Question

CAPITAL ASSET PRICING MODEL -

(A) Use Capital Asset Pricing Model (CAPM) to calculate the expected return on a stock that has a beta of 2.5 if the risk-free rate is 3 percent and the market portfolio is expected to pay 11 percent? (PLEASE INCLUDE FORMULAS USED TO SOLVE PROBLEM FOR EXCEL).

BETA -

(B) Company X was a steel company for the first hundred years of its existence but it has been a health care company for the past 25 years. In estimating Company X current beta, why would you get an inaccurate beta if you used all 125 years of its stock returns? (PLEASE INCLUDE FORMULAS USED TO SOLVE PROBLEM FOR EXCEL).

AVERAGE RETURN -

(C) You own a stock that has paid a 10% return for the past five years. In Years 1 and 2, it paid a return of 8 percent and in Years 3 and 4 it paid a return of 12 percent. What return did it pay in Year 5? (PLEASE INCLUDE FORMULAS USED TO SOLVE PROBLEM FOR EXCEL).

Answer 1

a.

Risk free rate = 3.00%

Market return = 11.00%

Beta = 2.50

required rate of return of company stock is calculated below using CAPM formula:

required rate of return = Risk free rate + (Market Return - Risk free rate) × Beta

                                    = 3.00% + (11.00% - 3.00%) × 2.50

                                    = 3.00% + (8% × 2.50)

                                    = 3.00% + 20%

                                    = 23.00%

Hence, required rate of return of company stock is 23.00%.

b.

Company X is healthcare business from last 25 year and its current business is healthcare system. So an analyst should use last 25 year data form estimating the beta of company X. Steel business and helathcare business is totally different and their risk level of also different. So it is inaccurate to use 125 year data for estimation of beta.

c.

Return in fifth year = R

(1 + R) = [(1 + 10%) ^ 5] / [(1 + 8%) ^ 2] × [(1 + 12%) ^ 2]

(1 + R) = 1.61051 / (1.1664 × 1.2544)

(1 + R) = 1.61051 / 1.4631

(1 + R) = 1.1007

R = 10.07%

Return in fifth year is 10.07%.