Chapter VTutorial

Risk and Return

P5-1: Rate of return, kt=(Pt-Pt-1+Ct)/Pt-1

• Douglas Keel, a financial analyst for Orange Industries, wishes to estimate the rate of return for two similar-risk investments, X and Y. Keel’s research indicates that the immediate past returns will serve as reasonable estimates of future returns. A year earlier, investment X had a market value of $20,000, investment Y of $55,000. During the year, investment X generated cash flow of $1,500 and investment Y generated cash flow of $6,800. The current market values of investments X and Y are $21,000 and $55,000, respectively.

a. Calculate the expected rate of return on investments X and Y using the most recent year’s data.

b. Assuming that the two investments are equally risky, which one should Keel recommend? Why?

Solution P5-1

P5-1: Rate of return, kt=(Pt-Pt-1+Ct)/Pt-1

X: Pt-1=20000, Ct=1500, Pt=21000

Y: Pt-1=55000, Ct=6800, Pt=55000

a) X: kt = (21000-20000+1500)/20000= 12,5%

Y: kt= (55000-55000+6800)/55000= 12,36%

b) Investment X should be selected because it has a higher rate of return for the same level of risk.

Problem 5-2

P5-2: Return calculations, kt=(Pt-Pt-1+Ct)/Pt-1

For each of the investments shown in the following table, calculate the rate of return earned over the unspecified time period.

Solution P5-2

P5-2: Rate of return, kt=(Pt-Pt-1+Ct)/Pt-1

A: kt=(1100-800-100)/800= 25%

B: kt=(118000-120000+15000)/120000= 10,83%

C: kt=(48000-45000+7000)/45000= 22,22%

D: kt=(500-600+80)/600= -3,33%

E: kt=(12400-12500+1500)/12500= 11,2

Problem 5-5

P5-5: Risk and Profitability

Micro-Pub, Inc., is considering the purchase of one of two microfilm cameras, R and S. Both should provide benefits over a 10-year period, and each requires an initial investment of $4,000. Management has constructed the following table of estimates of rates of return and probabilities for pessimistic, most likely, and optimistic results:

a. Determine the range for the rate of return for each of the two cameras.

b. Determine the expected value of return for each camera.

c. Purchase of which camera is riskier? Why?

Solution P5-5

P5-5: Risk and Profitability

a) Range: Camera R 30-20= 10%

Camera S 35-15= 20%

b) Expected Return

c) Camera S is considered more risky than camera R because it has a much broader range of outcomes.

Camera 

Probability, Pri

Expected return, ki

Weighted value of return, ki*Pri

Expected Return

RPessimistic 0,25 0,2 5,00%

25,00%Most likely 0,5 0,25 12,50%Optimistic 0,25 0,3 7,50%

SPessimistic 0,2 0,15 3,00%

25,50%Most likely 0,55 0,25 13,75%Optimistic 0,25 0,35 8,75%

Problem 5-7

P5-7: Coefficient of Variation, CV = σk/k

Coefficient of variation Metal Manufacturing has isolated four alternatives for meeting its need for increased production capacity. The data gathered relative to each of these alternatives is summarized in the following table.

a. Calculate the coefficient of variation for each alternative.

b. If the firm wishes to minimize risk, which alternative do you recommend? Why?

Solution P5-7

P5-7: Coefficient of Variation, CV = σk/k

a) A: CV= 7/20= 0,35

B: CV= 9,5/22= 0,4318

C: CV= 6/19= 0,3158

D: CV= 5,5/16= 0,3438

b) Asset C has the lowest CV and is the least risky relative to other choices

Problem 5-8

P5-8: Standard Deviation vs Coefficient of Variation

Greengage,Inc., a successful nursery, is considering several expansion projects. All of the alternatives promise to produce an acceptable return. The owners are extremely risk-averse; therefore, they will choose the least risky of the alternatives. Data on four possible projects follow.

a. Which project is least risky, judging on the basis of range?

b. Which project has the lowest standard deviation? Explain why standard deviation is not an appropriate measure of risk for purposes of this comparison.

c. Calculate the coefficient of variation for each project. Which project will Greengage’s owners choose? Explain why this may be the best measure of risk for comparing this set of opportunities.

Solution P5-8

P5-8: Standard Deviation vs Coefficient of Variation

a) Project A is least risky based on range with a value of 0,04.

b) Project A is least risky based on standard dev. with a value of 0,029. But standard dev. is not the appropriate measure of risk since the projects have different returns.

c) A: CV=0,029/0,12=0,2417

B: CV=0,032/0,125=0,256

C: CV=0,035/0,13=0,2692

D: CV=0,03/0,128=0,2344

In this case D is the best alternative since it provides the least amount of risk for each percent of return earned. CV is probably the best measure in this instance since it provides a standardized method of measuring the risk/return trade-off for investments with differing returns.

Problem 5-18

P5-18: Interpreting Beta

A firm wishes to assess the impact of changes in the market return on an asset that has a beta of 1.20.

a. If the market return increased by 15%, what impact would this change be expected to have on the asset’s return?

b. If the market return decreased by 8%, what impact would this change be expected to have on the asset’s return?

c. If the market return did not change, what impact, if any, would be expected on the asset’s return?

d. Would this asset be considered more or less risky than the market? Explain.

Solution P5-18

P5-18: Interpreting Beta

Beta = 1,2

a) 1,2*15%= 18% increase

b) 1,2*(-8%)= -9,6% decrease

c) 1,2*0= 0 no change

d) The asset is more risky than the market portfolio, which has a beta of 1. The higher beta makes the return move more than the market.

Problem 5-22

P5-22: Capital Asset Pricing Model, kj=RF+[bj*(km-RF)]

For each of the cases shown in the following table, use the capital asset pricing model to find the required return.

Solution P5-22

P5-22: Capital Asset Pricing Model, kj=RF+[bj*(km-RF)]

A: kj = 5+[1,3*(8-5)] = 8,9%

B: kj = 8+[0,9*(13-8)] = 12,5%

C: kj = 9+[-0,2*(12-9)] = 8,4%

D: kj = 10+[1*(15-10)] = 15%

E: kj = 6+[0,6*(10-6)] = 8,4%

Problems 5-10, 5-12, 5-16, 5-27 are included in excel spreadsheet

CH5

Reminder – MidTerm! On the 12th of NovemberChapters – 1, 2, 3, 4, 5

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