FINA 320 - FINAL EXAM
The major benefit of diversification is to:
Reduce the expected risk
Cost of Preferred Stock
Reminders: -Preferred generally pays a constant dividend every period -Dividends are expected to be paid every period forever Preferred stock is a perpetuity
As the rating of a bond increases (for example, from A, to AA, to AAA), it generally means that
the default risk decreases and the required rate of return decreases.
The value of common stock will likely decrease if:
the discount rate increases
The company cost of capital (WACC) may be an inappropriate discount rate for a capital budgeting proposal if:
the proposal has a different degree of risk
What is the present value of $100 to be deposited today into an account paying 8%, compounded semiannually for 2 years?
$100.00
The financial objective for a firm is to accumulate $6,000,000 in 6 years, investing money quarterly at the beginning of every quarter. If money is assumed to earn 3% annual interest, how much must be invested per quarter to accumulate the $6,000,000?
$227,403 FV = 6,000,000 PV = 0 N = 6 x 4 = 24 I/Y = 3/4 = 0.75 PMT = 227,403
As a financial analyst, you are estimating the value of a stock, ABC. You expect the stock do not pay any dividend for the next five years, and then start to pay $10 dividend per year for the next 20 years. After that, the stock is expected to stop paying dividend forever and the company's assets will be worth nothing. If the required rate of return of the stock is 10%, what is your best estimate of the value of the stock today?
$52.86 CF1 = 0 F1 = 5 CF2 = 10 F2 = 20 NPV = $52.86
How much more would you be willing to pay today for an investment offering $10,000 in 4 years rather than in 5 years? Your discount rate is 8%.
$544.47 4 years: FV = 10,000 I/Y = 8 N = 4 PMT = 0 PV = -7,350.30 5 years: FV = 10,000 I/Y = 8 N = 5 PMT = 0 PV = -6,805.83 7,350.30 - 6,805.83 = 544.47
You plan to save $650 per year for the next 8 years. If your bank offers you an annual interest rate of 10%, how much money (round to the nearest dollar) will you have at the end of year 8? Assume each cash flow is deposited into your account at the end of the year.
$7,433 N = 8 I/Y = 10 PMT = 650 PV = 0 FV = 7,433.33
Kwak Motors, Inc. pays a $1.77 preferred dividend every quarter and will maintain this policy forever. What price should you pay for one share of preferred stock if you want an annual return of 9.25% on your investment?
$76.54 (1.77 x 4) / 0.0925 = 7.08 / 0.0925 = 76.54
A real estate investment has the following expected cash flows: Year Cash Flows 1 $10,000 2 25,000 3 50,000 4 35,000
$96,110
Most of the beneficial effects of diversification will have been received by the time a portfolio of common stocks contains __________ stocks.
25
If a stock is purchased for $25 per share and held one year, during which time a $1.75 dividend is paid and the price climbs to $29.5, the rate of return is:
25.00%
The market price of a bond is $1,236.94, it has 14 years to maturity, a $1,000 face value, and pays an annual coupon of $100 in semiannual installments. What is the yield to maturity?
7.27% PV=-1236.94, FV=1000, PMT=100/2=50, N=14*2=28, => I/Y = 3.637 YTM= 3.637%*2 = 7.27%
You own a stock portfolio invested 25 percent in Stock Q, 20 percent in Stock R, 15 percent in Stock S, and 40 percent in Stock T. The betas for these four stocks are .9, 1.4, 1.1 and 1.8, respectively. What is the portfolio beta?
Bp = .25(.9) + .20(1.4) + .15(1.1) + .40(1.8) = 1.39
Suppose you have $15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security? $2000 of DCLK $3000 of KO $4000 of INTC $6000 of KEI
DCLK: 2000/15,000 = .133 KO: 3000/15,000 = .2 INTC: 4000/15,000 = .267 KEI: 6000/15,000 = .4
Which of the following actions will INCREASE the present value of an investment?
Decrease the interest rate.
A cash-strapped young professional offers to buy your car with four, equal annual payments of $3,000, beginning 2 years from today. Assuming you're indifferent to cash versus credit, that you can invest at 10%, and that you want to receive $9,000 for the car, should you accept?
No, present value is $8,645 N = 4 PMT = 3,000 I/Y = 10 FV = 0 PV = 9,509.60 9,509.60/(1 + 10%) = 8,645
Which of the statements below is TRUE? A. Inventory turnover is cost of goods sold divided by accounts receivables. B. Receivables turnover is accounts receivables divided by sales. C. Total asset turnover is profits divided by total assets. D. A higher inventory turnover ratio signifies that inventory level is too high. E. None of the above
None of the above
What is the expected yield on the market portfolio at a time when treasury bills yield 6% and a stock with a beta of 1.4 is expected to yield 18%
None of the above 18% = 6% + 1.4(rm - 6%) 18% = 6% + 1.4rm - 8.4% 20.4% = 1.4rm 14.57% = rm
Assume a firm's current ratio equals 3.5. Which of the following actions would increase it?
Paying off a short-term bank loan with the proceeds from new long-term debt.
One method for estimating the growth rate is to use the historical average Year Dividend -1995 1.23 -1996 1.30 -1997 1.36 -1998 1.43 -1999 1.50
Percent Change (1.30 - 1.23) / 1.23 = 5.7% (1.36 - 1.30) / 1.30 = 4.6% (1.43 - 1.36) / 1.36 = 5.1% (1.50 - 1.43) / 1.43 = 4.9% Average = (5.7% + 4.6% + 5.1% + 4.9%) / 4 = 5.1%
Portfolio Variance
Portfolio variance is NOT the weighted average of the variance of each of the stock in the portfolio.
Which of the following statements is most correct?
If an asset to be used by a potential project is already owned by the firm, and if that asset could be leased to another firm if the new project were not undertaken, then the net rent that could be obtained should be charged as a cost to the project under consideration.
If a firm sells inventory for cash at a profit, then the current ratio will always:
Increase
Which of the following changes in working capital will result in an increase in cash flows?
Increase in accounts payable
Measuring Market Risk:The Market Risk Premium
Market Risk Premium - Risk premium of market portfolio; the difference between the market return and the return on risk-free Treasury bills.
Dividend 0
Multiply by 1 + g. The last dividend, the most recent dividend, current dividend, dividend today all mean DIV0.
Suppose that your company is expected to pay a dividend of $1.50 per share next year. There has been a steady growth in dividends of 5.1% per year and the market expects that to continue. The current price is $25. What is the cost of equity?
RE = 1.50/25 + .051 = .111
Which of the following items would not be included in cash flow from investing?
Selling stock of the company
Most U.S. corporate and government bonds choose to make _______ coupon payments.
Semiannual
Which of the following is not a capital budgeting question?
The proper mix of stocks and bonds to hold for financing assets
Which of the following is false regarding risk and return? a. The risk-free asset earns the lowest expected rate of return. b. The reward for bearing risk is known as the standard deviation. c. Based on historical data, there are rewards for bearing risk. d. An increase in the risk of an investment will result in an increased risk premium.
The reward for bearing risk is known as the standard deviation.
The Seattle Corporation has been presented with an investment opportunity that will yield end-of-year cash flows of $30,000 per year in Years 1 through 4, $35,000 per year in Years 5 through 9, and $40,000 in Year 10. This investment will cost the firm $150,000 today, and the firm's cost of capital is 10 percent. a. What is the NPV for this investment? b. The packback period for this investment is closest to:
a. $51,138 Using cash flow keys, we enter: CF0= -150,000, CF1=30,000 F1=4 CF2=35,000 F2=5 CF3=40,000 I=10 Solve for NPV= 51,138. b. 4.86 years
A firm with negative net working capital .
has more current liabilities than current assets
If a project has a cost of $50,000 and a profitability index of 0.4, then:
its NPV is $20,000
Dividends that are expected to be paid far into the future have:
lesser impact on current stock price due to discounting
Which of the following changes would be likely to increase the NPV of a project? a. increasing the firms opportunity cost of capital b. permitting a net increase in working capital c. spreading the total cash inflows over a longer interval d. increasing the projects estimated expenses e. none of the above
none of the above
If a security plots below the security market line, it is:
offering too little return to justify its risk.
When firms develop a WACC for individual projects based on the cost of capital for other firms in similar lines of business as the project, the firm is utilizing a:
pure play approach
What rate of return should an investor expect on a share of stock with a $2 expected dividend and 8% growth rate that sells today for $60?
r = 2/60 + 0.08 = 11.33%
Standard deviation is one of the most common measures of _________.
return volatility
Investors buy and sell stocks in ________markets.
secondary
The relevant risk for the fair market pricing of financial securities is the _______________.
systematic risk
The financial data of company ABC on Yahoo! Finance's includes cost of revenue. You would like to break the cost of revenue into its two major components: cost of goods sold and depreciation. To do so, we would need to look at _________ for the cost of goods sold.
the income statement
Risk Premiums
•The "extra" return earned for taking on risk •Treasury bills are considered to be risk-free •The risk premium is the return over and above the risk-free rate
Cost of Debt
•The cost of debt is the required return on our company's debt •We usually focus on the cost of long-term debt or bonds •The required return is best estimated by computing the yield-to-maturity on the existing debt •The cost of debt is NOT the coupon rate •We may also use estimates of current rates based on the bond rating we expect when we issue new debt
Portfolio Returns
•The return of a portfolio is the weighted average of the returns for each asset in the portfolio
Diversifiable (Unsystematic) Risk
•The risk that can be eliminated by combining assets into a portfolio is called diversifiable risk •Diversifiable risk is also called unsystematic, idiosyncratic risk, unique or asset-specific risk •Risk factors that affect a limited number of assets •Includes such things as labor strikes, part shortages, etc.
Total Risk
•Total risk = systematic risk + unsystematic risk •The standard deviation of returns is a measure of total risk •For well diversified portfolios, unsystematic risk is very small •Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk
Divisional and Project Costs of Capital
•Using the WACC as our discount rate is only appropriate for projects that are the same risk as the firm's current operations •If we are looking at a project that does NOT have the same risk as the firm, then we need to determine the appropriate discount rate for that project •Divisions also often require separatediscount rates
The Weighted Average Cost of Capital (WACC)
•We can use the individual costs of capital that we have computed to get our "average" cost of capital for the firm. •This "average" is the required return on our assets, based on the market's perception of the risk of those assets •The weights are determined by how much of each type of financing that we use
A bond's indenture least likely specifies the
source of funds for repayment
Your company has invested $5 million in R&D on self-driving car technology. What is the initial cash flow of the self-driving car manufacturing project at year 0?
$12 million cash outflow
Assume your firm has an unused machine that originally cost $75,000, has a book value of $20,000, and a market value of $25,000. Ignoring taxes, what is the opportunity cost of this machine?
$25,000
You have purchased a savings bond that will pay $10,000 to your newborn child in fifteen years. If the bank discounts this bond at a rate of 3.875% per year, what is today's price (the present value) for this bond?
$5,654
If a 4-year bond with a 7% coupon and a 10% yield to maturity is currently worth $904.90, how much will it be worth 1 year from now if interest rates are constant?
$925.39 FV = 1,000 PMT = 70 N = 3 I/Y = 10 PV = 925.39
The profitability index for a project costing $40,000 and returning $15,000 annually for 4 years at an opportunity cost of capital of 12% is:
0.139 CF0 = -40,000 CF1 = 15,000 F1 = 4 I/Y = 12 NPV = 5560 PI = 5560/40000 = 0.139
Treasury bills currently have a return of 2.5% and the market risk premium is 7%. If a firm has a beta of 1.4, what is its cost of equity?
12.3% 2.5% + (1.4 x 7%) = 12.30%
Treasury bills currently have a return of 2.5% and the market risk premium is 7%. If a firm has a beta of 1.4, what is its cost of equity?
12.3% 2.5% + 1.4 x 7% = 12.30%
Last year's asset turnover ratio was 2.0. Sales have increased by 25% and average total assets have increased by 10% since that time. What is the current asset turnover ratio?
2.27 Sales/Total Assets = 100/2 = 50 100(1 + 25%) = $125 50(1 + 10%) = $55 125/55 = 2.27
Your grandfather placed $5,000 in a trust fund for you. In 12 years the fund will be worth $10,000. What is the rate of return on the trust fund? (round to the nearest one hundredth of 1%)
5.95% PV = -5000 FV = 10,000 PMT = 0 N = 12 I/Y = 5.946
Your company has the following balance sheet: Total Assets: 2,000 Common Stock: 800 What is the company's debt ratio?
60% (2,000 - 800)/2,000 = 60%
The managers at Kenforest Grocers are trying to determine the company's optimal capital budget for the upcoming year. Kenforest is considering the following projects:
A, B, C, F
Which of the following bonds would be considered to be of investment grade?
A Baa-rated bond
Which of the following would likely have the greatest amount of systematic risk?
A portfolio half invested in the market portfolio and half invested in stocks with betas = 1.50.
Lena invested $1,000 in each of several alternative investments. In fifty years, which investment would you expect to have the highest value?
A portfolio of common stock
The Mid-American Utility Company's preferred stock pays an annual dividend of 8% per year on its par value of $60. If you want to earn 10% on your investment how much should you offer for this preferred stock?
Annual dividend = .08 x $60 = $4.80 Price = $4.80/0.10 = $48
Which of the following is fixed (cannot change) for the life of a given bond?
Coupon rate
Holding all else equal, if the beta of a stock increases, the stock's price will:
Decrease
The income statement begins with revenue and subtracts various operating expenses until arriving at the intermediate point of ________.
EBIT
Formulas
EBIT = revenue - expense - depreciation Tax = EBIT x tax rate OCF = revenue - cash expense - tax
A stock has an expected return of 10 percent, its beta is .9 and the risk-free rate is 6 percent. What must the expected return on the market be?
E[Ri] = .10 = .06 + (E[RM] - .06)(.9) ; E[RM] = .1044
Which of the following calculations ignores the impact of the time value of money? I. Payback II. IRR III. Profitability index
I only
Which of the following does NOT address the question: What are the duties of the financial manager? I. Deciding the price of the company's current outstanding bond II. Deciding the mix of long-term debt and equity III. Deciding which projects a firm should undertake. IV. Deciding how much short-term debt to use.
I only
The current ratio is a good proxy for a firm's:
Liquidity
The standard deviation for historical stock returns can be calculated as:
The positive square root of the variance.
Which of the following portfolios might be expected to exhibit less unsystematic risk?
Thirty random stocks; portfolio beta unknown
Suppose you have a market value of equity equal to $500 million and a market value of debt = $475 million. What are the capital structure weights?
V = 500 million + 475 million = 975 million wE = E/V = 500 / 975 = .5128 = 51.28% •wD = D/V = 475 / 975 = .4872 = 48.72%
Calculate the beta of a portfolio that consists of 25% Ford, 25% Boeing, and 50% McDonald's.
We multiple the beta of each stock by its weight, and then add them up, we end up with a portfolio beta of 1.26.
Security: A Return: 16% Standard Deviation: 20% Beta: 1.2 Security: B Return: 12% Standard Deviation: 25% Beta: 0.8 Risk-Free Asset: 4% Standard Deviation: ??? Beta: ??? a. Which of A and B has the least total risk? The least systematic risk? b. What is the value of systematic risk (as measured by beta) for a portfolio with 2/3 of the funds invested in A and 1/3 of the funds invested in B? c. What is the portfolio expected return and the portfolio beta if you invest 35% in A, 45% in B, and 20% in the risk-free asset?
a. A; B b. 1.067 Portfolio beta = (2/3) x 1.2 + (1/3)*0.8 = 1.067 c. 11.8%; 0.78 Expected return = 35% x 16% + 45% x 12% + 20% x 4% = 11.8% Portfolio beta = 35% x 1.2 + 45% x 0.8 + 20% x 0 = 0.78
Which of the following would not be expected to affect the decision of whether to undertake an investment?
cost of feasibility study done for the project
Investors who own bonds with lower credit ratings should expect
higher default possibilities
For a discount bond, the current yield is ____ the coupon rate, and the coupon rate is _____ the yield to maturity.
greater than; less than
A project whose NPV equals zero __________.
has a discounted payback period that exactly matches the life of the project
The slope of an asset's security market line is the __________.
market risk premium
Regarding diversification, _____________________________.
most of the benefits are realized with about 20 to 30 stocks
Whenever a new product competes against a company's already existing products and reduces the sales of those products, ________ occur.
negative side effects
The SEC has a site named EDGAR that ________.
provides an on-line platform that will help investors find a company and its financial statements
The discount rate that makes the present value of a bond's payments equal to its price is termed the:
yield to maturity
A firm has a times interest earned ratio of 4.5 times. This means:
The firm has sufficient EBIT to cover its interest expense 4.5 times over.
A total debt ratio of 0.35:
Would exist if a firm had liabilities of $700 and assets of $2,000
The building of the project's ______________ cash flow is the cornerstone of the financial decision models.
Incremental
In a firm with both a treasurer and a controller, which of the following would most likely be handled by the controller?
Internal auditing
IRR and Mutually Exclusive Projects
Intuitively you would use the following decision rules: -NPV: choose the project with the higher NPV -IRR: choose the project with the higher IRR
Which of the following statements about the internal rate of return (IRR) for a project with the following cash flow pattern is CORRECT? Year 0: -$2,000 Year 1: $10,000 Year 2: -$10,000
It has 2 IRRs of approximately 38.2% and 261.8%
Which of the following statements regarding dividend yields is true?
It is analogous to the current yield for a bond.
As illustrated using the dividend growth model, the total return on a share of common stock is comprised of a _____________.
dividend yield and a capital gains yield
Net income is ________.
not cash flow
A new machine will cost $100,000 and generate after-tax cash inflows of $35,000 for 4 years. What is the payback period?
$100,000/$35,000 = 2.86 years
How much interest can be accumulated in two years on a $1,000 deposit paying annual interest rate of 10%, compounded monthly? (Round to the nearest dollar)
$220 PV = 1,000 N = 2 x 12 = 24 I/Y = 10/12 = 0.83333 PMT = 0 FV = 1,220.39 1,220.39 - 1,000 = 220.39
Which of the statements below is TRUE?
Accounting Identity is: Assets = Liabilities + Owner's Equity
What will happen to a stock that offers a lower risk premium than predicted by the CAPM?
It's price will decrease until the expected return is increased
The fundamental goal of financial management should be:
Maximize the current value per share of the existing stock.
Cost of Equity
•The cost of equity is the return required by equity investors given the risk of the cash flows from the firm •There are two major methods for determining the cost of equity -Dividend growth model -SML or CAPM
Value of a common stock does not directly depend on _________.
The maturity date of common stock
If a 5-year ordinary annuity has a present value of $1,000, and if the interest rate is 10 percent, what is the amount of each annuity payment? (round to the nearest cent)
$263.80 N = 5 I/Y = 10 PV = 1000 FV=0 PMT = -263.80
J&J Manufacturing just issued a bond with a $1,000 face value and a coupon rate of 8%. If the bond has a life of 20 years, pays annual coupons, and the yield to maturity is 7.5%, what will the bond sell for?
$1,050.97 I/Y=7.5, FV=1,000, PMT=80, N=20, => PV = -1050.97
Approximately how much must be saved for retirement in order to withdraw $100,000 per year for the next 25 years if the balance earns 8% annually, and the first payment occurs 1 year from now?
$1,067,000 PMT = 100,000 N = 25 I/Y = 8 FV = 0 PV = 1,067,477.62
If a stock's P/E ratio is 13.5 at a time when earnings are $3 per share, what is the stock's current price?
$40.50 13.5 = current price/3 Current price = 40.50
Assume that you invested $2,566.70 at Year 0 in a project that is promising to return 12 percent per year. The cash flows are expected to be as follows: End of Year: 1, Cash Flow $325 Determine the expected cash flow (whose values is missing) at Year 4.
$1,156.99
How much must be saved annually, beginning 1 year from now, in order to accumulate $50,000 over the next 10 years, earning 9% annually?
$3,291 PV = 0 FV = 50,000 N = 10 I/Y = 9 PMT = 3,291
Sedgwick, Inc. has a 12% required rate of return. It does not expect to initiate dividends for fifteen years, at which time it will pay $2.00 per share in dividends. At that time, Sedgwick expects its dividends to grow at 7% forever. If you currently own the stock and will sell it following the first dividend, what is your estimated selling price at T15?
$42.80 (2 x 1.07) / (.12 - .07) = 42.80
You just won the lottery. You and your heirs will receive $40,000 per year forever, with the first payment received immediately. What is the present value at a 9% discount rate?
$484,444 40,000/9% = 444,444 + 40,000 = 484,444
A firm generates sales of $250,000, depreciation expense of $50,000, taxable income of $50,000, and has a 35% tax rate. By how much does net cash flow deviate from net income?
$50,000
Which of the following statements is true for a stock that sells now for $60, pays an annual dividend of $4.00, and experienced a 20% return on investment over the past year? Its price one year ago was:
$53.33 20% = (69 - P0 + 4)/P0 = 53.33
List a capital budgeting, a capital structure decision, and a working capital management decision that a business might make
-Capital budgeting decision: what projects to invest in, where to expand, etc.? -Capital structure decision: what should be the optimal debt and equity mixture? -Working capital management: what should be the credit policy?How much cash balance the firm should keep?
What are the three areas of finance? Give an example of a financial activity that would fall into each area.
-Investment: deciding how much retirement savings are invested in stocks and bonds -Corporate finance: managing working capital -Financial market and intermediation: taking deposits and making loans
Depreciation
-The depreciation expense used for capital budgeting should be the depreciation schedule required by the IRS for tax purposes. -Depreciation itself is a non-cash expense, consequently, it is only relevant because it affects taxes. -Depreciation tax shield = DT D = deprecation expense T = marginal tax rate
Relevant Cash Flows
-We should base the investment decision on project csh flows rather than accounting income. -However, not all cash flows related to a project should be considered. -The cash flows that should be included in a capital budgeting analysis are those that will only occur if the project is accepted -These cash flows are called incremental cash flows: cash flow with project - cash flow without project Asking the right question: You should always ask yourself "Will this cash flow occur ONLY if we accept the project?" -if the answer is yes, it should be included -if this answer is no, it should not be included -if the answer is part of it, then we should include the part that occurs because of the project
IRR and Non-conventional Cash Flows
-When the cash flows change signs more than once, there is more than one IRR -When you solve for IRR, you are solving for the root of an equation and when you cross the x-axis more than once, there will be more than one return that solves the equation -If you have more than one IRR, which one do you use to make the decision?
Computing Depreciation
/Straight-line depreciation D = (Initial cost - salvage) / number of years /Initial Cost includes delivery charges, installation costs, and all other related costs /very few assets are depreciated straight-line for tax purposes Accelerated Depreciation -Depreciates large portion of the asset early in its life -Reduces net income, but increases cash flow from operation (why?) -Increases the NPV of investment project
For the cash flows in the previous problem, what is the NPV at a discount rate of 0%? What if the discount rate is 10%? If it is 20%? If it is 30%?
0%: NPV= - $4,000 + $1,500 + $2,100 + $2,900 = $2,500 10%: NPV= - $4,000 + $1,500/1.1 + $2,100/1.12 + $2,900/1.13 = $1,277.99 20%: NPV= - $4,000 + $1,500/1.2 + $2,100/1.22 + $2,900/1.23 = $386.57 30%: NPV= - $4,000 + $1,500/1.3 + $2,100/1.32 + $2,900/1.33 = - $283.57
The beta of an investment in U.S. Treasury bills is:
0.0
A company's zero coupon bond issue matures in 16 years and has a yield to maturity of 10.60%. Each zero has a face value of $1,000 and there are 4,000 of the bonds outstanding. If the market values the equity at $1,800,000, what capital structure weight for debt would you use in calculating the WACC, assuming the firm's only debt consists of the zeros?
0.299 N = 32 I/Y=10.6/2 = 5.3, PMT=0 FV = 1000 => PV = -$191.554 The market value of debt = 191.554 x 4000 =$766,216 Value of firm = 1,800,000 + 766,216 = $2,566,216 Weight of debt = 766216/2566216 = 0.299
Use the information below for the Greek Corporation to answer the following questions. 1. The value of total assets for the year-end is ________. 2. The value of net working capital at the year-end is ________. 3. The value of equity for the year-end is ________.
1. $20,940 Total Asset = Cash + A/R + Inventory + PPE = 1500 + 3200 + 4500 + 11740 = 20,940 2. $6,450 NWC = CA - CL = (Cash + A/R + Inventory) - A/P = (1500 + 3200 + 4500) - 2750 = 6,450 3. $11,090 Equity = Common Stock + Retained Earnings = 6250 + 4840 = 11,090
What should be the beta of a replacement stock if an investor wishes to achieve a portfolio beta of 1.0 by replacing stock C in the following equally weighted portfolio: stock A = .9 beta; stock B = 1.1 beta; stock C = 1.35 beta?
1.00 New portfolio beta = (.333 x .9) + (.333 x 1.1) + (.333 x Beta C) 1.0 = .3 + .366 + .333 x beta C .334 = .333 x beta C 1.00 = beta C
What would you estimate to be the required rate of return for equity investors if a stock sells for $40.00 and will pay a $4.40 dividend next year that is expected to grow at a constant rate of 5%?
16.0%
Given the following information for Dunhill Power Co. find the WACC. Assume the company's tax rate is 35 percent. Debt: 3,000 8 percent coupon bonds outstanding, $1,000 par value, 20 years to maturity, selling for 103 percent of par; the bonds make semiannual payments. Common Stock: 90,000 shares outstanding, selling for $45 per share; the beta is 1.20. Preferred Stock: 13,000 shares of 7 percent preferred stock outstanding, currently selling for $108 per share. The preferred stock has a par value of $100. Market: 8 percent market risk premium and 6 percent risk-free rate.
10.27% MVD = 3,000($1,000)(1.03) = $3.09M; MVE = 90,000($45) = $4.05M MVP = 13,000($108) = $1.404M; V = $3.09M + 4.05M + 1.404M = $8.544M RE = .06 + 1.20(.08) = 15.60% YTM of the bond = 7.703% RD = (1 - .35)(.07703) = 5.007% RP = $7/$108 = 6.481% WACC = .05007(3.09/8.544) + .1560(4.05/8.544) + .06481(1.404/8.544) = 10.27%
Calculate the risk premium on stock C given the following information: risk-free rate = 5%, market return = 13%, stock C beta = 1.3.
10.4% Stock C risk premium = beta x market risk premium = 1.3 x (13% - 5%) = 10.4%
Given the following information, what is the WACC? Common Stock: 1 million shares outstanding, $40 per share, $1 par value, beta = 1.3 Bonds: 10,000 bonds outstanding, $1,000 face value each, 8% annual coupon (paid annually), 22 years to maturity, market price = $1,101.23 per bond Market risk premium = 8.6%, risk-free rate = 4.5%, marginal tax rate = 34%
13.30%
What is the WACC for a firm with 50% debt and 50% equity that pays 12% on its debt, 20% on its equity, and has a 40% tax rate?
13.6%
Assume the following information about the market and JumpMasters' stock. JumpMasters' beta = 1.50, the risk-free rate is 3.50%, the market risk premium is 10.0%. Using the SML, what is the expected return for JumpMasters' stock?
18.50%
According to CAPM estimates, what is the cost of equity for a firm with beta of 1.5 when the risk-free interest rate is 6% and the expected return on the market portfolio is 15%?
19.5%
When you were born, your grandparents opened a savings account on your behalf and deposited $1,000. Neither additional deposit nor withdrawal has ever been made since. The account pays an annual interest rate of 5%. The account balance today is $3,920.1. How old are you now (round to the nearest year)?
28 years old PV = 1,000 FV = -3,920.q I/Y = 5 PMT = 0 N = 28
The Stack has just written and recorded the single greatest rock song ever made. The boys in the band believe that the royalties from this song will pay the band a handsome $200,000 every year forever. The record studio is also convinced that the song will be a smash hit and the royalty estimate is accurate. The record studio wants to pay the band up front and not make any more payments for the song. What should the record studio offer the band if it uses a 5% discount rate, a 7.5% discount rate, or a 10% discount rate?
5%: PV of perpetuity = pmt/r = 200000/5% = $4,000,000 7.5%: PV of perpetuity = pmt/r = 200000/7.5% = $2,666,667 10%: PV of perpetuity = pmt/r = 200000/10% = $2,000,000
Buying your own home is often mentioned as "the best investment you can make." In 1930, the average home sale price was $3,845. By 1990, the average home sale price had risen to $123,000. What was the average annual rate of return of investing in house over this time period?
5.95% per year N = 60 PV= -3845, FV=123,000 PMT=0 I/Y= 5.95
You are interested in a corporate bond with the current market price of $873.36 and yield to maturity of 7%. The bond carries a coupon rate of 6%, paid semi-annually. If you buy the bond today, how many semi-annual coupon payments will you receive until the final maturity?
6 PV = -973.36 FV = 1,000 I/Y = 7/2 = 3.5 PMT = 6% x 1,000/2 = 30 N = 6
Kelvin has $2,500 but needs $5,000 to purchase a new golf cart. If he can invest his money at a rate of 12% per year, approximately how many years will it take the money in Kelvin's account to grow to $5,000? Use the Rule of 72 to determine your answer.
6 years 72/12 = 6
After winning the lottery, you state that you are indifferent between receiving twenty $500,000 end of the year payments (first payment one year from today) and receiving a lump sum payment of $5,734,961 today. What interest rate are you using in your decision making process such that you are indifferent between the two choices?
6%
South Penn Trucking is financing a new truck with a loan of $10,000 to be repaid in 5 annual end-of-year installments of $2,504.56. What annual interest rate is the company paying? (round to the nearest one hundredth of 1%)
8.00% N = 5 I/Y= 8 PV = 10,000 PMT = -2,504.56 FV = 0
The Canadian government decided to issue a consol (a bond with a never-ending interest payment and no maturity date). The bond will pay $50 in interest each year (at the end of the year), but it will never return the principal. The current discount rate for Canadian government bonds is 6.5%. What should this consol bond sell for in the market? What if the interest rate should fall to 4.5%? Rise to 8.5%? Why does the price go up when interest rates fall? Why does the price go down when interest rates rise?
6.5%: $50/0.065 = $769.23 4.5%: $50/0.045 = $1,111.11 8.5%: $50/0.085 = $588.24 The price rises when interest rates fall because the present value of each future interest payment is worth more in present value due to the lower discount rate. The price falls when interest rates rise because the present value of each future interest payment is worth less in present value due to the higher discount rate.
A firm has $1,000 par value bonds outstanding that have an annual coupon rate of 8.00% and make semiannual payments. These bonds have twenty-three years remaining to maturity and currently sell for $1,133.42. What is the cost of debt for the firm?
6.84%
A firm has $100 million in equity and $300 million in debt. The firm recently issued bonds at the market required rate of return of 9%. The firm's beta is 1.124, the risk-free rate is 6%, and the expected return in the market is 14%. Assume the firm is at their optimal capital structure and the firm's tax rate is 40%. What is the firm's weighted average cost of capital (WACC)
7.80% 6% + 1.125 x (14% - 6%) = 15% 0.25 x 15% + 0.75 x 9% x (1 - 40%) = 7.8%
Kant Miss Company is promising its investors that it will double their money every three years. Is this promise too good to be true? What annual rate is Kant Miss promising? If you invest $250 now and Kant Miss is able to deliver on its promise, how long will it take your investment to reach $32,000? Use the Rule of 72.
72/3 = 24. Based on the Rule of 72, the annual rate must be 24% to double the money every three years. From $250 to $32,000, the investment increases by 128 times. In other words, the initial investment has doubled itself 7 times. If money is doubled every 3 years, then it would take approximately 21 years. More specifically, to increase from $250 to $32,000, it is an increase of 128 times, or 32,000=250(1+100%)7 In other words, the money needs to be doubled 7 times, or from 250 to 500 (1 times, or 3 years) from 500 to 1,000 (2 times, or 6 years) from 1,000 to 2,000 (3 times, or 9 years) from 2,000 to 4,000 (4 times, or 12 years) from 4,000 to 8,000 (5 times, or 15 years) from 8,000 to 16,000 (6 times, or 18 years) from 16,000 to 32,000 (7 times, or 21 years).
What is the coupon rate for a bond with 3 years until maturity, a price of $1,053.45, and a yield to maturity 6%?
8% N = 3 I/Y = 6 FV = 1,000 PV = -1,053.46 PMT = 80 80/100 = 8%
Asset A has an expected return of 14.5% and a beta of 1.15. The risk-free rate is 5%. What is the market risk premium?
8.26% R = Rf + beta* (Rm- Rf) 14.5% = 5% + 1.15*(Rm- Rf) Rm - Rf = 8.26%
Assume that you have taken out a 30-year mortgage of $240,000 and that your monthly payments are $1,853.90. What is your annual interest rate on the mortgage loan?
8.55% PV = 240,000 N = 30 x 12 = 360 PMT = -1,853.90 FV = 0 I/Y = 0.7125 0.7125 x 12 = 8.55%
ABC Corporation's common stock dividend yield is 3.61%, it just paid a dividend of $2.75, and is expected to pay a dividend of $2.89 one year from now. Dividends are expected to grow at a constant rate indefinitely. What is the required rate of return on ABC stock?
8.7% DIV1 = DIV0*(1+g) 2.89 = 2.75*(1+g) g = 5.09% R = DIV1/P0 + g = 3.61% + 5.09% = 8.7%
You have the following data for a company. What is the return on assets (ROA)? Return on equity = 15%; Earnings before taxes = $50,000; Total asset turnover = 1.2; Profit margin = 7.5%; Tax rate = 35%.
9% Net Income = EBT - Tax = EBT - EBT x (Tax Rate) = 50000 - 50000 x 35% = 32,500 Profit Margin = Net Income/Sale 7.5% = 32500/Sale Sale = 433,333 Total Asset Turnover = Sale/Total Asset 1.2 = 433,333/Total Asset Total Asset = 36,1111 ROA = Net Income/Total Asset = 32,500/36,1111 = 9%
Billick Brothers is estimating its WACC. The company has collected the following information: · Its capital structure consists of 40 percent debt and 60 percent common equity. · The company has 20-year bonds outstanding with a 9 percent annual coupon that are trading at par. · The company's tax rate is 40 percent. · The risk-free rate is 5.5 percent. · The market risk premium is 5 percent. · The stock's beta is 1.4. What is the company's WACC?
9.66% Since the bond sells at par, the YTM is the same as coupon rate. Thus, the cost of debt is 9%. Using the CAPM, we can find cost of equity as follows: Re = 5.5% + 1.4 x 5% = 12.5% WACC = 60% x 12.5% + 40% x 9% x (1- 40%) = 7.5% + 2.16% = 9.66%
Which of the following events will reduce a company's weighted average cost of capital (WACC)?
A reduction in the market risk premium
Which of the following would most likely be considered the most liquid asset?
A share of IBM common stock
A stock investor owns a diversified portfolio of 15 stocks. What will be the most likely effect on the portfolio's standard deviation if one more stock is added?
A slight decrease will occur.
Which of the following statements about zero-coupon bonds is FALSE?
A zero coupon bond may sell at a premium or when interest rates decline.
Takelmer Industries has a different WACC for each of three types of projects. Low-risk projects have an 8% WACC, average-risk projects a 10% WACC, and high-risk projects a 12% WACC. Which of the following projects do you recommend that the firm accept? Project: A Level of Risk: Low IRR: 9.50% Project: B Level of Risk: Average IRR: 8.50% Project: C Level of Risk: Average IRR: 7.50% Project: D Level of Risk: Low IRR: 9.50% Project: E Level of Risk: High IRR: 14.50% Project: F Level of Risk: High IRR: 17.50% Project: G Level of Risk: Average IRR: 11.50%
A, D, E, F, and G
Last year, ABC and XYZ both had the same level of cost of goods sold, but ABC turned its inventory over 8 times during the year while XYZ turned its inventory over every 55 days. If the objective is to keep inventory as low as possible on average, which of the following is true?
ABC did a better job since its inventory turnover was higher.
Consider the following four-year project. The initial outlay or cost is $180,000. The respective cash inflows for years 1, 2, 3 and 4 are: $100,000, $80,000, $80,000 and $20,000. What is the discounted payback period if the discount rate is 11%?
About 2.427 years First, find the PV of the annual cash flows as follows: PV of CF1 = 100000/(1+11%) = 90,090 PV of CF2 = 80000/(1+11%)2 = 64,930 PV of CF3 = 80000/(1+11%)3 = 58,495 PV of CF4 = 20000/(1+11%)4 = 13,175. Next, subtract the PV of each cash flow from the initial cost: 180,000 - 90,090 = 89,910 (to be recovered after year 1) 89,910 - 64,930 = 24,980 (to be recovered after year 2) Since 24,980 < the PV of year three cash flow, it will take 24980/58496 = 0.427 of the third year to fully recover the initial cost, or the discounted payback is 2.427 years.
NPV: Accounting Income - Example Year 1: Cash Inflow 1,500 Depreciation -1,000 Accounting Income 500 Year 2: Cash Inflow 500 Depreciation -1,000 Accounting Income -500
Accounting-based NPV = 0 + (500/1.10) + (-500/(1.10^2)) = $41.32
Which of the following best explains the combination of a high level of sales combined with a low cash flow during an accounting period?
Acquisition of equipment
SML Approach
Advantages: -Explicitly adjusts for systematic risk -Applicable to all companies, as long as we can compute beta Disadvantages: -Have to estimate the expected market risk premium, which does vary over time -Have to estimate beta, which also varies over time -We are relying on the past to predict the future, which is not always reliable
Assume a project has normal cash flows (that is, the initial cash flow is negative, and all other cash flows are positive). Which of the following statements is most correct?
All else equal, a project's NPV increases as the cost of capital declines.
Normal projects C and D are mutually exclusive. Project C has a higher (positive) net present value if the cost of capital is less than 12 percent, whereas Project D has a higher (positive) net present value if the cost of capital exceeds 12 percent. Which of the following statements is most correct? a. Project D has a higher internal rate of return. b. Project D and Project C have a crossover rate of 12%. c. You should be indifferent between the two projects if the cost of capital is 12% d. Statements b and c are correct. e. All of the statements above are correct.
All of the statements above are correct.
Normal projects C and D are mutually exclusive. Project C has a higher (positive) net present value if the discount rate is less than 12 percent, whereas Project D has a higher (positive) net present value if the discount rate exceeds 12%. Which of the following statements is most correct?
All of the statements above are correct.
Which of the statements below is true? a. The increase in working capital accounts necessary to support a project also provides for cost increases at the end of the project. b. An increase in working capital can be brought about by an increase in inventory or accounts receivable. c. Decreases in accounts receivable constitute a use of cash flow because you are helping your customers finance their purchases. Decreases in accounts payable constitute a source of cash flow because you are using your suppliers to help finance your business operations.
An increase in working capital can be brought about by an increase in inventory or accounts receivable.
The present value of annuity stream of $100 per year is $614 when valued at a 10% rate. By approximately how much would the value change if these were annuities due? (Round to the nearest dollar).
An increase of $61 614(1 + 10%) = 675.4 675.4 - 614 = 61.4
The price and yield to maturity on a bond have:
An inverse relation
The discounted payback rule can be best stated as:
An investment is acceptable if its discounted payback period is less than some pre-specified number of years.
A firm is considering purchasing two assets. Asset A will have a useful life of fifteen years and cost $3 million. It will have installation costs of $400,000, but no salvage or residual value. Asset B will have a useful life of six years and cost $1.3 million. It will have installation costs of $180,000 and a salvage or residual value of $300,000. Which asset will have a greater annual straight-line depreciation?
Asset A has $30,000 more in depreciation per year
Calculating capital component weights: T.J. Enterprises is trying to determine the weights to be used in estimating their cost of capital. The firm's market information regarding the price and number of securities outstanding are listed below. Market Information Debt Preferred Stock Common Stock Outstanding 48,000 102,000 1,300,000 Market Price $850 $95.40 $40 Calculate the firm's capital component weights using market values.
Based on market value: Market value of Debt = $40,800,000 = $850*48,000 Market Value of P/S= $9,730,800 = $95.4 x 102,000 Market Value of C/S= $52,000,000 = $40 x 1,300,000 Total Market Value = $102,530,000 Weight of Debt = $40,800/$102,530 = 39.79% Weight of P/S= $9,730.8/$102,530 = 9.49% Weight of C/S = $52,000/$102,530 = 50.72%
The band from the previous problem agrees to the one-time payment at a 5% discount rate, but it wants to figure the royalty payments from the beginning of the year, not the end of the year. How much more will the band receive with annuity due payments on the royal checks?
By shifting it to perpetuity due, the present value will increase to $4 million x (1+5%) = $4.2 million.
Your company has preferred stock that has an annual dividend of $3. If the current price is $25, what is the cost of preferred stock?
RP = 3 / 25 = 12%
You believe that the required return on Dynegy stock is 16% and that the expected dividend growth rate is 12%, which is expected to remain constant for the foreseeable future. Is the stock currently overvalued, undervalued, or fairly priced?
Cannot tell without more information
The means by which a company is financed refers to the firm's _________.
Capital structure
Why does the double taxation problem exist for corporations?
Corporations earn taxable income, pays taxes on that income, and then pay dividends to the stockholders, who also have net taxable income.
Lifehouse Software has 10 percent coupon bonds on the market with 7 years to maturity. The bonds make semiannual payments and currently sell for 104 percent of par. What is the current yield on Lifehouse's bonds? The YTM?
Current Yield = (annual coupon payment) / current price = 100/1,040 = 9.615% N = 7 X 2 = 14 I/Y (PTM) = ? PV = 1,000 * 1.04 = -1,040 PMT = 10 x 10 = 100/2 = 50 FV = 1,000 I/Y (PTM) = 4.606 x 2 = 9.21%
Massey Co. has 12 percent coupon bonds making annual payments with YTM of 9 percent. The current yield on these bonds is 9.80 percent. How many years do these bonds have left until they mature?
Current Yield Yield = (annual coupon payment) / current price = 12 x 10 = 120/9.8 = 1,224.49 N = ? I/Y (PTM) = 9% PV = -1,224.49 PMT = 12 x 10 = 120 FV = 1,000 N = 12.98
The quick ratio is measured as:
Current assets minus inventory, divided by current liabilities.
The advantage of MACRS over straight-line depreciation is that you can write off more of your capital costs in the _________ year(s).
Earlier
Mack Industries just laid a dividend of $1.00 per share (DIV0 = $1.00). Analysts expect the company's dividend to grow 20 percent this year and 15 percent next year. After two years the dividend is expected to grow at a a constant rate of 5 percent. The required rate of return on the company's stock is 12 percent. What should be the company's current stock price?
DIV1 = 1 x (1 + 0.2) = 1.2DIV2 = 1.2 x (1 + .15) = 1.38DIV3 = 1.38 * (1 + 0.05) = 1.45P2 = DIV3 /(r - g) = 1.45/(.12 - .05) = 20.70P0 = 1.2/(1 + .12) + 1.38(1 + .12)^2 + 20.70(1 + 0.12)^2= 1.071 + 1.10 + 16.502 = 18.67
ABC Corporation's common stock dividend yield 3.61%, it just paid a dividend of $2.75, and is expected to pay a dividend of $2.89 one year from now. Dividends are expected to grow at a constant rate indefinitely. What is the required rate of return on ABC stock?
DIV1=DIV0 x (1+g)2.89=2.75 x (1+g)g= 5.09%R=DIV1/P0 + g = 3.61% + 5.09%= 8.7%
Which of the following will increase the present value of annuity, other things equal?
Decreasing the interest rate
Identifying Cash Flows: Cash Flow vs. Accounting Income
Discount actual cash flows, not necessarily net income. Use accounting income, rather than cash flow, could lead to erroneous decisions.
Suppose you know that a company's stock currently sells for $60 per share and the required return on the stock is 14 percent. You also know that the total return on the stock is evenly divided between a capital gain yield and a dividend yield. If it's the company's policy to always maintain a constant growth rate in its dividends, what is the current dividend per share?
Dividend yield = ½(.14) = 0.07 D1 = 0.07 x $60 = $4.20 D0(1 + g) = D1 D0 = $4.20/(1.07) = $3.93 or $4
Dweller, Inc. is considering a four-year project that has an initial after-tax outlay or after-tax cost of $80,000. The future after-tax cash inflows from its project are $40,000, $40,000, $30,000, and $30,000 for years one, two, three, and four, respectively. Dweller uses the NPV method and has a discount rate of 12%. Will Dweller accept the project?
Dweller accepts the project because the NPV is greater than $28,000.
Which of the following is correct for a bond prices at $1,100 that has 10 years remaining until maturity, and a 10% coupon rate, with semiannual payments?
Each payment of interest equals $50 Semiannual coupon payment = (.10 x 1000)/2 = $50
Use the four assets from the previous problem in the same three portfolios. What are the expected returns of each of the four individual assets and the three portfolios if the current SML is plotting with an intercept of 4% (risk-free rate) and a market premium of 10% (slope of the line)?
Expected Return of Asset G = 4% + 0.45 (10%) = 8.5% Expected Return of Asset H = 4% + 0.8 (10%) = 12% Expected Return of Asset I = 4% + 1.15 (10%) = 15.5% Expected Return of Asset J = 4% + 1.6 (10%) = 20% Expected Return of Portfolio 1 = 4% + 1.0 (10%) = 14% Expected Return of Portfolio 2 = 4% + 0.845 (10%) = 12.45% Expected Return of Portfolio 3 = 4% + 1.145 (10%) = 15.45%
Assume that a company has equal amounts of debt, common stock, and preferred stock. An increase in the corporate tax rate of a firm will cause its weighted average cost of capital (WACC) to
Fall
For the following firms, find the return on equity using the three components of the DuPont identity: operating efficiency, as measured by the profit margin (net income/sales); asset management efficiency, as measured by asset turnover (sales/total assets); and financial leverage, as measured by the equity multiplier (total assets/total equity).
First find the equity of each company i.e. Total Assets less Total Liabilities: Pepsi's Equity = $77,487 - $53,199 = $24,288 Coca-Cola's Equity = $90,055 - $56,882 = $33,173 McDonald's Equity = $36,626 - $20,617 = $16,009 Last, take the three components to find the ROE, Pepsi = 0.10148 × 0.8574 × 3.1903 = 0.2776 or 27.76% ROE Coca-Cola = 0.1832 × 0.5203 × 2.7147 = 0.2588 or 25.88% ROE McDonald's = 0.2084 × 0.7674 × 2.2878 = 0.3659 or 36.59% ROE McDonald's is the most operationally efficient of the 3 firms and despite having the lowest amount of leverage, it provides the highest return on equity to its shareholders McDonald's is the most operationally efficient of the 3 firms and despite having the lowest amount of leverage, it provides the highest return on equity to its shareholders.
Which of the following is/are false regarding the balance sheet and income statement? I. The income statement reflects a summary of activity that occurs over some period of time while the balance sheet is a snapshot taken at a single point in time. II. Both represent a summary of activity that occurs over some time period. III. The two statements, taken together, give an accurate estimate of the firm's cash flows and market value.
II and III only
Which of the following statements is true? I. The dividend growth model only holds if, at some point in time, the dividend growth rate exceeds the stock's required return. II. An increase in the dividend growth rate will increase a stock's market value, all else the same. III. An increase in the required return on a stock will increase its market value, all else the same.
II only
Non-conventional Cash Flows: Suppose an investment will cost $90,000 initially and will generate the following cash flow: Year 1: $132,000 Year 2: $100,000 Year 3: -$150,000 The required rate of return is 15%. Should we accept/reject the project?
IRR = 10.11% NPV = 1,770 Based on NPV rule, accept the project. This is non-conventional because there is more than one IRR.
Internal Rate of Return
IRR is the return that makes NPV = 0 Decision Rule: Accept the project if the IRR is greater than the required return -This is the most important alternative to NPV -It is often used in practice and is intuitively appealing -It is based entirely on estimated cash flows and is independent of interest rates found elsewhere Advantages: -Knowing a return is intuitively appealing -It is a simple way to communicate the value of a project to someone who doesn't know all the estimations details. -If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task.
Consider a project with an initial investment and positive future cash flows. As the discount rate is decreased the ______.
IRR remains constant while the NPV increases
What is the IRR of the following set of cash flows? Year 0, Cash Flow -4,000 Year 1, Cash Flow 1,500 Year 2, Cash Flow 2,100 Year 3, Cash Flow 2,900
IRR: the discount rate, or interest rate, such that the NPV is zero. 0 = - $4,000 + $1,500/(1+IRR) + $2,100/(1+IRR)2 + $2,900/(1+IRR)3 ; IRR = 25.43%
You bought a bond for $950 1 year ago. You have received two coupons of $30 each. You can sell the bond for $975 today. What is your total dollar return?
Income = 30 + 30 = 60 Capital gain = 975 - 950 = 25 Total dollar return = 60 + 25 = $85
From the following income statement account, produce the income statement for the year Cost of goods sold $345000 Interest expense $82000 Taxes $2000 Revenue $744000 Selling, general, and administrative expense $66000 Depreciation $112000
Income Statement Revenue $744,000 -Cost of Goods Sold $345,000 -SG&A Expenses $ 66,000 -Depreciation = $112,000 EBIT $221,000 -Interest Expense $ 82,000 Taxable Income = $139,000 -Taxes $ 2,000 Net Income = $137,000
The financial statement that displays how much profit a business earned or lost is referred to as the
Income statement
A firm is considering an investment in a project whose risk is greater than the current risk of the firm, based on any method for assessing risk. In evaluating this asset, the decision maker should
Increase the cost of capital used to evaluate the project to reflect the project's higher risk.
Which of the following actions are likely to reduce agency conflicts between stockholders and managers?
Increasing the threat of corporate takeover
What would you recommend to an investor who is considering an investment that, according to its beta, plots above the security market line (SML)?
Invest; return is high relative to risk
Which of the following statements regarding investment in working capital is incorrect?
Investment in working capital, unlike investment in plant and equipment, represents a positive cash flow
________________ is the area of finance concerned with the activities of buying and selling financial assets such as stocks and bonds
Investments
Which of the following statements about IPO is false?
Investors trade a company's stocks among themselves during an IPO
Your financial team has done a detailed analysis of a proposed 10-year project and reported that the project NPV is $456 at a discount rate of 10%. A later review by the marketing team suggests that the project requires an additional $2,000 of inventory at year 0, which will be maintained through out the life of the project but liquidated (without any loss or gain) at the end of the project. How does the requirement for additional inventory impact the estimated project NPV?
It will decrease the NPV by $1,228.91 2,000/(1 + 10%)^10 = 771.08 2,000 - 771.08 = 1,228.91
When Tri-C Corp. compares its ratios to industry averages, it has a higher current ratio, an average quick ratio, and a low inventory turnover. What might you assume about Tri-C?
Its average inventory is too high.
You have $10,000 to invest in a stock portfolio. Your choices are Stock X with a return of 15 percent and Stock Y with a return of 10 percent. If your goal is to create a portfolio with a return of 13.5 percent, how much money will you invest in Stock X? In Stock Y?
Let Wx be the percentage of stock X, Rp = .135 = .15WX + .10(1 - WX); WX = 0.70 investment in X = 0.70($10,000) = $7,000; investment in Y = (1 - 0.70)($10,000) = $3,000
A firm that uses its WACC as a cutoff without consideration of project risk:
Likely will see its WACC rise over time.
Which of the following is not an advantage of a sole proprietorship?
Limited liability
SDJ, Inc., has net working capital of $1,050, current liabilities of $4,300, and inventory of $1,300. What is the current ratio? What is the quick ratio?
NWC = $1,050 = CA - CL; CA = $1,050 + 4,300 = $5,350 Current ratio = CA / CL = $5,350/$4,300 = 1.24 times Quick ratio = (CA - inventory) / CL = ($5,350 - 1,300) / $4,300 = 0.94 times
An investment earned the following returns 1998 through 2001:
None of the above
The following data pertains to a common stock:• It will pay no dividends for two years.• The dividends three years from now is expected to be $1.• Dividends are expected to grow at a 7% rate from that point onward.If an investor requires a 17% rate of return on this stock, what will they be willing to pay for this stock now?
P2 = 1/(.17 - .07)= $10 P0 = P2/(1 + r)^2= $10/(1.17)^2 = 7.31
ABC common stock is expected to have extraordinary growth of 20% per year for two years, at which time the growth rate will settle into a constant 6%. If the discount rate is 15% and the most recent dividend was $2.50, what should be the approximate current share price?
Price = ($2.50 × 1.2)/1.15 + ($2.50 × 1.22)/1.152+ [($2.50 × 1.22×1.06)/(0.15 − 0.06)]/1.152= $37.39 = 37.40
New projects or products can have a side effect on the firm as well as a direct effect. Which of the following appears to be a side effect of launching a new product?
Sales of a similar product of your firm's will decline
List the advantages and disadvantages of the three different types of business organization.
Sole proprietorship: PROS: -Easiest to start -Least regulated -Single owner keeps all the profits -Taxed once as personal income CONS: -Limited to life of owner -Limited equity capital -Unlimited liability -Difficult to sell ownership interest Partnership: PROS: -Two or more owners -More capital available -Relatively easy to start -Taxed once as personal income CONS: -Unlimited liability for general partner -Partnership dissolves when one partner dies or wishes to sell -Difficult to transfer ownership Corporation: PROS: -Limited liability -Unlimited life -Separation of ownership and management -Transfer of ownership is easy -Easier to raise capital CONS: -Agency conflicts -Double taxation
A bonds indenture least likely species the
Source of funds for repayment
The principle of diversification tells us that:
Spreading an investment across many diverse assets will eliminate some of the risk.
Prepare common-size income statements for Wal-Mart and Starbucks using the information provided below. Which company is doing a better job of getting sales dollars to net income? Where is the one company having an advantage over the other company in turning revenue into net income?
Starbucks brings a little over 10.79% of its sales revenue to the bottom line, while Wal-Mart brings only 3.36%. Starbuck's has a significant advantage over Wal-Mart in the cost of goods sold but Wal-Mart has a much smaller selling, general and administrative expense. Why these companies enjoy these different advantages is a question that will take more financial and economic investigation into the operations of the two companiesand the industries in which they operate.
Which of the following statements about the call provision of a bond is most accurate? A call provision
Stipulates whether and under what circumstances the issuer can redeem or depart the bond prior to maturity.
If we know the __________ and the EBIT, we can estimate the taxes for a project for the year.
Tax rate
Flynn, Inc. is considering a four-year project that has an initial outlay or cost of $80,000. The future cash inflows from its project are $40,000, $40,000, $30,000, and $30,000 for years 1, 2, 3 and 4, respectively. Flynn uses the internal rate of return method to evaluate projects. What is the approximate IRR for this project?
The IRR is about 28.88%. Using cash flow keys, we enter: CF0= -80000, CF1=40000, CF2=40000, CF3=30000, CF4=30000, and solve for IRR, we get IRR = 28.88%
Flynn, Inc. is considering a four-year project that has an initial after-tax outlay or after-tax cost of $80,000. The future after-tax cash inflows from its project for years one, two, three, and four are $40,000, $40,000, $30,000, and $30,000, respectively. Flynn uses the internal rate of return method to evaluate projects. What is the approximate IRR for this project?
The IRR is about 28.89%
Brock Florist Company sold its delivery truck (see previous problem) after three years of service. If MACRS was used for the depreciation schedule, what is the after-tax cash flow from the sale of the truck (continue to use a 30% tax rate) if a. The sales price was $15,000? b. The sales price was $10,000? c. The sales price was $5,000?
The accumulated depreciation after three years using MACRS is $29,000 × (0.20 + 0.32 + 0.192) = $20,648. The book value of the truck is therefore $29,000 - $20,648 = $8,352. a. If the sales price is $15,000 then the truck had a gain on sale of $15,000 - $8,352 = $6,648 and the tax liability is $6,648 × 0.30 = $1,994.40. The after tax cash flow is $15,000 - $1,994.40 = $13,005.60 b. If the sales price is $10,000 then the truck had a gain on sale of $10,000 - $8,352 = $1,648 and the tax liability is $1,648 × 0.30 = $494.40. The after tax cash flow is $10,000 - $494.40 = $9,505.60 c. If the sales price is $5,000 then the truck had a loss on sale of $5,000 - $8,352 = $3,352 and the tax credit is $3,352 × 0.30 = $1,005.60. The after tax cash flow is $5,000 + $1,005.60 = $6,005.60
The current yield on a bond is equal to:
The annual coupon payment divided by the current market price
St. John's Paper is considering purchasing equipment today that has a depreciable cost of $1 million. The equipment will be depreciated on a MACRS 5-year basis, which implies the following depreciation schedule: Year 1, MACRS DR: 0.20 Year 2, MACRS DR: 0.32 Year 3, MACRS DR: 0.19 Year 4, MACRS DR: 0.12 Year 5, MACRS DR: 0.11 Year 6, MACRS DR: 0.06 Assume that the company sells the equipment after three years for $400,000 and the company's tax rate is 40 percent. What would be the tax consequences resulting from the sale of the equipment?
The company would have to pay $44,000 in taxes. Year 1 depreciation = $1 million*0.2 = 200,000 Year 2 depreciation = $1 million*0.32 = 320,000 Year 3 depreciation = $1 million*0.19 = 190,000 Book value at end of year 3 = 1,000,000 - 200,000 - 320,000 - 190,000 = 290,000 Capital gain/loss = 400,000 - 290,000 = 110,000 Capital gain tax = 40%*110,000 = 44,000
In calculating the weighted average cost of capital (WACC), which of the following statements is least accurate?
The cost of debt is equal to one minus the marginal tax rate multiplied by the coupon rate on outstanding debt
Which of the following is false regarding the estimation of a firm's cost of equity capital?
The cost of equity is equal to the weighted average cost of capital
Which of the following is false regarding the estimation of a firm's cost of equity capital?
The cost of equity is equal to the weighted average cost of capital.
A bond sold five weeks ago for $1,100. The bond is worth $1,150 in today's market. Assuming no changes in risk, which of the following is false?
The coupon payment of the bond must have decreased.
What happens to the coupon rate of a bond that pays $80 annually in interest if yield to maturity changes from 9% to 10%
The coupon rate remains at 8%
Which of the following statements regarding bond pricing is true?
The lower the discount rate, the more valuable the coupon payments are today.
Net Present Value
The difference between the instristic value of a project and its cost. How much value is created from undertaking an investment? -The first step is to estimate expected future cash flows. -The second step is to estimate the required return for projects of this risk level. -The third step is to find the present value of the cash flows and subtract the initial investment. (+) desirable, creates value (-) not desirable, destroys value
Which of the following statements about preferred stock is false?
The dividends on preferred stocks could be increased or decreased
Which of the following describes a stock that plots above the security market line?
The expected return of the stock is too high
Which of the statements below is true?
The graphic plot of project NPV against discount rate is called the NPV profile
Which of the following is not an example of annuity cash flows?
The grocery bill that changes every week
What is the typical relationship between the return standard deviation of an individual common stock and the return standard of a diversified portfolio of common stocks?
The individual stock's return standard deviation is higher
What happens when a bond's expected cash flows are discounted at a rate lower than the bond's coupon rate?
The price of the bond is higher than the par value
Which of the following is false regarding risk and return? a. The risk-free asset earns the lowest rate of return. b. The reward for bearing risk is known as the standard deviation. c. Based on historical data, there are rewards for bearing risk. d. An increase in the systematic risk of an investment will result in an increased risk premium. e. None of the above
The reward for bearing risk is known as the standard deviation.
Your firm disposes of an asset which is worthless in the open market, but still has remaining undepreciated book value. The tax benefit to the firm from the write-off of this asset is equal to:
The tax rate multiplied by the remaining book value.
Massey Machine Shop is considering a four-year project to improve its production efficiency. Buying a new machine press for $450,000 is estimated to result in $150,000 in annual pretax cost savings. The press falls in the MACRS five year class, and it will have a salvage value at the end of the project of $90,000. The press also requires an initial investment in spare parts inventory of $18,000, along with an additional $3,000 in inventory for each succeeding year of the project. If the shop's tax rate is 35% and its discount rate is 14%, should Massey buy and install the machine press?
The total investment in the new machine is $450,000. Since the machine falls into the five-year class, it will has the following depreciation schedule: Year 1: 20%(450,000) = 90,000 Year 2: 32%(450,000) = 144,000 Year 3: 19.20%(450,000) = 86,400 Year 4: 11.52%(450,000) = 51,840 Year 5: 11.52%(450,000) = 51,840 Year 6: 5.76%(450,000) = 25,920 Ending Book Value = Initial investment - accumulated depreciation = $450,000 - ($90,000 + 144,000 + 86,400 + 51,840) = $77,760 After-tax salvage value = Salvage value - Tax Rate * Capital gain = Salvage value - Tax Rate*(Salvage value -Book value) = $90,000 - 0.35*( $90,000 -$77,760) = $85,716 The system is going to save the firm $150,000 per year. This is equivalent to a net of gross profit of $150,000.
You want to create a portfolio equally as risky as the market (i.e, a portfolio with beta equal to 1), and you have $1,000,000 to invest. Given this information, fill in the rest of the following table: Asset: Stock A Investment: $200,000 Beta: .70 Asset: Stock B Investment: $250,000 Beta: 1.10 Asset: Stock C Investment: Beta: 1.60 Risk-free asset
WA = $200,000 / $1,000,000 = .20; WB = $250,000/$1,000,000 = .25 ; WC + WRf = 1 - WA - WB = .55 bp = 1.0 = WA(.7) + WB(1.1) + WC(1.6) + WRf(0); Hence, WC = .365625, and invest .365625($1,000,000) = $365,625 in C. WRf = 1 - .20 - .25 - .365625 = .184375 and invest .184375($1,000,000) = $184,375 in the risk-free asset
Investment Criteria
We need to ask ourselves the following questions when evaluating decision criterion: -Does the decision rule adjust for the time value of money? -Does the decision rule adjust for risk? -Does the decision rule provide information on whether we are creating value for the firm?
Levenworth Industries has the following capital structure on December 31, 2006: What are the weights on debt and preferred stock in the firm's capital structure?
Weight on debt 0.41; Weight on preferred stock: 0.06
Levenworth Industries has the following capital structure on December 31, 2006:
Weight on debt: 0.41; Weight by on preferred stock: 0.10
Deighton Industries has 200,000 bonds outstanding. The par value of each corporate bond is $1,000, and the current market price of the bonds is $965. Deighton also has 6 million common shares outstanding, with a market price of $28 per share. At a recent board of directors netting, Deighton board members decided not to change the company's capital structure in a material way for the future. To calculate the weighted average cost of Deighton's capital, what weights should be assigned to debt and to equity?
Weight on debt: 53.46%; weight on equity: 46.54% 6,000,000 x 28 = 168,000,000 200,000 x 965 = 193,000,000 168,000,000/(168,000,000 + 193,000,000) = 46.54% 193,000,000/(168,000,000 + 193,000,000) = 53.46%
Simpson, Inc. is considering a five-year project that has an initial after-tax outlay or after-tax cost of $48,000. The respective future cash inflows from its project for years 1, 2,3 4, and 5 are: $15,000, $25,000, $35,000, $45,000, and -$70,000. The appropriate discount rate for this project is 9%. Should Simpson accept the project?
Yes because the NPV is positive
Your neighbor owns a perpetuity of $100 per year that has a discount rate of 6% per year. He offers to sell to you all but the next 20 cash flows (the first to be received one year from today) for $500. In other words, he keeps the first 20 cash flows of his perpetuity and you get all of the rest. Is this a good price for you if the appropriate discount rate is 6%?
Yes, because the present value of the remaining cash flows is $519.68 and you are buying them for only $500. PV = 100/6% = 1,666.667 PMT = 100 I/Y = 6 N = 20 FV = 0 PV = 1,146.992 1,666.667 - 1,146.992 = 519.68
A lottery ticket states that you will receive $250 every year for the next ten years. a. What is the present value of the winning lottery ticket if the discount rate is 6% and it is an ordinary annuity? b. What is the present value of the winning lottery ticket if the discount rate is 6% and it is an annuity due? c. What is the difference between the ordinary annuity and annuity due in parts (a) and (b)?
a. N = 10 I/Y = 6 PV = 0 PMT = 250 FV = 0 PV = 1,840 b. The present value of annuity due = PV of ordinary annuity*(1+r) = 1,840 x 1.06 = $1,950.40 c. 1,950.40 - 1,840 = 110.40
Suppose a stock had an initial price of $69 per share, paid a dividend of $1.95 per share during the year, and had an ending share price of $53. a) What was the dividend yield for the year? b) What was the capital gain yield for the year? c) What is the percentage total return for the year?
a. dividend yield = 1.95/69 = 2.83% capital gain yield = (53 - 69)/69 = -23.19% b. capital gain yield = (53 - 69)/69 = -23.19% c. total return = 2.83% + (-23.19%) = -20.36%
The type of risk that can be diversified away is called ________.
all of the above (diversifiable risk, unique risk, idiosyncratic risk)
In capital budgeting analysis, an increase in working capital can be shown as:
an outflow at the beginning and an equal inflow at the end of the project.
The cost of debt capital for a firm _________.
can be estimated even if the firm's bonds are not publicly traded, by looking at the yield to maturity on bonds outstanding from peer group firms with similar ratings and maturity
When managers' compensation plans are tired in a meaningful manner to the profits of the firm, agency problems:
can be reduced
___________ refers to the way a company finances itself through some combination of loans, bond sales, preferred stock sales, common stock sales, and retention of earnings.
capital structure
If a project is expected to increase inventory by $17,000, increase accounts payable by $10,000, and decrease accounts receivable by $1,000, what effect does working capital have during the life of the project?
cash outflow of $6,000
You are attempting to value a stock in a mature industry that is steadily shrinking in size. Of the stock valuation models studied, the most appropriate is the .
constant growth model
The ________ is the annual coupon payment divided by the current price of the bond, and is not always an accurate indicator.
current yield
Shocking Co. is expected to maintain a constant 7 percent growth rate in its dividends, indefinitely. If the company has a dividend yield of 4.2 percent, what is the required return on the power company's stock?
required return = R = dividend yield + capital gains yield = 0.042 + 0.7 = 11.2%
Suppose that the Federal Reserve takes actions that cause the risk-free rate to fall. All else the same, we would expect a firm's cost of equity to .
decrease if we are using the SML
Suppose a stock had an initial price of $69 per share, paid a dividend of $1.95 per share during the year, and had an ending share price of $53. •What was the dividend yield for the year? •What was the capital gain yield for the year? •What is the percentage total return for the year?
dividend yield = 1.95/69 = 2.83% capital gain yield = (53 - 69)/69 = -23.19% total return = 2.83% + (-23.19%) = -20.36%
Although non-systematic risk is present in differing amounts, individual stocks are:
exposed to differing amounts of systematic risk also
Which of the following does NOT offer the protection of limited liability?
sole proprietorship
The MACRS allows an increase
in annual depreciation during earlier years
The modified accelerated cost recovery system (MACRS) allows an increase:
in annual depreciation during earlier years
Landen, Inc. uses several methods to evaluate capital projects. An appropriate decision rule for Landen would be to invest in a project if it has a positive:
net present value (NPV)
The ________ model is usually considered the best of the capital budgeting decision-making models.
net present value (NPV)
Which of the following is not accurate in depicting cash flows from operations?
net profit + depreciation + tax paid
An NPV of zero implies that an investment ___________________. a. is not making money for its shareholders b. has the sum of the total cash flows equal to zero c. destroys shareholder wealth d. all of the above e. none of the above
none of the above
The main variables of the TVM equation are
present value, future value, time, interest rate, and payment.
The accelerated depreciation of capital investments in MACRS depreciation provides a taxable expense that reduces taxed at a faster rate than with straight-line depreciation. Therefore, according to _________ concepts, we can surmise that lower tax expenses in the earlier years and higher tax expenses in the later years are better than a steady tax expense each year.
time-value of money
The variance of an investment's returns is a measure of the:
volatility of the rates of return.
Which of the following is a correct interpretation of a total asset turnover of 3.0?
For each $1 of assets owned by the firm it generates $3 in sales.
You deposited $1,000 in a savings account that pays 8 percent annual interest compounded quarterly, planning to use it to finish your last year in college. Eighteen months later, you decide to go to the Rocky Mountains to become a ski instructor rather than continue in school, so you close out your account. How much money will you receive? (round to the nearest dollar)
$1,126 N = 6 I/Y = 2 PV = 1,000 PMT = 0 FV =-1,126
Braxton Ltd issued a 30-year 10% coupon bond ten years ago. Braxton bonds have a maturity (face) value $1,000 and make semiannual interest payments. If investors require an 8% nominal annual return on bonds with the same risk rating as Braxton, at what price should the bonds be selling for currently?
$1,197.93 I/Y = 8/2 = 4 FV = 1,000 PMT = 100/2 = 50 N = (30 - 10) x 2 = 40 PV = 1,197.93
What is the future value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest rate? (round to the nearest cent)
$1,348.48 N=5 I/Y =15 PV = 0 PMT = 200 FV= -1,348.48
Biogenetics, Inc. plans to retain and reinvest all of their earnings for the next 30 years. Beginning in year 31, the firm will begin to pay a $30 per share dividend. The dividend will not subsequently change. Given a required return of 18%, what should the stock sell for today?
$1.16 P30 = 30/18% = 166.67. P0 = P30/(1+18%)30 = 1.16
Assume that a firm takes on a project that requires an initial investment in year 0 of $20,000. Also assume that the project procedures cash inflows of $1,800 in all future years. If the required rate of return for this project is 6%, then what is the net present value?
$10,000
A firm has revenue of $50,000, the cost of goods sold is $23,000, other expenses (selling and administration) are $14,000 and depreciation is $5,000. The firms tax rate is 33%. What is the operating cash flow?
$10,360 50,000 - (23,000 + 14,000) - 5,000 = 8,000 8,000 x 33% = 2,460 8,000 - 2,460 + 5,000 = 10,360
What is the NPV of a project that costs $100,000 and returns $50,000 annually for 3 years if the opportunity cost of capital is 14%?
$16,082
An investment promises a payoff of $195 two and half years from today. At a discount rate of 7.5% per year, what is the present value of this investment?
$162.75 N=2.5 I/Y = 7.5 PMT = 0 FV=195 PV = -162.75
A corporation declares $25 million in net income, $1 million in interest expenses, $1 million in preferred stock dividends, and $7 million in common stock dividends. By how much will shareholder's equity increase on the balance sheet?
$17 million 25 - 1 - 7 = 17
Your parents plan to spend $20,000 on a car for you upon graduation from college. If you will graduate in three years and your parents can earn 4.125% annually on their investment, how much money must they set aside today for your car?
$17,716 N=3 I/Y =4.125 PMT=0 FV= 20,000 PV = -17,716.
Your uncle has agreed to deposit $3,000 in your brokerage account at the beginning of each of the next five years (t = 0, 1, 2, 3, and 4). You estimate that you can earn 9 percent a year on your investments. How much will you have in your account right after the last deposit is made? (Assume that no money is withdrawn from the account)
$17,954.13 N = 5 I/Y = 9 PV = 0 PMT = 3000 FV = 19,570
Suppose that sales and profits of Oly Enterprises are growing at a rate of 30% per year. At the end of four years, the growth rate will drop to a steady 6%. At the end of year 5, Oly will issue its first dividend in the amount of $3 per share. If the required return is 15%, what is the value of a share of stock? Assume dividends grow at the same rate as earnings after year 4.
$19.06 Assume that an investor buys the stock today and sell it at year 4. P4 = DIV5/(r-g) = 3/(15%-6%) = 33.33 P0 = P4/(1+r)4 = 33.33/(1.15)4 = 19.06
Harry decided he was tired of being a poor college student when he visited a local electronics store and experienced its finest theatre system. He determined that he would invest today a portion of the remaining money he earned last summer cleaning animal cages at the veterinary clinic. He plans to invest the money into an international mutual fund for 3.5 years and expects to earn an average annual dollar rate of return of 15%. If Harry wants to have $4,000 in the account at the end of this time, how much must he invest today? (Round your answer to the nearest dollar)
$2,453 FV = 4,000 I/Y = 15 N = 3.5 PMT = 0 PV = 2,452.55
The furniture store offers you no-money-down on a new set of living room furniture. Further, you may pay for the furniture in three equal annual end-of-the-year payments if $1,000 each with the first payment to be made one year from today. If the discount rate is 6%, what is the present value of the furniture payments?
$2,673.01 PMT = 1,000 N = 3 I/Y = 6 FV = 0 PV = -2,673.01
What is the net effect on a firm's net working capital if a new project requires $30,000 increase in inventory, $10,000 increases in accounts receivable, $35,000 increase in machinery, and a $20,000 increase in accounts payable?
$20,000 increase in NWC $10,000 + $30,000 - $20,000 = $20,000
Your parents agree to pay half of the purchase price of a new car when you graduate from college. You will graduate and buy the car two years from now. You have $9,000 to invest today and can earn 12% on invested funds. If your parents match the amount of money you have in two years, what is the maximum you can spend on the new car?
$22,579 PV = 9,000 N = 2 PMT = 0 I/Y = 12 FV = 11,289.60 x 2 = $22,579
Boomer Products, Inc. manufactures "no-inhale" cigarettes. As their target customers age and pass on, sales of the product are expected to decline. Thus, demographics suggest that earnings and dividends will decline at a rate of 5% annually forever. The firm just paid a dividend of $4; given a required rate of return is 10%, the price of the stock in 2 years will be:
$22.86 P2 = DIV3/(r-g) = 4*(1 - 5%)3/(10%+5%) = 3.43/15% = 22.86
Your company is considering investing in a new system that will cost $160,000. What is the total cash outflow in year 0?
$225,000 Investment cash outflow = 160,000 + 40,000 = 200,000 Cash outflow due to change in NWV = 25,000 Total cash outflow in year 0 = 200,000 + 25,000 = 225,000
Calculate the value of a common stock that last paid a $2.00 dividend if the required rate of return on the stock is 14 percent and the expected growth rate of dividends and earnings is 6 percent forever. What growth model is an example of this calculation?
$26.50 with constant growth model 2 x (1 + 6%)/(14% - 6%) = $26.50
You receive a credit card application from Shady Banks Savings and Loan offering an introductory rate of 2.90 percent per year, compounded monthly for the first six months, increasing thereafter to 15 percent compounded monthly. Assuming you transfer the $3,000 balance from our existing credit card and make no subsequent payments, how much interest will you owe at the end of the first year? (round to the nearest cent)
$279.30 N = 6 PV = 3,000 I/Y = 2.9/12 = 0.24167 PMT = 0 FV = 3,043.76 Then, find the balance at the end of 12 months: N = 6 PV = 3043.76 I/Y = 15/12 = 1.25 PMT = 0 FV = 3,279.30 Thus, interest = 3,279.30 - 3,000 = 279.30
Your company is considering investing in a new system that will cost $160,000. What is the after-tax salvage value at the end of year 5?
$28,608 Book value = (160,000 + 40,000)*(1-.20 - -.32 - .192 -.1152 -.1152) = 11,520 After tax salvage value = 40,000 - (40,000 - 11,520)*40% = 28,608
What would you pay today for a stock that is expected to make a $2 dividend in one year if the expected dividend growth rate is 5% forever and you require a 12% return on your investment?
$28.57 P0 = DIV1/(r-g) = 2/(12%-5%) = 28.57
Bertha plans to purchase 500 shares of preferred stock in five years and wants to know how much she must save each year to make the purchase. The preferred stock pays $6 dividend per share and has a 16% required return. Bertha can deposit her money in an account paying 7% interest rate. How much must Bertha save at the end of the next five years to have enough money to purchase the 500 shares at the end of year 5?
$3,001 to $5,000 Per share price = 6/16% = $37.5 Amount needed = 37.5 x 500 = $18,750 N = 5 PV = 0 I/Y = 7 FV = 18,750 PMT = $3,260.45
Anthony, Ltd. purchases a duplicating machine for $15,000. This machine qualifies as a five-year recovery asset under MACRS. The company has a tax rate of 33%. If the company sells the machine at the end of four years for $4,000, what is the cash flow from disposal?
$3,535.36
Western Inc. purchases a machine for $15,000. This machine qualifies as a five-year recovery asset under MACRS with the fixed depreciation percentages as follows: year 1 = 20.00%; year 2 = 32.00%; year 3 = 19.20%; year 4 = 11.52%. Western has a tax rate of 33%. If the machine is sold at the end of four years for $4,000, what is the after-tax cash flow from disposal?
$3,535.36 Year 1: $15,000(0.2000) = $3,000 Year 2: $15,000(0.3200) = $4,800 Year 3: $15,000(0.1920) = $2,880 Year 4: $15,000(0.1152) = $1,728 Accumulated Depreciation = $3,000 + $4,800 + $2,880 + $1,728 = $12,408 Book Value of machine = $15,000 - $12,408 = $2,592 Gain on disposal is $4,000 - $2,592 = $1,408 Tax rate = $1,408(0.33) = $464.64 After-Tax Cash Flow at disposal = $4,000 - $464.64 = $3,535.36
How much must be invested today in order to generate a 5-year annuity of $1,000 per year, with the first payment 1 year from today, at an interest rate of 12%?
$3,604.78 PMT = 1,000 N = 5 I/Y = 12 FV = 0 PV = 3,604.78
You have an annuity of equal annual end-of-year cash flows of $500 that begin two years from today and last for a total of ten cash flows. Using a discount rate of 4%, what are those cash flows worth in today's dollars?
$3,899.47
The BBM Corp. The net operating cash flow in year 5 from the production of Wuk is:
$3.5 million to 4.2 million
Assume that a share of common stock has just paid a dividend (D0) of $2.00. Also assume that investors expect this stock to have a long-run sustainable growth rate of 5 percent and that they require an annual rate of return of 12%. Determine the current price of this stock.
$30.00 2 x (1 + 5%)/(12% - 5%) = 30.00
The most recent paid dividend (Dic0) is $1.80, the growth rate (g) is 6%, and the required rate of return (r) is 12%. What is the stock price according to the constant growth dividend model?
$31.80
The most recent paid dividend (Div0) is $1.80, the growth rate (g) is 6%, and the required rate of return (r) is 12%. What is the stock price according to the constant growth dividend model?
$31.80 (1.80 X 1.06) / (.12 - .06) = 31.80
What is the required return for a stock that has a 6% constant-growth rate, a price of $25, an expected dividend of $2 next year, and a P/E ratio of 10?
14% 2/25 + 6% = 14%
Approximately how much should be accumulated by the beginning of retirement to provide a $2,500 monthly check that will last for 25 years, during which time the fund will earn 8% interest with monthly compounding? (Round to the nearest hundred dollar)
$323,900.00 PMT = 2,500 N = 25 x 12 = 300 I/Y = 8/12 = 0.6667 FV = 0 PV = 323,911
Depreciable assets were purchased for $70,000 five years ago. Accumulated depreciation is $37,000. The asset is sold for $40,000. If the company faces a 40% tax rate, how much total net after-cash will the sale of these assets generate?
$37,200 70,000 - 37,000 = 33,000 40,000 - ((40,000 - 33,000)* 40%) = 37,200
You are given the cash flows listed below at Years 3, 5, and 6, but you aren't sure about the cash flow at Year 4. Assume that the appropriate interest rate for these cash flows is 12% and that the value of all the cash flows in Years 3 to 6, evaluated as if Year 10 is $1,982.47. Determine the value of the cash flow at Year 4. Year 3, Cash Flow $100 Year 4, Cash Flow $? Year 5, Cash Flow $200 Year 6, Cash Flow $425
$375.00 FV Year 10 = 100 x (1 + 12%)^(10 - 3) + X(1 + 12%)^(10 - 4) + 200(1 + 12%)^(10 - 5) + 425(1 + 12%)^(10 - 6) = 1,982.47 = 221.068 + X(1.12)^6 + 352.468 + 668.746
Your firm intends to finance the purchase of a new construction crane. The cost is $1,500,000. The loan has an annual interest rate of 8.5% and requires annual installment payment. If the loan is to be completely paid off by the end of year five, what should be the annual payment? (Round to the nearest dollar)
$380,649 PV = 1,500,000 I/Y = 8.5 N = 5 FV = 0 PMT = 380,649
You are interested in saving money for your first house. Your plan is to make regular deposits into a brokerage account that will earn 14 percent. Your first deposit of $5,000 will be made today. You also plan to make four additional deposits at the beginning of each of the next four years. Your plan is to increase your deposits by 10 percent a year. (That is, you plan to deposit $5,500 at t = 1, and $6,050 at t = 2, etc.) How much money will be in your account right after the last deposit is made?
$39,363
The revenue is $24,000, the cost of goods sold is $12,000, other expenses (from selling and administration) are $6,000, and depreciation is $2,000. What is the EBIT?
$4,000
You are evaluating whether to retire your current computer modem product and replace it with a new modem that incorporates new features. Which of the following would not be relevant to your decision-making process? a. $50,000 spent on research and development costs over time on the older modem. b. A loss in revenues of $30,000 from terminating the old modem line. c. Equipment you own with a market value of $30,000 that can be used to build the new modems. d. $25,000 in salvage value you will receive for scrapping the old modem's obsolete production equipment.
$50,000 spent on research and development costs over time on the older modem.
Your employer has agreed to place a year-end deposits of $1,000, $2,000 and $3,000 into your retirement account. The $1,000 deposit will be one year from today, the $2,000 deposit two years from today, and the $3,000 deposit three years from today. If your account earns 5% per year, how much money will you have in the account at the end of year three when the last deposit is made?
$6,202.50
You have the opportunity to buy a perpetuity that pays $1,000 annually. Your required rate of return on this investment is 15 percent. You should be essentially indifferent to buying or not buying the investment if it were offered at a price of
$6,666.67 PV = 1000/15% = 6,666.67
What is the present value of receiving $100 monthly for two years, followed by $200 monthly for the next three years, payments? Assuming that the annual interest rate is 13%, compounded monthly. (Round to the nearest dollar)
$6,687 CF 1 = 100 F1 = 2 x 12 = 24 CF 2 = 200 F2 = 3 x 12 = 36 I = 13/12 = 1.08333 NPV = 6,686.61
A wealthy woman just died and left her pet cats the following estate: $50,000 per year for the next fifteen years, with the first cash flow today. At a discount rate of 3.2%, what is the feline estate worth in today's dollars?
$607,180.14
A firm has sales of $800, total assets of $500, and a debt ratio of 0.30. If its return on equity is 18%, what is its net income?
$63 debt ratio = total debt/total asset = 0.3 total debt = 0.3 x 500 = $150 Total asset = total equity + Total debt 500 = total equity + 150 Total equity = 350 ROE = NI/Total Equity = 18% NI = 18% x 350 = 63
Cash and equivalents are $1561; short-term investments are $1052; accounts receivable are $3616; accounts payable are $5173; short-term debt (due in six months) is $288; inventories are $1816; other current liabilities are $1401; and other current assets are $707. What is the amount of total current liabilities?
$6862
Assume you are to receive a 20-year annuity with annual payments of $50. The first payment will be received at the end of Year 1, and the last payment will be received at the end of Year 20. You will invest each payment in an account that pays 10 percent. What will be the value in your account at the end of Year 30? (round to the nearest dollar)
$7,428 N=30 I/Y=10 PV = -425.678 PMT=0 FV =7428
How much interest is earned in just the third year on a $1,000 deposit that earns 7% interest compounded annually?
$80.14 Year 1: 1,000 x 7% = 70 Year 2: (1,000 + 70) x 7% = 74.90 Year 3: (1,000 + 70 + 74.90) x 7% = 80.14
A firm purchased an asset that cost $1 million 3 years ago. In additional, the firm paid $100,000 in installation costs. The asset is classified as MACRS 3-year property class (MACRS depreciation schedule for 3-year property class is 33.33%, 44.45%, 14.81%, 7.41% for years 1, 2, 3, and 4 respectively). What is the book value today (at the end of year 3)?
$81,510
Randy Harris is contemplating whether to add a. Kms to his portfolio. It is a semiannual, 6.5% bond with 7 years to maturity. He is concerned about the charge in value due to interest rate fluctuations and would like to know the bonds value given various scenarios. At a yield to maturity of 7.5% or 5.0%, the bonds fair value is closest to:
$946.30 at 7.5% or $1,087.68 at 5%
The stock of MTY Golf World currently sells for $89.92 per share. The firm has a constant dividend growth rate of 6% and just paid a dividend of $5.09. If the required rate of return is 12%, what will the stock sell for one year from now?
$95.32 Recall that under the constant growth model, the growth rate, g, is not just the growth rate of the dividend, but the stock price also grows at the same rate. In this case, we know the growth rate is 6% and current price is $89.92. Thus, P1=P0 x (1+6%)= $89.92 x 1.06= $95.32.
Your company just sold a product with the following payment plan: $50,000 today, $25,000 next year, and $10,000 the following year. If your firm places the payments into an account earning 10% per year, how much money will be in the account after collecting the last payment?
$98,000
What is the expected return on asset A if it has a beta of 0.6, the expected market return is 15%, and the risk-free rate is 6%?
11.4% R = Rf + beta* (Rm- Rf) = 6% + 0.6*(15% - 6%) = 11.4%
Discounted Payback Period
-Compute the present value of each cash flow and then determine how long it takes to pay back on a discounted basis. -Compare to a specified required period -Decision Rule: accept the project if it pays back on a discounted basis within the specified time Advantages: -Includes time value of money -Easy to understand -Adjusts for uncertainty of later cash flow -Biased towards liquidity Disadvantages: -May reject positive NPV investments -Requires an arbitrary cutoff point -Ignores cash flows beyond the cutoff point -Biased against long0term projects, such as R&D and new products
NPV - Decision Rule
-If the NPV is positive, accept the project. -If the NPV is negative, reject the project. -A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners. -Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal. -For normal projects, NPV decreases when discount rate increases. -The relative attractiveness of mutually exclusive projects depend on the discount rate.
NPV vs. IRR
-NPV & IRR will generally give us the same decision Exceptions: -Non-conventional cash flows - cash flow signs change more than once -Mutually exclusive projects - initial investment and timing of cash flows are substantially different Conflicts between 2: -NPV directly measures the increase in value to the firm -Whenever there is a conflict between NPV and another decision rule, you should ALWAYS use NPV. -IRR is unreliable in the following situations: -non-conventional cash flows -mutually exclusive projects
Salvage Value
-Salvage value is the residual value of the equipment when the project is liquidated -Salvage value usually differs from the book value -After-tax Salvage = salvage - T(salvage - book value)
Common Types of Cash Flows
-Sunk costs: costs that have occurred in the past (irrelevant) -Opportunity costs - costs of lost options (relevant) -Side effects (relevant) Positive side effects - benefits to other projects Negative side effects - costs to other projects -Changes in net working capital (relevant) -Financing costs (irrelevant) -Taxes (relevant) / Remember Terminal Cash Flows (from liquidation of assets with market value but not necessarily accounting value and from liquidation of working capital / Beware of Allocated Overhead Costs / Separation of investment & financing decisions
Using the NPV Rule to Choose among Projects
-When choosing among mutually exclusive projects, calculate the NPV of each alternative and choose the highest positive NPV Project. -Projects with 0 or (- reject) NPV can still be profitable. -Sometimes firms must take on a negative NPV project. (like machine replacement, environmental cleanup, etc.) -When there are alternatives, the rule is to choose the project with the least negative NPV. EX) 9.5% OC Project A: C0 = -1,050 C1 = $700 C2 = $500 NPV = $6.27 Project B: C0 = -1,050 C1 = $500 C2 = $718 NPV = $5.44 Both projects have + NPVs, both accepted if not mutually exclusive. Since this is mutually exclusive, Project A has higher NPV and should be chosen over Project B.
An investor divides her portfolio equally into three parts, with one part in Treasury bills, one part in a market index, and one part in a diversified portfolio with beta of 1.50. What is the beta of the investor's overall portfolio?
0.83 (1/3 x 0) + (1/3 x 1) + (1/3 x 1.5) = 0.83
What is the beta for a portfolio equally weighted in four assets: A, the market portfolio; B, which has half the risk of A; C, which has twice the risk of A; and D, which is risk-free?
0.875 Portfolio beta = 0.25*1 + 0.25*0.5 + 0.25*2 +0.25* 0 = 0.875
Assume a portfolio is made up of the following three stocks: Selecting the closest answer, the beta for this portfolio is:
0.92
Annie is curious to know what her portfolio's CAPM-based expected rate of return should be. After doing some research she figures out the market values and betas of each of her 5 stocks (next slide) and is told by her consultant that the risk-free rate is 3% and the market risk premium is 8%. Help Annie calculate her portfolio's expected rate of return.
1 $35,000 0.1400 1.6 2 $40,000 0.1600 1.2 3 $45,000 0.1800 1.0 4 $50,000 0.2000 -0.8 5 $80,000 0.3200 0.8 = $250,000
Mercer Shaved Ice Co. has identified an investment project with the following cash flows. If the discount rate is 10 percent, what is the present value of these cash flows? What is the present value at 18 percent? At 24 percent?
1, $1,300 2. 500 3, 700 4, 1,620
Rasputin, Inc., has identified an investment project with the following cash flows. If the discount rate is 8 percent, what is the future value of these cash flows in Year 4? What is the future value at a discount rate of 11 percent? At 24 percent?
1, 900 2, 1,000 3, 1,100 4, 1,200
Company XYZ is evaluating a project and here is some information for the project. The unit sales price is projected to be $40 and sales volume to be 1,000 units in year 1, 1,250 units in year 2, and 1,325 units in year 3. The project has a 3 year life. Variable costs amount to $22.5 per unit and fixed costs are $10,000 per year. The project requires an initial investment of $16,500, which is depreciated straight-line to zero over the 3 year project life. The actual market value of the initial investment at the end of year 3 is $3,500. Initial net working capital investment of $7,500 and NWC will maintain a level equal to 20% of sales each year thereafter. The tax rate is 34% and the required return on the project is 10%. 1. What is EBIT for the project in the first year? 2. Given the $7,500 initial investment in NWC, what change occurs for NWC during year 1? 3. What is the operating cash flow for the project in year 2? 4. What is the effect of the $3,500 salvage value on year 2 cash flows?
1. $2,000 Sales = $40*1000=40,000 Variable cost = $22.5*1000 = $22,500 Depreciation = 16,500/3 = 5,500 EBIT = Sale - VC - FC - Depreciation = 40,000 - 22,500 - 10,000 - 5,500 = 2,000 2. There is a $500 increase in NWC. Year 1 NWC = 20%*40,000 = 8,000 Change in NWC = 8000 - 7500 = 500 3. $9,708 Sales = $40*1250=50,000 Variable cost = $22.5*1250 = $28,125 Depreciation = 16,500/3 = 5,500 EBIT = Sale - VC - FC - Depreciation = 50,000 - 28,125 - 10,000 - 5,500 = $6,375 Tax= 6375*34% =2167.50 OCF = EBIT - Tax + Depreciation = 6,375 - 2167.50 + 5,500 = 9,707.5 or 9708. 4. Salvage value does not affect incremental cash flow until year 3.
Kevin would like to increase the balance of his savings account by 300%. If the interest rate on the bank account is 12%, approximately how long would it take to achieve Kevin's goal?
12 years PV = -1 FV = 4 I/Y = 12 PMT = 0 N = 12.23
You have been asked by the president of your company to evaluate the proposed acquisition of a new special-purpose truck. The truck's basic price is $50,000, and it will cost another $10,000 to modify it for special use by your firm. The truck falls in the MACRS 3-year class, and it will be sold after three years for $20,000. Use of the truck will require an increase in net operating working capital (spare parts inventory) of $2,000. The truck will have no effect on revenues, but it is expected to save the firm $20,000 per year in before-tax operating costs, mainly labor. The firm's marginal tax rate is 40 percent. The three-year MACRS schedule is as follows: Year, Percentage 1, 33.3333% 2, 44.4444% 3, 14.8149% 4, 7.4074 % 1. What is the cash flow at year 0? 2. What is the operating cash flow in Year 1? 3. If the cost of capital for this project is 10 percent. What is its NPV?
1. -$62,000 50,000 + 10,000 + 2,000 = 62,000 2. $20,000 Depreciation in year 1 = (50,000 +10,000)*33.33333% = 20,000 Note a dollar saved is a dollar made. We can treat the $20,000 saved as revenue. In addition, there is no other additional cost related. Thus, we can find the operating profit, or EBIT, of the truck as: EBIT = 20,000 - 20,000 = $0 Tax = $0*40% = $0 OCF = EBIT + depreciation - tax = 0 + 20,000 + 0 = 20,000 3. -$ 1,544 Doing the same for years 2 and 3 as the previous problems, we can find the OCF_year2= $22,667, OCF_year3=$15,556. Investment Cash outflow in year 0 = $50,000 + $10,000 = $60,000 NWC cash outflow in year 0 = $2,000 So, total cash flow in year 0 = 60,000 +2,000 =62,000 At the end of year three, the book value of the truck = 60,000 * (1-33.3333% - 44.4444% - 14.8149%) = $4,444 After-tax salvage value = $20,000 - (20,000 -4,444)*40% = $13,778 Finally, we recover the $2,000 investment in NWC by the end of year 3. So, total cash flow in year 3 = 15,556 + 13,778 + 2,000 = $31,334. Given the cash flows, we can find the NPV as follows: CF0 = -62,000 CF1 = 20,000 CF2 = 22,667 CF3 = 31,334 I = 10, NPV = -$1,544
Computing WACC: New Ideas Inc. currently has 30,000 of its 9% semi-annual coupon bonds outstanding (Par value =1000). •The bonds will mature in 15 years and are currently priced at $1,340 per bond. •The firm also has an issue of 1 million preferred shares outstanding with a market price of $11.00. The preferred shares offer an annual dividend of $1.20. •New Ideas Inc. also has 2 million shares of common stock outstanding with a price of $30.00 per share. The firm is expected to pay a $3.20 common dividend one year from today, and that dividend is expected to increase by 7 percent per year forever. If the firm is subject to a 35 percent marginal tax rate, then what is the firm's weighted average cost of capital?
1. Determine the component costs Cost of Debt: P = $1340 Input N = 30 I/Y = ? PV = -1340 PMT = 45 FV = 1000 CPT I/Y = 2.808 Before - Tax Rd = 2.808% x 2 = 5.62% Cost of preferred stock: Dp = $1.20; Pp = $11 Dp = Dp/Pp = $1.20/($11) = 10.91% Cost of common stock: PC=$30; D1=$3.2; g=7%; Using the constant dividend growth model: Re = [D1/(PC)+g = [3.2/$30]+.07 = 17.67% 2. Determine the market value weights of the components: Market value of bonds = $1340 x 30,000 = $40,200,000 Market value of P/S = $11 x 1,000,000 = $11,000,000 Market value of C/S = $30 x 2,000,000 = $60,000,000 Total Market value = $111,200,000 Weight of debt = 40.2m/111.2m = 36.15% Weight of P/S = 11m/111.2m = 9.89% Weight of C/S = 60m/111.2m = 53.96% 3. Calculate the adjusted WACC WACC = .5396*17.67% + .0989*10.91% +.3615*5.62%*(1-.35) =9.53% +1.08%+1.32% = 11.93%
Assume that stock ABC will pay a dividend of $1.25 for next year (or Year 1), which will then grow at a constant rate of 6 percent every year after that. The stock is currently selling at $31.25. Given the information, what is the required rate of return on the stock?
1.25/31.25 + 6% = 10%
You own a stock portfolio invested 25 percent in Stock Q, 20 percent in Stock R, 40 percent in Stock S, and 40 percent in Stock T. The betas for these four stocks are .9, 1.4, 1.1, and 1.8, respectively. What is the portfolio beta?
1.39 (1.37-1.41)
Your assistant has estimated the cash flows of a new proposed 4-year project as follows. Somehow, he forgot to report cash flow in year 4. However, he did report that the project NPV is $0 at a discount rate of 10%. What is the IRR of the project?
10%
What is the ROA of a firm with $150,000 in average receivables, which represents 60 days sales, total assets of $750,000, and a profit margin of 9%?
10.95% Daily sales = 150,000/60 = 2,500 Annual sales = 2,500 x 365 = 912,500 Net profit margin = net profit/sales 9% = net profit/912,500 Net profit = 82,125 ROA = net profit/total asset = 82,125/750,000 = 10.95%
The business requires an investment of $100,000 of fixed assets (store furniture, computers, etc.), which will be depreciated in 8 years using straight line depreciation. You expect the fixed assets can be liquidated at half of its original value by the end of year 4. The tax rate if 35%. Please find the projected OCF.
100,000/8 = $12,500
Assume you invested $1,000 in stocks 10 years ago, and that your account is now worth $2,839.42. Determine the annual rate of return that you have earned on this investment.
11% PV = -1,000 N = 10 FV = 2,838.42 PMT = 0 I/Y = 11
What is the WACC for a firm using 55% equity with a required return of 15%, 35% debt with a required return of 8%, 10% preferred stock with a required return of 10%, and a tax rate of 35%?
11.07% 35% x 8%(1 - 35%) + 10% x -0% + 55% x 15% = 11.07%
What is the WACC for a firm using 55% equity with a required rate of return of 15%, 35% debt with a required return of 8%, 10% preferred stock with a required return of 10%, and a tax rate of 35%?
11.07% WACC = 35% x 8% x (1 - 35%) + 10% x 10% + 55% x 15% = 11.07%
In the previous problem, suppose the most recent dividend was $4 and the dividend growth rate is 6 percent. Assume that the overall cost of debt is the weighted average of that implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 35 percent. What is the company's WACC?
12.33% By the dividend growth model, we can find the cost of equity as follows: RE = [$4.00(1.06)/$52] + .06 = .1415 As to the cost of debt, it is more complicated. Since we have two outstanding bonds, we will take the weighted average of the YTM of the two bonds as the pretax cost of debt. Given the information on the price, coupon rate and maturity of the two bonds, we can easily find the YTMs of the two bonds. YTM1 = 7.426% and YTM2 = 8.142% Total market value of the first bonds = 1.04($70M) + 0.97($50M) = $121.3M Hence, the weight of the first bond = 1.04($70M)/121.3 = 0.6002 and the weight of the second bond = 0.97($50M)/$121.3M = 0.3998 Therefore, the weighted average cost of debt can be found as follows: RD = (1 - .35)[(.6002)(.07426) + (.3998)(.08142)] = .05013 Given the weights of equity and debt found in problem 12, we can find the WACC as follows: WACC = .7785(.1415) + .2215(.05013) = 12.13%
Suppose that you have just purchased a share of stock for $40. The most recent dividend was $2 and dividends are expected to grow at a rate of 7% indefinitely. What must your required return be on the stock?
12.35% R= DIV1/P0 + g = 2(1+7%)/40 + 7% = 12.35%
Using the following data, calculate the standard deviation of returns of. Round your answer to the nearest bias point, or hundredth of percent.
12.7
What is the IRR of an investment that costs $18,500 and pays $5,250 a year for 5 years?
12.92%
Julian was given a gold coin originally purchased for $1 by his great grandfather 50 years ago. Today the coin is worth $450. The rate of return realized on the sale of this coin is approximately equal to
13% PV = -1 FV = 450 N = 50 PMT = 0 I/Y = 13
You own a portfolio that is 50 percent invested in Stock X, 30 percent in Stock Y, and 20 percent in Stock Z. The returns on these three stocks are 10 percent, 18 percent and 13 percent, respectively. What is the return on the portfolio?
13.00%
Your company is considering taking on a new project that will cost $200,000. It is estimated that the system will increase sales/revenues by $150,000 annually for Years 1-6. Operating expenses, other than depreciation, are expected to be equal to 60 percent of sales in each year. The system will be depreciated on a MACRS basis over 5 years (depreciation rates are 20%, 32%, 19.2%, 11.52%, 11.52% and 5.76% for years 1 to 6 respectively) to a zero book value, but the expected salvage at Year 6 is $40,000. The firm will also be required to invest $25,000 in net working capital at Year 0, but will recapture this amount at Year 6. You may assume that the tax rate on ordinary income is 40 percent (record negative taxes as a positive cash flow). As you can calculate, the IRR for this project is 13.03%. If we assume that the firm's cost of capital for this project is 12 percent, then what is the NPV for this project?
13.03%
Stock in Parrothead Industries has a beta of 1.10. The market risk premium is 8 percent, and T-bills are currently yielding 5.5 percent. Parrothead's most recent dividend was $2.20 per share, and dividends are expected to grow at a 5 percent annual rate indefinitely. If the stock sells for $32 per share, what is your best estimate of Parrothead's cost of equity?
13.26% By the CAPM, RE1 = Rf + βE(E(Rm)-Rf) = .055 + 1.10(.08) = .1430; By the dividend growth model, RE2 = D1/P +g = D0(1+g)/P + g =[$2.20(1.05)/$32] + .05 = .1222; Our best estimate of the cost of equity would be the average of the two estimates: RE = (.1430 + .1222)/2 = 13.26%
Cost of Equity for a firm: R.K. Boats Inc. is in the process of making some major investments for growth and is interested in calculating their cost of equity so as to be able to correctly estimate their adjusted WACC. The firm's common stock is currently trading for $43.25 and their annual dividend, which was paid last year, was $2.25, and should continue to grow at 6% per year. Moreover, the company's beta is 1.35, the risk-free rate is at 3%, and the market risk premium is 9%. Calculate a realistic estimate of RKBI's cost of equity.
13.33% Using the SML Approach: Rf = 3%; Rm-Rf = 9%; β = 1.35; Re=3%+(9%) x 1.35 è15.15% Using the Dividend Growth Model (constant growth) P0 = $43.25; Do= $2.25; g=6%; ($2.25 x (1.06)/$43.25) + .06 = 11.51% A realistic estimate of RKBIs cost of equity = Average of the 2 estimates = (15.15% + 11.51%)/2 = 13.33%
If you can earn 5.25% per year on your investments, how long, exactly, will it take to double your money? (hint: do not use the Rule of 72)
13.55 years I/Y = 5.25 PV = -100 FV = 200 PMT = 0 N = 13.55
What is the standard deviation of a portfolio's returns if the mean return is 15%, the variance of returns is 0.0184, and there are three stocks in the portfolio?
13.56% (0.0184)^1/2 = 13.56%
What is the standard deviation of a portfolio's returns if the mean return is 15%, the variance of returns is 0.0184, and there are three stocks in the portfolio?
13.57%
What is the approximate standard deviation of returns if over the past 4 years an investment returned 8.0%, -12.0%, -11.0%, and 15.0%?
13.59%
You have a balance of $2,000 on your credit card and your monthly minimum payment is $35. The credit card company charges an APR of 18%, compounded monthly. If you just make the minimum payment and do not add additional charges on the card, how long does it take you to pay the balance off? (round to the nearest month)
131 months PV = 2,000 FV = 0 PMT = -35 I/Y = 18/12 = 1.5 N = 131
What is the approximate standard deviation of returns if over the past 4 years an investment returned 8.0%, -12.0%, and 16.0%?
14%
An investment offers $4,100 per year for 15 years, with the first payment occurring one year from now. If the required return is 10 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever?
15 years: N = 15 I/Y = 10 PV = ? PMT = 4,100 FV = 0 PV = $31,184.93 40 years: N = 40 I/Y = 10 PV = ? PMT = 4,100 FV = 0 PV = $40,094.11 75 years: N = 75 I/Y = 10 PV = ? PMT = 4,100 FV = 0 PV = $3,162.45 Perpetuity: PVA = $4,100/.10 = $41,000.00 Perpetuity cannot be solved with financial calculator. Note the difference in present values between perpetuity and a 75-year annuity is very small, less than $35.
Your company is considering the installation of a new production system that will cost $150,000. It is estimated that the system will increase revenues by $65,000 annually for Years 1-4, followed by $50,000 annually for Years 5-7, although operating expenses other than depreciation will also increase by $15,000 per year for Years 1- 7. The system will be depreciated on a MACRS basis over 5 years (depreciation rates are 20%, 32%, 19.2%, 11.52%, 11.52% and 5.76% for years 1 to 6 respectively) to a zero book value. If we assume that the tax rate on ordinary income is 40 percent, and the firm's cost of capital for this project is 10 percent, then, as you can calculate, the NPV for this project is $27,161. What is the IRR for this project?
16.13%
Marie has a $1,000,000 investment portfolio, and she wishes to spend $87,500 per year as an ordinary annuity. If the investment account earns 6% annually. How long will her portfolio last?
19.86 years
The Wilson Corporation has the following relationships: Sales/Total assets = 2.0, return on assets (ROA) = 4.0%, Return on equity (ROA) = 6.0%. What is Wilson's profit margin?
2% 4% = (NI/Sale) x 2 = 2%
A firm has a net profit margin of 15 percent on sales of $20,000,000. If the firm has a debt of $7,500,000, total assets of $22,500,000, and an after-tax interest cost on total debt of 5 percent, what is the firm's ROE?
20.0% 15% = net income/20,000,000 = 3,000,000 22,500,000 = total equity + 7,500,000 = 15,000,000 3,000,000/15,000,000 = 20%
Suppose Massey Ltd. just issued a dividend of $.68 per share on its common stock. The company paid dividends of $.40, $.45, $.52 and $.60 per share in the last four years. If the stock currently sells for $12, what is your best estimate of the company's cost of equity capital?
20.66% g1 = (.45 - .40)/.40 = .1250; g2 = (.52 - .45)/.45 = .1556 g3 = (.60 - .52)/.52 = .1538; g4 = (.68 - .60)/.60 = .1333 g = (.1250 + .1556 + .1538 + .1333)/4 = .1419 RE =D1/P + g =D0(1+g)/P+ g =[$0.68(1.1419)/$12.00] + .1419 = 20.66%
Your credit card has a balance of $3,000. The bank requires a minimum monthly payment of $64.90 and states that it will take 100 months to pay off the balance if you only make minimum payment every month and do NOT make additional charges on the card. What is the annual interest rate charges by your credit card?
21.60% PV = 3,000 PMT = -64.90 N = 100 FV = 0 I/Y = 1.80 1.80 x 12 = 21.69%
Dividend models suggest that ______________ determine the value of a financial asset to which the owner is entitled while holding the asset.
Future cash flows
Company X has 2 million shares of common stock outstanding at a book value of $2 per share. The stock trades for $3 per share. It also has $2 million in face value of debt that trades at 90% of par. What is the weight of debt for WACC purposes?
23.1% 2 million shares x $3.00 = $6,000,000 $2 million debt x 90% = $1,800,000 Total value = $7,800,000 $1.8 million/$7.8 million = 23.1%
Using the following returns, calculate the average returns, the variances, and the standard deviations for X and Y. Year 1: X: 16%, Y: 34% Year 2: X: 18, Y: -7 Year 3: X: -9, -12 Year 4: X: 21, Y: 41 Year 5: X: 2, Y: 10
23.76%
An investment with a cost of $5,000 is expected to have cash inflows of $3,000 in year 1, an $4,000 in year 2. The internal rate of return (IRR) for this investment is closest to:
24% CF0 = -5,000 CF1 = 3,000 CF2 = 4,000 IRR = 24.33
Given the following information, what is your best estimate for the firm's cost of equity on January 2, 2003, if the stock sells for $42 on that day? 12/31/97, $1.50 12/31/98, $1.73 12/31/99, $2.01 12/31/00, $2.34 12/31/01, $2.71 12/31/02, $3.17
24.91% Year-over-year dividend growth rates: 1998: (1.73-1.50)/1.50 = 15.33% 1999: (2.01 -1.73)/1.73 = 16.18% 2000: (2.34 -2.01)/2.01 = 16.42% 2001: (2.71 -2.34)/2.34 = 15.81% 2002: (3.17 -2.71)/2.71 = 16.97% Taking the average, we get annual growth rate: (15.33% + 16.18% +16.42% + 15.81% +16.97%)/5 = 16.14% Using constant growth model; we get: Re = D1/Po + g = 3.17*(1+16.14%)/42 +16.14% = 24.91%
What is the percentage return on a stock that was purchased for $50.00, paid a $3.00 dividend after one year, and was then sold for $49.00?
3% (49 - 50 + 3)/50 = 4%
Mercer Shaved Ice Co. has identified an investment project with the following cash flows. If the discount rate is 10 percent, what is the present value of these cash flows?
3,227
A project costs $100 and has cash flows of $40 per year for the next seven years. If the discount rate is 15%, what is the discounted payback period?
3.38 years
Project costs $100 and has cash flows of $40 per year for the next seven years. If the discount rate is 15%, what is the discounted payback period?
3.38 years
A new machine will cost $100,000 and generate after-tax cash inflows of $35,000 for 4 years. Find the discounted payback if the firm uses a 12% discount rate.
3.72
Assume that a share of stock, priced at $52.5 per share, just paid a dividend of $2. The dividend is expected to grow at a long-run constant rate. The required rate of return is 4% higher than the dividend growth rate (or R - g = 4%). Given this information, determine the dividend yield of the stock.
4.00%
You currently have $67,000 in an interest-earning account. From this account, you wish to make twenty year-end payments of $5,000 each. What annual rate of return must you make on this account to meet your objective?
4.16%
Ferryville Radar Technologies has five-year, 7.5% bonds outstanding that trade at a yield to maturity of 6.8%. The company's marginal tax rate is 35%. Ferryville plans to issue new five-year notes to finance an expansion. Ferryville's after-tax cost of debt capital is closest to:
4.4% 6.8% x (1 - 35%) = 4.42%
A firm sold 10-year bond issue 3 years ago. The bond has a 6.45% annual coupon and a $1,000 face value. The coupons are paid semi-annually. If the current market price of the bond is $951.64 and the tax rate is 35%, what is the after-tax cost of debt?
4.77% N = (10 - 3) = 7 x 2 = 14 PMT = 64.5/2 = 32.25 FV = 1,000 PV = -951.64 I/Y = 3.673 2.673 x 2 = 7.35% 7.35% x (1 - 35%) = 4.77%
Two rival football fans have made the following wager: if one fan's college football team wins the conference title outright, the other fan will donate $1,000 to the winning school. Both schools have had relatively unsuccessful teams, but are improving each season. If the two fans must put up their potential donation today and the discount rate is 8% for the funds, what is the required upfront deposit if both expect a team to win the conference title in five years? Ten years? Twenty years?
5 years: N = 5 I/Y = 8 PV = ? PMT = 0 FV = -1,000 PV = $680.58 10 years: N = 10 I/Y = 8 PV = ? PMT = 0 FV = -1,000 PV = $463.19 20 years: N = 20 I/Y = 8 PV = ? PMT = 0 FV = -1,000 PV = $214.55
A company has a bond issue outstanding that has an 8% coupon, pays semiannual interest, matures in 7 years at a face value of $1,000. What after-tax cost of debt should the company use?
5.51%
Approximately how long will it take to double your money if you get a 5.5%, 7.5%, or 9.5% annual return on your investment? Verify the approximate doubling period with the time value of money equation.
5.5: N = ? I/Y = 5.5 PV = 100 PMT = 0 FV = -200 N = 12.95 7.5: N = ? I/Y = 7.5 PV = 100 PMT = 0 FV = -200 N = 9.58 9.5: N = ? I/Y = 9.5 PV = 100 PMT = 0 FV = -200 N = 7.64
Cost of debt for a firm: You have been assigned the task of estimating the after-tax cost of debt for a firm as part of the process in determining the firm's cost of capital. After doing some checking, you find out that the firm's original 20-year 9.5% coupon bonds (paid semi-annually), currently have 14 years until they mature and are selling at a price of $1,100 each. You are also told that the investment bankers charge a commission of $25 per bond when new bonds are sold. If these bonds are the only debt outstanding for the firm, what is the after-tax cost of debt for this firm if the marginal tax rate for the firm is 34 percent?
5.66% Calculate the YTM on the currently outstanding bonds, after adjusting the price for the $25 commission. i.e. Net Proceeds = $1100-$25 =$1075 Input 28 ? -1075 47.5 1000 Key N I/Y PV PMT FV Output 4.285% After-tax cost of debt =4.285%*2*(1-.34) = 5.66%
Both assets A and B plot on the SML. Asset A has an expected return of 15% and a beta of 1.7, and asset B has an expected return of 12% and a beta of 1.1. What is the risk-free rate of return?
6.5% Given the information, we can set up two equations as follows: 15% = Rf + 1.7*MRP (A) 12% = Rf + 1.1*MRP (B) MRP stands for market risk premium, or Rm-Rf. Multiply equation A by 1.1, and equation B by 1.7, we get 16.5% = 1.1*Rf + 1.87*MRP (C) 20.4% = 1.7*Rf + 1.87*MRP (D) Subtract equation C from equation D, we get 3.90% = 0.6Rf, Then we can solve for Rf=3.90%/0.6 = 6.5%.
On January 1, 2002, HomeSafe Cab Co. will issue new bonds to finance its expansion plans. Currently outstanding 8%, January 1, 2017 HomeSafe bonds are selling for $1,091.96. If interest is paid semiannually for both bonds, what must the coupon rate of the new bonds be in order for the issue to sell at par?
7.00% First, we can find the yield to maturity of the bond currently outstanding as follows: PV=-1091.96, PMT=8% x 1000/2=40, N=15 x2 =30, FV=1000 => I/Y = 3.5 YTM =3.5%*2 = 7%. Given the two bonds are issued by the same company and have the same risk, they YTM of the new bond should be same as the existing bond, or 7%. Further, to issue the new bond at par value, its coupon rate must be set to equal its YTM. Thus, the coupon rate of the new bond must be 7%.
Your firm has preferred stock outstanding that pays a current dividend of $3.00 per year and has a current price of $39.50. You anticipate the economy will grow steadily at a rate of 3.00% per year for the foreseeable future. What is the market required rate of return on your firm's preferred stock?
7.60%
A bond with a 7% coupon with an original maturity of 20 years was issued 4 years ago. If the bond is currently selling for $940, what is its yield to maturity? (The bond pays coupons annually).
7.66% N = 20 - 4 = 16 FV = 1,000 PV = -940 PMT = 70 I/Y = 7.66
An analyst has gathered the following information about a company: What is the ROE?
9.26% ROE = net income/total equity = 150/(1,000 + 620) = 9.26%
Dividend Growth Model
Advantages: -easy to understand and use Disadvantages: -Only applicable to companies currently paying dividends -Not applicable if dividends aren't growing at a reasonably constant rate -Extremely sensitive to the estimated growth rate - an increase in g of 1% increases the cost of equity by 1% -Does not explicitly consider risk
Which of the following is NOT a component of the Du Pont identity?
All of the above are component of the Du Pont identity.
Which of the following statements is most correct? a. If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series. b. To increase present consumption beyond present income normally requires either the payment of interest or else an opportunity cost of interest forgone. c. Disregarding risk, if money has time value, it is impossible for the present value of a given sum to be greater than its future value. d. Disregarding risk, if the present value of a sum is equal to its future value, then the interest rate must be zero e. All of the statements above are correct.
All of the statements above are correct.
Which of the following will result in a future value of greater than $100?
All the future values are greater than $100
Bush Boomerang, Inc., is considering a new three year expansion project that requires an initial fixed asset investment of $2.1 million. The fixed asset will be depreciated straight-line to zero over its three-year tax life, after which time it will be worthless. The project is estimated to generate $1,900,000 in annual sales, with costs of $850,000. If the tax rate is 35%, what is the OCF for this project?
Annual Depreciation = (Beginning value - Ending book value)/(Number of years) = (2.1 million -0)/3 = 0.7 million EBIT = Sale - Cost - Depreciation = 1.9 m- 0.85 m - 0.7 m = 0.35 m Since we do not have interest expenses, Tax = Tax rate * EBIT = 0.35%*0.35 m =0.1225 m OCF = EBIT + Depreciation - Tax = 0.35 m + 0.7 m - 0.1225 m = $0.9275 m
Dog Up! Franks is looking at a new sausage system with an installed cost of $410,000. This cost will be depreciated straight-line to zero over the project's five-year life, at the end of which the sausage system can be scrapped for $70,000. The sausage system will save the firm $115,000 per year in pretax operating costs, and the system requires an initial investment in new working capital of $15,000. If the tax rate is 34% and the discount rate is 10%, what is the NPV of this project?
Annual depreciation = Beginning value - Ending book value)/(Number of years) = $410,000/5 = $82,000 After tax salvage value = Salvage value - Tax Rate * Capital gain (or Loss) = Salvage value - Tax Rate*(Salvage value -Book value) = $70,000 -0.34*( $70,000 - 0) = $46,200 The system is going to save the firm $115,000 per year. This is equivalent to a net of gross profit of $115,000. EBIT = $ 115,000 - Depreciation = $115,000 - 82,000 = $33,000 Tax = Tax rate * EBIT = 0.34%* $33,000 =$11,220 OCF = EBIT + Depreciation - Tax = $33,000 + 82,000 -11,220 = $103,780 Therefore, the NPV can be found by discounting the cash flows or using calculator as: NPV = $6,408
A firm is considering purchasing two assets. Asset L will have a useful life of 20 years and cost $5 million; it will have installation costs of $1 million but no salvage or residual value. Asset S will have a useful life of 8 years and cost $2 million; it will have installation costs of $500,000 and a salvage or residual value of $400,000. Which asset will have a greater annual straight-line depreciation?
Annual depreciation for Asset A= (Asset Cost + Installation Cost - Salvage Value) / Useful Life = ($3 million + $0.4 million - 0) / 15 years = $226,666.67, or about $226,667 per year. Annual depreciation for Asset B= (Asset Cost + Installation Cost - Salvage Value) / Useful Life = ($1.3 million + $0.18 million - $0.3 million) / 6 years = $196,666.67, or about $196,667 per year.
A company is considering a new project. The company's CFO plans to calculate the project's NPV by discounting the relevant cash flows (which include the initial investment, the operating cash flows, and the salvage values) at the company's cost of capital. Which of the following factors should the CFO include when estimating the relevant cash flows?
Any opportunity costs associated with the project.
Marie is 65 years old and ready to retire. She has a $1 million nest egg and wishes to spend $90,000 per year as an ordinary annuity. If her investment portfolio earns 6% annually, at what age will she run out of money? (Longevity risk)
Around 84 years old PV = $1,000,000 PMT = -90,000 I/Y = 6 FV = 0 N = 18.85 65 + 19 = 84
Which of the following is false concerning diversification? Assume that the securities being considered for selection into a portfolio are not perfectly correlated. a. As more securities are added to the portfolio, the unsystematic risk of the portfolio declines. b. As more securities are added to the portfolio, the total risk of the portfolio declines. c. As more securities are added to the portfolio, the systematic risk of the portfolio declines. d. As more securities are added to the portfolio, the portfolio risk eventually approaches the level of systematic risk in the market.
As more securities are added to the portfolio, the systematic risk of the portfolio declines.
If Annie wants to form a 2-stock portfolio of the most undervalued stocks with a beta of 1.3, how much will she have to weight each of the stocks by?
Based on the results in (4), Stocks 1 and 2 are most undervalued and would be chosen by Annie to form the 2-stock portfolio with a beta = 1.3. Stock 1's beta = 1.8; Stock 2's beta = 0.9; Desired Portfolio beta = 1.3 Since the portfolio beta = weighted average of individual stock betas Let Stock 1's Weight be X%; Thus Stock 2's Weight would be (1-X)% 1.8*X% + 0.9 x (1-X)% = 1.3 1.8X + 0.9 -0.9X = 1.3 0.9X = 0.4 X = 0.4/0.9 = 0.4444 or 44.44% = Stock 1's Weight (1-X) = 1 - 0.4444 = .5556 or 55.56 = Stock 2's Weight Check....0.4444 x 1.8 + 0.5556 x 0.9 = 0.79992 + 0.50004 = 1.3
The betas of four stocks - G, H, I, and J - are .45, 0.8, 1.15, and 1.6 respectively. What is the beta of a portfolio with the following weights in each asset?
Beta of Portfolio 1 = 0.25 × 0.45 + 0.25 × 0.8 + 0.25 × 1.15 + 0.25 × 1.6 βportfolio - 1 = 0.1125 + 0.2 + 0.2875 + 0.4 = 1.0 Beta of Portfolio 2 = 0.30 × 0.45 + 0.40 × 0.8 + 0.20 × 1.15 + 0.10 × 1.6 βportfolio - 2 = 0.135 + 0.32 + 0.23 + 0.16 = 0.845 Beta of Portfolio 3 = 0.10 × 0.45 + 0.20 × 0.8 + 0.40 × 1.15 + 0.30 × 1.6 βportfolio - 3 = 0.045 + 0.16 + 0.46 + 0.48 = 1.145
The restrictive covenants of a bond indenture are intended to protect the interest of _______.
Bondholders
Using the operating cash flow information from the previous problem, determine whether Grady Precision Measurement Tools should add the GPS system to its set of products. The initial investment is $1,440,000 for manufacturing equipment, which will be depreciated over six years (straight line) and will be sold at the end of five years for $380,000. The cost of capital is 10%, and the tax rate is still 35%.
Book Value (Basis at end of five years) Original Cost $1,440,000 Depreciation expense per year is $1,440,000 / 6 = $240,000 Accumulated depreciation is 5 × $240,000 = $1,200,000 Basis = $1,440,000 - $1,200,000 = $240,000 Gain on Disposal = $380,000 - $240,000 = $140,000 Tax on Disposal = $140,000 × 0.35 = $49,000 After-tax cash flow at disposal = $380,000 - $49,000 = $331,000 NPV = -$1,440,000 + $320,808 × 3.7908 + $331,000 × 0.6209 NPV = -$1,440,000 + $1,216,114.72 + $205,524.96 = -$18,360.32 Reject the project. On financial calculator, you can find the NPV as follows: CF0= -1,440,000 C01= 320,808 F01=4 C02 = 651,808 I=10 NPV = -18,360.31
Firms that make investment decisions based on the payback rule may be biased toward rejecting projects:
Both B and C
Which of the following is likely to be correct for a CCC-rated bond, compared to a BBB-rated bond?
Both B and C
A company has a target capital structure of 40% debt and 60% equity. The company is a constant growth firm that just paid a dividend of $2.00, sells for $27.00 per share, and has a growth rate of 8%. The company's bonds pay 10% coupon (semi-annual payment), mature in 20 years, and sell for $849.54. The company's stock beta is 1.2. The company's marginal tax rate is 40%. The risk-free rate is 4%. The market premium is 10%. The cost of equity using the capital asset pricing model (CAPM) and the constant growth model is:
CAPM: 16.0%; CGM: 16.0% Under CAPM model, 4% + 1.2 x 10% = 16% UndEr CGM model, (1 + 8%)/27 + 8% = 16%
What are the returns on the following investments?
CD: $500.00 $540.00 $0.00 $40 8% Stock $23.00 $34.00 $2.00 $13 56.52% Bond $1,040.00 $980.00 $88.00 $28 2.69% Bicycle $400.00 $220.00 $0.00 -$180 -45%
Cool Waters, Inc. sells bottled water. The firm keeps in inventory plastic bottles at 10% of the monthly projected sales. These plastic bottles cost $0.005 each. The monthly sales for the coming year are as follows: January: 2,000,000 February: 2,200,000 March: 2,700,000 April: 3,000,000 May: 3,600,000 June: 5,500,000 July: 7,000,000 August: 9,000,000 September: 6,000,000 October: 4,000,000 November: 2,500,000 December: 1,300,000 January one year out: 2,200,000 Show the anticipated cost of plastic bottles each month for these project sales, the beginning inventory volume and ending inventory volume each month, and the monthly increase or decrease in cash flow for inventory given that an increase is a use of cash and a decrease is a source of cash.
COGS = Monthly Sales × $0.005 Beginning Inventory Balance = Current Month's Sales Projection × 10% Ending Inventory Balance = Next Month's Sales Projection × 10% Increase in Working Capital Cash = Ending Inventory - Beginning Inventory × $0.005
Your company is faced with an investment project. The following information is associated with this project: 1 2 3 4 Year Net Income* $100,000 120,000 140,000 120,000 for 3-Yr. MACRS class 0.330.450.15 0.07*Assume no interest expense and a zero tax rate. Allowable Depreciation The project involves an initial investment of $300,000 in equipment that falls in the 3-year MACRS class and has an estimated salvage value (after-tax) of $45,000. In addition, the company expects an initial increase in net operating working capital of $25,000 that will be recovered in year 4. The cost of capital for the project is 14 percent. Determine the project's net present value.
Calculate depreciation for each year: Dep1 = ($300,000)(0.33) = $ 99,000 Dep2 = ($300,000)(0.45) = $135,000 Dep3 = ($300,000)(0.15) = $ 45,000 Dep4 = ($300,000)(0.07) = $ 21,000 Now calculate cash flows for each year: CF0 = -$300,000 - $25,000 = - $325,000 CF1 = $100,000 + $99,000 = $199,000 CF2 = $120,000 + $135,000 = $255,000 CF3 = $140,000 + $45,000 = $185,000 CF4 = $120,000 + $21,000 + $25,000 + $45,000 = $211,000 I = 14% Solve for NPV = $295,574.29
Which of the following statements is correct for a firm in which depreciation expense exceeds EBIT? The firm:
Can still have a positive net income
Bradshaw Steel has a capital structure with 30 percent debt (all long-term bonds) and 70 percent common equity. The coupon rate on the company's long-term bonds is 8 percent and the bond is sell at a premium. The firm estimates that its overall composite WACC is 10 percent. The risk-free rate of interest is 5.5 percent, the market risk premium is 5 percent, and the company's tax rate is 40 percent. Bradshaw uses the CAPM to determine its cost of equity. What is the beta on Bradshaw's stock?
Cannot be solved because not enough information is provided
The process of planning, evaluating, selecting, and managing the financing of long-term operating projects of the company is termed _________.
Capital budgeting
___________ is at the heart of corporate finance because it is concerned with making the best choices about project selection.
Capital budgeting
Financing costs for a capital project are
Captured in the project's required rate of return
Which of the following statements is false?
Cash Flow is an accounting measure of performance during the specified period of time
Which of the following expenses cannot be used to reduce taxable corporate income?
Cash dividends
Calculating Cash Flows
Cash flows are made up of 3 separate parts: Total cash flow = CF from initial investments + CF from changes in working capital + Operating CF
Your company is considering an expansion into a new product area. The company has collected the following information about the proposed product. The project has an anticipated economic life of 5 years. The company will have to purchase a new machine to produce the product. The machine has an up-front cost (T = 0) of $750,000. The machine will be depreciated on a straight-line basis over 5 years (that is, the company's depreciation expense will be $150,000 in each of the first five years (T = 1, 2, 3, 4, and 5). If the company goes ahead with the project, it will affect the company's net working capital. At the outset, T = 0, inventory will increase by $50,000 and accounts payable will increase by $30,000. At T = 5, the net working capital will be recovered. The project is expected to produce EBIT of $200,000 the first year (T = 1), $300,000 the second and third years (T = 2 and 3), $200,000 the fourth year (T = 4), and $150,000 the final year (T = 5). The company's tax rate is 40 percent. What is the total cash flow in year 0 (T=0)?
Cash outflow due to investment = $750,000 Cash outflow due to change in net working capital = $50,000 - 30,000 = $20,000 No cash in or outflow due to operation Total cash out flow = $750,000 + $20,000 = $770,000
The December 31, 2001, balance sheet of Venus's Tennis Shop, Inc., showed current assets of $1,200 and current liabilities of $720. The December 31, 2002, balance sheet showed current assets of $1,440 and current liabilities of $525. What was the company's 2002 change in net working capital, or NWC?
Change in NWC = NWCend - NWCbeg = (CAend - CLend) - (CAbeg - CLbeg) = ($1,440 - 525) - ($1,200 - 720) = $915 - 480 = $435 Hence, there is an increase in NWC of $435.
Which of the following choices best describes the role of taxes on the after-tax cost of capital in the U.S. from the different capital sources!
Common equity: no effect; preferred equity: no effect; debt: decrease
Which of the following would decrease a portfolio's systematic risk?
Common stock with positive beta is sold and replaced with Treasury bills.
Preferred stocks are different from common stocks in that
Common stockholders have voting rights while preferred stockholders do not
What is the current yield of a bond with a 6% coupon, 4 years until maturity, and a price of $750?
Current yield = coupon payments/price = (.06 x 1000)/750 = 8%
A firm has $100,000 in common equity. Preferred stock has a value of $10,000 and long-term debt totals $120,000. For purposes of estimating the firm's WACC, what are the weights of long-term debt, preferred stock, and equity?
D/V = 52.17%, PS/V = 4.35%, and E/V = 43.48%
A firm expects to pay a dividend over each of the next four years of $2.00, $1.50, $2.50, and $3.50. Of growth is then expected to level off at 8% per year, and if you require a 14% rate of return, then how much should you be willing to pay for this stock?
D5 = 3.50 x (1+.08) = 3.78 P4 = D5/(r-g) = 3.78/(.14-.08) = 63 P0 = 2(1+.14) + 1.5/(1+.14)^2 + 2.5/(1+.14)^3 + 3.5/(1+.14)^4 + 63/(1+.14)^4 P0 = 1.754 + 1.154 + 1.687 + 2.072 + 37.301 = 43.97
To determine the present value of a future amount, one should ________ the future cash flows.
Discount
Dividend 1
Do not multiply by 1 + g. The next dividend, dividend next year, expected dividend in one year all mean DIV 1.
Which of the statements below is TRUE?
Dupont analysis shows that ROE is (Net Income/Sales) x (Sales/Total Assets) x (Total Assets/Total Equity)
The income statement begins with revenue and subtracts various operating expenses until arriving at __________.
Earnings before interest and taxes (EBIT)
Ed Lawrence has $100,000 invested. Of that, $30,000 is invested in IBM stock, $25,000 is invested in T-bills, and the remainder is invested in corporate bonds. Which of the following is true regarding his portfolio?
Ed has 30% of his portfolio invested in stocks. Amount invested in stocks = 30,000 Weight of stock = 30,000/100,000 =30%
The weighted average of betas of all individual assets is:
Exactly 1
A stock's risk premium is equal to the:
Expected market risk premium times beta
Which of the following would correctly differentiate general partners from limited partners in a partnership?
General partners have unlimited personal liability
Which of the following would be considered an example of systematic risk?
Greater new jobless claims than expected.
A $1,000 par value, 10% coupon bond with 15 years to maturity is priced at $951. The bond pays coupon annually. The bonds yield to maturity is:
Greater than its current yield N = 15 I/Y = ? PV = -951 PMT = 10% x 1,000 = 100 FV = 1,000 Current Yield = 100/951 = 10.52%
Given a set future value, which of the following will contribute to a lower present value?
Higher discount rate
The ________ the beta coefficient the ____ the expected return, on average.
Higher, higher
Payback Method
How long does it take to get the initial cost back in a nominal sense? Computation: -Estimate the cash flows -Subtract the future cash flows from the initial cost until the initial investment has been recovered. Decision Rule: Accept if the payback period is less than some preset limit. Advantages: -Easy to understand -Adjusts for uncertainty of later cash flows -Biased towards liquidity Disadvantages: -Ignores time value of money -May reject positive NPV investments -Requires an arbitrary cutoff point -Biased against long-term projects, such as R&D and new projects
A chief financial officer (CFO) is the top finance officer in a firm. Which function is CFO involved with?
I, II and III
If dividends on a common stock are expected to grow at a constant rate forever, and if you are told the most recent dividend paid, the dividend growth rate, and the appropriate discount rate today, you can calculate ______________. I. the price of the stock today II. the dividend that is expected to be paid ten years from now III. the expected stock price five years from now
I, II, and III
Which of the following statements is most correct?
If an asset to be used by a potential project is already owned by the firm, and if that asset could be leased to another firm if the new project were not undertaken, then the net rent that could be obtained should be charged as a cost to the project under consideration.
Which is not a step in the estimation of after-tax cash flow at disposal? a. If selling price is greater than book value: selling price - tax on gain. b. If selling price is less than book value: selling price + tax credit on loss. c. If book value is less than selling price: selling price + tax credit on loss. If selling price equals book value: selling price.
If book value is less than selling price: selling price + tax credit on loss.
Which of the following statements regarding making investment decisions using net present value (NPV) and internal rate of return (IRR) is least accurate?
If projects are mutually exclusive, one should always choose the project with the highest IRR
Which of the following statements is true? a. If a project has a profitability index less than one the project should be accepted. b. If the cost of capital is greater than the IRR, the project should be accepted. c. If a project has a payback which is longer than the company requires, the project should be accepted. d. If the NPV of a project is positive, it should be accepted.
If the NPV of a project is positive, it should be accepted.
Which of the following statements is incorrect least correct)?
If the discount (or interest) rate is positive, the future value of an annuity due will always be less than the future value of an equivalent regular annuity, and the present value of an annuity due will always be less than present value of an equivalent regular annuity.
You are helping your aging parents, who had taken out a fixed-interest rate mortgage loan many years ago. The most recent mortgage statement shows a remaining balance of $100,000 and a monthly payment of $1,760.16. Your parents told you that the annual interest rate on the mortgage loan is 6%. They would like to know when the mortgage loan will be completely paid off. Your answer is:
In 67 months PV = 100,000 PMT = -1,760.16 I/Y = 6/12 = 0.5 FV = 0 N = 67
The value of a proposed capital budgeting project depends on the:
Incremental cash flows produced
A bond sold five weeks ago for $1,100. The bond is worth $1,150 in today's market. Assuming no changes in risk, which of the following is true?
Interest rates must be lower now than they were five weeks ago.
If a firm suffers reduced profits to the point of moving into a lower tax bracket, one would expect the depreciation tax shield, all else the same, to become ____________________.
Less valuable.
Accelerated Depreciation
MACRS -congress allows accelerated depreciation to encourage capital investment -modified accelerated cost recovery system -break assets into different classes that have different depreciation schedules -multiply percentage given in depreciation table by the initial cost to find annual depreciation -depreciate to 0
If treasury bills are yielding 10% at a time when the market risk premium is 6%, then the:
Market portfolio should yield 16%
Two mutual fund managers, Martha and David, have been discussing whose fund is the top performer. Martha states that investors bought shares in her mutual fund ten years ago for $21 and those shares are now worth $65. David states that investors bought shares in his mutual fund for only $3 six years ago and they are now worth $7.30 which mutual fund manager had the higher growth rate for the management period?
Martha: N = 10 I/Y = ? PV = -21 PMT = 0 FV = 65 I/Y = 11.96 David: N = 6 I/Y = ? PV = -3 PMT = 0 FV = 7.30 I/Y = 15.98 David generated a better rate of return.
Cash Flow from Operations: 3 methods of calculation
Method 1: Dollars in - Dollars out Operating Cash Flow = Revenue - Cash Expenses - Taxes Method 2: Adjusted Accounting Profits Operation Cash Flow (OCF) = After-tax Profit + non-cash expenses = EBIT - tax + non cash expenses Method 3: Tax Shields OCF = (Revenue - cash expenses) x (1 - tax rate) + (tax rate x depreciation)
Cooley Landscaping Company needs to borrow $30,000 for a new front-end dirt loader. The bank is willing to loan the funds at 8.5% interest with annual payments at the end of the year for the next ten years. The loan is fully amortized, i.e., the loan will be fully paid off at the end of year ten. What is the annual payment on this loan for Cooley Landscaping?
N = 10 I/Y = 8.5 PV = 30,000 PMT = ? FV = 0 PMT = $4,572.23
Your broker faxed to you the following information about two semiannual coupon bonds that you are considering as a potential investment. Unfortunately, your fax machine is blurring some of the items, and all you can read from the fax on the two different bonds is the following: Fill in the missing data from the information that the broker sent. Features IBM Coupon Bond AOL Coupon Bond Face value (par) $1,000 $1,000 Coupon rate 9.5% 238 Yield to maturity 7.5% 9.5% Years to maturity 10 20 Price 1,138.96 $689.14
N = 10 x 2 = 20 I/Y (PTM) = 7.5/2 = 3.75 PV = ? PMT = 9.5 x 10 = 95/2 = -47.5 FV = -1,000 PV = 1,138.96 IBM Coupon Bond: N = 20 x 2 = 40 I/Y (PTM) = 0.095/2 = 4.75 PV = -689.14 PMT = ? FV = 1,000 PMT = 29.99 = 30/1,000 = 6%
Mullineaux Co. issued 11-year bonds one year ago at a coupon rate of 8.6 percent. The bonds make semiannual payments. If the YTM on these bonds is 7.5 percent, what is the current bond price?
N = 11 - 1 = 10 x 2 = 20 I/Y (YTM) = R = 7.5/2 = 3.75000 PMT = 8.6 x -10 / 2 = -43.00 PV = ? FV = -1,000 PV = 1,076.43
Your coin collection contains fifty 1952 silver dollars. If your parents purchased them for their face value when they were new, how much will your collection be worth when you retire in 2067, assuming they appreciate at 4% annual rate?
N = 115 I/Y = 4 PV = -50 PMT = 0 FV = ? FV = $4,547.83
Clapper Corp. issued 12-year bonds 2 years ago at a coupon rate of 7.8 percent. The bonds make semiannual payments. If these bonds currently sell for 108 percent of par value, what is the YTM?
N = 12 - 2 = 10 x 2 = 20 I/Y (YTM) = ? PMT = 7.8 x 10 = 78/2 = 39 FV = 1,000 PV = -1,000 * 1.08 = -1,080 I/Y (PTM) = 3.345 x 2 = 6.69%
Benson Biometrics, Inc. has outstanding $1,000 face value 8% coupon bonds that make semiannual payments and have fourteen years remaining to maturity. If the current price for these bonds is $1,118.74, what is the annualized yield to maturity?
N = 14 x 2 = 28 I/Y (PTM) = ? PV = -1,118.74 PMT = 8 x 10 = 80/2 = 40 FV = 1,000 I/Y (PTM) = 3.34 x 2 = 6.68%
Barely Heroes Corporation has bonds on the market with 14.5 years to maturity, YTM of 9 percent, and a current price of $850. The bonds make semiannual payments. What must the coupon rate be on Barely Heroes' bonds?
N = 14.5 X 2 = 29 I/Y (PTM) = 9/2 = 4.5% PV = -850 PMT = ? FV = 1,000 PMT = 35.64 X 2 = 71.28/1,000 = 7.13%
Upstate Bank is offering long-term certificates of deposit with a face value of $100,000 (future value). Bank customers can buy these CDs today for $67,000 and will receive the $100,000 in fifteen years. What interest rate is the bank paying on these CDs?
N = 15 I/Y = ? PV = -67,000 PMT = 0 FV = 100,000 I/Y = 2.706
Assume that a corporate bond has a par value of $1,000 and 15 years until it matures. Also assume that investors require an annual rate of return of 12% (compounded semi-annually), that coupon interest is paid semi-annually, and that the current price for this bond is $931.18. What is the annual coupon rate on this bond?
N = 15 x 2 = 30 I/Y = 12/2 = 6 PV = -931.18 PMT = FV = 1,000 PMT = 55 Coupon rate = (55 x 2)/1000 = 11%
Standard Insurance is developing a long-life insurance policy for people who outlive their retirement nest egg. The policy will pay out $250,000 on your eighty-fifth birthday. You must buy the policy on your sixty-fifth birthday. The insurance company can earn 7% on the purchase price of your policy. What is the minimum purchase price the insurance company should charge for this policy?
N = 20 I/Y = 7 PV = ? PMT = 0 FV = -250,000 PV = $64,604.75
Imprudential, Inc., has an unfunded pension liability of $650 million that must be paid in 20 years. To assess the value of the firm's stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 8.5%, what is the present value of this liability?
N = 20 I/Y = 8.5 PV = ? PMT = 0 FV = -650,000,000 PV = $127,150,652.40
The State of Confusion wants to change the current retirement policy for state employees. To do so, however, the state must pay the current pension fund members the present value of their promised future payments. There are 240,000 current employees in the state pension fund. The average employee is twenty-two years away from retirement, and the average promised future retirement benefit is $400,000 per employee. If the state has a discount rate of 5% on all its funds, how much money will the state have to pay to the employees before it can start a new pension plan?
N = 22 I/Y = 5 PV = ? PMT = 0 FV = -96,000,000,000 PV = $32,820,000
County Ranch Insurance Company wants to offer a guaranteed annuity in units of $500, payable at the end of each year for twenty-five years. The company has a strong investment record and can consistently earn 7% on its investments after taxes. If the company wants to make 1% on this contract, what price should it set on it? Use 6% as the discount rate. Assume it is an ordinary annuity and the price is the same as present value.
N = 25 I/Y = 6 PV = ? PMT = -500 FV = 0 PV = $6,391.68
A local government is about to run a lottery, but does not want to be involved in the payoff if a winner picks an annuity payoff. The government contracts with a trust to pay the lump-sum payout to the trust and have the trust (probably a local bank) pay the annual payments. The first winner of the lottery chooses the annuity and will receive $150,000 a year for the next twenty-five years. The local government will give the trust $2,000,000 to pay for this annuity. What investment rate must the trust earn to break even on this arrangement?
N = 25 I/Y = ? PV = 2,000,000 PMT = -150,000 FV = 0 I/Y = 5.56
Five years ago Thompson Tarps, Inc. issued twenty-five-year 10% annual coupon bonds with a $1,000 face value. Since then, interest rates in general have risen, and the yield to maturity on the Thompson Tarps bonds is now 12%. Given this information, what is the price today for a Thompson Tarps bond?
N = 25 - 5 = 20 I/Y (PTM) = 12 PV = ? PMT = 1,000 (face value) x 10 (coupon rate) = -100 FV = -1,000 PV = $850.61
Suppose we have a bond issue currently outstanding that has 25 years left to maturity. The coupon rate is 9% and coupons are paid annually. The bond is currently selling for $908.72 per $1000 par. What is the cost of debt?
N = 25; PMT = 90; FV = 1000; PV = -908.72; I/YR = 10.01%; YTM = 10.01%
Marty received an offer for an injury settlement of $10,000 payable in three years. He wants to know what the present value of the injury settlements is if his opportunity cost is 5% (The opportunity cost is the interest rate in this problem.)
N = 3 I/Y = 5 PV = ? PMT = 0 FV = -10,000 PV = $8,638.38
What is the yield to maturity of a bond with the following characteristics? 8% coupon rate is annual payments, $1000 par value and current price of $960, 3 years until maturity. Round your answer to the nearest hundredth percent.
N = 3 I/Y = ? PV = -960 PMT = 80 FV = 1,000
A zero-coupon bond matures three years from today, has a par value of $1,000 and a yield to maturity of 8.5% (assuming semi-annual compounding). What is the current value of this issue?
N = 3 x 2 = 6 I/Y = 8.5/2 = 4.25 PV = ? PMT = 0 FV = 1,000 PV = 779.01
Endicott Enterprises, Inc. has issued thirty-year semiannual coupon bonds with a face value of $1,000. If the annual coupon rate is 14% and the current yield to maturity is 8%, what is the firm's current price per bond?
N = 30 x 2 = 60 I/Y (PTM) = 8/2 = 4 PV = ? PMT = 14 (face value) x 10 (coupon rate) = -140/2 = -70 FV = -1,000 PV = 1,678.70
How much would an investor lose if she purchased a 30-year zero-coupon bond with a $1,000 par value and 10% yield to maturity, only to see market interest rates increase to 12% 1 year later?
N = 30 x 2 = 60 I/Y = 10/2 = 5 PV = ? PMT = 0 FV = 1,000 PV = 53.54 Price 1 year later at YMT of 12%: N = 29 x 2 = 58 I/Y = 12/2 = 6 PV = ? PMT = 0 FV = 1,000 PV = -34.06 34.06 - 53.54 = 19.48 loss
You want to invest in a stock that pays $6.00 annual cash dividends for the next five years. At the end of the five years, you will sell the stock for $30.00. If you want to earn 10% on this investment, what is a fair price for this stock if you buy it today?
N = 5 I/Y = 10 PV = ? PMT = -6 FV = -30 PV = $41.37
By how much will a bond increase in price over the next year if it currently sells for $925, has 5 years until maturity, and an annual coupon rate of 7%?
N = 5 x 2 = 10 I/Y = ? PV = -925 PMT = 7% x 1,000 / 2 = 35 FV = 1,000 I/Y = 4.445 YTM = 4.445 x 2 = 8.89 Price of next year: N = 4 x 2 = 8 I/Y = 8.89/2 = 4.445 PV = ? PMT = 7% x 1,000 / 2 = 35 FV = 1,000 PV = 937.53 937.53 - 925 = 12.53 increase
Sam Hinds, a local dentist, is going to remodel the dental reception area and add two new workstations. He has contacted A-Dec, and the new equipment and cabinetry will cost $18,000. A-Dec will finance the equipment purchase at 7.5% over a six-year period. What will Hinds have to pay in annual payments for this equipment?
N = 6 I/Y = 7.5 PV = 18,000 PMT = ? FV = 0 PMT = $3,834.81
A smooth used-car salesman who smiles considerably is offering you a great deal on a "preowned" car. He says, "For only six annual payments of $2,500, this beautiful 2008 Honda Civic can be yours." If you can borrow money at 8%, what is the price of this car?
N = 6 I/Y = 8 PV = ? PMT = -2,500 FV = 0 PV = $11,557.20
Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 1995, Christie's auctioned the William de Kooning painting Untitled. The highest bid of $2.2 million was rejected by the owner, who had purchased the painting at the height of the art market in 1989 for $3.52 million. Had the seller accepted the bid, what would his annual rate of return have been?
N = 6 I/Y = ? PV = -3,520,000 PMT = 0 FV = 2,200,000 I/Y = 7.53
You bought a 30-year bonds many years ago. The bond has a par value of $1,000 and coupon rate of 12%, paid semi-annually. The current price of the bond is $1,137.99 and the yield to maturity is 10%. How many years ago did you buy the bond?
N = ? I/Y = 10/2 = 5 PV = -1.137.99 PMT = .12 x 1,000/2 = 60 FV = 1,000 N = 24 = 24/2 = 12 = 30 - 12 = 18 18 years ago
You expect to receive $10,000 at graduation in 2 years. You plan on investing it at 12% until you have $120,000. How long will you wait from now?
N = ? I/Y = 12 PV = -10,000 PMT = 0 FV = 120,000 N = 21.93 From now, you'll wait 2 + 21.93 = 23.93 years
You're trying to save to buy a new $120,000 Ferrari. You have $40,000 today that can be invested at your bank. The bank pays 5.5% annual interest on its accounts. How long will it be before you have enough to buy the car?
N = ? I/Y = 5.5 PV = 40,000 PMT = 0 FV = -120,000 N = 20.52
Your grandfather will sell you a piece of beachfront property for $72,500. He says the price is firm whenever you can pay him cash. You know your finances will allow you to save only $5,000 a year and you can make 8% on your investment. If you invest faithfully every year at the end of the year, how long will it take you to accumulate the necessary $72,500 future cash for the beachfront property?
N = ? I/Y = 8 PV = 0 PMT = -5,000 FV = 72,500 N = 10
Bethesda Co. had additions to retained earnings for the year just ended of $275,000. The firm paid out $150,000 in cash dividends, and it has ending total equity of $6 million. If Bethesda currently has 125,000 shares of common stock outstanding, what are earnings per share? Dividends per share? Book value per share? If the stock currently sells for $95 per share, what is the market to book ratio? The price earnings ratio?
NI = addition to retained earnings + dividends = $275K + 150K = $425K EPS = NI / shares = $425K / 125K = $3.40 per share DPS = dividends / shares = $150K / 125K = $1.20 per share BVPS = TE / shares = $6M / 125K = $48.00 per share Market-to-book ratio = share price / BVPS = $95 / $48 = 1.98 times P/E ratio = share price / EPS = $95 / $3.40 = 27.9 times
Which mutually exclusive project would you select, if both are priced at $1,000 and your required return is 15%: Project A with three annual cash flows of $1,000; or Project B, with 3 years of zero cash flow followed by 3 years of $1,500 annually?
NPV = Project A: 1,283.23 Project B: 1,251.89 Choose Project A.
Net Present Value Example: Assume you plan to invest $1,000 today and will receive $600 each year for two years (assume the cash is received at the end of the year). What is the net present value if there is a 10% opportunity cost of capital?
NPV = -$1,000 + ($600/((1+.10)^1) + ($600/((1+.10)^2) = -$1,000 + $1,041.32 = $41.32
Net Present Value Terms
NPV = C0 + (C1/((1+r)^1) + (C2/((1+r)^2) + ... + (Ct/((1+r)^t) C0 = Initial Cash Flow (often negative) C1 = Cash Flow at time 1 C2 = Cash Flow at time 2 Ct = Cash Flow at time t t = Time period of the investment r = opportunity cost of capital
As the director of capital budgeting for Denver Corporation, you are evaluating two mutually exclusive projects with the following net cash flows: Year 0 Project X CF: -$100,000 Project Z CF: -$100,000 Year 1 Project X CF: 50,000 Project Z CF: 10,000 Year 2 Project X CF: 40,000 Project Z CF: 30,000 Year 3 Project X CF: 30,000 Project Z CF: 40,000 Year 4 Project X CF: 10,000 Project Z CF: 60,000 If Denver's cost of capital is 15 percent, which project would you choose? (hint: you can choose only one of the projects, or neither of them, but not both of them)
Neither project. NPV of project X is -833. NPV of project Z is -8014. Given both projects have negative NPV, neither project should be accepted.
Pags Industrial Systems Company (PISC) is trying to decide between two different conveyor belt systems. System A costs $405,000, has a three-year life, and requires $105,000 in pretax annual operating costs. System B costs $450,000, has a five-year life, and requires $60,000 in pretax annual operating costs. Both systems are to be depreciated straight-line to zero over their lives and will have zero salvage value. Whichever project is chosen, it will not be replaced when it wears out. If the tax rate is 34% and the discount rate is 20%, which project should the firm choose?
Neither system is going to bring in any revenue. The system to be chosen should have a less negative System A: Annual depreciation = (Beginning value - Ending book value)/(# of years) = $405,000/3 = $135,000 NPVA = -$454,291.67 System B: Annual depreciation = (Beginning value - Ending book value)/(Number of years) = $450,000/5 = $90,000 NPVB = -$476,915.51 System A should be chosen, because it has the more positive NPV.
Given the following info the Soprano Pizza Co., calculate the depreciation expense: sales = $21,000; costs = $10,000; addition to retained earnings = $4,000; dividends paid = $800; interest expense = $1,200; tax rate = 35%.
Net income = dividends + addition to ret. earnings = $800 + 4,000 = $4,800 EBT = NI / ( 1- tax rate) = $4,800 / 0.65 = $7,385 EBIT = EBT + interest = $7,385 + 1,200 = $8,585 Sales - costs = EBDIT = $21,000 - 10,000 = $11,000 Depreciation = EBDIT - EBIT = 11,000 - 8,585 = $2,415
A firm is considering a project which would increase accounts receivable by $10,000, accounts payable by $55,000, and inventory by $30,000. Which of the following is true? a. Net working capital has increased. b. Sales will increase. c. Net working capital has decreased. d. This is a net use of cash.
Net working capital has decreased.
If a firm's cash flow statement shows that cash was used for investments, which of the following would seem most likely?
New machines were acquired.
A home improvement firm has quoted a price of $9,800 to fix up John's backyard. Five years ago John put $7,500 into a home improvement account that has earned an average of 5.25% per year. Does John have enough money in his account to pay for the backyard fix-up?
No. John has only $9687 in his home improvement account.
Given no change in required returns, preferred stock prices will:
None of the above
The standard deviations of individual stocks are generally higher than the standard deviation of the market portfolio because individual stocks:
None of the above
An investment earned the following returns for the returns 1998 through 2001: 30%, 40%, 15%, and 7%. What is the variance of returns for this investment?
None of the above (the correct answer is 0.0219) First, find the mean return: (0.3+.4+.15+.07)/4 = 0.23 Variance = [(.3-.23)2 + (.4-.23)2 +(.15-.23)2 +(.07-.23)2 ]/(4-1) = 0.0219
Your subscription to Jogger's World Monthly is about to run out and you have the choice of renewing it by sending in the $10 a year regular rate or of getting a lifetime subscription to the magazine by paying $100. Your cost of capital is 7 percent. How many years would you have to live to make the lifetime subscription the better buy? Payments for the regular subscription are made at the beginning of each year. (Round up if necessary to obtain a whole number of years.)
None of the above Use the BGN mode: I/Y = 7 PV = 100 PMT = -10 FV = 0 N=15.7
Haig Aircraft is considering a project that requires some initial investment today (t = 0). The project will generate positive cash flows of $60,000 a year for the next five years (from t=1 to t=5). The project's NPV is $75,000 and the company's cost of capital is 10 percent. What is the project's regular payback?
None of the above (the correct answer should be 2.54 years) First, we need to find the initial cost of the project. Given the NPV of $75,000, we know the initial cost is $75,000 less than the present value of the future value, which can be found as follows: N= 5 I/Y= 10 PV = ? PMT= 60,000 FV= 0 PV= -227,447 So, the initial cost = 227,447 - 75,000 = $152,447 Next, we can find the payback period as follows: After 1 year, we still have $92,447 ($152,447- $60,000) to recover. After 2 years, we still have $32,447 ($92,447 - $60,000) to recover. For the remaining $32,447, it takes 0.54 (32,447/60,000) of a year (of the third year) to recover. Thus, the payback period is 2.54 years.
Stocks A and B have the same required rate of return and the same expected year-end dividend (D1). Stock A's dividend is expected to grow at a constant rate of 10 percent per year, while Stock B's dividend is expected to grow at a constant rate of 5 percent per year. Which of the following statements is most correct?
None of the statements above is correct.
Your company is considering an expansion into a new product area. The company has collected the following information about the proposed product. The project has an anticipated economic life of 5 years. The company will have to purchase a new machine to produce the product. The machine has an up-front cost (T = 0) of $750,000. The machine will be depreciated on a straight-line basis over 5 years (that is, the company's depreciation expense will be $150,000 in each of the first five years (T = 1, 2, 3, 4, and 5). If the company goes ahead with the project, it will affect the company's net working capital. At the outset, T = 0, inventory will increase by $50,000 and accounts payable will increase by $30,000. At T = 5, the net working capital will be recovered. The project is expected to produce EBIT of $200,000 the first year (T = 1), $300,000 the second and third years (T = 2 and 3), $200,000 the fourth year (T = 4), and $150,000 the final year (T = 5). The company's tax rate is 40 percent.What is the operating cash flow in year 2 (T=2)?
OCF = EBIT + Depreciation - TaxOCF = 300,000 + 150,000 - EBIT*Tax Rate OCF = 450,000 - 300,000 * 40% = 330,000
Below is the balance sheet information on two companies. Prepare a common-size balance sheet for each company. Review each company's percentage of total assets. Are these companies operating with similar philosophies or in similar industries? What appears to be the major difference in financing for these two companies?
One major difference is the use of debt financing by company one and the lack of debt financing for company two. Company two has been using equity financing and internally generated cash flow for financing (it is Starbucks). Company one also has much higher intangible assets such as patents and registration rights (it is Johnson and Johnson).
Which of the following statements is most correct?
One of the disadvantages of the sole proprietorship form of organization is that there is unlimited liability
Your company is considering an expansion into a new product area. The company has collected the following information about the proposed product. The project has an anticipated economic life of 5 years. The company will have to purchase a new machine to produce the product. The machine has an up-front cost (T = 0) of $750,000. The machine will be depreciated on a straight-line basis over 5 years (that is, the company's depreciation expense will be $150,000 in each of the first five years (T = 1, 2, 3, 4, and 5). If the company goes ahead with the project, it will affect the company's net working capital. At the outset, T = 0, inventory will increase by $50,000 and accounts payable will increase by $30,000. At T = 5, the net working capital will be recovered. The project is expected to produce EBIT of $200,000 the first year (T = 1), $300,000 the second and third years (T = 2 and 3), $200,000 the fourth year (T = 4), and $150,000 the final year (T = 5). The company's tax rate is 40 percent. What is the total cash flow in year 5 (T=0)?
Operating cash flow in year 5 = EBIT + Depreciation - Tax Operating cash flow in year 5 = $150,000 + $150,000 - $150,000*40% = $240,000 Cash flow due to changes in net working capital = $30,000 +50,000 =$80,000 No salvage value or cash flow due to investmentTotal cash flow in year 5 = $240,000 + $80,000 = $320,000 = 260,000?
___________ involve(s) a cash flow that never occurs, but we need to add it as a cost or outflow of a new project.
Opportunity costs
Kiessling Corp. pays a constant $9 dividend on its stock. The company will maintain this dividend for the next eight years and will then cease paying dividends forever. If the required return on this stock is 11 percent, what is the current share price?
P0 = 9/(1+11%)^1 + 9/(1+11%)^2 + 9/(1+11%)^3 + 9/(1+11%)^4 + 9/(1+11%)^5 + 9/(1+11%)^6 + 9/(1+11%)^7 + 9/(1+11%)^8 = 8.11 + 7.30 + 6.58 + 5.93 + 5.34 + 4.81 + 4.33 + 3.91 = $46.32
Corn, In., has an odd dividend policy. The company has just paid a dividend of $6 per share and has announced that it will increase the dividend by $2 per share for each of the next four years, and then never pay another dividend. If you require an 11 percent return on the company's stock, how much will you pay for a share today?
P0 = $8/(1.11) + 10/(1.11)^2 +12/(1.11)^3 + 14/(1.11)^4 = 7.20 + 8.12 + 8.77 + 9.22 = $33.32
What should the price of a share of stock be if the firm will pay a $4 dividend in 1 year that is expected to grow at a constant rate of 5%? Assume a discount rate of 10%.
P0 = 4/(0.1 - 0.5) = $80
If next year's dividend is forecasted to be $5.00, the constant-growth rate is 4%, and the discount rate is 16%, then the current stock price should be:
P0 = 5/(0.16 - 0.04) = 41.67
Assume that you plan to buy a share of XYZ stock today to hold it for 2 years. Your expectations are that you will not receive a dividend at the end of Year 1, but you will receive a dividend of $9.25 at the end of Year 2. In addition, you expect to sell the stock for $150 at the end of Year 2. If your expected rate of return is 16 percent, how much should you be willing to pay for this stock today?
P0 = 9.25/(1 + 0.16)^2 + 150/(1 + 0.16)^2 = 6.874 + 111.474 = 118.35
Antiques R Us is a mature manufacturing firm. The company just paid a $9 dividend, but management expects to reduce the payout by 8 percent per year, indefinitely. If you require a 14 percent return on this stock, what will you pay for a share today?
P0 = D0 (1 + g)/ (r - g) = $9.00(0.92) / (.14 - .08) = $37.64
Cannons Corporation will pay a $4.00 per share dividend next year. The company pledges to increase its dividend by 4 percent per year, indefinitely. If you require a 13 percent return on your investment, how much will you pay for the company's stock today?
P0 = D1/(R - g) = $4.00/(.13 - .04) = $44.44
Albright Motors is expected to pay a year-end dividend of $3.00 a share (DIV1 = $3.00). The stock currently sells for $30 a share. The required (and expected) rate of return on the stock is 16 percent. If the dividend is expected to grow at a constant rate, g, what is g?
P0 = DIV1/(r-g) 30 = 3/(16% - g)g = 6%
Roxie Inc has just paid a dividend of $4.00. It's stock is now selling for $65 per share, and the required rate of return on a stock like Roxie inc. is 14%. Assuming Roxie is a constant growth stock, determine the implied growth rate for Roxie's dividends.
P0 = DIV1/(r-g) 65 = 4 x (1+g)/(.14 - g) g = 7.4%
What should be the expected price next year if the firm will pay a $4 dividend in 1 year that is expected to grow at a constant rate of 5%? Assume a discount rate of 10%.
P1 = (4(1 + 0.05))/(0.1 - 0.05) = $84 Note that stock price increases from $80 today to $84 in one year. Growth rate = (84-80)/80 = 5%
If next year's dividend is forecasted to be $5.00, the constant-growth rate is 4%, and the discount rate is 16%, then the stock price next year should be:
P1 = (5(1 + 0.04)/(0.16 - 0.04) = 5.2/0.12 = 43.33
How much should you pay for a share of stock that offers a constant-growth rate of 10%, requires a 16% rate of return, and is expected to sell for $50 one year from now? (round to the nearest cent)
P1 = P0 x (1 + g) 50 = P0 x (1 + .1)P0 = 45.45
Super Growth Co. is growing quickly. Dividends are expected to grow at a 32 percent rate for the next three years, with the growth rate falling off to a constant 7 percent thereafter. If the required return is 15 percent and the company just paid a $2.25 dividend, what is the current share price?
P3 = D3 (1 + g)/(r - g) = D0 (1 + g1)^3(1 + g) / (r - g) = $2.25 (1.32)^3 (1.07) / (.15 -.07) = 5.53717 / 0.08 = $69.21 P0 = [$2.25(1.32)/(1.15)] + [2.25(1.32)^2/(1.15)^2] + [2.25(1.32)^3/(1.15)^3] = [69.21/(1.15)^3] = $54.46
Metallica Bearings, Inc. is a young start-up company. No dividends will be paid on the stock over the next nine years, because the firm needs to plow back its earnings to fuel growth. The company will pay a $7 per share dividend in 10 years and will increase the dividend by 6 percent per year, thereafter. If the required return on this stock is 14 percent, what is the current share price?
P9 = D10/(r - g) = $7.00/(.14-.06) = $87.50 P0 = $87.50/1.14^9 = $26.91
A newly-issued 15-year, $1,000 face value 6.75% semi-annual coupon bond is priced at $1,075. Which of the following choices describes the bond and the relationship of the bond's market yield to the coupon?
Premium bond, required market yield is less than 6.75%
Agnes wants to purchase common stock of New Frontier Inc. and hold it for 4 years. The directors of the company just announced that they expect to pay an annual cash dividend of $4.00 per share for the next 4 years. Agnes believes that she will be able to sell the stock for $40.00 at the end of four years. In order to earn 12% on this investment, how much should Agnes pay for this stock?
Price = Future Price x (1/(1 + r)^n + Dividend Stream x (1 - (1/(1 + r)^n) / r) Price = $40.00 x (1/(1 + 0.12)^4) + $4.00 x (1 - (1/(1 + 0.12)^4 / 0.12) Price = $40.00 x 0.635518 + $4.00 x 3.03734 Price = $25.42 + $12.15 = $37.57 CALCULATOR: N = 4 I/Y = 12% PV = ? PMT = 4 FV = 40 PV = -37.57
What is the difference between the primary market and the secondary market?
Primary market is where firms and government raise money from investors. Secondary market is where trading of financial assets takes place between investors.
Which of the following could be calculated with only the use of an income statement?
Profit margin
Music Row, Inc. has sales of $32 million, total assets of $43 million, and total debt of $9 million. If the profit margin is 7%, what is net income? What is ROA? What is ROE?
Profit margin = net income / sales; net income = ($32M)*(0.07) = $2,240,000 ROA = net income / TA = $2.24M / $43M = 5.21% ROE = net income / TE = net income / (TA - TD) = $2.24M / ($43M - 9M) = 6.59%
Other Investment Criteria: Profitability Index
Profitability Index = NPV/Initial Investment
Quark industries has four potential projects, all with an initial cost of $2,000,000. The capital budget for the year will allow Quark to accept only one of the four projects. Given the discount rate and the future cash flow of each project, determine which project Quark should accept. Cash Flow Project 1 Project 2 Project 3 Project 4 Cash flow year 1 $ 500,000 $ 600,000 $ 1,000,000 $ 300,000 Cash flow year 2 $ 500,000 $ 600,000 $ 800,000 $ 500,000 Cash flow year 3 $ 500,000 $ 600,000 $ 600,000 $ 700,000 Cash flow year 4 $ 500,000 $ 600,000 $ 400,000 $ 900,000 Cash flow year 5 $ 500,000 $ 600,000 $ 200,000 $ 1,100,000 Discount rate 6% 9% 15% 22%
Project 2 should be accepted, it has the highest NPV.
Allied, Inc. is considering Project A and Project B, which are two mutually exclusive. Project A is an eight- year project that has an initial outlay or cost of $180,000, its future cash inflows for years 1 through 8 are $38,000. Project B is also an 8 year project that has an initial outlay or cost of $160,000 . Its future cash inflows for years 1 through 8 are the same at $34,500. The appropriate discount rate for both project is 7.5%. Which project should Allied accept?
Project A because it has a higher NPV
The financial manager at Johnson & Smith estimates that its required rate of return is 11%. Which of the following independent projects should Johnson & Smith accept?
Project C requires an up-front expenditure of $600,000 and generates a positive internal rate of return of 12.0%
A firm is evaluating two mutually exclusive projects of the same risk class, Project X and Project Y. Both have the same initial cash outlay and both have positive NPVs. Which of the following is a sufficient reason to choose Project X over Project Y?
Project Y has a lower profitability index than Project X
Allocations of overhead should not affect a project's incremental cash flows unless the:
Project actually increased overhead expenses
Project selection ambiguity can arise if one relies on IRR instead of NPV when:
Project cash flows are not conventional.
The current quarterly dividend on the common shares of your company is $0.30, the risk-adjusted annual discount rate is 16%, and the management of the firm believes that the dividends will increase by 1.2% per quarter. What is the current share price of this company?
R = 16%/4 = 4% P0 = DIV1(r-g) P0 = 0.3 x (1+1.2%)/(4% - 1.2%) = 10.84
Consider the following two stocks: -Year A B 2005 22% -5% 2006 -10% 15% •Invest 45% of your money in A and another 55% in B What is the return and standard deviation for each stock? What is the return and standard deviation for the portfolio?
R2005 = 45%*22% + 55%*(-5%) = 7.15% R2006 = 45%*(-10%) + 55%*(15%) = 3.75% Returns on the portfolio are more stable than either stock A or stock B
Suppose your company has an equity beta of .58 and the current risk-free rate is 6.1%. If the expected market risk premium is 8.6%, what is your cost of equity capital?
RE = 6.1% + .58(8.6%) = 11.1%
If the total assets of a firm increase while all other components of ROE remain unchanged, you would expect the firm's:
ROE to remain unchanged.
Consider the portfolio weights computed previously. If the individual stocks have the following returns, what is the return for the portfolio? DCLK: 19.65% KO: 8.96% INTC: 9.67% KEI: 8.13%
RP = .133(19.65%) + .2(8.96%) + .267(9.67%) + .4(8.13%) = 10.24%
Grady Precision Measurement has forecasted the following sales and costs for a new GPS system: annual sales of 48,000 units at $18 a unit, production costs at 37% of sales price, annual fixed costs for production at $180,000, and straight-line depreciation expense of $240,000 per year. The company tax rate is 35%. What is the annual operating cash flow of the new GPS system?
Revenue (48,000 × $18) $864,000 COGS (48,000 × $18 × 0.37) 319,680 Fixed Costs 180,000 Depreciation 240,000 EBIT $124,320 Taxes ($124,320 × 0.35) 43,512 Net Income $ 80,808 Add Back Depreciation $240,000 Operating Cash Flow (per year) $320,808
You own a portfolio that is 50 percent invested in Stock X, 30 percent in Stock Y, and 20 percent in Stock Z. The returns on these three stocks are 10 percent, 18 percent, and 13 percent respectively. What is the return on the portfolio?
Rp = .50(.10) + .30(.18) + .20(.13) = .1300
A proposed new investment has projected sales of $700,000. Variable costs are 60 percent of sales, and fixed costs are $175,000; depreciation is $75,000. Prepare a pro forma income statement assuming a tax rate of 35 percent. What is the projected net income?
Sales $700,000 Variable costs 420,000 (60%*700,000) Fixed costs 175,000 Depreciation 75,000 EBT $30,000 Taxes @ 35% 10,500 Net income $19,500
Winnebagel Corp. currently sells 20,000 motor homes per year at $45,000 each, and 8,000 luxury motor coaches per year at $78,000 each. The company wants to introduce a new portable camper to fill out its product line; it hopes to sell 16,000 of these campers per year at $12,000 each. An independent consultant has determined that if Winnebagel introduces the new campers, it should boost the sales of its existing motor homes by 5,000 units per year, and reduce the sales of its motor coaches by 1,000 units per year. What is the amount to use as the annual sales figure when evaluating this project? Why?
Sales due solely to the new product line are 16,000($12,000) = $192 million. Increased sales of the motor home line occur because of the new product line introduction; thus 5,000($45,000) = $225 million in new sales is relevant. Erosion of luxury motor coach sales is also due to the new mid-size campers; thus 1,000($78,000) = $78 million loss in sales is relevant. The net sales figure to use in evaluating the new line is thus: $192 million + 225 million - 78 million = $339 million.
Find the following financial ratios for Smolira Golf Corp. Short-term solvency ratios a. Current ratio b. Quick ratio c. Cash ratio Asset turnover ratios d. Total asset turnover e. Inventory turnover f. Receivables turnover Long-term solvency ratios g. Total debt ratio h. Equity multiplier i. Times interest earned ratio j. Cash coverage ratio Profitability ratios k. Profit margin l. Return on assets m. Return on equity
Short-term solvency ratios: CR01 = $7,440 / $1,717 = 4.33 times CR02 = $7,798 / $2,163 = 3.61 times QR01 = ($7,440 - 4,408) / $1,717 = 1.77 times QR02 = ($7,798 - 4,982) / $2,163 = 1.30 times Cash ratio01 = $650 / $1,717 = 0.38 times Cash ratio02 = $710 / $2,163 = 0.33 times Asset utilization ratios: TAT = $28,000 / $26,382 = 1.06 times Inventory turnover = $11,600 / $4,982 = 2.33 times Receivables turnover = $28,000 / $2,106 = 13.30 times Long-term solvency ratios: Debt ratio01 = ($21,432 - 15,397) / $21,432 = 0.28 Debt ratio02 = ($26,382 - 20,029) / $26,382 = 0.24 EM01 = Total asset/Total Equity =21432/15397 = 1.39 EM02 = 26382/20029 = 1.32 TIE ratio = $14,260 / $980 = 14.55 times Cash coverage ratio = ($14,260 + 2,140) / $980 = 16.73 times Profitability ratios: PM = $8,632 / $28,000 = 30.83% ROA = $8,632 / $26,382 = 32.72% ROE = $8,632 / $20,029 = 43.10%
Over the past 75 years, which of following investments has provided the largest average return?
Small company stocks
You have just made your first $2,000 contribution to your individual retirement account. Assuming you earn a 9% rate of return and make no additional contributions, what will your account be worth when you retire in 45 years? What if you wait 10 years before contributing?
Start now: N = 45 I/Y = 9 PV = 2,000 PMT = 0 FV = ? FV = $96,654.57 10 Years: N = 35 I/Y = 9 PV = 2,000 PMT = 0 FV = ? FV = $40,827.94
Ashlyn Lutz makes the following statements to her supervisor, Paul Ulring, regarding the basic principles of capital budgeting: Statement 1: The timing of expected cash flows is crucial for determining the profitability of a capital budgeting project. Statement 2: Capital budgeting decisions should be based on the after-tax net income produced by the capital project. Which of the following regarding Lutz's statements is most accurate?
Statement 1 Correct Statement 2 Incorrect
A firm is expected to pay $2/share in dividends next year. Those dividends are expected to grow by 8% for the next three years and, starting with year 4, the dividends will grow at 6% thereafter. If the discount rate is 10%, what is the current price of this security?
Step 1: Find the dividends until year 4: DIV1 = 2 DIV2 = 2(1+0.08) = 2.16 DIV3 = 2(1+0.08)^2 = 2.33 DIV4 = 2(1+0.08)^3 = 2.52 Step 2: Find the dividend at year 5: DIV5 = DIV4(1 + 0.06) = 2.67 Step 3: Apply the constant growth model to find P4: P4 = DIV5/(r - g1) = 2.67/(0.10 - 0.06) = 66.75 Step 4: Discount all the cash flows back to present and add them up: P0 = (2/1.10) + (2.16/1.10^2) + (2.33/1.10^3) + (2.52/1.10^4) + (66.75/1.10^4) = 52.68
Stock A has a beta coefficient of 0.9, and stock B has a beta coefficient of 1.2. Which of the following statements is false regarding these two stocks? a. Stock A is less risky from the market's perspective than a typical stock, and stock B is more risky than a typical stock. b. Stock B, if purchased, will increase the market risk of a portfolio more than stock A would (if purchased). c. Stock A necessarily must have a lower standard deviation of returns than stock B. d. Stock B must have a higher expected return than stock A if both of them are priced properly.
Stock A necessarily must have a lower standard deviation of returns than stock B.
Bud is an undiversified investor and is considering two alternative stocks for purchase. Stock A has a beta of 0.85 and stock B a beta of 1.6. If Bud expects the stock market to boom next year (strong bull market), which stock should he purchase?
Stock B
Annie is curious to know whether the following 5 stocks (in the next slide) are appropriately valued in the market. Accordingly, she creates a table (shown below) listing the betas of each stock along with their expected return values that have been calculated using a probability distribution. She also lists the current risk-free rate and the expected rate of return on the broad market index. Help her out and state your steps.
Stock Expected Return Beta 1 26.00% 1.8 2 16.00% 0.9 3 14.00% 1.2 4 16.15% 1.1 5 20.00% 1.4 Rf 3.50% ---- Rm15.00%1.0 1 - undervalued 2 - undervalued 3 - overvalued 4 - correct 5 - undervalued
Listed below are the annual rates of return earned on Stock X and Stock Y over the past 6 years. Which stock was riskier and why? 2004; 20%; 16% 2005; 15%; 17% 2006; -10%; 20% 2007; 30%; 24% 2008; 25%; 23% 2009; 14%; -10%
Stock X was riskier than Stock Y since it had the higher Standard Deviation of the two, and its average return was not much higher than Stock Y's average return .
Stocks are different from bonds because
Stocks, unlike bonds, represent ownership
For a project with conventional cash flows, if Pl is greater than 1, then:
The NPV is greater than zero
Which is greater, the present value of a $1,000 five-year ordinary annuity discounted at 10%, or the present value of a $1,000 five-year annuity due discounted at 10%?
The PV of annuity due is worth $379.08 more
Double taxation refers to which of the following scenarios?
The corporation pays taxes on its earnings, and shareholders pay taxes on dividends received.
Which of the statements below is false? a. To account for the time value of money with the payback period model, you need to restate the future cash flow in current dollars. b. The discounted payback period method is the time it takes to recover the initial investment in future dollars. c. When we discount a future cash flow with our standard time value of money concepts, we inherently assume that the company received the entire cash flow at the end of the year. d. The discounted payback period method does not correct for the cash flow after the recovery of the initial outflow.
The discounted payback period method is the time it takes to recover the initial investment in future dollars.
What will happen to the expected return on a stock with a beta of 1.5 and a market risk premium of 9% if the treasury bill yield increases from 3 to 5%?
The expected return will increase by 2.0%
Which of the following statements is true? a. The graphic plot of project NPV against discount rate is called the NPV profile b. NPV profile is always downward sloping, i.e., NPV decreases with higher discount rate c. At the intercept point of the NPV profile with the horizontal axis, the project IRR is zero d. All of the above e. None of the above
The graphic plot of project NPV against discount rate rate is called NPV profile
An investment of $100 today is worth $116.64 at the end of two years if it earns an annual interest rate of 8%. How much interest is earned in the first year and how much in the second year of this investment?
The interest earned in year one is $8.00 and the interest earned in year two is $8.64 100 x 8% = 8 (100 + 8) x 8% = 8.64
Which of the following statements about independent projects is least accurate?
The internal rate of return and net present value methods can yield different accept/reject decisions for independent projects
Reginal is about to lease an apartment for the year. The landlord wants him to make the lease payments at the start of the month. The twelve monthly payments are $1,300 per month. The landlord says he will allow Reginal to prepay the rent for the entire year with a discount. The one-time annual payment due at the beginning of the lease is $14,778. What is the implied monthly discount rate for the rent? If Reginal is earning 1.5% on his savings monthly, should he pay by month or make the single annual payment?
The month rent is due at the beginning of each month. Thus, it is an annuity due. The one-time annual payment is the present value of the annuity due. We can use the financial calculator to find the implied monthly discount rate. It is important to use the BEG mode in the calculator because the lease is an annuity due. N = 12 I/Y = ? PV = 14,778 PMT = -1300 FV = 0 I/Y = 1
If the market portfolio is expected to offer returns of 16%, then what can be said about a portfolio expected to return 13%?
The portfolio's beta is less than 1.0
Which of the statements below is FALSE?
The times interest earned ratio tells us the number of times a company has resorted to debt financing over the year.
Mr. Malone wants to change the overall risk of his portfolio. Currently, his portfolio is a combination of risky assets with a beta of 1.25 and an expected return of 14%. He will add a risk-free asset (U.S. Treasury bill) to his portfolio. If he wants a beta of 1.0, what percent of his wealth should be in the risky portfolio and what percentage should be in the risk-free asset? If he wants a beta of 0.75? If he wants a beta of 0.50? If he wants a beta of 0.25? Is there a pattern here?
The weight in the risk-free asset is 1- w, and the weight in the risky portfolio is w and the total of the two reflects 1 or 100% of his wealth. Beta of 1.0 = (1-w) × (0) + (w) × (1.25) 1.0 = w (1.25) w = 1 / 1.25 = 0.80 Thus, 80% of wealth in the risky portfolio and 20% of wealth in risk-free asset. Beta of 0.75 = (1-w) × (0) + (w) × (1.25) 0.75 = w (1.25) w = 0.75 / 1.25 = 0.60 Thus, 60% of wealth is in the risky portfolio and 40% of wealth in risk-free asset. Beta of 0.50 = (1-w) × (0) + (w) × (1.25) 0.50 = w (1.25) w = 0.50 / 1.25 = 0.40 Thus, 40% of wealth in risky portfolio and 60% of wealth in risk-free asset. Beta of 0.25 = (1-w) × (0) + (w) × (1.25) 0.25 = w (1.25) w = 0.25 / 1.25 = 0.20 Thus, 20% of wealth in risky portfolio and 80% of wealth in risk-free asset. The pattern is for every beta change of 0.25 Sam will need to switch 20% of his wealth out of the risky portfolio and into the risk-free asset. This constant ratio means that there is a linear relationship between portfolio weights and beta.
The type of risk that we can diversify away is ____________.
Unsystematic risk
MACRS Schedule for assets with five-year life. Format: Year, MACRS Percent
Year 1, 20% Year 2, 32% Year 3, 19.20% Year 4, 11.52% Year 5, 11.52% Year 6, 5.76%
The rate of return required by investors in the market for owning a bond is called the:
Yield to maturity
You are evaluating a project for The Ultimate recreational tennis racket, guaranteed to correct that wimpy backhand. a. What is EBIT for the project in the first year? b. What is the operating cash flow in year 2?
a. $20,000 EBIT = sales - cash expenses - depreciation EBIT Year 1 = 400,000 - 325,000 - 55,000 = 20,000 b. $97,075 Annual depreciation = 165,000/3 = 55,000 EBIT = 500,000 - 381,250 - 55,000 = 63,750 Tax = 63,750 * 34% = 21,675 OCF = 63.750 - 21,675 + 55,000 = 97,075
From the following balance sheet accounts, a) Construct a balance sheet for 2013 and 2014 b) List all the working capital accounts c) Find the net working capital for the years ending 2013 and 2014 d) Calculate the change in net working capital for the year 2014 Account Balance 12/31/2013 Balance 12/31/2014 Accounts payable $1000 $1100 Accounts receivable $2480 $2690 Cash $1300 $1090 Common stock $4990 $4990 Inventory $5800 $6030 Long-term debt $7800 $8200 Three-month Notes payable $ 800 $ 960 Plant, property, and equipment $6380 $6530 Retained earnings $1370 $1090
a. b. The Working Capital Accounts are: Cash, Accounts Receivable, Inventory, Accounts Payable, and Three-month Note Payable. c. The Net Working Capital for 2013 and 2014: Net Working Capital = Cash + Accounts Receivable + Inventory - Current liabilities 2013 Net Working Capital = $1,300 + $2,480 + $5,800 - $1,800 = $7,780 2014 Net Working Capital = $1,090 + $2,690 + $6,030 - $2,060 = $7,750 d. The Change in Net Working Capital for 2014 is, $7,750 - $7,780 = -$30 or a decrease in Net Working Capital of $30.
Moore Company is about to issue a bond with semiannual coupon payments, a coupon rate of 8%, and a par value of $1,000. The yield to maturity for this bond is 10%. a. What is the bond price if it matures in five, ten, fifteen, or twenty years? b. What do you notice about the bond price in relationship to the bond's maturity?
a. 5 years: N = 5 x 2 = 10 I/Y (PTM) = 10/2 = 5 PV = ? PMT = 8 x 10 = 80/2 = -40 FV = -1,000 PV = 922.78 10 years: N = 10 x 2 = 20 I/Y (PTM) = 10/2 = 5 PV = ? PMT = 8 x 10 = 80/2 = -40 FV = -1,000 PV = 875.38 15 years: N = 15 x 2 = 30 I/Y (PTM) = 10/2 = 5 PV = ? PMT = 8 x 10 = 80/2 = -40 FV = -1,000 PV = 846.28 20 years: N = 20 x 2 = 40 I/Y (PTM) = 10/2 = 5 PV = ? PMT = 8 x 10 = 80/2 = -40 FV = -1,000 PV = 828.41 b. The longer the maturity of a bond selling at a discount, all else held constant, the lower the price of the bond.
Your dreams of becoming rich have just come true. You have won the State of Tranquility's lottery. The state offers you two payment plans for the $5,000,000 advertised jackpot. You can take the annual payments of $250,000 for the next twenty years or $2,867,480 today. a. If your investment rate over the next twenty years is 8%, which payoff will you choose? b. If your investment rate over the next twenty years is 5%, which payoff will you choose? c. At what investment rate will the annuity stream of $250,000 be the same as the lump-sum payment of $2,867,480?
a. N = 20 I/Y = 8 PV = ? PMT = 250,000 FV = 0 PV = 2,454,537 At 8%, the present value of installment payments is $2,454,537 million, less than the lump sum of $2,867,480. Take the lump sum. b. N = 20 I/Y = 5 PV = ? PMT = 250,000 FV = 0 PV = 3,115,553 At 5%, the present value of installment payments is $3,115,553 million, greater than the lump sum of $2,867,480. Take the installment payments. c. N = 20 I/Y = ? PV = -2,867,480 PMT = 250,000 FV = 0 I/Y = 6 At 6%, the two options are equivalent.
Addison Company will issue a zero-coupon bond this coming month. The bond's projected yield is 7%. If the par value is $1,000, what is the bond's price using a semiannual convention if a. The maturity is 20 years? b. The maturity is 30 years? c. The maturity is 50 years? d. The maturity is 100 years?
a. N = 20 x 2 = 40 I/Y (PTM) = 7/2 = 3.5 PV = ? PMT = 0 FV = -1,000 PV = 252.57 b. N = 30 x 2 = 60 I/Y (PTM) = 7/2 = 3.5 PV = ? PMT = 0 FV = -1,000 PV = 126.93 c. N = 50 x 2 = 100 I/Y (PTM) = 7/2 = 3.5 PV = ? PMT = 0 FV = -1,000 PV = 32.06 d. N = 100 x 2 = 200 I/Y (PTM) = 7/2 = 3.5 PV = ? PMT = 0 FV = -1,000 PV = 1.03
Jack and Jill are saving for a rainy day and decide to put $50 away in their local bank every year for the next twenty-five years. The local Up-the-Hill Bank will pay them 7% on their account. a. If Jack and Jill put the money in the account faithfully at the end of every year, how much will they have in it at the end of twenty-five years? b. Unfortunately, Jack was hurt in an accident after only ten years of savings. The medical bill has come to $700. Is there enough in the rainy-day fund to cover it?
a. N = 25 I/Y = 7 PV = 0 PMT = -50 FV = ? FV = $3,162.45 b. N = 10 I/Y = 7 PV = 0 PMT = -50 FV = ? FV = $690.82 Not enough $ to cover medical bill.
Brock Florist Company buys a new delivery truck for $29,000. It is classified as a light-duty truck. a. Calculate the depreciation schedule using a five-year life, straight-line depreciation, and the half-year convention for the first and last years. b. Calculate the depreciation schedule using a five-year life and MACRS depreciation. c. Compare the depreciation schedules from parts (a) and (b) before and after taxes using a 30% tax rate. What do you notice about the difference between these two methods?
a. Annual depreciation is cost of truck divided by five; $29,000/ 5 =$5,800 And for the first and last year we have $5,800 / 2 = $2,900. b. Depreciation schedule using MACRS; Year 1 Depreciation = $29,000 × 0.2000 = $5,800 Year 2 Depreciation = $29,000 × 0.3200 = $9,280 Year 3 Depreciation = $29,000 × 0.1920 = $5,568 Year 4 Depreciation = $29,000 × 0.1152 = $3,340.80 Year 5 Depreciation = $29,000 × 0.1152 = $3,340.80 Year 6 Depreciation = $29,000 × 0.0576 = $1,670.40 c. The difference is that the MACRS moves up the tax shield to the early years of depreciation yet the total tax shield is the same under both depreciation schedules.
Filer Manufacturing has 8.2 million shares of common stock outstanding. The current share price is $52, and the book value per share is $5. Filer Manufacturing also has two bond issues outstanding. The first bond issue has a face value of $70 million, an 8 percent coupon, and sells for 104 percent of par. The second issue has a face value $50 million, a 7.5 percent coupon, and sells for 97 percent of par. The first issue matures in 10 years, the second in 6 years.(assume each unit of bond has a face value of $1,000) a. What are Filer's capital structure weights on book value basis? b. What are Filer's capital structure weights on a market value basis? c. Which are more relevant, the book or market value weights? Why?
a. BVE = number of share * BV per share = 8.2M*($5) = $41M; BVD = $70M + $50M = $120M; BVA = BVE + BVD = $41M + 120M = $161M; E/V = 41/161 = 0.2547; D/V = 1 - E/V = 0.7453 In terms of book value, 25.47% of the capital is composed of equity and the remaining 74.53% is composed of debt. b. MVE = number of share * per share price = 8.2M* ($52) = $426.4M; MVD = 1.04($70M) + 0.97($50M) = $121.3M; MVA = MVE + MVD = $426.4 + 121.3M = $547.7; E/V = 426.4/547.7 = 0.7785; D/V = 1 - E/V = 0.2215 In terms of market value, 77.85% of the capital is composed of equity and the remaining 22.15% is composed of debt. c. The market value weights are more relevant.
Jiminy's Cricket Farm issued a 30-year, 9 percent annual coupon bond 8 years ago. The bond makes coupon payments semiannually. The par value of the bond is $1,000. The bond currently sells for 105 percent of its face value. The company's tax rate is 35 percent. a. What is the pretax cost of debt? b. What is the after-tax cost of debt? c. Which is more relevant, the pretax or the after-tax cost of debt? Why?
a. Cost of debt is the yield to maturity (YTM) of the outstanding bonds of the company. Given the price, maturity and coupon rate of the bond, we can use the financial calculator to find the YTM = 8.49%. Hence, the pretax cost of debt is 8.49%. b. RD = .0849(1 - .35) = 5.52% c. The after-tax rate is more relevant because that is the actual cost to the company.
You bought a stock for $35 and you received dividends of $1.25. The stock is now selling for $40. a. What is your dollar return? b. What is your percentage return?
a. Dollar return = 1.25 + (40 - 35) = $6.25 b. Dividend yield = 1.25 / 35 = 3.57% Capital gains yield = (40 - 35) / 35 = 14.29% Total percentage return = 3.57 + 14.29 = 17.86%
Titan Mining Corporation has 8 million shares of common stock outstanding, 5 million shares of preferred stock outstanding, and 100,000 units of 9 percent semiannual bonds outstanding, par value $1,000 each. The preferred stock pays a dividend of $6 per share. The common stock currently sells for $32 per share and has a beta of 1.15, the preferred stock currently sells for $67 per share, and the bonds have 15 years to maturity and sell for 91 percent of par. The market risk premium is 10 percent, T-bills are yielding 5 percent, and Titan Mining's tax rate is 35 percent. a. What is the firm's market value capital structure? b. If Titan Mining is evaluating a new investment project that has the same risk as the firm's typical project, what rate should the firm use to discount the project's cash flows?
a. MVD = 100,000($1,000)(0.91) = $91M; MVE = 8M($32) = $256M MVP = 5 million*($67) = $335M; V = $91M + 256M + 335M = $682M D/V = 91/682 = .1334; P/V = 335/682 = .4912; E/V = 256/682 = .3754 b. For projects equally as risky as the firm itself, the WACC should be used as the discount rate. RE = .05 + 1.15(.10) = 16.50% RD = 10.18% (by calculator) RP = $6/$67 = 8.96% WACC = .3754(16.50%) + .4912(8.96%) + 0.1334(1-0.35)(10.18%) = 11.48%
Kong Petroleum, Inc. is trying to evaluate a generator project with the following cash flows: Year 0, Cash Flow -28,000,000 Year 1, Cash Flow 53,000,000 Year 2, Cash Flow -8,000,000 a. If the company requires a 10% return on its investments, should it accept this project? Why? b. Compute the IRR for this project. How many IRRs are there? If you apply the IRR decision rule, should you accept the project or not? What's going on here? *(Part B is a challenging question and will NOT be in quiz or final exam.)*
a. NPV = - $28M + $53M/1.1 - $8M/1.12 = $13,570,247.93; NPV > 0 so accept the project. b. 0 = -$28M + $53M/(1+IRR) - $8M/(1+IRR)^2 IRR = 72.75%, -83.46% When there are multiple IRRs, the IRR decision rule is ambiguous; in this case, if the correct IRR is 72.75%, then we would accept the project, but if the correct IRR is -83.46%, we would reject the project.
Bumble's Bees, Inc., has identified the following two mutually exclusive projects: Year 0, Cash Flow (A) -17,000, Cash Flow (B) -17,000 Year 1, Cash Flow (A) 8,000, Cash Flow (B) 2,000 Year 2, Cash Flow (A) 7,000, Cash Flow (B) 5,000 Year 3, Cash Flow (A) 5,000, Cash Flow (B) 9,000 Year 4, Cash Flow (A) 3,000, Cash Flow (B) 9,500 a. What is the IRR for each of these projects? If you apply the IRR decision rule, which project should the company accept? Is this decision necessarily correct? b. If the required return is 11%, what is the NPV for each of these projects? Which project will you choose if you apply the NPV decision rule? c. Over what range of discount rates would you choose Project A? Project B? At what discount rate would you be indifferent between these two projects? Explain. *(Part C is a challenging question and will NOT be in quiz or final exam.)*
a. Project A, IRR = 15.86% Project B, IRR = 14.69% IRRA > IRRB, so IRR decision rule implies accepting project A. This may not be a correct decision; however, because the IRR criterion has a ranking problem for mutually exclusive projects. To see if the IRR decision rule is correct or not, we need to evaluate the project NPVs. b. Project A: NPV can = $1,520.71 Project B NPV = $1,698.58 NPVB > NPVA, so NPV decision rule implies accepting project B. c. Crossover rate: a discount rate such that the two investment project has the same NPV. Let R be the crossover rate. By definition, NPVA=NPVB when discount rate =R. Hence, we have the following: NPVA = -17,000 + 8,000/(1+R)+ 7,000/(1+R)2 + 5,000/(1+R)3 + 3,000/(1+R)4 =NPVB =-17,000 + 2,000/(1+R)+ 5,000/(1+R)2 + 9,000/(1+R)3 + 9,500/(1+R)4 Rearranging the equation, we get the following: 0 = $6,000/(1+R) + $2,000/(1+R)2 - $4,000/(1+R)3 - $6,500/(1+R)4 Solving the above equation, we get R = 12.18% At discount rates above 12.18% choose project A; for discount rates below 12.18% choose project B; indifferent between A and B at a discount rate of 12.18%.
An all-equity firm is considering the following projects: Project: W Beta: .70 Expected Return: 11% Project: X Beta: .95 Expected Return: 13 Project: Y Beta: 1.05 Expected Return: 14 Project: Z Beta: 1.60 Expected Return: 16 The T-bill rate is 5 percent, and the expected return on the market is 12 percent. Assume the company's overall WACC is 12%. a. Which projects have a higher expected return than the firm's 12 percent cost of capital? b. Which projects should be accepted? c. Which projects would be incorrectly accepted or rejected if the firm's overall cost of capital were used as a hurdle rate?
a. Projects X, Y and Z. b. Using the firm's overall cost of capital as a hurdle rate, projects Y and Z. However, after considering risk via the SML: E[W] = .05 + .70(.12 - .05) = .0990 < .11, so accept W. E[X] = .05 + .95(.12 - .05) = .1165 < .13, so accept X. E[Y] = .05 + 1.05(.12 - .05) = .1235 < .14, so accept Y. E[Z] = .05 + 1.60(.12 - .05) = .1620 > .16, so reject Z. c. Project W would be incorrectly rejected; project Z would be incorrectly accepted.
One of the basic principles of capital budgeting is that:
decisions are based on cash flows, not accounting income.
Sunk Costs are ______ in estimating an investment's cash flow, since sunk costs are______.
ignored, not recoverable
The standard deviations of individual stocks are generally higher than the standard deviation of the market portfolio because individual stocks:
none of the above
A bond with an annual coupon of $100 originally sold at par for $1,000. The current market interest rate on this bond is 9%. Assuming no change in risk, this bond will sell at a and present the seller (who bought the bond at initial issuance) of the bond today with a capital .
premium; gain
The ________ is the market of first sale in which companies first sell their authorized shares to the public.
primary market
In agency theory, the owners of the business are _______ and the managers are _______
principals, age
Stocks are different from bonds because ________.
stocks, unlike bonds, represent residual ownership
All else the same, a higher corporate tax rate ________.
will decrease the WACC of a firm with some debt in its capital structure
A bond that makes no coupon payments (and thus is initially priced at a deep discount to par value) is called a bond.
zero coupon
Portfolios
•A portfolio is a collection of assets •An asset's risk and return is important in how it affects the risk and return of the portfolio •The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets
Subjective Approach
•Consider the project's risk relative to the firm overall •If the project is more risky than the firm, use a discount rate greater than the WACC •If the project is less risky than the firm, use a discount rate less than the WACC •You may still accept projects that you shouldn't and reject projects you should accept, but your error rate should be lower than not considering differential risk at all
The Pure Play Approach
•Find one or more companies that specialize in the product or service that we are considering •Compute the beta for each company •Take an average •Use that beta along with the CAPM to find the appropriate return for a project of that risk •Often difficult to find pure play companies
Measuring Systematic Risk
•How do we measure systematic risk? •We use the beta coefficient to measure systematic risk •What does beta tell us? -A beta of 1 implies the asset has the same systematic risk as the overall market -A beta < 1 implies the asset has less systematic risk than the overall market -A beta > 1 implies the asset has more systematic risk than the overall market
Percentage Returns
•It is generally more intuitive to think in terms of percentages than dollar returns •Dividend yield = income / beginning price •Capital gains yield = (ending price - beginning price) / beginning price •Total percentage return = dividend yield + capital gains yield
Cost of Capital
•Knowing our cost of capital can help us determine our required return for capital budgeting projects •The return to an investor is the same as the cost to the company •We know that the return earned on assets depends on the risk of those assets •Our cost of capital provides us with an indication of how the market views the risk of our assets
Risk, Return and Financial Markets
•Lesson from capital market history -There is a reward for bearing risk -The greater the potential reward, the greater the risk -This is called the risk-return trade-off •We can examine returns in the financial markets to help us determine the appropriate returns on non-financial assets
Diversification
•Portfolio diversification is the investment in several different asset classes or sectors •The objective of diversification is to reduce the risk (or return variance) of a portfolio without an equivalent reduction in expected returns -The reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another •Diversification is not just holding a lot of assets -If the worse than expected returns from one asset occurs when the other asset also experiences worse than expected returns, then there will not be significant reduction in risk of the portfolio
Systematic Risk
•Risk factors that affect a large number of assets •Also known as non-diversifiable risk or market risk •Includes such things as changes in GDP, inflation, interest rates, etc.
Portfolio Beta
•The beta of your portfolio will be a weighted average of the betas of the securities in the portfolio. •What would be the average beta if you owned all of the S&P Composite Index stocks? -1 by definition •What is the beta of the risk-free return, U.S. Treasury Bills? -0 by definition
Systematic Risk Principle
•There is a reward for bearing risk •There is not a reward for bearing risk unnecessarily •The expected return on a risky asset depends only on that asset's systematic risk since unsystematic risk can be diversified away
Investment Risk and Return Variance
•Variance (or standard deviation) of the returns on an investment measures the risk of the investment •Investments with high return variances have higher probabilities of very small or negative returns. •Investments with low return variances usually have realized returns very close to expected returns •Everything else equal, risk averse investors would prefer less risky investments, or investments with lower return variances.
Variance and Standard Deviation
•Variance and standard deviation measure the volatility of asset returns •The greater the volatility the greater the uncertainty •Historical variance = sum of squared deviations from the mean / (number of observations - 1) •Standard deviation = square root of the variance
Taxes and the WACC
•We are concerned with after-tax cash flows, so we need to consider the effect of taxes on the various costs of capital •Interest expense reduces our tax liability -This reduction in taxes reduces our cost of debt -After-tax cost of debt = RD(1-TC) •Dividends are not tax deductible, so there is no tax impact on the cost of equity