ch13 internet answers

Foundations of Fin. Mgt. 8/E Cdn. • Block, Hirt, Short S-425

Practice Problems Chapter 13 Recommended 1-3, 6, 8, 21,22,24

Discussion Questions 13-1. Risk-averse corporate managers are not unwilling to take risks, but will require a higher

return from risky investments. There must be a premium or additional compensation for risk taking.

13-2. Risk may be defined in terms of the variability of outcomes from a given investment. The

greater the variability, the greater the risk. Risk may be measured in terms of the coefficient of variation, in which we divide the standard deviation (or measure of dispersion) by the mean. We also may measure risk in terms of beta, in which we determine the volatility of returns on an individual stock relative to a stock market index.

13-3. The standard deviation is an absolute measure of dispersion, while the coefficient of

variation is a relative measure that allows us to relate the standard deviation to the mean. The coefficient of variation is a better measure of dispersion when we wish to consider the relative size of the standard deviation or compare two or more investments of different size.

13-4. Risk may be introduced into the capital budgeting process by requiring higher returns for

risky investments. One method of achieving this is to use higher discount rates for riskier investments. This risk-adjusted discount rate approach specifies different discount rates for different risk categories as measured by the coefficient of variation or some other factor. Other methods, such as the certainty equivalent approach, may also be used.

13-5. Referring to Table 13-3, the following order would be correct:

• repair old machinery (c) • new equipment (a) • addition to normal product line (f) • new product in related market (e) • completely new market (b) • new product in foreign market (d)

13-6. In order to minimize risk, the firm that is positively correlated with the economy should

select the two projects that are negatively correlated with the economy. 13-7. A discount rate combines the effects of risk and time value of money in one evaluation

tool. A certainty equivalent deals first with risk by converting uncertain cash flows to ‘certainty equivalents’, and then discounts at the risk free rate to consider the time value of money.


13-8. Simulation is one way of dealing with the uncertainty involved in forecasting the outcomes of capital budgeting projects or other types of decisions. A Monte Carlo simulation model uses random variables for inputs. By programming the computer to randomly select inputs from probability distributions, the outcomes generated by a simulation are distributed about a mean and instead of generating one return or net present value, a range of outcomes with standard deviations are provided.

13-9. Sensitivity analysis only adjusts one variable at a time. In all likelihood variables are

interdependent and if one changes the others will likely change as well. Sensitivity analysis misses this dynamism. As well sensitivity analysis does not assess risk, it only points out possible outcomes and we are left to assign probabilities. With today’s ease of spreadsheet production on the PC one can turn out endless analysis, which, without a plan will become meaningless.

13-10. Decision trees help lay out the sequence of decisions that are to be made and present a

tabular or graphical comparison resembling the branches of a tree which highlights the difference between investment choices.

13-11. The firm should attempt to construct a chart showing the risk-return characteristics for

every possible set of 20. By using a procedure similar to that indicated in Figure 13-11, the best risk-return trade-offs or efficient frontier can be determined. We then can decide where we wish to be along this line.

13-12. High profits alone will not necessarily lead to a high market value for common stock. To

the extent large or unnecessary risks are taken, a higher discount rate and lower valuation may be assigned to shares. Only by attempting to match the appropriate levels for risk and return can we hope to maximize our overall value in the market.

Internet Resources and Questions 1. www.standardandpoors.com

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Problems 13-1. Myers Business Systems

a. DPD ∑=

D P DP 20 .10 2 40 .30 12 55 .40 22 70 .20 14 50 = D

b. ( )∑ −= PDD

2σ

D D (D– D ) (D– D )2 P (D– D )2P 20 50 – 30 900 .10 90 40 50 – 10 100 .30 30 55 50 + 5 25 .40 10 70 50 + 20 400 .20 80 210

49.14210 ==σ 13-2. Shack Homebuilders Limited

a. DPD ∑=

D P DP 40 .20 8 60 .50 30 140 .30 42 80 = D


b. ( )∑ −= PDD2

σ

D D (D– D ) (D– D )2 P (D– D )2P 40 80 – 40 1,600 .20 320 60 80 – 20 400 .50 200 140 80 + 60 3,600 .30 1,080 1,600

0.40600,1 ==σ 13-3. Five alternatives

( )D

V variation of tCoefficien σ=

Ranking from lowest to highest A $1,200/ $5,000 = .24 E (.08) B $600/ $4,000 = .15 B (.15) C $800/ $4,000 = .20 C (.20) D $3,200/ $8,000 = .40 D (.24) E $800/ $10,000 = .08 A (.40) 13-4. You would not need to use the coefficient of variation. Since B and

C have the same expected value, they can be evaluated based solely on their standard deviations of return. C has a larger standard deviation and so is riskier than B for the same expected return.


13-5. Sensor Technology a. Profits: Standard Coefficient of Year Expected Value Deviation Variation

1 90 31 .34 3 120 52 .43 6 150 83 .55 9 200 146 .73 b. Yes, the risk appears to be increasing over time. This

may be related to the inability to make forecasts far into the future. There is more uncertainty.

13-6. Tim Trepid & Mike Macho Coefficient of variation Stocks $4,000/ $7,000 0.57 Bonds $1,560/ $5,000 0.31 Commodities $15,100/ $12,000 1.26 Options $8,850/ $8,000 1.11

a. Tim should select bonds, which have the least risk. b. Mike should select commodities, which have the greatest risk.

13-7. Wildcat Oil & Richmond Construction

Project Coefficient of variation A $138,000/ $262,000 0.53 B $403,000/ $674,000 0.60 C $108,000/ $88,000 1.23 D $207,000/ $125,000 1.66

a. Wildcat Oil should select project D, which has the greatest risk. b. Richmond Construction should select project A, which has the least risk.


13-8. Three Investment Alternatives

Alternative 1 Alternative 2 Alternative 3 D × P = DP D × P = DP D × P = DP $50 .2 $10 $90 .3 $27 $80 .4 $32 80 .4 32 160 .5 80 200 .5 100 120 .4 48 200 .2 40 400 .1 40 D = $90 D= $147 D= $172

Standard Deviation: Alternative 1: D D (D– D ) (D– D )2 P (D– D )2P $50 90 – 40 1,600 .20 $320 80 90 – 10 100 .4 40 120 90 + 30 900 .4 360 $720

83.26720 ==σ Alternative 2: D D (D– D ) (D– D )2 P (D– D )2P $90 $147 – 57 3,249 .3 $974.70 160 147 + 13 169 .5 84.50 200 147 + 53 2,809 .2 561.80 $1,621.00

26.40621,1 ==σ

Alternative 3: D D (D– D ) (D– D )2 P (D– D )2P $80 $172 $-92 $8,464 .4 $3,385.60 200 172 +28 784 .5 392.00 400 172 +228 51,984 .1 5,198.40 $8,976.00

74.94976,8 ==σ


Rank by Coefficient of Variation: least risk to most

( ) 274.0147

26.402 ===D

V eAlternativ σ

( ) 298.090

83.261 ===D

V eAlternativ σ

( ) 551.0172

74.943 ===D

V eAlternativ σ


13-9. Bridget’s Modeling Studios

Standard Deviations of Sites A and B

Site A D D (D– D ) (D– D )2 P (D– D )2P $80 $120 $40 $1,600 .15 $ 240 110 120 10 100 .50 50 140 120 +20 400 .30 120 220 120 +100 10,000 .05 500 $ 910

17.30$910 ==σ

Site B D D (D– D ) (D– D )2 P (D– D )2P $50 $120 $70 $4,900 .10 $ 490 80 120 40 1,600 .20 320 120 120 0 0 .40 0 160 120 +40 1,600 .20 320 190 120 +70 4,900 .10 490 $1,620

25.40$620,1 ==σ

VA = $30.17/$120 = .2514 VB = $40.25/$120 = .3354

Site A is the preferred site since it has the smaller coefficient of variation. Because both alternatives have the same expected value, the standard deviation alone would have been enough for a decision. A will be just as profitable as B but with less risk.


13-10. Micro Systems

The coefficient of variation suggests a discount rate of 12%.

Year Cash flow PV@12% 1 $ 9,000 $ 8,036 2 12,000 9,566 3 18,000 12,812 4 16,000 10,168 5 24,000 13,618 PV of cash flows 54,200 Investment 50,000 NPV $ 4,200 Based on a positive NPV, the project should be undertaken. 13-11. Payne Medical Labs

Product 1 Product 2

Year Cash flow PV@10% Year Cash flow PV@15% 1 $25,000 $22,727 1 $16,000 $13,913 2 30,000 24,793 2 22,000 16,635 3 38,000 28,550 3 34,000 22,356 4 31,000 21,173 4 29,000 16,581 5 19,000 11,798 5 70,000 34,802 PV of Inflows $109,041 $104,287 Investment 90,000 90,000 NPV $ 19,041 $ 14,287

Select Product 1 The instructor may wish to point out that Product 2 has higher undiscounted total cash flows than Product 1 (the numbers are $171,000 versus $143,000), but has a lower NPV because of the higher discount rate.


13-12. Debby’s Dance Studios

a. Expected Cash Flow

Cash Flow P $3,600 × .2 $ 720 5,000 × .3 1,500 7,400 × .4 2,960 9,800 × .1 980 $6,160

b. NPV (Net Present Value)

$6,160 (%i = 11%, n = 5) = $22,767

$ 22,767 Present value of inflows 25,000 Present value of outflows $(2,233) Net present value IRR (Internal Rate of Return)

Calculator: PV = $25,000 FV = 0 PMT = $6,160 %i =? N = 5 Compute: %i = 7.38%

c. Debby should not buy this new equipment because the net present value is negative and the internal rate of return is less than the cost of capital. The answer assumes that Debby’s probability distribution of the possible outcomes is accurate.


13-13. Silverado Mining Company

a. Calculate the net present value for each project.

The Yukon Mine Years Cash Flow Present Value @ 10% 5-15 $400,000 $1,774,486 16-25 $800,000 $1,176,768 Present value of inflows $2,951,254 Present value of outflows $2,000,000 NPV (Net present value) $ 951,254 The Labrador Mine Years Cash Flow Present Value @ 10% 1-25 $300,000 $2,723,112 Present value of inflows $2,723,112 Present value of outflows $2,400,000 NPV (Net present value) $ 323,112

Both projects are attractive based on positive NPVs. Select the Yukon Mine if projects are mutually exclusive.

b. Recalculate the NPV of the Yukon Mine at a 15% discount rate.

The Yukon Mine Years Cash Flow Present Value @ 15% 5-15 $400,000 $1,196,957 16-25 $800,000 $ 493,423 Present value of inflows $1,690,380 Present value of outflows $2,000,000 NPV (Net Present Value) $ (309,620) Reject the Yukon Mine. Purchase the Labrador Mine.


13-14. Mr. Monty Terry

a. DPD ∑=

Wrigley Village Crosley Square

D P DP D P DP 10 .10 $ 1 20 .10 $ 2 30 .20 6 30 .30 9 40 .30 12 35 .40 14 50 .30 15 50 .20 10 60 .10 6 Expected cash flow $35

Expected cash flow $40 (thousands) (thousands)

b. Find the standard deviation. Then the coefficient of variation.

Wrigley Village D D (D– D ) (D– D )2 P (D– D )2P $10 $40 $30 $900 .10 $90 30 40 10 100 .20 20 40 40 0 0 .30 0 50 40 +10 100 .30 30 60 40 +20 400 .10 40 $180

thousands 42.13180 ==σ

( ) 336.040$

42.13$===

DV variation of tCoefficien σ


Crosley Square D D (D– D ) (D– D )2 P (D– D )2P $20 $35 $15 225 .10 22.5 30 35 5 25 .30 7.5 35 35 0 0 .40 0 50 35 +15 225 .20 45.0 $75.0

thousands 66.875 ==σ

( ) 247.035$66.8$

===D

V variation of tCoefficien σ

Based on the coefficient of variation, Wrigley Square has more risk (0.336 vs. 0.247).

13-15. Mr. Monty Terry (Continued)

a. Risk-adjusted net present value

Wrigley Village

Crosley Square With V = 0.336,

discount rate = 11% With V = 0.247, discount rate = 8%

Expected cash flow $40,000 $35,000 IFPVA (n = 25) Present value of inflows $336,870 $373,617 Present value of outflows 300,000 300,000 Net present value $ 36,870 $ 73,617

b. If these two investments are mutually exclusive, he should accept

Crosley Square because it has a higher net present value.

If the investments are non-mutually exclusive and no capital rationing is involved, they both should be undertaken.


13-16. Allison’s Dresswear Manufacturers a. (1) (2) (3) (4) (5) (6)

Expected

Sales

Probability

Present Value of cash flows

from sales

Initial cost

(3) – (4)

Expected NPV

(2) × (5) Enter Fantastic .20 $180,000 $110,000 $70,000 $14,000

Wool Moderate .60 130,000 110,000 20,000 12,000

Sweater

Dismal .20 85,000 110,000 (25,000) (5,000)

Line

Expected NPV

$21,000

Enter Fantastic .40 $300,000 $125,000 $175,000 $70,000

Cashmere Moderate .20 230,000 125,000 105,000 21,000

Sweater Dismal .40 0 125,000 (125,000) (50,000)

Line Expected NPV

$41,000

b. The indicated investment, based on the expected NPV, is in the Cashmere sweater line.

However, there is more risk in this alternative so further analysis may be necessary. It is not an automatic decision.


13-17. Probability calculations

Expected value = $40,000, σ = $8,000

a. $32,000 to $48,000 expected value + 1 σ 0.6826 = 68.26%

b. $28,000 to $52,000 expected value + 1.5 σ 0.8664 = 86.64%

c. greater than $32,000

$32,000

Compare to expected value:

1000,8$000,8$

000,8$000,40$000,32$

−=−

=− This represents 0.3413 or

34%

Total distribution under the curve: .3413 .5000 .8413 = 84.13%


d. Less than $55,680

$55,680


96.1000,8$680,15$

000,8$000,40$680,55$

+==− This represents 0.4750 or

48%.

Total distribution under the curve: .4750 .5000 .9750 = 97.50%

e. Less than $32,000 or greater than $52,000

$32,000 $52,000


1000,8$000,8$

000,8$000,40$000,32$

−=−

=− This represents 0.3413 or 34%

5.1000,8$000,12$

000,8$000,40$000,52$

+==− This represents 0.4332 or 43%

Total distribution under the curve, in the tails: 0.5000 – 0.3413 = 0.1587 + 0.5000 – 0.4332 = 0.0668 = 0.2255 = 22.55%


13-18. The Palo Alto Microchip Corporation

a. Standard deviation: year 1

D D (D– D ) (D– D )2 P (D– D )2P 50 60 – 10 100 .20 20 60 60 0 0 .60 0 70 60 + 10 100 .20 20 40

32.640 ==σ Standard deviation: year 5

D D (D– D ) (D– D )2 P (D– D )2P 40 60 – 20 400 .25 100 60 60 0 0 .50 0 80 60 + 20 400 .25 100 200

14.14200 ==σ Standard deviation: year 10

D D (D– D ) (D– D )2 P (D– D )2P 30 60 – 30 900 .30 270 60 60 0 0 .40 0 90 60 + 30 900 .30 270 540

24.23540 ==σ


b. Risk over time


c. Table: (1) (2) (3)

Year PVIF PVIF PVIF

5%

10%

Difference

1

.952

.909

.043

5

.784

.621

.163

10

.614

.386

.228

d. Yes. The larger risk over time is consistent with the larger differences in the present value interest factors (PVIFs) over time. In effect, future uncertainty is being penalized by a lower present value interest factor (PVIF). This is one of the consequences of using progressively higher discount rates to penalize for risk.

e. NPV

Year Inflow PV @ 10%

1

$60

$ 54.5

5

60

37.3

10

60

23.1

PV of inflows

$114.9

Investment

110.0 NPV $ 4.9

Accept the investment.


13-19. Gifford Western Wear

a. Purchase of the Toy Company would provide some reduction in risk because of the low correlation with Gifford Western Wear, while purchase of Boot Company would do very little to reduce portfolio risk because of the high correlation coefficient. A combination with the Jewelry Company would provide a fairly large degree of risk reduction.

b. Students may or may not calculate the coefficient of variation to get

some idea about the riskiness of each project. If they do, they will find the following:

VGWW = $3/ $10 = 0.3 VBC = $5/ $10 = 0.5 VToy = $6/ $10 = 0.6 VJC = $7/ $10 = 0.7

Although the Jewelry Company has the highest risk as measured by the coefficient of variation, its negative correlation coefficient of – 0.6 should provide the best risk reduction for Gifford Western Wear. This is an example of a risky company being added to a portfolio but reducing total risk. Buy the Jewelry Company.

c. Since the Boot Company is most like Gifford Western Wear, its

selection would provide the least amount of risk reduction. Therefore, add the Toy Company to the Jewelry Company selected in part (b). The Toy Company offers the next best risk reduction after the Jewelry Company because of its low positive correlation coefficient. You might also want to know more about the relationship of the other companies to each other.


13-20. Hopper Chemical Co.

a. Before acquisition: DPD ∑= D P DP

$20 .30 6 40 .40 16 60 .30 18 $40($ millions)

( )∑ −= PDD2

σ D D (D– D ) (D– D )2 P (D– D )2P $20 40 – 20 400 .30 120 40 40 0 0 .40 0 60 40 + 20 400 .30 120 240

49.15240 ==σ

( ) 388.040

49.15===

DV variation of tCoefficien σ

After the acquisition: Expected value 43.0 ($ millions) Standard deviation 27.2 ($ millions) Coefficient of variation 0.633

b. No, it doesn’t appear desirable. Although the expected value is $3 million higher, the coefficient of variation is more than twice as high (.633 vs. 388). The slightly added return probably does not adequately compensate for the added risk.

c. Probably not. There may be a higher discount rate applied to the firm's earnings to compensate for the additional risk. The share price may actually go down.

d. The oil company may provide the best diversification benefits. Since petroleum is used as part of the firm’s production process, an increase in the price of oil would normally hurt the chemical company, but this would be offset by the increased profits for the oil company. The same type of


offsetting risk reduction benefits would take place if the price of oil were going down.


13-21. Jimmy

a. Investment D is riskier by itself with the higher standard deviation (5.2% vs. 4.1%), and D is also riskier in a portfolio context as its beta is higher (1.25 vs. 0.94).

b. %6.15156.084.0072.014.060.018.04.0 ==+=×+×=D

c. %0.40400081.0

6.04.0041.0052.055.02041.06.0052.04.0 2222

==×××××+×+×=

DE

DE

σσ

d. Β = 0.4 × 1.25 + 0.6 × 0.94 = 1.064

e. The standard deviation of the portfolio is less than either investment individually. The key variable in determining the portfolio standard deviation is the correlation coefficient (how the two investments move together). The portfolio beta is an easier calculation of risk than the portfolio standard deviation.

13-22. Astrid

a. Investment N is riskier by itself with the higher standard deviation (3.9% vs. 3.1%). However M is also riskier in a portfolio context as its beta is higher (1.40 vs. 0.85).

b. %15.151515.0855.0066.019.045.012.055.0 ==+=×+×=D

c. %79.2027897.0

45.055.0039.0031.030.02039.045.0031.055.0 2222

==×××××+×+×=

DE

DE

σσ

d. Β = 0.55 × 1.40+ 0.45 × 0.85 = 1.1525

e. The standard deviation of the portfolio is less than either investment individually. The key variable in determining the portfolio standard deviation is the correlation coefficient (how the two investments move together). Beta is an easier calculation of risk than the portfolio standard deviation.


13-23. Albert & China Projects

a. Albert DPD ∑= D P DP

– 0.10 .30 –.03 0.20 .40 .08 0.50 .30 .15 .20 = 20%

( )∑ −= PDD2

σ D D (D– D ) (D– D )2 P (D– D )2P – 0.10 .20 – .30 .09 .30 .027 0.20 .20 .00 0 .40 0 0.50 .20 .30 .09 .30 .027 .054 %2.23232.054. ===σ

China D P DP

0.10 .30 .03 0.10 .40 .04 0.10 .30 .03 .10 = 10%

( )∑ −= PDD2

σ D D (D– D ) (D– D )2 P (D– D )2P 0.10 .10 0 0 .30 0 0.10 .10 0 0 .40 0 0.10 .10 0 0 .30 0 0 %000 ===σ


b. covAC = (D D i) (F ) (D– D ) × (F– ) × P – 0.10 – 0.10 0.10 – 0.10 .30 0 0.20 – 0.10 0.10 – 0.10 .40 0 0.50 – 0.10 0.10 – 0.10 .30 0 0 covAC = 0 Ƿ = 0

c. %0.1515.05.010.010.050.020.050.0 ==+=×+×=D

σ2AC

σ2

AC = (.5)2(.054) + (.5)2 (0) + 2(0)(.5)(.5)

%62.111162.0

0135.0==

=

AC

AC

σσ


13-24. . Alpha & Omega Projects

a. Alpha DPD ∑= D P DP

0.25 .10 .025 0.20 .40 .080 0.15 .40 .060 0.10 .10 .010 .175 = 17.5%

( )∑ −= PDD2

σ D D (D– D ) (D– D )2 P (D– D )2P 0.25 .175 .075 .005625 .10 .0005625 0.20 .175 .025 .000625 .40 .0002500 0.15 .175 – .025 .000625 .40 .0002500 0.10 .175 – .075 .005625 .10 .0005625 .0016250 %03.40403.0016250. ===σ

Omega DPD ∑= D P DP

0.10 .10 .010 0.15 .40 .060 0.20 .40 .080 0.25 .10 .025 .175 = 17.5%

( )∑ −= PDD2

σ D D (D– D ) (D– D )2 P (D– D )2P 0.10 .175 – .075 .005625 .10 .0005625 0.15 .175 – .025 .000625 .40 .0002500 0.20 .175 .025 .000625 .40 .0002500 0.25 .175 .075 .005625 .10 .0005625 .0016250


%03.40403.0016250. ===σ

b. covAO = (D D i) (F ) (D– D ) × (F– ) × P 0.25 – 0.175 0.10 – 0.175 .10 – .0005625 0.20 – 0.175 0.15 – 0.175 .40 – .0002500 0.15 – 0.175 0.20 – 0.175 .40 – .0002500 0.10 – 0.175 0.20 – 0.175 .10 – .0005625 – .0016250 covAO = 0 Ƿ = – .0016250/ 0.0403 × 0.0403 = –1.0

c. %5.17175.0875.00875.0175.050.0175.050.0 ==+=×+×=D

σ2

AC

σ2AC = (.5)2(.001625) + (.5)2 (001625) + 2(– .0016250)(.5)(.5)

%00

0==

=

AC

AC

σσ


13-25. Mr. Boone

a. b.

c. Achieve the highest possible return for a given risk level. Allow the lowest possible risk at a given return level.

d. No. Each investor must assess his or her own preferences about

their risk and return trade-off.

0 1 2 3 4 5 6 7 8

17

16

15

14

13

12

11

10

Risk (percent)

(percent)Return

AB

C

H

GF

E

D

ch13 internet answers

Documents

gifford western

higher discount

higher standard

portfolio

outflows net

standard deviation

crosley square

toy company