Finance 350: Final

A 10-year bond, $1,000 face value bond with a 11% coupon rate and semi-annual coupons has a yield to maturity of 8%. The bond should be trading at a price of $

(1) With an 11% coupon rate and semiannual coupons, the coupon payment per six months is: CPN = FV × Coupon Rate / Number of Payments per year = $1,000 × 11% / 2 = $55. (2) YTM is 8% per year, so YTM per six months is 4%. N = 10 years × 2 =20. (3) t=0 t=1 t=2 t=19 t=20 |----------------|----------------|--------- ··········-----|----------------| $55 $55 $55 $55 + $1000 Use this formula to find the price: P=CPNYTM×(1−1(1+YTM)N)+FV(1+YTM)N, where P is the price of the bond, CPN is the coupon payment, N is the number of payments, FV is the face value paid at maturity, and y is the yield to maturity. So in this case: P = $55/0.04 × (1 - 1/(1+0.04)20 ) + $1,000 / (1+0.04)20

Anle Corporation has a current price of $21, is expected to pay a dividend of $2 in one year, and its expected price right after paying that dividend is $22. (a) What is Anle's expected dividend yield? Answer 9.5 %. (Round to two decimal places.) (b) What is Anle's expected capital gain rate? Answer 4.76 %. (Round to two decimal places.) (b) What is Anle's equity cost of capital? Answer 14.26 %. (Round to two decimal places.)

(a) Anle's expected dividend yield is: Dividend⋅yield=Div1P0, where Div1 is the dividend and P0 is the current share price. Dividend yield = $2 / $21 (b) Anle's expected capital gain rate is: Capital⋅gain⋅rate=P1−P0P0, where P1 is the expected share price in one year and P0 is the current share price. Capital Gain Rate = ($22 - $21) / $21 (c) Anle's equity cost of capital is: Equity Cost of Capital = Dividend yield + Capital gain rate

Andrew Industries is contemplating issuing a 30-year bond with a coupon rate of 7.50% (annual coupon payments) and a face value of $1,000. Andrew believes it can get a rating of A from Standard Poor's. However, due to recent financial difficulties at the company, Standard and Poor's is warning that it may downgrade Andrew Industries bonds to BBB. Yields on A-rated long-term bonds are currently 7.00%, and yields on BBB-rated bonds are 7.40%. (a) What is the price of the bond if Andrew maintains the A rating for the bond issue? $Answer 1062 . (Round to the nearest cent.) (b) What will the price of the bond be if it is downgraded? $Answer

(a) If Andrew Industries maintains a rating of A, it should have a YTM = 7%. With an 7.5% coupon rate and annual coupons, the coupon payment per year is: CPN = FV × Coupon Rate / Number of Payments per year = $1,000 × 7.5% / 1 = $75. YTM is 7% per year. N = 30 years. t=0 t=1 t=2 t=29 t=30 |----------------|----------------|--------- ··········-----|----------------| $75 $75 $75 $75 + $1000 Use this formula to find the price: P=CPNYTM×(1−1(1+YTM)N)+FV(1+YTM)N, where P is the price of the bond, CPN is the coupon payment, N is the number of payments, FV is the face value paid at maturity, and y is the yield to maturity. So in this case: P = $75/0.07 × (1 - 1/(1+0.07)30 ) + $1,000 / (1+0.07)30 (b) If Andrew Industries maintains a rating of BBB, it should have a YTM = 7.4%. So in this case: P = $75/0.074 × (1 - 1/(1+0.074)30 ) + $1,000 / (1+0.074)30

The last four years of returns for a stock are as follows: 1 2 3 4 -3.5% +28.5% +12.5% +4.5% (a) What is the average annual return? Answer 10.5 %. (Round to two decimal places.) (b) What is the variance of the stock's returns? Answer 0 . (Round to five decimal places.) (c) What is the standard deviation of the stock's returns? Answer 13.66

(a) The average return is: E(R) = 1/T × (R1 + R2 + ... + RT) =1/4 × (-3.5% + 28.5% + 12.5% + 4.5%) (b) The variance of the return is: VAR(R) = 1/ (T-1) × [ (R1 - E(R))2 + (R2 - E(R))2 +... + (RT - E(R))2 ] VAR(R) = 1/ 3 × [ (-3.5% - 10.50%)2 + (28.5% - 10.50%)2 + (12.5% - 10.50%)2 + (4.5% - 10.50%)2 ] Note, when taking the average, we divide with (T-1) instead of T. (c) The standard deviation is: SD(R) = ( VAR(R) )0.5

Krell Industries has a share price of $20.50 today. If Krell is expected to pay a dividend of $1.00 this year, and its stock price is expected to grow to $25 at the end of the year, what is Krell's dividend yield and equity cost of capital? (a) Krell's dividend yield is Answer 4.88 %. (Round to two decimal places.) (b) Krell's equity cost of capital is Answer 26.83

(a) The dividend yield is the percentage return the investor expects to earn from the dividend paid by the stock. It is given by: DividendYield=Div1P0, where Div1 is the dividend to be paid within the year, and P0 is the current stock price. Substituting the appropriate values, we have: Dividend Yield = $1 ÷ $20.50 (b) The equity cost of capital should equal to the expected return that the investor will earn for a one-year investment in the stock. It is equal to the sum of the dividend yield and the capital gain rate: rE = Dividend Yield + Capital Gain Rate The capital gain rate is the ratio between the capital gain and the current stock price: CapitalGainRate=P1−P0/P0, that is: CapitalGainRate=25.00−20.50/20.50 Therefore, the Equity Cost of Capital = Dividend Yield + Capital Gain Rate

The table below shows the one-year return distribution for RCS stocks. Possible Return Ri Probability pi -40% 0.10 -20% 0.20 0% 0.15 20% 0.25 40% 0.30 (a) The expected return is: Answer 9 (b) The standard deviation is Answer 27.18 Correct

(a) The expected return is calculated as a weighted average of the possible returns, where the weights correspond to the probabilities. Use this formula to calculate the expected return: E(R)=p1×R1+p2×R2+...+pi×Ri , where E(R) is the expectation of return R, pi is the probability of the return being Ri. E(R) = 0.10 × (-40%) + 0.20 × (-20%) +0.15 × (0%) +0.25 × (20%) +0.30 × (40%) (b) The variance is the average squared deviation from the mean: VAR(R)=∑Ii=1pi×[Ri−E(R)]2 VAR(R) = 0.10 × (-40% - 9%)2 + 0.20 × (-20% - 9%)2 + 0.15 × (0% - 9%)2 + 0.25 × (20% - 9%)2 +0.30 × (40% - 9%)2

Suppose the current, zero-coupon, yield curve for risk-free bonds is as follows: Maturity (years) 1 2 3 4 5 Yield to Maturity 4.70% 5.20% 5.45% 5.65% 5.80% (a) What is the price per $100 face value of a 3-year, zero-coupon risk-free bond? The price is $Answer 85.28 . (Round to two decimal places.) (b) What is the price per $100 face value of a 5-year, zero-coupon, risk-free bond? The price is $Answer 75.43 . (Round to two decimal places.) (c) What is the risk-free interest rate for 3-year term? The risk-free interest rate for 3-year maturity is Answer 5.45 %. (Round to two decimal places.)

(a) The formula for the price of a zero-coupon bond is as follows: P=FV(1+YTMn)n, where FV is the face value of $100, YTM is the yield to maturity and n is the number of periods. Therefore: P = $100 ÷ (1+5.45%)3 (b) The formula for the price of a zero-coupon bond is as follows: P=FV(1+YTMn)n, where FV is the face value of $100, YTM is the yield to maturity and n is the number of periods. Therefore: P = $100 ÷ (1+5.80%)5 (c) The risk-free interest rate for a 3-year term should equal the YTM on a risk-free bond with 3 year maturity: r3 = YTM3 = 5.45%

A bond will make payments every six months as shown on the following timeline (using six-month periods): t=0 t=1 t=2 t=27 t=28 |----------------|----------------|--------- ··········-----|----------------| $60 $60 $60 $1,060 (a) What is the maturity of the bond (in years)? Answer 14 years. (b) What is the face value? $Answer 1000 (c) What is the coupon rate (in percent)? Answer

(a) To determine the maturity of the bond, find the number of periods on timeline and divided by two because there are two payments in each year. (b) The face value is the amount paid at maturity, so the last payment is made up of the semi-annual coupon payment and the face value, or $60,00 and $1,000, in this case. (c) To determine the coupon rate, use the formula: Coupon Payment= (Coupon Rate × Face Value) / Number of Payments per year. This implies: $60 = $1,000 × Coupon Rate / 2

The expected return on the market portfolio is closest to

.50(24%) + .50(-8%) = 8% The correct answer is: 8%

The beta for security "Y" is closest to:

Change in Market = 24% - (-8%) = 32%, change in security = -16% - (16%) = -32%, Beta = -32%/32% = -1.00 The correct answer is: -1

You are a shareholder in a C corporation. The corporation earns $9 per share before taxes. Once it has paid taxes, it will distribute the rest of its earnings to you as a dividend. The corporate tax rate is 40%, and the personal tax rate on dividend income is 39%. How much is left for you after all taxes are paid? The amount that remains is $ ____ per share.

After-tax earnings = $9 × (1-40%) × (1-39%) =$3.294. The correct answer is: 3.29

Summit Systems will pay a dividend of $1.40 in one year. If you expect Summit's dividend to grow by 5.0% per year, what is its share price if its equity cost of capital is 10%? The price per share is $Answer

Below is the timeline for the cash flows (which continue into perpetuity): t=0 t=1 t=2 t=3 |----------------|----------------|----------------|--------- ·········· $1.40 $1.40(1+g) $1.40(1+g)2 According to the constant dividend growth model, the value of the firm depends on the current dividend level divided by the equity cost of capital adjusted by the growth rate. Then, P0=Div1rE−g, where P0 is the current stock price, Div1 is the next dividend payment, rE is the equity cost of capital, and g is the expected dividend growth rate. Substituting values, we have: P0 = $1.40 / (0.100 - 0.050)

Your firm is preparing to open a new retail strip mall and you have multiple businesses that would like lease space in it. Each business will pay a fixed amount of rent each month plus a percentage of the gross sales generated each month. The NPVs from each of the businesses has approximately the same amount of risk. The business names, square footage requirements, and monthly expected NPVs for each of the businesses that would like to lease space in your strip mall are provided below: Business Name Square Feet Required Expected Monthly NPV Videos Now 4,000 70,000 Gords Gym 3,500 52,500 Pizza Warehouse 2,500 52,500 Super Clips 1,500 25,500 30 1/2 Flavors 1,500 28,500 S-Mart 12,000 180,000 WalVerde Drugs 6,000 147,000 Multigular Wireless 1,000 22,250 If your new strip mall will have 15,000 square feet of retail space available to be leased, what is the maximum monthly NPVs to be generated?

Business Name Square Feet Required Expected Monthly NPVS NPV per S.F. Project Rank Videos Now 4,000 70,000 17.5 5 Gords Gym 3,500 52,500 15 7 Pizza Warehouse 2,500 52,500 21 3 Super Clips 1,500 25,500 17 6 30 1/2 Flavors 1,500 28,500 19 4 S-Mart 12,000 180,000 15 8 WalVerde Drugs 6,000 147,000 24.5 1 Multigular Wireless 1,000 22,250 22.25 2 So we select projects based upon their ranking until we run out of space. The optimal combination is shown below: WalVerde Drugs 6,000 147,000 24.5 1 Multigular Wireless 1,000 22,250 22.25 2 Pizza Warehouse 2,500 52,500 21 3 30 1/2 Flavors 1,500 28,500 19 4 Videos Now 4,000 70,000 17.5 5 Total 15,000 $320,250 The correct answer is: $320,250

The weight on Wyatt Oil stock in the market portfolio is closest to:

Calculations B × C D/1950 Stock Price per Share Number of Shares Outstanding (Millions) Market Cap Weight Taggart Transcontinental $15.60 25 $390.00 0.2 Rearden Metal $13.00 45 $585.00 0.3 Wyatt Oil $29.25 10 $292.50 0.15 Nielson Motors $26.25 26 $682.50 0.35 Total $1950.00 The correct answer is: 15%

Suppose all possible investment opportunities in the world are limited to the four stocks list in the table below: Stock Price per Share Number of Shares Outstanding (Millions) Taggart Transcontinental $15.60 25 Rearden Metal $13.00 45 Wyatt Oil $29.25 10 Nielson Motors $26.25 26 1) The weight on Taggart Transcontinental stock in the market portfolio is closest to:

Calculations B × C D/1950 Stock Price per Share Number of Shares Outstanding (Millions) Market Cap Weight Taggart Transcontinental $15.60 25 $390.00 0.2 Rearden Metal $13.00 45 $585.00 0.3 Wyatt Oil $29.25 10 $292.50 0.15 Nielson Motors $26.25 26 $682.50 0.35 Total $1950.00 The correct answer is: 20%

Suppose that you are holding a market portfolio and you have invested $9,000 in Rearden Metal. The amount that you have invested in Nielson Motors is closest to:

Calculations B × C D/1950 Stock Price per Share Number of Shares Outstanding (Millions) Market Cap Weight Taggart Transcontinental $15.60 25 $390.00 0.2 Rearden Metal $13.00 45 $585.00 0.3 Wyatt Oil $29.25 10 $292.50 0.15 Nielson Motors $26.25 26 $682.50 0.35 Total $1950.00 Amount Neilson = Weight Neilson / Weight Rearden * Amount Rearden = 0.35/0.30 * $9,000 = $10,500 The correct answer is: $10,500

Suppose that the market portfolio is equally likely to increase by 24% or decrease by 8%. Security "X" goes up on average by 29% when the market goes up and goes down by 11% when the market goes down. Security "Y" goes down on average by 16% when the market goes up and goes up by 16% when the market goes down. Security "Z" goes up on average by 4% when the market goes up and goes up by 4% when the market goes down. The beta for security "X" is closest to:

Change in Market = 24% - (-8%) = 32%, change in security = 29% - (-11%) = 40%, Beta = 40%/32% = 1.25 The correct answer is: 1.25

The beta for security "Z" is closest to:

Change in Market = 24% - (-8%) = 32%, change in security = 4% - (4%) = 0%, Beta = 0%/32% = 0 The correct answer is: 0

Which firm has the highest cost of equity capital?

Cost of capital is measured using the CAPM and is a linear function of beta. Therefore the firm with the highest beta (Moe) has the highest cost of equity capital. The correct answer is: Moe

Who checks the accuracy of financial statements?

Financial statements in form 10-K are required to be audited by a neutral third party who checks them and ensures that the financial statements are prepared according to GAAP and that the information contained is reliable.

You have decided to form a new start-up company developing applications for the iPhone. Match each example listed below with the type of decision you would make as a Chief Financial Offer. Determining which types of iPhone application projects will offer your company the best value and therefore which project your company should develop. Ensuring that your company has the necessary funds to make investments, pay interest on loans, and pay your employees Determining how to fund your iPhone application investments what what mix of bonds and stocks will sell.

Financing decision (Decisions to raise money). Investment Decision (Decisions to spend money). Cash Management Decision (Decisions to manage day-to-day cash needs). The correct answer is: Determining which types of iPhone application projects will offer your company the best value and therefore which project your company should develop. → Investment Decision, Ensuring that your company has the necessary funds to make investments, pay interest on loans, and pay your employees → Cash Management Decision, Determining how to fund your iPhone application investments what what mix of bonds and stocks will sell. → Financing Decision

When you purchased your house, you took out a 30-year mortgage with an interest rate of 4.8% per year. The monthly payment on the mortgage $1,500. You have just made a payment and have now decided to pay the mortgage off by repaying the outstanding balance. What is the payoff amount if you have lived in the house for 18 years (so there are 12 years left on the mortgage)? Payoff amount is $Answer 163954

Given a monthly payment of $1,500, the payoff amount is equal to the present value of an n-month annuity, n being the number of monthly payments remaining on the mortgage. The monthly interest rate is: rm = r ÷ 12 = 4.8% ÷ 12 = 0.4% = 0.004 The present value of 144-month annuity is: PV = $1,500 ÷ 0.004 × [ 1 - 1 ÷ (1+0.004)144 ] = $163,954

Assume Evco, Inc., has a current stock price of $60 and will pay a $2.20 dividend in one year; its equity cost of capital is 19%. What price must you expect Evco stock to sell for immediately after the firm pays the dividend in one year to justify its current price? $Answer

In order to justify the current price of $60, the price that the stock sells for must take into account both the cost of capital for the investment as well as the dividend that is paid out.P0=Div1+P11+rE. $60 = ($2.20 + P1) ÷ (1+19%) Expected Price = $60 × (1+0.19) - $2.20

What is the present value of $14,000 received: (a) 12 years from today when the interest rate is 4% per year. $Answer 8744 (b) 20 years from today when the interest rate is 5% per year. $Answer 5276 (c) 6 years from today when the interest rate is 2% per year. $Answer 12432

Hint: PV = FV ÷ (1+r)n

You are thinking of retiring. Your retirement plan will pay you either $250,000 immediately on retirement or $350,000 five years after the date of your retirement. (a) If the interest rate is 0% per year, which alternative should you choose? Take the money now. Waiting until 5 years after retirement. Mark 1.00 out of 1.00 The correct answer is: Waiting until 5 years after retirement. (b) If the interest rate is 8% per year, which alternative should you choose? Take the money now. Waiting until 5 years after retirement. Mark 1.00 out of 1.00 The correct answer is: Take the money now. (c) If the interest rate is 20% per year, which alternative should you choose? Take the money now. Waiting until 5 years after retirement. Mark 1.00 out of 1.00 The correct answer is: Take the money now.

Hint: PV = FV ÷ (1+r)n

You currently have a four-year-old mortgage outstanding on your house. You make monthly payments of $1,700. You have just made a payment. The mortgage has 26 years to go (i.e., it had an original term of 30 years). Show the timeline of the loan from the bank's perspective.

Hint: Since you have just made a monthly payment, you do not have any payment due TODAY and the next payment is due at the end of the month. The correct answer is: Year: 0 1 2 3 4 312 ------------------|-------------|------------|------------|------------|-- - - - - - - - - --| Cash Flow: $1700 $1700 $1700 $1700 $1700

You have just taken out a five-year loan from a bank to buy an engagement ring. The ring costs $5,000. You plan to put down $2,000 and borrow $3,000. You will need to make annual payments of $1,100 at the end of each year. Show the timeline of the loan from your perspective.

Hint: from your perspective on the loan, you received $3,000 today and you will make 5 installments of $1,100 at the end of each of the next five years. The correct answer is: Year 0 1 2 3 4 5 ------------------|-------------|-------------|-------------|-------------|------------| Cash Flow $3000 -$1100 -$1100 -$1100 -$1100 -$1100

Which firm has the least market risk:

Market risk is measured using beta and Eenie has the lowest beta, hence the lowest market risk. The correct answer is: Eenie

Consider a project with the following cash flows: Year Cash Flow 0 -10,000 1 14,000 Assume the appropriate discount rate for this project is 15%. The IRR for this project is closest to:

NPV = -$10,000 + $14,000÷ (1+IRR), solve for IRR, IRR = 40% The correct answer is: 40%

A project costs $200 million and is expected to generate cash flows of $25 million per year, starting at the end of the first year and lasting forever. What is the internal rate of return?

Note that the cash flow stream is a perpetuity. So its present value is: C / r NPV = -$200 + $25 ÷ IRR. Set NPV = 0, solve for IRR, IRR=12.5% The correct answer is: 12.5%

Consider a project with the following cash flows: Year Cash Flow 0 -10,000 1 4,000 2 4,000 3 4,000 4 4,000 Assume the appropriate discount rate for this project is 15%. The payback period for this project is closest to:

Payback = 10000 / 4000 = 2.5, Round upward to 3. The correct answer is: 3

You are a shareholder in an S corporation. The corporation earns $2 per share before taxes. Once it has paid any applicable taxes it will distribute the rest of its earnings to you as a dividend. The corporate tax rate is 50%, and the personal tax rate on income is 35%. How much is left for you after all taxes are paid? The amount that remain is $ ____ per share.

S corporations are only subject to income tax. After-tax income = $2 × (1 - 35%) = $1.3. The correct answer is: 1.30

The risk-free rate is closest to:

Security "Z" is the risk-free asset since its return is constant regardless of the market. Therefore the risk-free rate is the return on security Z which is 4%. The correct answer is: 4%

The expected return on security with a beta of 1.2 is closest to:

Security "Z" is the risk-free asset since its return is constant regardless of the market. Therefore the risk-free rate is the return on security Z which is 4%. The expected return on the market rate is .50(24%) + .50(-8%) = 8%. Using the CAPM, the return on this security is .04 + 1.2(.08 -.04) = 8.8% The correct answer is: 8.8%

You just purchased a car for $24,000 and the auto loan is 60-month fixed rate loan with annual interest of 2.4%. What is your monthly payment? Your monthly payment is $Answer 425

The auto loan is a 60-month annuity with monthly cash flow of $C and monthly interest rate of 0.2% (=2.4%÷12). Given that the present value is $24,000, you can back out $C. $24,000 = C / 0.002 * [ 1 - 1 / (1+0.002)^60]

What is the present value of $5,000 paid at the beginning of each of the next 78 years if the interest rate is 9% per year? The present value is $Answer

The cash flow at t=0 is $5,000 and the last cash flow stops at the end of 77 years (that is, the beginning of 78 years). Therefore, the stream is not a standard annuity model. The timeline can be split into two parts: $5,000 cash flow at t=0 and a 77-year annuity of $5,000 cash flows. Total PV = $5,000 today + PV (77-year Annuity)

What four financial statements can be found in a firm's 10-K filing?

The correct answer is: Balance sheet, Income Statement, Statement of cash flows, and statements of shareholders' equity

Shareholders of a corporation can exercise control by all of the following except:

The correct answer is: electing the chief executive officer.

You bought a house worth $900,000 and the loan is a 30-year fixed rate mortgage with 4.5% annual interest rate. What is your monthly payment? Your monthly payment is $Answer

The loan is a 360-month annuity. The present value of the annuity equals to the loan amount, so PV = $900,000. C = unknown. Monthly Interest rate: rm= r ÷ 12 = 4.5% ÷ 12 = 0.375% =0.00375. n = 30 years × 12 = 360. We have an equation with one unknown. Use the present value formula of annuity, back out C. $900,000 = c / 0.00375 * [1 - 1 / (1+0.00375)^ 360]

Your lender now offers you a 30-year fixed-rate home mortgage with 3.6% interest per year. If you can afford a monthly payment of $3,000, what is maximum price of a house that you can afford? The maximum house price is $Answer

The maximum monthly payment C = $3,000. the monthly interest rate can be derived from annual rate: rm= r ÷ 12 = 3.6% ÷ 12 = 0.3% =0.003. n = 30 years × 12 = 360 month. Apply the PV formula for annuity and you can figure out the max affordable loan. PV = $3000 / 0.003 * [1 - 1 / (1+0.003)^360]

The promised cash flows of three securities are listed below. If the cash flows are risk-free, and the risk-free interest rate is 6.0%, determine the no-arbitrage price of each security before the first cash flow is paid. Security Cash Flow Today ($) Cash Flow in One Year ($) A 700 700 B 0 1,400 C 1,400 0

The no-arbitrage price of Security A is $ Answer 1360.37 The no-arbitrage price of Security B is $ Answer 1320.75 The no-arbitrage price of Security C is $ Answer 1400

You are 20 years old and decide to start saving for your retirement. You plan to save $4,000 at the end of the first year and then increase your savings by 3% per year until you make the very last deposit at age 65. Suppose you earn 6% per year on your retirement savings. How much will you have saved for retirement right at age 65? $Answer 1331069

The question is about calculating the future value of a stream of cash flows involving a Growing Annuity structure. The cash flow will become 3% larger than the previous cash flow each year. The time line can be drawn as: t=0 t=1 t=2 t=3 t=45 |----------------|----------------|----------------|----- ··············------| $0 $4000 $4000×(1+g) $4000×(1+g)2 $4000×(1+g)44 C = $4,000 r = 0.06 g = 0.03 n = 45 Thus, PV =C / (r-g) * [ 1 - (1+g)n / (1+r)n ] FV = PV * (1+r)n

Your oldest daughter is about start kindergarten in a private school. Tuition is $20,000 per year, payable at the beginning of the school year. You expect to keep your daughter in private school through high school. You expect tuition to increase at a rate of 3% over the 13 years of her schooling. What is the present value of your tuition payments if the interest rate is 8% per year? That is, you would need to have $Answer 198730 (Round to the nearest dollar) in the bank now to fund all 13 years of tuition.

The question is about calculating the present value of a stream of cash flows involving a Growing Annuity structure. This is a challenging question. To get it right, the timeline must be carefully drawn. Given that tuition payments are made at the beginning of a year, the first payment of $20k will take place today at t=0. And the last payment will made at t=12, which is the beginning of the 13th year. The cash flow at the end of the 13th year, t=13, is $0. The time line can be drawn as: t=0 t=1 t=2 t=3 t=12 t=13 |----------------|----------------|----------------|----- ··········-----|----------------| $20k $20k×(1+g) $20k×(1+g)2 $20k×(1+g)3 $20k×(1+g)12 $0 The stream of cash flow above can be decomposed into two parts: a single cash flow of $20k at t=0, and a 12-year growing annuity. For the 12-year growing annuity, C, the cash flow at t=1, is $20k×(1+g), not $20k. Remember, C is always referring to the cash flow at t=1; r = 8%; g = 3%. Therefore, PV = $20,000 + PV(growing annuity) = $20,000 + [$20,000 ×(1+0.03)] ÷ (0.08 - 0.03) × [1 - (1.03/1.08)12]

A rich relative has bequeathed you a growing perpetuity. The first payment will occur in one year and will be $4,000 each. Each year after that, you will receive a payment on the anniversary of the last payment that is 4% larger than the last payment. This pattern of payments will go on forever. If the interest rate is 11% per year, what is the present value of the bequest? The PV of the growing perpetuity is $Answer 57143

The question is about calculating the present value of a stream of cash flows involving a Growing Perpetuity structure. The cash flow will become 4% larger than the previous cash flow each year. The time line can be drawn as: t=0 t=1 t=2 t=3 |----------------|----------------|----------------|----- ·············· $0 $4000 $4000×(1+g) $4000×(1+g)2 C = $4,000 r = 0.11 g = 0.04 Thus, PV =C / (r-g) = $4,000 ÷ (0.11- 0.04)

Your buddy in mechanical engineering has invested a machine. It takes one year for the machine to manufacture $400 worth of goods. Once built, the machine will last forever and will require no maintenance. The machine can be built immediately and will cost $4,000 to build. If the interest rate is 3.5%, the NPV of the machine is $Answer

The question is about calculating the present value of a stream of cash flows involving a perpetuity structure. The cost of building the machine is $400 paid today. It takes the machine one year to manufacture $400, so the very first cash flow (+) will arrive at t=1. The time line can be drawn as: t=0 t=1 t=2 t=3 |----------------|----------------|----------------|----- ·············· - $4,000 $400 $400 $400 The stream of cash flow above can be decomposed into two parts: a single cash flow of - $4,000 at t=0, and a standard perpetuity afterwards. Thus, PV =CF0 + PV(perpetuity) = -$4,000 + C / r = - $4,000+ $400 / 0.035

Your buddy in mechanical engineering has invested a machine. It takes one year for the machine to manufacture $400 worth of goods. Once built, the machine will last forever and will require no maintenance. The machine can be built immediately and will cost $4,000 to build. If the interest rate is 3.5%, the NPV of the machine is $Answer 7428.57

The question is about calculating the present value of a stream of cash flows involving a perpetuity structure. The cost of building the machine is $400 paid today. It takes the machine one year to manufacture $400, so the very first cash flow (+) will arrive at t=1. The time line can be drawn as: t=0 t=1 t=2 t=3 |----------------|----------------|----------------|----- ·············· - $4,000 $400 $400 $400 The stream of cash flow above can be decomposed into two parts: a single cash flow of - $4,000 at t=0, and a standard perpetuity afterwards. Thus, PV =CF0 + PV(perpetuity) = -$4,000 + C / r = - $4,000+ $400 / 0.035

What is the present value of $5,000 paid at the end of each of the next 78 years if the interest rate is 9% per year? The present value is $Answer

The stream of cash flows described above is a standard Annuity. Therefore, you can apply directly the Present Value formula for Annuity. Identify C, r and n, and use PV = C/r × [ 1 - 1/(1+r)n ].

You are 22 years old and decide to start saving for your retirement. You plan to save $6,000 at the end of each year (so the first deposit will be one year from now), and will make the last deposit when you retire at age 65. Suppose you earn 6% per year on your retirement savings. How much will you have saved for retirement right at age 65? 1125045

This is a question about the future value of an annuity. First figure out the present value of this 43-year annuity; then get the future value by compounding the present value with a factor of (1+r)43. Constant Cash Flow: C = $6,000. Annual Interest Rate: r = 0.06. n = 65 - 22 = 43. FV = PV * (1+r)^n = 6000 / 0.06 * [ 1 - 1 / (1+0.06)^43 ] * (1+0.06)^43

Your grandmother has been putting $2,000 into a savings account on every birthday since your first (that is, when you turned 1). The account pays an interest rate of 5%. How much money will be in the account on your 18th birthday immediately after your grandmother makes the deposit on that birthday? The amount in the account upon your 18th birthday is $Answer 56265

This is an 18-year annuity of annual cash flow of $2,000 and annual interest rate of 5%. First, compute the present value of the annuity (back to the point when you are born); then, multiply the PV with a factor of (1+r)n to get FV. C = $2000; r=0.05; n= 18

d) Why is the amount of interest earned in part (a) less than half the amount of interest earned in part (b)?

This is because you earn interest on past interest. Since the beginning of the second 5 year starts off with more money than the beginning of the first 5 years, the money grows faster.

Use the following information to answer the question(s) below. Beta Volatility "Eenie" 0.45 20% "Meenie" 0.75 18% "Miney" 1.05 35% "Moe" 1.20 25% Assume that the risk-free rate of interest is 3% and you estimate the market's expected return to be 9%. 1) Which firm has the most total risk?

Total risk is measured using volatility and Miney has the highest volatility, hence the most total risk. The correct answer is: Miney

Your firm has a risk-free investment opportunity where it can invest $160,000 today and receive $171,000 in one year. For what level of interest rate is this project attractive? The project will be attractive when the interest rate is any positive value less than or equal to

Under what interest rate would an investment of $160,000 grow to $171,000 in one year?

Luther Industries has 25 million shares outstanding trading at $18 per share. In addition, Luther has $150 million in outstanding debt. Suppose Luther's equity cost of capital is 13%, its debt cost of capital is 7%, and the corporate tax rate is 40%. Luther's weighted average cost of capital is closest to:

Weighted Average Cost of Capital E = 25 million * $18 = $450 million D = $150 million The correct answer is: 10.8%

In July 2007, Apple had cash of $7.08 billion, current assets of $18.74 billion, current liabilities of $6.98 billion, and inventories of $0.21 billion.

What was Apple's current ratio? Answer 2.68 (b) What was Apple's quick ration? Answer 2.65

Consider the following two quotes for ABC Stock: March 14th March 21st Ask: 30.24 Ask: 30.42 Bid: 30.21 Bid: 30.39 Suppose you purchase 1225 shares of ABC stock on March 14th and then sell them one week later on March 21st. What are your net proceeds?

You buy at the asking price and sell to the biding price. You bought at $30.24 on March 14th and you sold at $30.39 on March 21st. You made a profit of ($30.39 - $30.24=) $0.15 per share. The correct answer is: 183.75

Consider the following information regarding corporate bonds: Rating AAA AA A BBB BB B CCC Average Default Rate 0.0% 0.0% 0.2% 0.4% 2.1% 5.2% 9.9% Recession Default Rate 0.0% 1.0% 3.0% 3.0% 8.0% 16.0% 43.0% 1) Wyatt Oil has a bond issue outstanding with seven years to maturity, a yield to maturity of 7.0%, and a BBB rating. The bondholders expected loss rate in the event of default is 70%. Assuming a normal economy the expected return on Wyatt Oil's debt is closest to:

rd = ytm - prob(default) × loss rate = 7% - 0.4%(70%) = 6.72% The correct answer is: 6.7%

Wyatt Oil has a bond issue outstanding with seven years to maturity, a yield to maturity of 7.0%, and a BBB rating. The bondholders expected loss rate in the event of default is 70%. Assuming the economy is in recession, then the expected return on Wyatt Oil's debt is closest to:

rd = ytm - prob(default) × loss rate = 7% - 3.0%(70%) = 5.53% The correct answer is: 4.9%