A share of stock with a beta of 0.67 now sells for $51. Investors expect the sto

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.)

Explanation / Answer

Solution:

Given that Risk free rate = 4%, beta is 0.67,and market risk premium is 9%.

We can find the expected return on the equity using CAPM model

Expected return = Risk free rate + Beta * Market risk premium

Expected return = 4% + 0.67 * 9% = 4% +6.03% = 10.03%

Current share price = $51 and it is expected that we will get $3 dividend in year end,

Using Dividend discount model

P0 = Div1/ (expected return - growth )

51 = 3 /(10.03% - growth)

10.03% - growth = 3/51

Growth = 10.03% -5.88% = 4.1476%

Share price after one year = Div 1 *(1+growth rate) / (cost of equity - growth rate) = 3 *(1+ 4.1476%)/(10.03% - 4.1476%) = 3.1244/5.882% = $

Q1.

Is this a good buy ?

Ans: yes, as expected share price is 53.1135 after one year as compared to $53 which the investor believes

Q2. Stock price will be at equilibrium if it reaches at $53.11

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