Question

LG6 5-24 Manipulating CAPM Use the basic equation for the capital asset pricing model (CAPM) to work each of the following problems. a. Find the required return for an asset with a beta of.90 when the risk-free rate and market return are 8% and 12%, respectively. 58 PART 2 Important Financial Concepts b. Find the risk-free rate for a firm with a required return of 15% and a beta of 1.25 when the market return is 14%. c. Find the market return for an asset with a required return of 16% and a beta of 1.10 when the risk-free rate is 9%. d. Find the beta for an asset with a required return of 15% when the risk-free rate and market return are 10% and 12.5%, respectively.

Answer 1

According to Capital asset pricing model,

E(r) = Rf + Beta*(M(r) –Rf)

E(r) = Expected rate of return

Rf = Risk free return

Beta

M(r) = Market return

(a) E(r) = Expected rate of return = ?

Rf = Risk free return = 8%

Beta = 0.90

M(r) = Market return = 12 %

Insert above data in the formula, E(r) = Rf + Beta*(M(r) –Rf)

E(r) = 8 % + 0.90 * (12% - 8%)

= 8 % + 0.90 * (4%)

= 8 % + 3.6 %

= 11.6 %

(b)

E(r) = Expected rate of return = 15 %

Rf = Risk free return = ?

Beta = 1.25

M(r) = Market return = 14 %

Insert above data in the formula, E(r) = Rf + Beta*(M(r) –Rf)

15 % = Rf + 1.25 (14% - Rf)

15 % = Rf - 1.25 Rf + 17.5 %

Rf (1.25 - 1) = 17.5 - 15 %

Rf (0.25) = 2.5 %

Rf = 2.5 % / 0.25

Rf = 10 %

(c)

E(r) = Expected rate of return = 16 %

Rf = Risk free return = 9%

Beta = 1.10

M(r) = Market return = ?

Insert above data in the formula, E(r) = Rf + Beta*(M(r) –Rf)

16 % = 9 % + 1.1(M(r) - 9%)

16% - 9 % = 1.1 ( M(r) - 9%)

7 % = 1.1 ( M(r) - 9%))

7 / 1.1 = M(r) - 9 %

6.36 = M(r) - 9 %

M(r) = 15.36%

(d)

E(r) = Expected rate of return = 15 %

Rf = Risk free return = 10 %

Beta = ?

M(r) = Market return = 12.5 %

Insert above data in the formula, E(r) = Rf + Beta*(M(r) –Rf)

15 % = 10 % + Beta * ( 12.5% - 10%)

15% = 10% + Beta * (2.5%)

5% = Beta * 2.5%

Beta = 5% / 2.5%

Beta = 2