Question

Risk &Return Company is expected to pay a dividend of $3.50 in the coming year. Dividends are expected to grow at a rate of 10% per year. The risk-free rate of return is 5% and the expected return on the market portfolio is 13%. The stock is trading in the market today at a price of $90.00.

a- What is the expected rate of return of the stock?      

b- What is the beta of Risk &Return's stock if the required rate of return

and the expected rate of return are equal?

Answer 1

using Gordon Growth Model

Po = D1 / (Ke – g)

Where,

Po – Current share price = 90

D1 – Next year expected dividend = 3.50

Ke – Cost of equity = ?

G – Growth rate in dividend = 10%

90 = 3.5/(Ke-.1)

Ke-.1 = 3.5/90

= 0.03888888888

Ke = 0.03888888888+.1

= 13.89%

using Capital Asset Pricing Model

required rate of return = Rf + b ( Rm – Rf )

Where,

Rf – Risk free return = 5%

b – Beta = ?

Rm – Expected return on market portfolio = 13%

13.89 = 5 + b*(13-5)

8b = 13.89-5 = 8.89

b = 8.89/8

= 1.11125

= ​​​​​​​1.11