Question

A share of stock with a beta of 0.77 now sells for $50. Investors expect the stock to pay a year-end dividend of $3. The T-bill rate is 4%, and the market risk premium is 8%. a. Suppose investors believe the stock will sell for $52 at year-end. Calculate the opportunity cost of capital. Is the stock a good or bad buy? What will investors do? b. At what price will the stock reach an “equilibrium” at which it is perceived as fairly priced today?

Correct answer:

a) Opportunity cost 0.04+(0.77*0.08)=10.16%

b) Stock price =3/(1+0.1016)+52/(1+0.1016) =$49.93

Answer 1

a)	Opportunity cost of capital per CAPM = 4%+0.77*8% =	10.16%
	Expected return = (3+52-50)/50 =	10.00%
	As the expected yield is less than the opportunity cost,
	investors will not invest in the stock. It is a bad buy.
b)	Equilibrium price = (3+52)/1.1016 =	$        49.93
	This is the fair price of the stock. Investors who hold
	the share will sell it, demand for the stock will be less
	at $50. The situation will continue till the price reaches
	$49.93.