Principles of Managerial Finance

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258 PART 2 Important Financial Concepts

b. Find the risk-free ratefor a firm with a required return of 15% and a beta of

1.25 when the market return is 14%.

c. Find the market returnfor an asset with a required return of 16% and a beta

of 1.10 when the risk-free rate is 9%.

d. Find the betafor an asset with a required return of 15% when the risk-free

rate and market return are 10% and 12.5%, respectively.

5–25 Portfolio return and beta Jamie Peters invested $100,000 to set up the follow-

ing portfolio one year ago:

a. Calculate the portfolio beta on the basis of the original cost figures.

b. Calculate the percentage return of each asset in the portfolio for the year.

c. Calculate the percentage return of the portfolio on the basis of original cost,

using income and gains during the year.

d. At the time Jamie made his investments, investors were estimating that the

market return for the coming year would be 10%. The estimate of the risk-

free rate of return averaged 4% for the coming year. Calculate an expected

rate of return for each stock on the basis of its beta and the expectations of

market and risk-free returns.

e. On the basis of the actual results, explain how each stock in the portfolio

performed relative to those CAPM-generated expectations of performance.

What factors could explain these differences?

5–26 Security market line, SML Assume that the risk-free rate, RF,is currently 9%

and that the market return, km,is currently 13%.

a. Draw the security market line (SML) on a set of “nondiversifiable risk

(xaxis)–required return (yaxis)” axes.

b. Calculate and label the market risk premiumon the axes in part a.

c. Given the previous data, calculate the required return on asset A having a

beta of .80 and asset B having a beta of 1.30.

d. Draw in the betas and required returns from part cfor assets A and B on the

axes in part a.Label the risk premiumassociated with each of these assets,

and discuss them.

5–27 Shifts in the security market line Assume that the risk-free rate, RF,is currently

8%, the market return, km,is 12%, and asset A has a beta, bA,of 1.10.

a. Draw the security market line (SML) on a set of “nondiversifiable risk

(xaxis)–required return (yaxis)” axes.

b. Use the CAPM to calculate the required return, kA,on asset A, and depict

asset A’s beta and required return on the SML drawn in part a.

c. Assume that as a result of recent economic events, inflationary expectations

have declined by 2%, lowering RFand kmto 6% and 10%, respectively.

Asset Cost Beta at purchase Yearly income Value today

A $20,000 .80 $1,600 $20,000

B 35,000 .95 1,400 36,000

C 30,000 1.50 — 34,500

D 15,000 1.25 375 16,500