Question

Assume that the risk-free rate of interest is 6% and the expected rate of return on the market is 16%. Consider the following questions.

a. A share of stock sells for $50 today. It will pay a dividend of $6 per share at the end of the year. Its beta is 1.2. What do investors expect the stock to sell for at the end of the year?

b. I am buying a firm with an expected perpetual cash flow of $1,000 but am unsure of its risk. If I think the beta of the firm is .5, when in fact the beta is really 1, how much more will I offer for the firm than it is truly worth?

c. A stock has an expected rate of return of 4%. What is its beta?

Answer 1

a.

Current stock price (P0) = 50

D1 = 6

Required rate of return of stock as per CAPM = risk free rate + (beta *(market return - risk free rate))

=6% + (1.2*(16%-6%))

=18%

Current price of stock (P0) = (D1+P1)/(1+ke)

50 = (6+P1)/(1+18%)

50*1.18 = 6+P1

P1 or price of stock at year 1 = 59-6 = 53

So  investors expect the stock to sell for at the end of the year is $53.

b.

perpetual cash flows or D1 = 1000

Expected beta = 0.5

Required rate of return of stock as per CAPM = risk free rate + (beta *(market return - risk free rate))

=6% + (0.5*(16%-6%))

=11%

Value or buying assumed by us = D1/ke

(growth is 0, so above formula is applicable in case of no growth)

=1000/11%

=9090.909091

Actual beta of firm = 1

Required rate of return of stock as per CAPM = risk free rate + (beta *(market return - risk free rate))

=6% + (1*(16%-6%))

=16%

Actual or true value of firm = 1000/16%

=6250

Over valuation of firm = 9090.9091 - 6250

=2840.9091

So I will offer $2840.91 more for the firm than it is truly worth

c.

expected return of stock = 4%

Expected return or required return as per CAPM = risk free rate + (beta *(market return - risk free rate))

4%=6% + (beta*(16%-6%))

4%-6% = beta*10%

-2%/10% = beta

beta=-0.2

So beta of stock is -0.2