Question

A share of stock with a beta of 0.67 now sells for $51. Investors expect the stock to pay a year-end dividend of $3. The T-bill rate is 4%, and the market risk premium is 9%. a. Suppose investors believe the stock will sell for $53 at year-end. Calculate the opportunity cost of capital. Is the stock a good or bad buy? What will investors do? (Do not round intermediate calculations. Round your opportunity cost of capital calculation as a whole percentage rounded to 2 decimal places.) b. At what price will the stock reach an “equilibrium” at which it is perceived as fairly priced today? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

a.

Under Capital Assets pricing model (CAPM), the expected return i.e opportunity cost of capital can be calculated with following equation -

where,

Ke = Opportunity cost of capital

Rf = Risk free rate i.e T bills rate

putting the values -

Opportunity cost of capital = 10.03%

To check whether the stock is good buy or bad buy, we need to calculate the holding period return and if holding period return is greater than opportunity cost of equity than it would be a good buy otherwise bad buy.

putting the values -

We can see, the Holding period return is less than opportunity cost of capital (required return) thus, It is bad buy and Investor shouldn't buy this stock.

b.

Equilibrium price of stock can be calculated with following equation and it is suggested by M&M theory.

where,

P0 = Today Price (Equilibrium price)

P1 = Expected Price at the end of period

D = Dividend during period

Ke = Cost of capital

putting the values -

Thus, Today's fair price = $50.90

Hope this will help, please do comment if you need any further explanation. Your feedback would be appreciated.