Final Exam MGT 320 Finance
How are limit orders and market orders different?
A limit order specifies a price that you are willing to buy or sell at. It will be executed when there is demand or supply at that price. A market order is to be executed immediately at the best outstanding limit order.
Assume Gillette Corporation will pay an annual dividend of $0.65 one year from now. Analysts expect this dividend to grow at 12.0% per year thereafter until the 5th year. Thereafter, growth will level off at 2.0% per year. According to thedividend-discount model, what is the value of a share of Gillette stock if the firm's equity cost of capital is 8.0%?
HELP
You have $600,000 to donate to your college. You want to endow a perpetual scholarship that makes its first payment in 1 year. If thecollege's discount rate is 8%, how large will the annual scholarship payment be?
However, since you are calculating the payment amount (CF), the formula can be rearranged as: CF=PV×r Therefore, CF=$600,000×0.08=$48,000 The annual scholarship payment will be $48,000.
NoGrowth Corporation currently pays a dividend of $0.55 per quarter, and it will continue to pay this dividend forever. What is the price per share of NoGrowth stock if the firm's equity cost of capital is 13.5%?
If the dividends are paid quarterly, we can value them as a perpetuity using a quarterly discount rate found using the following formula: Equivalent n-period discount rate=(1+rE)^1/n −1 Therefore, Equivalent n-period discount rate =(1+0.135)^1/4 −1=0.03216 The quarterly discount rate is 3.216%. To calculate the price per share, use the following formula: P0=Div1/rE−g Therefore, P0=$0.55/0.03216−0=$17.10 The stock price per share is $17.10.
What role do investment banks play in the economy?
Investment banks advise companies in major financial transactions such as buying or selling companies or divisions. Investment banks assist companies in raising capital by issue of stocks and bonds on behalf of corporate clients.
You are considering a car loan with a stated APR of 8% based on monthly compounding. What is the effective annual rate of this loan?
Monthly interest rate=0.08/12=0.00667 The montly interest rate is 0.667%. To calculate the effective annual rate, use the following formula: Effective annual rate=(1+Monthly interest rate)^12−1 Therefore, Effective annual rate=(1.00667)^12−1 =0.0830 =8.30% The effective annual rate is 8.30%.
If the rate of inflation is 6.2%, what nominal interest rate is necessary for you to earn a 4.1% real interest rate on your investment? (Note: Be careful not to round any intermediate steps less than six decimal places.)
Real Rate=Nominal Rate−Inflation Rate/ 1+Inflation Rate Nominal Rate=Real Rate×(1+Inflation Rate)+Inflation Rate Nominal rate=0.0410×1.0620+0.0620=0.1055=10.55% The nominal rate needed is 10.55%.
You have just purchased a share of stock for $21.45. The company is expected to pay a dividend of $0.65 per share in exactly one year. If you want to earn a 10.5% return on your investment, what price do you need if you expect to sell the share immediately after it pays the dividend?
Since the return on your investment must be 10.5%, use the following formula to determine the price needed: R1=Div1+(P1−P0)/P0 substituting the values into this formula: R1=$0.65+(P1−$21.45)/$21.45=0.105 Therefore, P1=$21.45×0.105−$0.65+$21.45=$23.05 The selling price after the dividend would need to be $23.05.
You sit on the board of a public corporation. Your CEO has proposed taking steps to offset the carbon impact of your company's manufacturing process. Doing so will add to the company's overall expenses. Your CEO argues, however, that this action will actually increase the stock price, maximizing shareholder wealth. Why might socially-responsible activities also be value-maximizing?
Socially responsible actions are not necessarily at odds with shareholder wealth maximization. If potential customers value these actions highly, they will be more likely to purchase your products and may even be willing to pay more for them if doing so helps a social goal that is important to them. Further, some potential employees may value working for socially responsible firms, helping you attract the best talent.
You are considering a savings bond that will pay $100 in 12 years. If the interest rate is 2.3%, what should you pay today for the bond?
The amount that you should pay today for the bond is: PV=C/(1+r)^n PV=$100/(1+0.023)^12=$76.12
If your bank pays you 1.7% interest and you deposit $650 today, what will be your balance in six years?
The bank balance will be: FV=C×(1+r)^n FV=$650×(1+0.017)^6=$719.18
You have credit card debt of $24,000 that has an APR (monthly compounding) of 14%. Each month you pay the minimum monthly payment. You are required to pay only the outstanding interest. You have received an offer in the mail for an otherwise identical credit card with an APR of 8%. After considering all your alternatives, you decide to switch cards, roll over the outstanding balance on the old card into the new card, and borrow additional money as well. How much can you borrow today on the new card without changing the minimum monthly payment you will be required to pay? (Note: Be careful not to round any intermediate steps less than six decimalplaces.)
The discount rate on the original card is: r=APR/m Therefore, r=14%/12 =1.16666667% Assuming that your current monthly payment is the interest that accrues, it equals: Original monthly payment=P×r Therefore, Original monthly payment=$24,000×0.011666667 =$280.00 The new discount rate is r=8%/12 =0.66666667% Next, use the formula for the present value of a perpetuity to find the present value of your monthly payments: PV=$280.00/0.0066666667 =$42,000
What is the most important type of decision that the financial manager makes?
The financial manager's most important job is to make the firm's investment decisions.
You are upgrading to better production equipment for your firm's only product. The new equipment will allow you to make more of your product in the same amount of time. Thus, you forecast that total sales will increase next year by 10% over the current amount of 115,000 units. If your sales price is $24 per unit, what are the incremental revenues next year from the upgrade?
The incremental revenues are given by the expression: Incremental Revenues=Additional Units Sold×Price per Unit Therefore, Incremental Revenues =115,000 units×10%×$24 per unit =$276,000
Assume that a bond will make payments every six months as shown on the following timeline (using six-month periods): a. What is the maturity of the bond (in years)? b. What is the coupon rate (as a percentage)? c. What is the face value?
The maturity of the bond is the number of years until the issuer returns the face value to the buyer. For the case of a bond that will make payments every six months, the maturity is the number of payments divided by 2. The maturity of the bond is 15 years b- By rearranging the equation above, we come up with: Coupon Rate=CPN×Number of Coupon Payments per Year/Face Value Therefore, Coupon Rate=$22.00×2/$1,000=4.4% c- What is the face value? The face value is the principal of the bond, which has to be repaid at maturity. Therefore, the face value is $1,000.
Marian Plunket owns her own business and is considering an investment. If she undertakes the investment, it will pay $6,840 at the end of each of the next 3 years. The opportunity requires an initial investment of $1,710 plus an additional investment at the end of the second year of $8,550. What is the NPV of this opportunity if the interest rate is 2.6% per year? Should Marian take it?
The net present value of the cash flows is: NPV=−CF0+ CF1/(1+r)+ CF2/(1+r)^2+ CF3(1+r)^3 Therefore, NPV=−$1,710 +$6,840/1+0.026+ (−$1,710/(1+0.026)^2) + $6,840/(1+0.026)^3 =$9,665.30 Should Marian take it? Yes, Marian should make the investment since it has a positive NPV of $9,665.30.
Your cousin is currently 15 years old. She will be going to college in 3 years. Your aunt and uncle would like to have $130,000 in a savings account to fund her education at that time. If the account promises to pay a fixed interest rate of 5.0% per year, how much money do they need to put into the account today to ensure that they will have $130,000 in 3 years?
The present value of a future amount is: PV=FV/(1+r)^n where r is the interest rate and n is the number of periods. PV=$130,000/(1+0.050)^3=$112,298.89
The current zero-coupon yield curve for risk-free bonds is as follows: What is the price per $100 face value of a two-year, zero-coupon, risk-free bond?
The price of the zero-coupon bond is given by: P=FV/(1+y)^n where FV is the face value, y is the yield to maturity, and n is the number of periods (years). Therefore, P=$100/(1+0.0560)^2 =$89.68
You bought a stock one year ago for $52.00 per share and sold it today for $58.00 per share. It paid a $1.25 per share dividend today. What was your realized return?
The realized return from t to t +1 is determined by using the following formula: Rt+1=Divt+1+(Pt+1−Pt)/Pt where Divt+1 is the dividend paid, Pt is the purchase price, and Pt+1 is the selling price. Therefore, R1=$1.25+($58.00−$52.00)/$52.00=13.9%
What is the difference between a public and private corporation?
The shares of a public corporation are traded on an exchange (or "over the counter" in an electronic trading system) while the shares of a private corporation are not traded on a public exchange.
if you own 18,000 shares of stock of Nike and it pays a dividend of $0.26 per share, then what is the total dividend you will receive?
The total dividend that you will receive is: Dividend=Dividend per Share×Number of Shares Therefore, Dividend=$0.26 per share×18,000 shares=$4,680
Daily Enterprises is purchasing a $10.7 million machine. It will cost $56,000 to transport and install the machine. The machine has a depreciable life of five years and will have no salvage value. If Daily uses straight-line depreciation, what are the depreciation expenses associated with this machine?
The yearly depreciation expenses associated with this machine are equal to the purchase cost plus installation cost of the machine divided by 5 years: Depreciation Expenses= (Purchase Cost+Installation)/Number of Years Depreciation Expenses= ($10,700,000+$56,000)/5 years= $2,151,200 per year
What is the discount factor that is equivalent to a 12% discount rate?
To calculate the discount factor, use the following formula: Discount factor=1/1+Interest rate Therefore, Discount factor=1/1.12=0.8929 The discount factor is 0.8929.
Ovit, Inc. has preferred stock with a price of $21.05 and a dividend of $1.64 per year. What is its dividend yield?
To calculate the dividend yield, use the following formula: Dividend Yield=Div1/P0 Therefore, Dividend Yield=$1.64/$21.05=0.078 The dividend yield is 7.8%.
You have found three investment choices for a one-year deposit: 13% APR compounded monthly, 13% APR compounded annually, and 11% APR compounded daily. Compute the EAR for each investment choice. (Assume that there are 365 days in the year.) (Note: Be careful not to round any intermediate steps less than six decimal places.)
To calculate the effective annual rate (EAR) from an account with 13% APR compounded monthly, use the following equation: EAR=(1+0.13/12)^12 −1=13.803% Therefore, the EAR=13.803%. To calculate the effective annual rate (EAR) from an account with 13% APR compounded annually, use the following equation: EAR=(1+0.13/1)^1 −1=13.000% Therefore, the EAR=13.000%. To calculate the effective annual rate (EAR) from an account with 11% APR compounded daily, use the following equation: EAR=(1+0.11/365)^365 −1=11.626% Therefore, the EAR=11.626%.
You expect KStreet Co's trade at $110 per share right after paying a $4.00 dividend per share in one year. What is the most you would pay to buy the stock now if you want to earn at least a return of 8%?
To calculate the most you would pay to buy the stock, solve for P0 in the following formula: Return=Div1+(P1−P0)/P0 Therefore, 0.08=$4.00+($110−P0)/P0 0.08P0=$114.00−P0 1.08P0=$114.00 P0=$114.00/1.08=$105.56 The most you would pay to buy the stock is $105.56.
You just purchased a share of SPCC for $110. You expect to receive a dividend of $8 in one year. If you expect the price after the dividend is paid to be $122, what toal return will you have earned over the year? What was your dividend yield? Your capital gain rate?
To calculate the total return, use the following formula: r=Div1+(P1−P0)/P0 Therefore, r=$8+($122−$110)/$110=0.1818=18.18% To calculate the dividend yield, use the following formula: Dividend yield=Dividend/P0 Therefore, Dividend yield=$8/$110=0.0727=7.27% To calculate the capital gain rate, use the following formula: Capital gain rate=P1−P0/P0 Therefore, Capital gain rate=($122−$110)/$110=0.1091=10.91%
You have a depreciation expense of $558,000 and a tax rate of 21%. What is your depreciation tax shield?
To determine the depreciation tax shield, use the following formula: Depreciation Tax Shield=Depreciation Expense×Tax Rate Therefore, Depreciation Tax Shield=$558,000×0.21=$117,180 The depreciation tax shield will be $117,180.
Krell Industries has a share price of $22.35 today. If Krell is expected to pay a dividend of $1.15 this year and its stock price is expected to grow to $24.08 at the end of the year, what is Krell's dividend yield and equity cost of capital?
To determine the dividend yield, use the following formula: Dividend Yield=Div1/P0 Therefore, Dividend Yield=$1.15/$22.35=0.051=5.1% Capital Gain Rate=$24.08−$22.35/$22.35=0.077=7.7% The capital gain rate is 7.7%. To determine the total return, use the following formula: rE=Dividend Yield+Capital Gain Rate Therefore, rE=5.1%+7.7%=12.8% The total return is 12.8%
Zoom Enterprises expects that one year from now it will pay a total dividend of $5.6 million and repurchase $5.6 million worth of shares. It plans to spend $11.2 million on dividends and repurchases every year after that forever, although it may not always be an even split between dividends and repurchases. If Zoom's equity cost of capital is 14.1% and it has 6.0 million shares outstanding, what is its share price today?
To determine the equity value, use the following formula: Equity Value=Total Payout/rE Therefore, Equity Value=$11.2 million/0.141=$79.43 million The equity value is $79.43 million. To calculate the price per share, use the following formula: P0=Equity Value/Number of Shares Therefore, P0=$79.43 million/6.0 million shares=$13.24 The price per share is $13.24.
You want to endow a scholarship that will pay $16,000 per year forever, starting one year from now. If the school's endowment discount rate is 11%, what amount must you donate to endow the scholarship?
To determine the present value of the perpetuity use the following formula: PV=C/r where C is the cash flow and r is the interest rate. PV=$16,000/0.11=$145,454.55
Your company wants to raise $8.5 million by issuing 25-year zero-coupon bonds. If the yield to maturity on the bonds will be 6.5% (annual compounded APR), what total face value amount of bonds must you issue?
To determine the total face value amount of bonds to be issued, use the following formula: FV=PV×(1+r)^n where PV is the amount to be raised, r is the interest rate, and n is the number of periods. Therefore, FV=$8,500,000×(1+0.065)^25 =$41,035,442.42
You have an opportunity to invest $115,000 now in return for $81,200 in one year and $43,200 in two years. If your cost of capital is 9.6%, what is the NPV of this investment?
To determine the NPV, use the following formula: NPV=PV (Benefits)−PV (Costs) Therefore, NPV=($81,200/1+0.096)+($43,200/(1+0.096)^2 −$115,000= −$4,948.85 keep negative
You have an opportunity to invest $48,900 now in return for $61,200 in one year. If your cost of capital is 8.6%, what is the NPV of thisinvestment?
To determine the NPV, use the following formula: NPV=PV (Benefits)−PV(Costs) Therefore, NPV=$61,200/(1+0.086)−$48,900 =$7,453.59
Daily Enterprises is purchasing a $10.7 million machine. It will cost $56,000 to transport and install the machine. The machine has a depreciable life of five years and will have no salvage value. The machine will generate incremental revenues of $4.5 million per year along with incremental costs of $1.8 million per year. If Daily's marginal tax rate is 21%, what are the incremental earnings (net income) associated with the new machine?
To find the annual incremental earnings, use the following formula: Annual Incremental Earnings=(Revenues−Costs−Depreciation)×(1−Tax Rate) Therefore, Annual Incremental Earnings=($4,500,000−$1,800,000−($10,700,000+$56,000/5)) ×(1−0.21)=$433,552
You are a real estate agent thinking of placing a sign advertising your services at a local bus stop. The sign will cost $6,300 and will be posted for one year. You expect that it will generate additional revenue of $1,386 a month. What is the payback period?
To find the payback period with an annuity situation, use the following formula: Payback Period=CF0/CF Therefore, Payback Period=$6,300/$1,386 per month=4.5 months
Suppose you currently have $5,300 in your savings account, and your bank pays interest at a rate of 0.56% per month. If you make no further deposits or withdrawals, how much will you have in the account in four years?
We calculate the future value as: FV=C×(1+r)^n Thus, FV=$5,300×(1+0.0056)^48=$6,929.29 You will have $6,929.29 in the account in 4 years' time.
You have $1,300 and a bank is offering 6.5% interest on deposits. If you deposit the money in the bank, how much will you have in oneyear?
You can exchange (1+r) dollars in the future per dollar today, where r is 6.5%. Use this formula to determine the amount of money you will have in one year: FV=PV×(1+r) FV=$1,300×(1+0.065)=$1,384.50
You expect to have $13,000 in one year. A bank is offering loans at 6.5% interest per year. How much can you borrow today?
You can say 1/(1+r) is the price today of one dollar in one year, where r is 6.5%. Use this formula to determine how much you could borrow today: PV=FV/1+r PV=$13,000/1+0.065 =$12,206.57
You are looking to buy a car and you have been offered a loan with an APR of 6.3%, compounded monthly. a. What is the true monthly rate of interest? b. What is the EAR?
a- .063/12= 0.00525 b- What is the EAR? The EAR is: EAR= (1+APR/m)^m −1 EAR=(1.00525)^12 −1= 6.4851%
Assume you can earn 8.8% per year on your investments. a. If you invest $140,000 for retirement at age 30, how much will you have 35 years later for retirement? b. If you wait until age 40 to invest the $140,000, how much will you have 25 years later for retirement? c. Why is the difference so large?
a. The future value is: FVn=C×(1+r)^n FV35=$140,000×(1+0.088)^35=$2,680,028 b. The future value is: FV25=$140,000×(1+0.088)^25=$1,153,056 c. Why is the difference so large? The difference is large because the compounding effect is accentuated the longer the time of investment.
What is the present value of $16,000 received: a. Twenty five years from today when the interest rate is 12% per year? b. Fifteen years from today when the interest rate is 12% per year? c. Eight years from today when the interest rate is 12% per year?
a. The present value of $16,000 received 25 years from today when the interest rate is 12% per year is below: PV =$16,000/(1+0.12)^25=$941 b. The present value of $16,000 received 15 years from today when the interest rate is 12% per year is below: PV =$16,000/(1+0.12)^15=$2,923 c. The present value of $16,000 received 8 years from today when the interest rate is 12% per year is below: PV=$16,000/(1+0.12)^8=$6,462
You are thinking about buying a savings bond. The bond costs $70 today and will mature in 16years with a value of $140. What annual interest rate will the bond earn?
r=(FV/P)^1/n −1 Solving for r: r=($140/$70)^1/16 −1 =0.04427=4.427%
You have an investment opportunity that requires an initial investment of $9,000 today and will pay $12,000 in one year. What is the rate of return of this opportunity?
where PV is the amount you invest today, FV is the future value you will receive in n, number of years, and solve for r, the annual rate. r=(FV/PV)^1/n −1 Therefore, r=($12,000/$9,000) −1=33.33%
You bought a stock one year ago for $52.00 per share and sold it today for $58.00 per share. It paid a $1.25 per share dividend today. How much of the return came from dividend yield and how much came from capital gain?
Therefore, R1=$1.25/$52.00=2.4% The dividend yield is 2.4%. Therefore, R1=($58.00−$52.00)/$52.00=11.5% The capital gain yield is 11.5%.
