final exam workout problems – Flashcards
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Consider the following two mutually exclusive projects:
Year Cash Flow
(A) Cash Flow
(B)
0 -$ 355,000 -$ 47,500
1 40,000 23,500
2 60,000 21,500
3 60,000 19,000
4 435,000 14,100
Whichever project you choose, if any, you require a 15 percent return on your investment.
What is the payback period for each project?
answer
Payback period
Project A
3.45%
years
Project B
2.13 %
years
The payback period for each project is:
A: 3 + ($195,000 / $435,000) = 3.45 years
B: 2 + ($2,500 / $19,000) = 2.13 years
question
If you apply the payback criterion, which investment will you choose?
answer
The payback criterion implies accepting Project B because it pays back sooner than Project A.
question
What is the NPV for each project?
answer
The discounted payback for each project is:
A: $40,000 / 1.15 + $60,000 / 1.152 + $60,000 / 1.153 = $119,602.20
$435,000 / 1.154 = $248,712.66
Discounted payback = 3 + ($355,000 - 119,602.20) / $248,712.66 = 3.95 years
B: $23,500 / 1.15 + $21,500 / 1.152 = $36,691.87
$19,000 / 1.153 = $12,492.81
Discounted payback = 2 + ($47,500 - 36,691.87) / $12,492.81 = 2.87 years
question
If you apply the NPV criterion, which investment will you choose?
answer
The discounted payback criterion implies accepting Project B because it pays back sooner than A.
question
What is the NPV for each project?
answer
The NPV for each project is:
A: NPV = -$355,000 + $40,000 / 1.15 + $60,000 / 1.152 + $60,000 / 1.153 + $435,000 / 1.154
NPV = $13,314.86
B: NPV = -$47,500 + $23,500 / 1.15 + $21,500 / 1.152 + $19,000 / 1.153 + $14,100 / 1.154
NPV = $9,746.40
question
If you apply the NPV criterion, which investment will you choose?
answer
The NPV criterion implies we accept Project A because Project A has a higher NPV than Project B.
question
What is the IRR for each project?
answer
The IRR for each project is:
A: $355,000 = $40,000 / (1 + IRR) + $60,000 / (1 + IRR)2 + $60,000 / (1 + IRR)3 + $435,000 / (1 + IRR)4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR = 16.27%
B: $47,500 = $23,500 / (1 + IRR) + $21,500 / (1 + IRR)2 + $19,000 / (1 + IRR)3 + $14,100 / (1 + IRR)4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR = 25.72%
question
If you apply the IRR criterion, which investment will you choose?
answer
The IRR decision rule implies we accept Project B because the IRR for B is greater than the IRR for A.
question
What is the profitability index for each project?
answer
The profitability index for each project is:
A: PI = ($40,000 / 1.15 + $60,000 / 1.152 + $60,000 / 1.153 + $435,000 / 1.154) / $355,000 = 1.038
B: PI = ($23,500 / 1.15 + $21,500 / 1.152 + $19,000 / 1.153 + $14,100 / 1.154) / $47,500 = 1.205
question
If you apply the profitability index criterion, which investment will you choose?
answer
The profitability index criterion implies we accept Project B because its PI is greater than Project A's.
question
Based on your answers in (a) through (e), which project will you finally choose?
answer
The final decision should be based on the NPV since it does not have the ranking problem associated with the other capital budgeting techniques.
question
plug into calculator
answer
CF(A) c. d. e.
CFo
-$355,000
CFo
-$355,000
CFo
$0
C01
$40,000
C01
$40,000
C01
$40,000
F01
1
F01
1
F01
1
C02
$60,000
C02
$60,000
C02
$60,000
F02
2
F02
2
F02
2
C03
$435,000
C03
$435,000
C03
$435,000
F03
1
F03
1
F03
1
I = 15% IRR CPT I = 15%
NPV CPT 16.27% NPV CPT
$13,314.86 $368,314.86
PI = $368,314.86 / $355,000 = 1.038
CF(B) c. d. e.
CFo
-$47,500
CFo
-$47,500
CFo
$0
C01
$23,500
C01
$23,500
C01
$23,500
F01
1
F01
1
F01
1
C02
$21,500
C02
$21,500
C02
$21,500
F02
1
F02
1
F02
1
C03
$19,000
C03
$19,000
C03
$19,000
F03
1
F03
1
F03
1
C04
$14,100
C04
$14,100
C04
$14,100
F04
1
F04
1
F04
1
I = 15% IRR CPT I = 15%
NPV CPT 25.72% NPV CPT
$9,746.40 $57,246.40
PI = $57,246.40 / $47,500 = 1.205
question
A project will produce cash inflows of $3,100 a year for 3 years with a final cash inflow of $4,400 in Year 4. The project's initial cost is $10,400. What is the net present value if the required rate of return is 16 percent?
answer
NPV = -$10,400 + $3,100([1 - (1 / 1.163)] / .16) + $4,400 / (1 + .16)4
NPV = -$1,007.66
question
You are considering two mutually exclusive projects. Both projects have an initial cost of $52,000. Project A produces cash inflows of $25,300, $37,100, and $22,000 for years 1 through 3, respectively. Project B produces cash inflows of $43,600, $19,800 and $10,400 for years 1 through 3, respectively. The required rate of return is 14.2 percent for Project A and 13.9 percent for Project B. Which project should you accept and why?
answer
NPVA = -$52,000 + $25,300 / 1.142 + $37,100 / 1.1422 + $22,000 / 1.1423
NPVA = $13,372.95
NPVB = -$52,000 + $43,600 / 1.139 + $19,800 / 1.1392 + $10,400 /1.1393
NPVB = $8,579.62
Project A; because it has the larger NPV.
question
Assume a project has cash flows of -$51,300, $18,200, $37,300, and $14,300 for years 0 to 3, respectively. What is the profitability index given a required return of 12.5 percent?
answer
PVInflows= $18,200 / 1.125 + $37,300 / 1.1252 + $14,300 / 1.1253 = $55,692.73
PI = $55,692.73 / $51,300 = 1.09
question
You estimate that a project will cost $27,700 and will provide cash inflows of $11,800 in year 1 and $24,600 in year 3. Based on the profitability index rule, should the project be accepted if the discount rate is 14 percent? Why or why not?
answer
PVInflows = $11,800 / 1.14 + $24,600 / 1.143 = $26,955.18
PI = $26,955.18 / $27,700 = .97
The PI is less than 1 so the project should be rejected.
question
You are considering a project with an initial cost of $8,600. What is the payback period for this project if the cash inflows are $2,100, $3,140, $3,800, and $4,500 a year over the next four years, respectively?
answer
Payback = 2 + ($8,600 - 2,100 - 3,140) / $3,800 = 2.88 years
question
JJ's is reviewing a project with a cost of $318,000, and cash inflows of $0, $47,000, $198,000, and $226,000 for Years 1 to 4, respectively. The required discount rate is 15.5 percent and the required discounted payback period is three years. Should the project be accepted? Why or why not?
answer
Total discounted cash inflow = $47,000 / 1.1552 + $198,000 / 1.1553 + $226,000 / 1.1554 = $290,729.70
The project should be rejected because it never pays back on a discounted basis.
question
ALUM, Inc. uses high-tech equipment to produce specialized aluminum products for its customers. Each one of these machines costs $1,520,000 to purchase plus an additional $48,000 a year to operate. The machines have a five-year life after which they are worthless. What is the equivalent annual cost of one these machines if the required return is 15.5 percent?
answer
NPV = -$1,520,000 - $48,000({1 - [1 / (1.155)5]} / .155) = -$1,679,016.85
-$1,679,016.85 = EAC({1 - [1 / (1.155)5]} / .155)
EAC = -$506,819.32
question
Precision Dyes is analyzing two machines to determine which one it should purchase. The company requires a rate of return of 14 percent and uses straight-line depreciation to a zero book value over the life of its equipment. Machine A has a cost of $512,000, annual aftertax cash outflows of $34,200, and a four-year life. Machine B costs $798,000, has annual aftertax cash outflows of $21,500, and has a six-year life. Whichever machine is purchased will be replaced at the end of its useful life. The firm should purchase Machine _____ because it lowers the firm's annual costs by approximately _______ as compared to the other machine.
answer
NPVA = -$512,000 - $34,200({1 - [1 / (1.14)4]} / .14) = -$611,648.96
- $611,648.96 = EACA({1 - [1 / (1.14)4]} / .14)
EACA= -$209,920.85
NPVB = -$798,000 - $21,500({1 - [1 / (1.14)6]} / .14) = -$881,606.35
-$881,606.35 = EACB({1 - [1 / (1.14)6]} / .14)
EACB = -$226,711.68
Difference in costs = -$209,920.85 - (-$226,711.68) = $16,790.83
Machine A lowers the firm's annual costs by about $16,791.
question
Garage, Inc., has identified the following two mutually exclusive projects:
Year Cash Flow (A) Cash Flow (B)
0 -$ 29,500 -$ 29,500
1 14,900 4,550
2 12,800 10,050
3 9,450 15,700
4 5,350 17,300
answer
The IRR is the interest rate that makes the NPV of the project equal to zero. The equation for the IRR of Project A is:
0 = -$29,500 + $14,900 / (1 + IRR) + $12,800 / (1 + IRR)2 + $9,450 / (1 + IRR)3 + $5,350 / (1 + IRR)4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR = 19.69%
The equation for the IRR of Project B is:
0 = -$29,500 + $4,550 / (1 + IRR) + $10,050 / (1 + IRR)2 + $15,700 / (1 + IRR)3 + $17,300 / (1 + IRR)4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
IRR = 18.07%
Examining the IRRs of the projects, we see that the IRRA is greater than the IRRB, so IRR decision rule implies accepting Project A. This may not be a correct decision; however, because the IRR criterion has a ranking problem for mutually exclusive projects. To see if the IRR decision rule is correct or not, we need to evaluate the project NPVs.
b.
The NPV of Project A is:
NPVA = -$29,500 + $14,900 / 1.10 + $12,800 / 1.102 + $9,450 / 1.103 + $5,350 / 1.104
NPVA = $5,378.01
And the NPV of Project B is:
NPVB = -$29,500 + $4,550 / 1.10 + $10,050 / 1.102 + $15,700 / 1.103 + $17,300 / 1.104
NPVB = $6,553.92
The NPVB is greater than the NPVA, so we should accept Project B.
c.
To find the crossover rate, we subtract the cash flows from one project from the cash flows of the other project. Here, we will subtract the cash flows for Project B from the cash flows of Project A. Once we find these differential cash flows, we find the IRR. The equation for the crossover rate is:
Crossover rate: 0 = $10,350 / (1 + R) + $2,750 / (1 + R)2 - $6,250 / (1 + R)3 - $11,950 / (1 + R)4
Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:
R = 14.41%
At discount rates above 14.41 percent choose Project A; for discount rates below 14.41 percent choose Project B; indifferent between A and B at a discount rate of 14.41 percent.
question
Garage, Inc., has identified the following two mutually exclusive projects:
Year Cash Flow (A) Cash Flow (B)
0 -$ 29,500 -$ 29,500
1 14,900 4,550
2 12,800 10,050
3 9,450 15,700
4 5,350 17,300
Calculator Solution:
answer
Project A
CFo
-$29,500
CFo
-$29,500
C01
$14,900
C01
$14,900
F01
1
F01
1
C02
$12,800
C02
$12,800
F02
1
F02
1
C03
$9,450
C03
$9,450
F03
1
F03
1
C04
$5,350
C04
$5,350
F04
1
F04
1
IRR CPT I = 10%
19.69% NPV CPT
$5,378.01
Project B
CFo
-$29,500
CFo
-$29,500
C01
$4,550
C01
$4,550
F01
1
F01
1
C02
$10,050
C02
$10,050
F02
1
F02
1
C03
$15,700
C03
$15,700
F03
1
F03
1
C04
$17,300
C04
$17,300
F04
1
F04
1
IRR CPT I = 10%
18.07% NPV CPT
$6,553.92
Crossover rate
CFo $0
C01 $10,350
F01 1
C02 $2,750
F02 1
C03 -$6,250
F03 1
CO4 -$11,950
FO4 1
IRR CPT
14.41%
question
Suppose a stock had an initial price of $58 per share, paid a dividend of $1.90 per share during the year, and had an ending share price of $68.
Compute the percentage total return.
answer
The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. The return of this stock is:
R = ($68 - 58 + 1.90) / $58
R = .2052, or 20.52%
question
Suppose a stock had an initial price of $70 per share, paid a dividend of $2.30 per share during the year, and had an ending share price of $55.
Compute the percentage total return.
What was the dividend yield and the capital gains yield?
answer
Using the equation for total return, we find:
R = ($55 - 70 + 2.30) / $70
R = −.1814, or −18.14%
And the dividend yield and capital gains yield are:
Dividend yield = $2.30 / $70
Dividend yield = .0329, or 3.29%
Capital gains yield = ($55 - 70) / $70
Capital gains yield = −.2143, or −21.43%
Here's a question for you: Can the dividend yield ever be negative? No, that would mean you were paying the company for the privilege of owning the stock. It has happened on bonds.
question
You've observed the following returns on Crash-n-Burn Computer's stock over the past five years: 6 percent, -9 percent, 25 percent, 13 percent, and 14 percent. The average inflation rate over this period was 3.4 percent and the average T-bill rate was 4.5 percent.
Requirement 1:
What was the average real return on Crash-n-Burn's stock?
Requirement 2:
What was the average nominal risk premium on Crash-n-Burn's stock?
answer
1:
To find the average return, we sum all the returns and divide by the number of returns, so:
Average return = (0.06 - 0.09 + 0.25 + 0.13 + 0.14)/5 = 0.0980 or 9.80%
To calculate the average real return, we can use the average return of the asset, and the average inflation in the Fisher equation. Doing so, we find:
(1 + R) = (1 + r)(1 + h)
formula55.mml= (1.0980/1.034) - 1 = 0.0619 or 6.19%
2:
The average risk premium is simply the average return of the asset, minus the average risk-free rate, so, the average risk premium for this asset would be:
formula56.mml
question
You've observed the following returns on Crash-n-Burn Computer's stock over the past five years: 19 percent, -13 percent, 16 percent, 21 percent, and 10 percent. Suppose the average inflation rate over this period was 1.4 percent and the average T-bill rate over the period was 4.5 percent.
What was the average real risk-free rate over this time period?
What was the average real risk premium?
answer
We can find the average real risk-free rate using the Fisher equation. The average real risk-free rate was:
(1 + R) = (1 + r)(1 + h)
formula23.mmlf = (1.045 / 1.014) - 1
formula23.mmlf = .0306, or 3.06%
To find the average return, we sum all the returns and divide by the number of returns, so:
Average return = (.19 - .13 + .16 + .21 + .10) / 5
Average return = .106, or 10.6%
To calculate the average real return, we can use the average return of the asset, and the average inflation in the Fisher equation. Doing so, we find:
(1 + R) = (1 + r)(1 + h)
formula6.mml = (1.106 / 1.014) - 1
formula6.mml = .0907, or 9.07%
And to calculate the average real risk premium, we can subtract the average risk-free rate from the average real return. So, the average real risk premium was:
Average real risk premium = Average real return - Average risk-free rate
Average real risk premium = 9.07% - 3.06%
Average real risk premium = 6.02%
question
You find a certain stock that had returns of 13 percent, −12 percent, 25 percent, and 21 percent for four of the last five years. The average return of the stock over this period was 12.16 percent.
What was the stock's return for the missing year?
What is the standard deviation of the stock's returns?
answer
Here we know the average stock return, and four of the five returns used to compute the average return. We can work the average return equation backward to find the missing return. The average return is calculated as:
5(.1216) = .13 - .12 + .25 + .21 + R
R = .138, or 13.8%
The missing return has to be 13.8 percent. Now we can use the equation for the variance to find:
Variance = 1/4[(.13 - .1216)2 + (-.12 - .1216)2 + (.25 - .1216)2 + (.21 - .1216)2 + (.138 - .1216)2]
Variance = .02075
And the standard deviation is:
Standard deviation = (.02075)1/2
Standard deviation = .1441, or 14.41%
question
A stock has had returns of 13 percent, 31 percent, 18 percent, −19 percent, 31 percent, and −7 percent over the last six years.
What are the arithmetic and geometric returns for the stock
answer
The arithmetic average return is the sum of the known returns divided by the number of returns, so:
Arithmetic average return = (.13 + .31 + .18 - .19 + .31 - .07) / 6
Arithmetic average return = .1117, or 11.17%
Using the equation for the geometric return, we find:
Geometric average return = [(1 + R1) × (1 + R2) × ... × (1 + RT)]1/T - 1
Geometric average return = [(1 + .13)(1 + .31)(1 + .18)(1 - .19)(1 + .31)(1 - .07)](1/6) - 1
Geometric average return = .0950, or 9.50%
Remember, the geometric average return will always be less than the arithmetic average return if the returns have any variation.
question
Over a 42-year period an asset had an arithmetic return of 12.6 percent and a geometric return of 10.5 percent.
Using Blume's formula, what is your best estimate of the future annual returns over 8 years? 12 years? 21 years?
answer
To find the best forecast, we apply Blume's formula as follows:
formula16.mml
formula17.mml
formula18.mml
question
Christina purchased 200 shares of stock at a price of $62.30 a share and sold them for $70.25 a share. She also received $148 in dividends. If the inflation rate was 4.2 percent, What was her approximate real rate of return on this investment?
answer
Nominal return = [$70.25 - 62.30 + ($148 /200)]/$62.30 = .1395, or 13.95 percent
Approximate real return = 13.95 percent - 4.2 percent = 9.75 percent
question
A stock had returns of 6 percent, -22 percent, 18percent, 12 percent, and -2 percent over the past five years. What is the standard deviation of these returns?
answer
Average return = (.06 - .22 + .18 + .12- .02)/5 = .024
σ = √[1/(5 - 1)] [(.06 - .024)2 + (-.22 - .024)2 + (.18 -.024)2 + (.12 - .024)2 + (-.02 - .024)2] = .1552, or 15.52 percent
question
A stock had annual returns of 16 percent, 8 percent, -17 percent, and 21 percent for the past four years. Based on this information, what is the 95 percent probability range of returns for any one given year?
answer
Average return = (.16 + .08 - .17 + .21)/4 =.07, or 7 percent
σ = [1/ (4 - 1)][(.16 -.07)2 +(.08 -.07)2+ (-.17 -.07)2+ (.21 -.07)2].5= .1687, or 16.87 percent
95% probability range = .07 ± (2 ×16.87 percent) = -26.74 to 40.74 percent
question
Over the past 15 years, the common stock of The Flower Shoppe has produced an arithmetic average return of 13.1 percent and a geometric average return of 12.8 percent. What is the projected return on this stock for the next five years according to Blume's formula?
answer
R(5) = (5 - 1) / (15 - 1) ×.128 + (15 - 5) / (15 - 1) ×.131 = .1301, or 13.01 percent
question
You bought one of Shark Repellant's 8 percent coupon bonds one year ago for $802. These bonds pay annual payments, have a face value of $1,000, and mature 14 years from now. Suppose you decide to sell your bonds today when the required return on the bonds is 12 percent. The inflation rate over the past year was 3.7 percent. What was your total real return on this investment?
answer
P = $80({1 - [1 / (1.12)14]} / .12) + $1,000 / 1.1214 = $734.87
Nominal return = ($734.87 - 802 + 80)/$802= .0160, or 1.6 percent
Real return = [(1 + .0160)/(1 + .037)] - 1 =-.0202, or -2.02 percent
question
You own a portfolio that has $2,400 invested in Stock A and $3,150 invested in Stock B. If the expected returns on these stocks are 11 percent and 16 percent, respectively, what is the expected return on the portfolio?
answer
The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. The total value of the portfolio is:
Total value = $2,400 + 3,150 = $5,550
So, the expected return of this portfolio is:
E(Rp) = ($2,400/$5,550)(0.11) + ($3,150/$5,550)(0.16) = 0.1384 or 13.84%
question
You own a stock portfolio invested 15 percent in Stock Q, 15 percent in Stock R, 10 percent in Stock S, and 60 percent in Stock T. The betas for these four stocks are 1.56, 0.55, 0.54, and 1.66, respectively. What is the portfolio beta?
answer
The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. So, the beta of the portfolio is:
βp = 0.15(1.56) + 0.15(0.55) + 0.1(0.54) + 0.6(1.66) = 1.37
question
A stock has an expected return of 9 percent, its beta is 0.5, and the risk-free rate is 4.5 percent. What must the expected return on the market be?
answer
Here we need to find the expected return of the market using the CAPM. Substituting the values given, and solving for the expected return of the market, we find:
E(Ri) = 0.09 = 0.045 + [E(RM) - 0.045](0.5)
E(RM) = 0.135 or 13.5%
question
Stock Y has a beta of 1.0 and an expected return of 13.5 percent. Stock Z has a beta of .6 and an expected return of 9 percent.
What would the risk-free rate have to be for the two stocks to be correctly priced?
answer
We need to set the reward-to-risk ratios of the two assets equal to each other, which is:
(.135 - Rf) / 1.0 = (.090 - Rf) / .6
We can cross multiply to get:
.6(.135 - Rf) = 1.0(.090 - Rf)
Solving for the risk-free rate, we find:
.0810 - .6Rf = .0900 - 1.0Rf
Rf = .0225, or 2.25%
question
Consider the following information about three stocks:
Rate of Return If State Occurs
State of Probability of
Economy State of Economy Stock A Stock B StockC
Boom .25 .25 .30 .56
Normal .45 .22 .17 .14
Bust .30 .00 −.30 −.46
answer
a.
We need to find the return of the portfolio in each state of the economy. To do this, we will multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get:
Boom: RP = .30(.25) + .30(.30) + .40(.56) = .3890, or 38.90%
Normal: RP = .30(.22) + .30(.17) + .40(.14) = .1730, or 17.30%
Bust: RP = .30(.00) + .30(−.30) + .40(−.46) = −.2740, or −27.40%
And the expected return of the portfolio is:
E(RP) = .25(.3890) + .45(.1730) + .30(−.2740)
E(RP) = .0929, or 9.29%
To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, then add all of these up. The result is the variance. So, the variance and standard deviation of the portfolio is:
σP2 = .25(.3890 − .0929)2 + .45(.1730 − .0929)2 + .30(−.2740 − .0929)2
σP2 = .06519
σP = (.06519)1/2
σP = .2553, or 25.53%
b.
The risk premium is the return of a risky asset minus the risk-free rate. T-bills are often used as the risk-free rate, so:
RPi = E(RP) − Rf = .0929 − .048
RPi = .0449, or 4.49%
c.
The approximate expected real return is the expected nominal return minus the inflation rate, so:
Approximate expected real return = .0929 − .043
Approximate expected real return = .0499, or 4.99%
To find the exact real return, we will use the Fisher equation. Doing so, we get:
1 + E(Ri) = (1 + h)[1 + e(ri)]
1.0929 = (1.043)[1 + e(ri)]
e(ri) = (1.0929 / 1.043) − 1
e(ri) = .0478, or 4.78%
The approximate real risk-free rate is:
Approximate expected real return = .048 - .043
Approximate expected real return = .005, or .50%
And using the Fisher effect for the exact real risk-free rate, we find:
1 + E(Ri) = (1 + h)[1 + e(ri)]
1.048 = (1.043)[1 + e(ri)]
e(ri) = (1.048 / 1.043) - 1
e(ri) = .0048, or .48%
The approximate real risk premium is the approximate expected real return minus the risk-free rate, so:
Approximate expected real risk premium = .0499 - .005
Approximate expected real risk premium = .0449, or 4.49%
The exact real risk premium is the exact real return minus the risk-free rate, so:
Exact expected real risk premium = .0478 - .0048
Exact expected real risk premium = .0430, or 4.30%
question
You are comparing Stock A to Stock B. Given the following information, what is the difference in the expected returns of these two securities?
State of Economy Probability of State of Economy Rate of Return if State Occurs
Stock A Stock B
Normal 45% 12% 17%
Recession 55% -22 -31
answer
E(rA) = (.45 × .12) + (.55 × -0.22) = -6.70 percent
E(rB) = (.45 × .17) + (.55 × -0.31) = -9.40 percent
Difference = -6.70 percent - (-9.40 percent) = 2.70 percent
question
Jerilu Markets has a beta of 1.09. The risk-free rate of return is 2.75 percent and the market rate of return is 9.80 percent. What is the risk premium on this stock?
answer
Risk premium = 1.09 (0.098 - 0.0275) = 7.68 percent
question
The rate of return on the common stock of Lancaster Woolens is expected to be 21 percent in a boom economy, 11 percent in a normal economy, and only 3 percent in a recessionary economy. The probabilities of these economic states are 10 percent for a boom, 70 percent for a normal economy, and 20 percent for a recession. What is the variance of the returns on this common stock?
answer
E(r) = (0.10 ×0.21) + (0.70 ×0.11) + (0.20 ×0.03) = 0.104
Var = 0.10 (0.21 - 0.104)2 + 0.70 (0.11 - 0.104)2 + 0.20 (0.03 - 0.104)2 = 0.002244
question
What is the expected return on a portfolio that is invested 25 percent in stock A, 55 percent in stock B, and the remainder in stock C?
State of
Economy Probability of
State of Economy Rate of Return
if State Occurs
Stock A Stock B Stock C
Boom 5% 19% 9% 6%
Normal 45 11 8 13
Recession 50 -23 5 25
answer
E(r)Boom = (0.25 × 0.19) + (0.55 × 0.09) + (0.20 × 0.06) = 0.109
E(r)Normal = (0.25 × 0.11) + (0.55 × 0.08) + (0.20 × 0.13) = 0.0975
E(r)Bust = (0.25 × -0.23) + (0.55 × 0.05) + (0.20 × 0.25) = 0.02
E(r)Portfolio = (0.05 × 0.109) + (0.45 × 0.0975) + (0.50 × 0.02) = 5.93 percent
question
The market has an expected rate of return of 11.2 percent. The long-term government bond is expected to yield 5.8 percent and the U.S. Treasury bill is expected to yield 3.9 percent. The inflation rate is 3.6 percent. What is the market risk premium?
answer
Market risk premium = 11.2 percent - 3.9 percent = 7.3 percent
question
You have $10,000 to invest in a stock portfolio. Your choices are stock X with an expected return of 13 percent and stock Y with an expected return of 8 percent. Your goal is to create a portfolio with an expected return of 12.4 percent. All money must be invested. How much will you invest in stock X?
answer
E(Rp) = 0.124 = .13× + .08(1 - ×); × = 88 percent
Investment in Stock X = 0.88($10,000) = $8,800
question
What is the expected return of an equally weighted portfolio comprised of the following three stocks?
State of
Economy Probability of
State of Economy Rate of Return
if State Occurs
Stock A Stock B Stock C
Boom 0.64 0.19 0.13 0.31
Bust 0.36 0.15 0.11 0.17
answer
E(RP)Boom = (0.19 + 0.13 + 0.31)/3 = 0.21
E(RP)Normal = (0.15 + 0.11 + 0.17)/3 = 0.1433
E(RP) = 0.64(0.21) + 0.36(0.1433) = 18.60 percent
question
The Pet Market has $1,000 face value bonds outstanding with 18 years to maturity, a coupon rate of 9 percent, annual interest payments, and a current price of $835. What is the aftertax cost of debt if the tax rate is 34 percent?
answer
$835 = (.09 × $1,000) × ({1 - [1 / (1 + r)18]} / r) + $1,000 / (1 + r)18
Using trial-and-error, a financial calculator, or a computer, r = 11.16 percent
Aftertax cost of debt = 11.16 percent × (1 - .34) = 7.37 percent
question
Chelsea Fashions is expected to pay an annual dividend of $1.10 a share next year. The market price of the stock is $21.80 and the growth rate is 4.5 percent. What is the firm's cost of equity?
answer
RE = ($1.10 / $21.80) + .045 = .0955, or 9.55 percent
question
Southern Home Cooking just paid its annual dividend of $.75 a share. The stock has a market price of $16.80 and a beta of 1.14. The return on the U.S. Treasury bill is 2.7 percent and the market risk premium is 7.1 percent. What is the cost of equity?
answer
RE = .027 + 1.14(.071) = .1079, or 10.79 percent
question
Dee's Fashions has a growth rate of 5.2 percent and is equally as risky as the market while its stock is currently selling for $28 a share. The overall stock market has a return of 12.6 percent and a risk premium of 8.7 percent. What is the expected rate of return on this stock?
answer
RE = (.126 - .087) + 1(.087) = .126, or 12.6 percent
question
Holdup Bank has an issue of preferred stock with a $4 stated dividend that just sold for $89 per share. What is the bank's cost of preferred stock?
answer
The cost of preferred stock is the dividend payment divided by the price, so:
RP = $4/$89 = 0.0449 or 4.49%
question
Fashion Wear has bonds outstanding that mature in 12 years, pay interest annually, and have a coupon rate of 7.5 percent. These bonds have a face value of $1,000 and a current market price of $1,060. What is the company's aftertax cost of debt if its tax rate is 35 percent?
answer
$1,060 = (.075 × $1,000) × ({1 - [1 / (1 + r)12]} / r) + $1,000 / (1 + r)12
Using trial-and-error, a financial calculator, or a computer, r = 6.75 percent
Aftertax cost of debt = 6.75 percent × (1 - .35) = 4.39 percent
question
The Downtowner has 950,000 shares of common stock outstanding valued at $38 a share along with 40,000 bonds selling for $1,020 each. What weight should be given to the debt when the firm computes its weighted average cost of capital?
answer
D = 40,000 × $1,020 = $40,800,000
E = 950,000 × $38= $36,100,000
V = $40,800,000 + 36,100,000 = $76,900,000
WE = $40,800,000 / $76,900,000 = .5306, or 53.06 percent
question
Phillips Equipment has 75,000 bonds outstanding that are selling at par. Bonds with similar characteristics are yielding 7.5 percent. The company also has 750,000 shares of 6 percent preferred stock and 2.5 million shares of common stock outstanding. The preferred stock sells for $64 a share. The common stock has a beta of 1.21 and sells for $44 a share. The U.S. Treasury bill is yielding 2.3 percent and the return on the market is 11.2 percent. The corporate tax rate is 34 percent. What is the firm's weighted average cost of capital?
answer
RE = .023 + 1.21(.112 - .023) = .13069
RP = (.06 × $100) / $64 = .09375
D = 75,000 × $1,000 = $75,000,000
P = 750,000 × $64 = $48,000,000
E = 2,500,000 × $44= $110,000,000
V = $75,000,000 + 48,000,000 + 110,000,000 = $233,000,000
WACC = ($110m / $233m)(.13069) + ($48m / $233m)(.09375) + ($75m / $233m)(.075)(1 - .34) = .0969, or 9.69 percent
question
Jiminy's Cricket Farm issued a 30-year, 8 percent, semiannual bond six years ago. The bond currently sells for 114 percent of its face value. What is the aftertax cost of debt if the company's tax rate is 31 percent?
answer
(1.14 × $1,000) = [(.08 × $1,000) / 2] × [(1 - {1 / [1 + (r / 2)]24 × 2}) / (r / 2)] + $1,000 / [1 + (r / 2)]24 × 2
Using trial-and-error, a financial calculator, or a computer, r = 6.81 percent
RDAftertax = 6.81 percent × (1 - .31) = 4.70 percent
