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 mid-terms, 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 end-of-year 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 20-year Treasury and corporate bonds are as follows:
T-bond = 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 risk-free 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 10-year corporate bond must have a higher
yield than a 5-year Treasury bond.
b. A 10-year Treasury bond must have a higher
yield than a 10-year corporate bond.
c. A 5-year corporate bond must have a higher
yield than a 10-year 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 1-year Treasury bill has a yield to
maturity of 7% and a 2-year Treasury bill has a yield to maturity of 8%, this
would imply the market believes that 1-year rates will be 7.5% one year from
now.
c. The yield on a 5-year corporate bond should
always exceed the yield on a 3-year Treasury bond.
d. Interest rate price risk is higher on long-term
bonds, but reinvestment rate risk is higher on short-term bonds.
e. Interest rate price risk is higher on
short-term bonds, but reinvestment rate risk is higher on long-term bonds.
d
4. If 10-year T-bonds
have a yield of 6.2%, 10-year corporate bonds yield 8.5%, the maturity risk
premium on all 10-year bonds is 1.3%, and corporate bonds have a 0.4% liquidity
premium versus a zero liquidity premium for T-bonds, 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%
T-bond yield = rRF
= 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 1-year T-bond is 5.0% and that on a 2-year T-bond is 7.0%. Assuming the pure expectations theory is
correct, what is the market's forecast for 1-year rates 1 year from now?
a. 7.36%
b. 7.75%
c. 8.16%
d. 8.59%
e. 9.04%
e
1-year rate today 5.00%
2-year rate today 7.00%
Maturity of longer
bond 2
Ending return if buy
the 2-year bond = needed return on series of 1-year bonds 1.1449
Rate of return, or yield, on a 1-year 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
5-year bonds yield 6.35%, and 5-year T-bonds yield 4.75%. The real risk-free rate is r* = 3.60%, the
default risk premium for Crockett's bonds is DRP = 1.00% versus zero for
T-bonds, the liquidity premium on Crockett's bonds is LP = 0.90% versus zero
for T‑bonds, 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
5-year 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
rCrockett Not needed in this problem 6.35%
LP Not needed in this problem 0.90%
DRP Not needed in this problem 1.00%
rT-bond Required data 4.75%
r* Required data 3.60%
Years to maturity Required data 5
MRP = (t – 1) × (0.1)
= 0.40%
IP = rT-bond − r* −
MRP 0.75%
7. Kelly Inc's 5-year
bonds yield 7.50% and 5-year T-bonds yield 4.90%. The real risk-free 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 T-bonds, and the
inflation premium (IP) is 1.5%. What is
the maturity risk premium (MRP) on all 5-year bonds?
a. 0.73%
b. 0.81%
c. 0.90%
d. 0.99%
e. 1.09%
c
Maturity 5
rKelly Yield 7.50%
rT-bond 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%
rT-bond =
r* + IP + MRP + DRP + LP
rKelly = r*
+ IP + MRP + DRP + LP
MRP = rKelly – r* – IP – LP – DRP = 0.90%
Or, MRP
= rT-bond − r* − IP = 0.90%
Chapter 7
1. A 15-year 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 10-year Treasury bond has an 8% coupon,
and an 8-year 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 10-year 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 10-year bond
will fall more due to its longer maturity and lower coupon. That leaves Answer
b as the only possibly correct statement.
Recognize that longer-term bonds, and ones where payments come late
(like low coupon bonds) are most sensitive to changes in interest rates. Thus, the 10-year, 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 1-year zero coupon
bond.
b. A 1-year bond with an 8% coupon.
c. A 10-year bond with an 8% coupon.
d. A 10-year bond with a 12% coupon.
e. A 10-year zero coupon bond.
e
4. McCue Inc.'s bonds currently sell for
$1,250. They pay a $90 annual coupon,
have a 25-year 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 25-year, $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 15-year
maturity, a 7.25% semiannual coupon, and a par value of $1,000. The going interest rate (rd) 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 = rd 6.20%
Periodic rate = rd/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:
Long-term 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 = rd = YTM 11.0%
Periodic rate = rd/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 risk-free 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 risk-free rate.
d
3. During the coming year, the market risk
premium (rM − rRF), is expected to fall, while the
risk-free rate, rRF, 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 take-home 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: (bE − bA)(%A) + bOld
= 1.125
6. Mikkelson Corporation's stock had a required
return of 11.75% last year, when the risk-free 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
risk-free 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
Risk-free rate 5.50%
Old market risk premium 4.75%
Old required return 11.75%
b = (old return − rRF)/old RPM 1.32
New market risk premium 6.75%
New required return = rRF
+ b(RPM) = 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 (rs) 10.20%
Market
risk premium, RPM 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 rs = rRF
+ b(RPM) 10.20%
RPM 6.00%
Percentage increase in beta: 30.00%
Increase in IP: 2.00%
Find new beta after increase = 1.30
Find old rRF:
Old rs = rRF+ b(RPM): 10.2% = rRF + 1.0(6.0%): rRF = 10.2% − 6.0% = 4.20%
Find new rRF:
Old rRF + increase in IP = 6.20%
Find new rs = new rRF + new beta(RPM) 14.00%
8. Mulherin's stock has a beta of 1.23, its
required return is 11.75%, and the
risk-free 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
Risk-free rate 4.30%
Required return on stock 11.75%
RPM = (rstock − rRF)/beta 6.06%
Required return on market = rRF + RPM = 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, D1 $3.00
Current Price, P0 $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.
D1 $3.00 D1/P0 6.0%
P0 $50.00 rX 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 = DP/rP
= $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 risk-free rate is 4.00%. What is the company's current stock price, P0?
a. $18.62
b. $19.08
c. $19.56
d. $20.05
e. $20.55
a
D0 $0.75
b 1.15
rRF 4.0%
RPM 5.0%
g 5.5%
D1 = D0(1
+ g) = $0.7913
rs = rRF
+ b(RPM) = 9.75%
P0 = D1/(rs
− 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, D0?
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%
P0 = D1/(rs
− g), so D1 = P0(rs − g) = $1.1250
Last dividend = D0
= D1/(1 + g) $1.05
7. Sorenson Corp.’s expected year-end dividend
is D1 = $1.60, its required return is rs = 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
= D1 = $1.60
Required return 11.0%
Dividend yield = D1/P0
= 6.0%
Find the growth rate:
g = rs − yield = 5.0%
Find P0 = D1/(rs
− 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
FCF1 -$50
FCF2 $100
g 5%
WACC 11%
First, find the
horizon, or terminal, value:
HV2 = FCF2(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
risk-free rate will have a greater
effect on the after-tax 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 before-tax 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 risk-free 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
= rd(1 − T), so if T increases, then
rd(1 − T) declines.
rd(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 after-tax cost of all the company's outstanding debt as shown on
its balance sheet.
b. The WACC is calculated on a before-tax 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 = before-tax cost of debt 7.74%
= After-tax cost of debt (A-T rd) 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: D0 = $0.90; P0 =
$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
D0 $0.90
P0 $27.50
g 7.00%
D1 = D0 × (1 + g) $0.963
rs = D1/P0 + 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 EPS1 $3.50
Payout ratio 65%
Expected dividend, D1 = EPS × Payout $2.275
Current stock price $32.50
g 6.00%
F 5.00%
re
= D1/(P0 × (1 − F)) + g 13.37%
7. Sorensen Systems Inc. is expected to pay a
$2.50 dividend at year end (D1 = $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 before-tax 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
D1 $2.50
g 5.50%
P0 $52.50
rd 7.50%
Tax rate 40%
Weight debt 45%
Weight equity 55%
rd(1 − T) 4.50%
rs = D1/P0 + g 10.26%
WACC = wd(rd)(1 − T) + wc(rs)
= 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 rd 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
CFS -$1,100 $550 $600 $100 $100
CFL -$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
CFS -$1,100 $550 $600 $100 $100
Compounded CFs: 673.77 686.94 107.00 100.00 $1,567.71 9.5469%
CFL -$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 high-quality 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 non-cash 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 before-tax
cash flows.
e. The WACC used to discount cash flows in a
capital budgeting analysis should be calculated on a before-tax basis.
a
4. Fool Proof Software is considering a new
project whose data are shown below. The
equipment that would be used has a 3-year 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 10-year 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
After-tax 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 3-year 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 10-year 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
After-tax 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 3-year tax life, would be depreciated by the
straight-line method over its 3-year 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 3-year life. What is the project's NPV?
Risk-adjusted
WACC 10.0%
Net
investment cost (depreciable basis) $65,000
Straight-line
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
After-tax 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 after-tax 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. Marshall-Miller & 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 after-tax 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 Year-end
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
