61 Questions for Extra Credit Points. Due 12/16 (Wednesday)
(Please show your work and provide your explanation)
You need to show your work and explanations. Jotting down only the answers is not acceptable. If you do all 100 questions, you will get up to 3 extra points added to your final total score (after I determine your total score based on midterms, HWs, and the final).
Chapter 5
1. You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would lower the calculated value of the investment?
a. The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for only 5 rather than 10 years, hence that each payment is for $20,000 rather than for $10,000.
b. The discount rate increases.
c. The riskiness of the investment’s cash flows decreases.
d. The total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less are received in the later years.
e. The discount rate decreases.
b
2. Which of the following statements is CORRECT?
a. The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
b. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity.
c. The cash flows for an annuity due must all occur at the beginning of the periods.
d. The cash flows for an annuity may vary from period to period, but they must occur at regular intervals, such as once a year or once a month.
e. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity.
c
3. You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?
a. The present value of ORD must exceed the present value of DUE, but the future value of ORD may be less than the future value of DUE.
b. The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD.
c. The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE.
d. The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD.
e. If the going rate of interest decreases from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant.
d
4. Your uncle is about to retire, and he wants to buy an annuity that will provide him with $75,000 of income a year for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much would it cost him to buy the annuity today?
a. $825,835
b. $869,300
c. $915,052
d. $963,213
e. $1,011,374
d
BEGIN Mode
N 20
I/YR 5.25%
PMT $75,000
FV $0.00
PV $963,213
5. Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?
a. $28,532
b. $29,959
c. $31,457
d. $33,030
e. $34,681
a
N 20
I/YR 8.25%
PV $275,000
FV $0.00
PMT $28,532
6. Suppose a bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $250.00 at the end of each quarter and then pay off the principal amount at the end of the year. What is the effective annual rate on the loan?
a. 8.46%
b. 8.90%
c. 9.37%
d. 9.86%
e. 10.38%
e
Interest payment: $250.00
0 1 2 3 4
CFs: 10,000 250 250 250 250
10,000
10,000 250 250 250 10,250
IRR (quarterly) = 2.50%
Annual effective rate = 10.38% vs. nominal rate = 10.00%
7. Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business. The terms require you to amortize the loan with 10 equal endofyear payments. How much interest would you be paying in Year 2?
a. $7,531
b. $7,927
c. $8,323
d. $8,740
e. $9,177
b
Find the required payment:
N 10
I 8.5%
PV $100,000
FV $0
PMT $15,241 Found with a calculator or Excel.
Amortization schedule (first 2 years)
Year Beg. Balance Payment Interest Principal End. Balance
1 100,000 15,241 8,500 6,741 93,259
2 93,259 15,241 7,927 7,314 85,945
Chapter 6
1. Assume that interest rates on 20year Treasury and corporate bonds are as follows:
Tbond = 7.72% AAA = 8.72% A = 9.64% BBB = 10.18%
The differences in these rates were probably caused primarily by:
a. Tax effects.
b. Default risk differences.
c. Maturity risk differences.
d. Inflation differences.
e. Real riskfree rate differences
b
2. A bond trader observes the following information:

The Treasury yield curve is downward sloping.

Empirical data indicate that a positive maturity risk premium applies to both Treasury and corporate bonds.

Empirical data also indicate that there is no liquidity premium for Treasury securities but that a positive liquidity premium is built into corporate bond yields.
On the basis of this information, which of the following statements is most CORRECT?
a. A 10year corporate bond must have a higher yield than a 5year Treasury bond.
b. A 10year Treasury bond must have a higher yield than a 10year corporate bond.
c. A 5year corporate bond must have a higher yield than a 10year Treasury bond.
d. The corporate yield curve must be flat.
e. Since the Treasury yield curve is downward sloping, the corporate yield curve must also be downward sloping.
c
3. If the pure expectations theory of the term structure is correct, which of the following statements would be CORRECT?
a. An upward sloping yield curve would imply that interest rates are expected to be lower in the future.
b. If a 1year Treasury bill has a yield to maturity of 7% and a 2year Treasury bill has a yield to maturity of 8%, this would imply the market believes that 1year rates will be 7.5% one year from now.
c. The yield on a 5year corporate bond should always exceed the yield on a 3year Treasury bond.
d. Interest rate price risk is higher on longterm bonds, but reinvestment rate risk is higher on shortterm bonds.
e. Interest rate price risk is higher on shortterm bonds, but reinvestment rate risk is higher on longterm bonds.
d
4. If 10year Tbonds have a yield of 6.2%, 10year corporate bonds yield 8.5%, the maturity risk premium on all 10year bonds is 1.3%, and corporate bonds have a 0.4% liquidity premium versus a zero liquidity premium for Tbonds, what is the default risk premium on the corporate bond?
a. 1.90%
b. 2.09%
c. 2.30%
d. 2.53%
e. 2.78%
a
Basic equation: r = r* + IP + MRP + DRP + LP
r*, IP, and MRP are included in both bonds, hence are not relevant.
Liquidity risk premium = LP is included in corporate only 0.40%
Corporate bond yield = r = r* + IP + MRP + DRP + LP 8.50%
Tbond yield = r_{RF} = r* + IP + MRP + 0 + 0 6.20%
Difference = DRP + LP = DRP + 0.40% = 2.30%
DRP = Difference – LP = 1.90%
5. Suppose the interest rate on a 1year Tbond is 5.0% and that on a 2year Tbond is 7.0%. Assuming the pure expectations theory is correct, what is the market's forecast for 1year rates 1 year from now?
a. 7.36%
b. 7.75%
c. 8.16%
d. 8.59%
e. 9.04%
e
1year rate today 5.00%
2year rate today 7.00%
Maturity of longer bond 2
Ending return if buy the 2year bond = needed return on series of 1year bonds 1.1449
Rate of return, or yield, on a 1year bond 1 year from now:
X in this equation: (1.05)(1 + X) = 1.1449
X = 1.1449/1.05 − 1 = 9.04%
6. Crockett Corporation's 5year bonds yield 6.35%, and 5year Tbonds yield 4.75%. The real riskfree rate is r* = 3.60%, the default risk premium for Crockett's bonds is DRP = 1.00% versus zero for Tbonds, the liquidity premium on Crockett's bonds is LP = 0.90% versus zero for Tbonds, and the maturity risk premium for all bonds is found with the formula MRP = (t – 1) × 0.1%, where t = number of years to maturity. What inflation premium (IP) is built into 5year bond yields?
a. 0.68%
b. 0.75%
c. 0.83%
d. 0.91%
e. 1.00%
b
Basic equation: r = r* + IP + MRP + DRP + LP
r_{Crockett } Not needed in this problem 6.35%
LP Not needed in this problem 0.90%
DRP Not needed in this problem 1.00%
r_{Tbond} Required data 4.75%
r* Required data 3.60%
Years to maturity Required data 5
MRP = (t – 1) × (0.1) = 0.40%
IP = r_{Tbond} − r* − MRP 0.75%
7. Kelly Inc's 5year bonds yield 7.50% and 5year Tbonds yield 4.90%. The real riskfree rate is r* = 2.5%, the default risk premium for Kelly's bonds is DRP = 0.40%, the liquidity premium on Kelly's bonds is LP = 2.2% versus zero on Tbonds, and the inflation premium (IP) is 1.5%. What is the maturity risk premium (MRP) on all 5year bonds?
a. 0.73%
b. 0.81%
c. 0.90%
d. 0.99%
e. 1.09%
c
Maturity 5
r_{Kelly }Yield 7.50%
r_{Tbond }Yield 4.90%
r* Included in both bonds 2.50%
LP Included in Kelly's only 2.20%
DRP Included in Kelly's only 0.40%
IP Included in both bonds 1.50%
r_{Tbond} = r* + IP + MRP + DRP + LP
r_{Kelly} = r* + IP + MRP + DRP + LP
MRP = r_{Kelly} – r* – IP – LP – DRP = 0.90%
Or, MRP = r_{Tbond} − r* − IP = 0.90%
Chapter 7
1. A 15year bond with a face value of $1,000 currently sells for $850. Which of the following statements is CORRECT?
a. The bond’s coupon rate exceeds its current yield.
b. The bond’s current yield exceeds its yield to maturity.
c. The bond’s yield to maturity is greater than its coupon rate.
d. The bond’s current yield is equal to its coupon rate.
e. If the yield to maturity stays constant until the bond matures, the bond’s price will remain at $850.
c
2. A 10year Treasury bond has an 8% coupon, and an 8year Treasury bond has a 10% coupon. Neither is callable, and both have the same yield to maturity. If the yield to maturity of both bonds increases by the same amount, which of the following statements would be CORRECT?
a. The prices of both bonds will decrease by the same amount.
b. Both bonds would decline in price, but the 10year bond would have the greater percentage decline in price.
c. The prices of both bonds would increase by the same amount.
d. One bond's price would increase, while the other bond’s price would decrease.
e. The prices of the two bonds would remain constant.
b
We can tell by inspection that c, d, and e are all incorrect. A is also incorrect because the 10year bond will fall more due to its longer maturity and lower coupon. That leaves Answer b as the only possibly correct statement. Recognize that longerterm bonds, and ones where payments come late (like low coupon bonds) are most sensitive to changes in interest rates. Thus, the 10year, 8% coupon bond should be more sensitive to a decline in rates. You could also do some calculations to confirm that b is correct.
3. If its yield to maturity declined by 1%, which of the following bonds would have the largest percentage increase in value?
a. A 1year zero coupon bond.
b. A 1year bond with an 8% coupon.
c. A 10year bond with an 8% coupon.
d. A 10year bond with a 12% coupon.
e. A 10year zero coupon bond.
e
4. McCue Inc.'s bonds currently sell for $1,250. They pay a $90 annual coupon, have a 25year maturity, and a $1,000 par value, but they can be called in 5 years at $1,050. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. What is the difference between this bond's YTM and its YTC? (Subtract the YTC from the YTM; it is possible to get a negative answer.)
a. 2.62%
b. 2.88%
c. 3.17%
d. 3.48%
e. 3.83%
a
If held to maturity: If called in 5 years:
N = Maturity 25 N = Call 5
Price = PV $1,250 PV $1,250
PMT $90 PMT $90
FV = Par $1,000 FV = Call Price $1,050
I/YR = YTM 6.88% I/YR = YTC 4.26%
Difference: YTM – YTC = 2.62%
5. A 25year, $1,000 par value bond has an 8.5% annual payment coupon. The bond currently sells for $925. If the yield to maturity remains at its current rate, what will the price be 5 years from now?
a. $884.19
b. $906.86
c. $930.11
d. $953.36
e. $977.20
c
First find the YTM at this time, then use the YTM with the other data to find the bond's price 5 years hence.
Par value $1,000
Coupon rate 8.50% Value in 5 years:
N 25 N 20
PV $925 I/YR 9.28%
PMT $85 PMT $85
FV $1,000 FV $1,000
I/YR 9.28% PV $930.11
6. Moerdyk Corporation's bonds have a 15year maturity, a 7.25% semiannual coupon, and a par value of $1,000. The going interest rate (r_{d}) is 6.20%, based on semiannual compounding. What is the bond’s price?
a. $1,047.19
b. $1,074.05
c. $1,101.58
d. $1,129.12
e. $1,157.35
c
Par value = FV $1,000
Coupon rate 7.25%
Periods/year 2
Yrs to maturity 15
Periods = Years × 2 = N 30
Going annual rate = YTM = r_{d} 6.20%
Periodic rate = r_{d}/2 = I/YR 3.10%
Coupon rate × Par/2 = PMT $36.25
PV $1,101.58
7. In order to accurately assess the capital structure of a firm, it is necessary to convert its balance sheet figures from historical book values to market values. KJM Corporation's balance sheet (book values) as of today is as follows:
Longterm debt (bonds, at par) $23,500,000
Preferred stock 2,000,000
Common stock ($10 par) 10,000,000
Retained earnings 4,000,000
Total debt and equity $39,500,000
The bonds have a 7.0% coupon rate, payable semiannually, and a par value of $1,000. They mature exactly 10 years from today. The yield to maturity is 11%, so the bonds now sell below par. What is the current market value of the firm's debt?
a. $17,436,237
b. $17,883,320
c. $18,330,403
d. $7,706,000
e. $7,898,650
b
Calculate the price of each bond:
Coupon rate 7.0%
Par value = FV $1,000
Yrs to maturity 10
Periods/Yr 2
Periods = Years × 2 = N 20
Going annual rate = r_{d} = YTM 11.0%
Periodic rate = r_{d}/2 = I/YR 5.5%
Coupon rate × Par/2 = PMT $35.00
Price of the bonds = PV $760.99
Determine the number of bonds:
Book value on balance sheet $23,500,000
Par value $1,000
Number of bonds = Book value/Par value 23,500
Calculate the market value of bonds:
Mkt value = PV × Number of bonds = $17,883,320
Chapter 8
1. Which of the following statements best describes what you should expect if you randomly select stocks and add them to your portfolio?
a. Adding more such stocks will reduce the portfolio's unsystematic, or diversifiable, risk.
b. Adding more such stocks will increase the portfolio's expected rate of return.
c. Adding more such stocks will reduce the portfolio's beta coefficient and thus its systematic risk.
d. Adding more such stocks will have no effect on the portfolio's risk.
e. Adding more such stocks will reduce the portfolio's market risk but not its unsystematic risk.
a
2. Which of the following statements is CORRECT? (Assume that the riskfree rate is a constant.)
a. If the market risk premium increases by 1%, then the required return will increase for stocks that have a beta greater than 1.0, but it will decrease for stocks that have a beta less than 1.0.
b. The effect of a change in the market risk premium depends on the slope of the yield curve.
c. If the market risk premium increases by 1%, then the required return on all stocks will rise by 1%.
d. If the market risk premium increases by 1%, then the required return will increase by 1% for a stock that has a beta of 1.0.
e. The effect of a change in the market risk premium depends on the level of the riskfree rate.
d
3. During the coming year, the market risk premium (r_{M} − r_{RF}), is expected to fall, while the riskfree rate, r_{RF}, is expected to remain the same. Given this forecast, which of the following statements is CORRECT?
a. The required return will increase for stocks with a beta less than 1.0 and will decrease for stocks with a beta greater than 1.0.
b. The required return on all stocks will remain unchanged.
c. The required return will fall for all stocks, but it will fall more for stocks with higher betas.
d. The required return for all stocks will fall by the same amount.
e. The required return will fall for all stocks, but it will fall less for stocks with higher betas.
c
4. Roenfeld Corp believes the following probability distribution exists for its stock. What is the coefficient of variation on the company's stock?
Probability Stock's
State of of State Expected
the Economy Occurring Return
Boom 0.45 25%
Normal 0.50 15%
Recession 0.05 5%
a. 0.2839
b. 0.3069
c. 0.3299
d. 0.3547
e. 0.3813
b
This is a relatively technical problem. It should be used only if calculations are emphasized in class, or on a takehome exam where students have time to look up formulas.
Probability of Return Deviation Squared State Prob.
This state This state from Mean Deviation × Sq. Dev.
0.45 25.00% 6.00% 0.36% 0.1620%
0.50 15.00% 4.00% 0.16% 0.0800%
0.05 5.00% 14.00% 1.96% 0.0980%
Expected return = 19.00% 0.34% 0.3400% = Expected variance
σ = 5.83%
Coefficient of variation = σ/Expected return = 0.3069
5. Jill Angel holds a $200,000 portfolio consisting of the following stocks. The portfolio's beta is 0.875.
Stock Investment Beta
A $ 50,000 0.50
B 50,000 0.80
C 50,000 1.00
D 50,000 1.20
Total $200,000
If Jill replaces Stock A with another stock, E, which has a beta of 1.50, what will the portfolio's new beta be?
a. 1.07
b. 1.13
c. 1.18
d. 1.24
e. 1.30
b
Original Portfolio New Portfolio
Stock Investment Percentage Beta Product Percentage Beta Product
A $50,000 25.00% 0.50 0.125
B $50,000 25.00% 0.80 0.200 25.00% 0.80 0.200
C $50,000 25.00% 1.00 0.250 25.00% 1.00 0.250
D $50,000 25.00% 1.20 0.300 25.00% 1.20 0.300
E 25.00% 1.50 0.375
Total $200,000 100.00% 0.875 New Portfolio Beta = 1.125
Alternative solution: (b_{E} − b_{A})(%A) + b_{Old} = 1.125
6. Mikkelson Corporation's stock had a required return of 11.75% last year, when the riskfree rate was 5.50% and the market risk premium was 4.75%. Then an increase in investor risk aversion caused the market risk premium to rise by 2%. The riskfree rate and the firm's beta remain unchanged. What is the company's new required rate of return? (Hint: First calculate the beta, then find the required return.)
a. 14.38%
b. 14.74%
c. 15.11%
d. 15.49%
e. 15.87%
a
Riskfree rate 5.50%
Old market risk premium 4.75%
Old required return 11.75%
b = (old return − r_{RF})/old RP_{M} 1.32
New market risk premium 6.75%
New required return = r_{RF} + b(RP_{M}) = 14.38%
7. Data for Dana Industries is shown below. Now Dana acquires some risky assets that cause its beta to increase by 30%. In addition, expected inflation increases by 2.00%. What is the stock's new required rate of return?
Initial beta 1.00
Initial required return (r_{s}) 10.20%
Market risk premium, RP_{M} 6.00%
Percentage increase in beta 30.00%
Increase in inflation premium, IP 2.00%
a. 14.00%
b. 14.70%
c. 15.44%
d. 16.21%
e. 17.02%
a
Old beta: 1.00
Old r_{s} = r_{RF} + b(RP_{M}) 10.20%
RP_{M} 6.00%
Percentage increase in beta: 30.00%
Increase in IP: 2.00%
Find new beta after increase = 1.30
Find old r_{RF}: Old r_{s} = r_{RF}+ b(RP_{M}): 10.2% = r_{RF} + 1.0(6.0%): r_{RF} = 10.2% − 6.0% = 4.20%
Find new r_{RF}: Old r_{RF} + increase in IP = 6.20%
Find new r_{s} = new r_{RF} + new beta(RP_{M}) 14.00%
8. Mulherin's stock has a beta of 1.23, its required return is 11.75%, and the riskfree rate is 4.30%. What is the required rate of return on the market? (Hint: First find the market risk premium.)
a. 10.36%
b. 10.62%
c. 10.88%
d. 11.15%
e. 11.43%
a
Beta 1.23
Riskfree rate 4.30%
Required return on stock 11.75%
RP_{M} = (r_{stock} − r_{RF})/beta 6.06%
Required return on market = r_{RF} + RP_{M} = 10.36%
Chapter 9
1. Stock X has the following data. Assuming the stock market is efficient and the stock is in equilibrium, which of the following statements is CORRECT?
Expected dividend, D_{1} $3.00
Current Price, P_{0} $50
Expected constant growth rate 6.0%
a. The stock’s required return is 10%.
b. The stock’s expected dividend yield and growth rate are equal.
c. The stock’s expected dividend yield is 5%.
d. The stock’s expected capital gains yield is 5%.
e. The stock’s expected price 10 years from now is $100.00.
b
The correct answer choice is b. One could quickly calculate the dividend yield and see that it equals the growth rate, but here are some numbers that provide more information.
D_{1} $3.00 D_{1}/P_{0} 6.0%
P_{0} $50.00 r_{X} 12.0%
g 6.0%
2. Which of the following statements is NOT CORRECT?
a. The corporate valuation model can be used both for companies that pay dividends and those that do not pay dividends.
b. The corporate valuation model discounts free cash flows by the required return on equity.
c. The corporate valuation model can be used to find the value of a division.
d. An important step in applying the corporate valuation model is forecasting the firm's pro forma financial statements.
e. Free cash flows are assumed to grow at a constant rate beyond a specified date in order to find the horizon, or terminal, value.
b
3. Which of the following statements is CORRECT?
a. Preferred stockholders have a priority over bondholders in the event of bankruptcy to the income, but not to the proceeds in a liquidation.
b. The preferred stock of a given firm is generally less risky to investors than the same firm’s common stock.
c. Corporations cannot buy the preferred stocks of other corporations.
d. Preferred dividends are not generally cumulative.
e. A big advantage of preferred stock is that dividends on preferred stocks are tax deductible by the issuing corporation.
b
4. Molen Inc. has an outstanding issue of perpetual preferred stock with an annual dividend of $7.50 per share. If the required return on this preferred stock is 6.5%, at what price should the stock sell?
a. $104.27
b. $106.95
c. $109.69
d. $112.50
e. $115.38
e
Preferred dividend $7.50
Required return 6.5%
Preferred price = D_{P}/r_{P} = $115.38
5. The Isberg Company just paid a dividend of $0.75 per share, and that dividend is expected to grow at a constant rate of 5.50% per year in the future. The company's beta is 1.15, the market risk premium is 5.00%, and the riskfree rate is 4.00%. What is the company's current stock price, P_{0}?
a. $18.62
b. $19.08
c. $19.56
d. $20.05
e. $20.55
a
D_{0} $0.75
b 1.15
r_{RF} 4.0%
RP_{M} 5.0%
g 5.5%
D_{1} = D_{0}(1 + g) = $0.7913
r_{s} = r_{RF} + b(RP_{M}) = 9.75%
P_{0} = D_{1}/(r_{s} − g) $18.62
6. Goode Inc.'s stock has a required rate of return of 11.50%, and it sells for $25.00 per share. Goode's dividend is expected to grow at a constant rate of 7.00%. What was the last dividend, D_{0}?
a. $0.95
b. $1.05
c. $1.16
d. $1.27
e. $1.40
b
Stock price $25.00
Required return 11.50%
Growth rate 7.00%
P_{0} = D_{1}/(r_{s} − g), so D_{1} = P_{0}(r_{s} − g) = $1.1250
Last dividend = D_{0} = D_{1}/(1 + g) $1.05
7. Sorenson Corp.’s expected yearend dividend is D_{1} = $1.60, its required return is r_{s} = 11.00%, its dividend yield is 6.00%, and its growth rate is expected to be constant in the future. What is Sorenson's expected stock price in 7 years, i.e., what is ?
a. $37.52
b. $39.40
c. $41.37
d. $43.44
e. $45.61
a
Next expected dividend = D_{1 }= $1.60
Required return 11.0%
Dividend yield = D_{1}/P_{0} = 6.0%
Find the growth rate: g = r_{s} − yield = 5.0%
Find P_{0} = D_{1}/(r_{s} − g) = $26.67
Years in the future 7
8. Kale Inc. forecasts the free cash flows (in millions) shown below. If the weighted average cost of capital is 11.0% and FCF is expected to grow at a rate of 5.0% after Year 2, what is the Year 0 value of operations, in millions?
Year 1 2
Free cash flow $50 $100
a. $1,456
b. $1,529
c. $1,606
d. $1,686
e. $1,770
a
FCF_{1} $50
FCF_{2} $100
g 5%
WACC 11%
First, find the horizon, or terminal, value:
HV_{2} = FCF_{2}(1 + g)/(WACC – g) = $100(1.05)/(0.11 – 0.05) = $1,750.00
Then find the PV of the free cash flows and the horizon value:
Value of operations = $50/(1.11) + ($100 + $1,750)/(1.11)^{2} =$1,456.46
Chapter 10
1. Which of the following statements is CORRECT?
a. When calculating the cost of debt, a company needs to adjust for taxes, because interest payments are deductible by the paying corporation.
b. When calculating the cost of preferred stock, companies must adjust for taxes, because dividends paid on preferred stock are deductible by the paying corporation.
c. Because of tax effects, an increase in the riskfree rate will have a greater effect on the aftertax cost of debt than on the cost of common stock as measured by the CAPM.
d. If a company’s beta increases, this will increase the cost of equity used to calculate the WACC, but only if the company does not have enough retained earnings to take care of its equity financing and hence must issue new stock.
e. Higher flotation costs reduce investors' expected returns, and that leads to a reduction in a company’s WACC.
a
Statement a is true, because interest payments on debt are tax deductible. The other statements are false.
2. Which of the following statements is CORRECT?
a. A change in a company’s target capital structure cannot affect its WACC.
b. WACC calculations should be based on the beforetax costs of all the individual capital components.
c. Flotation costs associated with issuing new common stock normally reduce the WACC.
d. If a company’s tax rate increases, then, all else equal, its weighted average cost of capital will decline.
e. An increase in the riskfree rate will normally lower the marginal costs of both debt and equity financing.
d
Statement d is true, because the cost of debt for WACC purposes = r_{d}(1 − T), so if T increases, then
r_{d}(1 − T) declines.
3. For a company whose target capital structure calls for 50% debt and 50% common equity, which of the following statements is CORRECT?
a. The interest rate used to calculate the WACC is the average aftertax cost of all the company's outstanding debt as shown on its balance sheet.
b. The WACC is calculated on a beforetax basis.
c. The WACC exceeds the cost of equity.
d. The cost of equity is always equal to or greater than the cost of debt.
e. The cost of retained earnings typically exceeds the cost of new common stock.
d
Statement d is true, because equity is more risky than debt and hence investors require a higher return on equity. Also, interest on debt is deductible, and this further reduces the cost of debt. The other statements are false.
4. Several years ago the Jakob Company sold a $1,000 par value, noncallable bond that now has 20 years to maturity and a 7.00% annual coupon that is paid semiannually. The bond currently sells for $925, and the company’s tax rate is 40%. What is the component cost of debt for use in the WACC calculation?
a. 4.28%
b. 4.46%
c. 4.65%
d. 4.83%
e. 5.03%
c
Coupon rate 7.00%
Periods/year 2
Maturity (yr) 20
Bond price $925.00
Par value $1,000
Tax rate 40%
Calculator inputs:
N = 2 × 20 40
PV = Bond's price $925.00
PMT = Coupon rate × Par/2 $35
FV = Par = Maturity value $1,000
I/YR 3.87%
Times periods/yr = beforetax cost of debt 7.74%
= Aftertax cost of debt (AT r_{d}) for use in WACC 4.65%
5. Assume that Kish Inc. hired you as a consultant to help estimate its cost of capital. You have obtained the following data: D_{0} = $0.90; P_{0} = $27.50; and g = 7.00% (constant). Based on the DCF approach, what is the cost of equity from retained earnings?
a. 9.29%
b. 9.68%
c. 10.08%
d. 10.50%
e. 10.92%
d
D_{0} $0.90
P_{0} $27.50
g 7.00%
D_{1} = D_{0} × (1 + g) $0.963
r_{s} = D_{1}/P_{0} + g 10.50%
6. Weaver Chocolate Co. expects to earn $3.50 per share during the current year, its expected dividend payout ratio is 65%, its expected constant dividend growth rate is 6.0%, and its common stock currently sells for $32.50 per share. New stock can be sold to the public at the current price, but a flotation cost of 5% would be incurred. What would be the cost of equity from new common stock?
a. 12.70%
b. 13.37%
c. 14.04%
d. 14.74%
e. 15.48%
b
Expected EPS_{1} $3.50
Payout ratio 65%
Expected dividend, D_{1} = EPS × Payout $2.275
Current stock price $32.50
g 6.00%
F 5.00%
r_{e} =_{ }D_{1}/(P_{0} × (1 − F)) + g 13.37%
7. Sorensen Systems Inc. is expected to pay a $2.50 dividend at year end (D_{1} = $2.50), the dividend is expected to grow at a constant rate of 5.50% a year, and the common stock currently sells for $52.50 a share. The beforetax cost of debt is 7.50%, and the tax rate is 40%. The target capital structure consists of 45% debt and 55% common equity. What is the company’s WACC if all the equity used is from retained earnings?
a. 7.07%
b. 7.36%
c. 7.67%
d. 7.98%
e. 8.29%
c
D_{1} $2.50
g 5.50%
P_{0} $52.50
r_{d} 7.50%
Tax rate 40%
Weight debt 45%
Weight equity 55%
r_{d}(1 − T) 4.50%
r_{s} = D_{1}/P_{0} + g 10.26%
WACC = w_{d}(r_{d})(1 − T) + w_{c}(r_{s}) = 7.67%
8. You were hired as a consultant to Quigley Company, whose target capital structure is 35% debt, 10% preferred, and 55% common equity. The interest rate on new debt is 6.50%, the yield on the preferred is 6.00%, the cost of retained earnings is 11.25%, and the tax rate is 40%. The firm will not be issuing any new stock. What is Quigley's WACC?
a. 8.15%
b. 8.48%
c. 8.82%
d. 9.17%
e. 9.54%
a
Tax rate = 40%
Weights r_{d} AT Costs
Debt 35% 6.50% 3.90%
Preferred 10% 6.00%
Common 55% 11.25%
WACC 100% 8.15%
Chapter 11
1. Which of the following statements is CORRECT?
a. The NPV method was once the favorite of academics and business executives, but today most authorities regard the MIRR as being the best indicator of a project’s profitability.
b. If the cost of capital declines, this lowers a project’s NPV.
c. The NPV method is regarded by most academics as being the best indicator of a project’s profitability, hence most academics recommend that firms use only this one method.
d. A project’s NPV depends on the total amount of cash flows the project produces, but because the cash flows are discounted at the WACC, it does not matter if the cash flows occur early or late in the project’s life.
e. The NPV and IRR methods may give different recommendations regarding which of two mutually exclusive projects should be accepted, but they always give the same recommendation regarding the acceptability of a normal, independent project.
e
Statement e is correct. The others are all false. If you draw an NPV profile for one project, you will see that if the WACC is less than the IRR, the NPV will be positive.
2. Which of the following statements is CORRECT?
a. For a project to have more than one IRR, then both IRRs must be greater than the WACC.
b. If two projects are mutually exclusive, then they are likely to have multiple IRRs.
c. If a project is independent, then it cannot have multiple IRRs.
d. Multiple IRRs can only occur if the signs of the cash flows change more than once.
e. If a project has two IRRs, then the smaller one is the one that is most relevant, and it should be accepted and relied upon.
d
3. Projects A and B have identical expected lives and identical initial cash outflows (costs). However, most of one project’s cash flows come in the early years, while most of the other project’s cash flows occur in the later years. The two NPV profiles are given below:
Which of the following statements is CORRECT?
a. More of Project A’s cash flows occur in the later years.
b. More of Project B’s cash flows occur in the later years.
c. We must have information on the cost of capital in order to determine which project has the larger early cash flows.
d. The NPV profile graph is inconsistent with the statement made in the problem.
e. The crossover rate, i.e., the rate at which Projects A and B have the same NPV, is greater than either project’s IRR.
a
Statement a is true and the other statements are false. Distant cash flows are more severely penalized by high discount rates, so if the NPV profile line has a steep slope, this indicates that cash flows occur relatively late.
4. Lasik Vision Inc. recently analyzed the project whose cash flows are shown below. However, before Lasik decided to accept or reject the project, the Federal Reserve took actions that changed interest rates and therefore the firm's WACC. The Fed's action did not affect the forecasted cash flows. By how much did the change in the WACC affect the project's forecasted NPV? Note that a project's projected NPV can be negative, in which case it should be rejected.
Old WACC: 8.00% New WACC: 11.25%
Year 0 1 2 3
Cash flows $1,000 $410 $410 $410
a. $59.03
b. $56.08
c. $53.27
d. $50.61
e. $48.08
a
Old WACC: 8.00% New WACC: 11.25%
Year 0 1 2 3
Cash flows $1,000 $410 $410 $410
Old NPV = $56.61
New NPV = $2.42
Change = $59.03
5. Hindelang Inc. is considering a project that has the following cash flow and WACC data. What is the project's MIRR? Note that a project's projected MIRR can be less than the WACC (and even negative), in which case it will be rejected.
WACC: 12.25%
Year 0 1 2 3 4
Cash flows $850 $300 $320 $340 $360
a. 13.42%
b. 14.91%
c. 16.56%
d. 18.22%
e. 20.04%
c
WACC: 12.25%
Year 0 1 2 3 4
Cash flows $850 $300 $320 $340 $360
Compounded values $424.31 $403.20 $381.65 $360.00
TV = Sum of comp'ed inflows: $1,569.16
MIRR = 16.56% Found as discount rate that equates PV of TV to cost, discounted back 4 years @ WACC
MIRR = 16.56% Alternative calculation, using Excel's MIRR function
6. Stern Associates is considering a project that has the following cash flow data. What is the project's payback?
Year 0 1 2 3 4 5
Cash flows $1,100 $300 $310 $320 $330 $340
a. 2.31 years
b. 2.56 years
c. 2.85 years
d. 3.16 years
e. 3.52 years
e
Year 0 1 2 3 4 5
Cash flows $1,100 $300 $310 $320 $330 $340
Cumulative CF $1,100 $800 $490 $170 $160 $500
Payback = 3.52     3.52 
7. Fernando Designs is considering a project that has the following cash flow and WACC data. What is the project's discounted payback?
WACC: 10.00%
Year 0 1 2 3
Cash flows $900 $500 $500 $500
a. 1.88 years
b. 2.09 years
c. 2.29 years
d. 2.52 years
e. 2.78 years
b
WACC: 10.00%
Year 0 1 2 3
Cash flows $900 $500 $500 $500
PV of CFs $900 $455 $413 $376
Cumulative CF $900 $445 $32 $343
Payback = 2.09    2.09
8. Tesar Chemicals is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. The CEO believes the IRR is the best selection criterion, while the CFO advocates the NPV. If the decision is made by choosing the project with the higher IRR rather than the one with the higher NPV, how much, if any, value will be forgone, i.e., what's the chosen NPV versus the maximum possible NPV? Note that (1) "true value" is measured by NPV, and (2) under some conditions the choice of IRR vs. NPV will have no effect on the value gained or lost.
WACC: 7.50%
Year 0 1 2 3 4
CF_{S} $1,100 $550 $600 $100 $100
CF_{L} $2,700 $650 $725 $800 $1,400
a. $138.10
b. $149.21
c. $160.31
d. $171.42
e. $182.52
a
First, recognize that NPV makes theoretically correct capital budgeting decisions, so the highest NPV tells us how much value could be added. We calculate the two projects' NPVs, IRRs, and MIRRs, but the MIRR information is not needed for this problem. We then see what NPV would result if the decision were based on the IRR (and the MIRR). The difference between the NPV is the loss incurred if the IRR criterion is used. Of course, it's possible that IRR could choose the correct project.
WACC: 7.5000%
Year 0 1 2 3 4 TV MIRR
CF_{S} $1,100 $550 $600 $100 $100
Compounded CFs: 673.77 686.94 107.00 100.00 $1,567.71 9.5469%
CF_{L} $2,700 $650 $725 $800 $1,400
Compounded CFs: 796.28 830.05 856.00 1400.00 $3,882.33 9.6663%
MIRR, L = 9.67% IRR, L = 10.71181% NPV, L = $224.3065
MIRR, S = 9.55% IRR, S = 12.24157% NPV, S = $86.2036
MIRR Choice: L IRR Choice: S NPV Choice: L
NPV using MIRR: $224.31 NPV using IRR: $86.20 NPV using NPV: $224.31
Lost value using IRR versus MIRR: $138.10 Loss below: 7.9850%
Lost value using MIRR versus NPV: $0.00 Loss below: 10.1638%
Lost value using IRR versus NPV: $138.10 Loss below: 10.1638%
Chapter 12
1. A company is considering a new project. The CFO plans to calculate the project’s NPV by estimating the relevant cash flows for each year of the project’s life (i.e., the initial investment cost, the annual operating cash flows, and the terminal cash flow), then discounting those cash flows at the company’s overall WACC. Which one of the following factors should the CFO be sure to INCLUDE in the cash flows when estimating the relevant cash flows?
a. All sunk costs that have been incurred relating to the project.
b. All interest expenses on debt used to help finance the project.
c. The investment in working capital required to operate the project, even if that investment will be recovered at the end of the project’s life.
d. Sunk costs that have been incurred relating to the project, but only if those costs were incurred prior to the current year.
e. Effects of the project on other divisions of the firm, but only if those effects lower the project’s own direct cash flows.
c
2. Which one of the following would NOT result in incremental cash flows and thus should NOT be included in the capital budgeting analysis for a new product?
a. Using some of the firm's highquality factory floor space that is currently unused to produce the proposed new product. This space could be used for other products if it is not used for the project under consideration.
b. Revenues from an existing product would be lost as a result of customers switching to the new product.
c. Shipping and installation costs associated with a machine that would be used to produce the new product.
d. The cost of a study relating to the market for the new product that was completed last year. The results of this research were positive, and they led to the tentative decision to go ahead with the new product. The cost of the research was incurred and expensed for tax purposes last year.
e. It is learned that land the company owns and would use for the new project, if it is accepted, could be sold to another firm.
d
3. A company is considering a proposed new plant that would increase productive capacity. Which of the following statements is CORRECT?
a. In calculating the project's operating cash flows, the firm should not deduct financing costs such as interest expense, because financing costs are accounted for by discounting at the WACC. If interest were deducted when estimating cash flows, this would, in effect, “double count” it.
b. Since depreciation is a noncash expense, the firm does not need to deal with depreciation when calculating the operating cash flows.
c. When estimating the project’s operating cash flows, it is important to include both opportunity costs and sunk costs, but the firm should ignore the cash flow effects of externalities since they are accounted for in the discounting process.
d. Capital budgeting decisions should be based on beforetax cash flows.
e. The WACC used to discount cash flows in a capital budgeting analysis should be calculated on a beforetax basis.
a
4. Fool Proof Software is considering a new project whose data are shown below. The equipment that would be used has a 3year tax life, and the allowed depreciation rates for such property are 33%, 45%, 15%, and 7% for Years 1 through 4. Revenues and other operating costs are expected to be constant over the project's 10year expected life. What is the Year 1 cash flow?
Equipment cost (depreciable basis) $65,000
Sales revenues, each year $60,000
Operating costs (excl. deprec.) $25,000
Tax rate 35.0%
a. $30,258
b. $31,770
c. $33,359
d. $35,027
e. $36,778
a
Equipment cost $65,000
Depreciation rate 33.0%
Sales revenues $60,000
− Operating costs (excl. deprec.) 25,000
− Depreciation 21,450
Operating income (EBIT) $13,550
− Taxes Rate = 35% 4,743
Aftertax EBIT $ 8,808
+ Depreciation 21,450
Cash flow, Year 1 $30,258
5. Your company, CSUS Inc., is considering a new project whose data are shown below. The required equipment has a 3year tax life, and the accelerated rates for such property are 33%, 45%, 15%, and 7% for Years 1 through 4. Revenues and other operating costs are expected to be constant over the project's 10year expected operating life. What is the project's Year 4 cash flow?
Equipment cost (depreciable basis) $70,000
Sales revenues, each year $42,500
Operating costs (excl. deprec.) $25,000
Tax rate 35.0%
a. $11,814
b. $12,436
c. $13,090
d. $13,745
e. $14,432
c
Equipment cost $70,000
Depreciation rate, Year 4 7.0%
Sales revenues $42,500
− Operating costs (excl. deprec.) 25,000
− Depreciation 4,900
Operating income (EBIT) $12,600
− Taxes Rate = 35% 4,410
Aftertax EBIT $ 8,190
+ Depreciation 4,900
Cash flow, Year 4 $13,090
6. Temple Corp. is considering a new project whose data are shown below. The equipment that would be used has a 3year tax life, would be depreciated by the straightline method over its 3year life, and would have a zero salvage value. No new working capital would be required. Revenues and other operating costs are expected to be constant over the project's 3year life. What is the project's NPV?
Riskadjusted WACC 10.0%
Net investment cost (depreciable basis) $65,000
Straightline deprec. rate 33.3333%
Sales revenues, each year $65,500
Operating costs (excl. deprec.), each year $25,000
Tax rate 35.0%
a. $15,740
b. $16,569
c. $17,441
d. $18,359
e. $19,325
e
WACC 10.0% Years 0 1 2 3
Investment cost $65,000
Sales revenues $65,500 $65,500 $65,500
− Operating costs (excl. deprec.) 25,000 25,000 25,000
− Depreciation rate = 33.333% 21,667 21,667 21,667
Operating income (EBIT) $18,833 $18,833 $18,833
− Taxes Rate = 35% 6,592 6,592 6,592
Aftertax EBIT $12,242 $12,242 $12,242
+ Depreciation 21,667 21,667 21,667
Cash flow $65,000 $33,908 $33,908 $33,908
NPV $19,325
7. Liberty Services is now at the end of the final year of a project. The equipment originally cost $22,500, of which 75% has been depreciated. The firm can sell the used equipment today for $6,000, and its tax rate is 40%. What is the equipment’s aftertax salvage value for use in a capital budgeting analysis? Note that if the equipment's final market value is less than its book value, the firm will receive a tax credit as a result of the sale.
a. $5,558
b. $5,850
c. $6,143
d. $6,450
e. $6,772
b
% depreciated on equip. 75%
Tax rate 40%
Equipment cost $22,500
− Accumulated deprec. 16,875
Current book value of equipment $ 5,625
Market value of equipment 6,000
Gain (or loss): Market value − Book value $ 375
Taxes paid on gain (−) or credited (+) on loss 150
AT salvage value = market value +/− taxes $ 5,850
8. MarshallMiller & Company is considering the purchase of a new machine for $50,000, installed. The machine has a tax life of 5 years, and it can be depreciated according to the following rates. The firm expects to operate the machine for 4 years and then to sell it for $12,500. If the marginal tax rate is 40%, what will the aftertax salvage value be when the machine is sold at the end of Year 4?
Year Depreciation Rate
1 0.20
2 0.32
3 0.19
4 0.12
5 0.11
6 0.06
a. $8,878
b. $9,345
c. $9,837
d. $10,355
e. $10,900
e
Deprec. Annual Yearend
Year Rate Basis Deprec. Book Value
1 0.20 $50,000 $10,000 $40,000
2 0.32 50,000 16,000 24,000
3 0.19 50,000 9,500 14,500
4 0.12 50,000 6,000 8,500
5 0.11 50,000 5,500 3,000
6 0.06 50,000 3,000 0
1.00 $50,000
Gross sales proceeds $12,500
Book value, end of Year 4 8,500
Profit $ 4,000
Tax on profit Rate = 40% 1,600
AT salvage value = market value +/− taxes $10,90
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