Question

Firm A has a beta of 1.5 and estimated cost of equity of 7%. Firm B has a beta of 0.7 and estimated cost of equity of 6%. What is the assumed market return and risk-free rate?

Answer 1

Let the risk free rate be Rf

As per CAPM, price of a stock is given by

Re = Rf + (Rm – Rf) x Beta

Where,

Re = Expected return on the stock

Rf = Risk free rate of return

Rm – Rf = Market risk premium

Beta = Beta of the stock

So, return of stock A will be given by

7 = Rf + (Rm – Rf) x 1.50 ---------- ( 1 ) and return of stock B will be given by

6 = Rf + (Rm – Rf) x 0.70 ------- ( 2 )

( 1 ) - ( 2 )

1 = Rf – Rf + (Rm – Rf) x (1.50 – 0.70)

So, Rm – Rf = 1 / 0.80

= 1.25

So, putting the value of Rm – Rf in equation 1 we get

7 = Rf + 1.25 x 1.50

So, Rf = 7 – 1.88

= 5.12 percent

Putting the value of Rf in Rm – Rf we get,

Rm – 5.12 = 1.25

So, Rm = 1.25 + 5.12

= 6.37