Question

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

Answer 1

Answer: Price of stock at year end =$53

Explanation:

we first compute the Expected rate of return using the CAPM FORMULAE that

Expected return =risk-free rate + Beta ( Market return - risk free rate)

Expected return=6% + 1.2 ( 16%-6%)

Expected return= 0.06 + 1.2 (10%)

Expected return=0.06+ 0.12

Expected return=0.18

Using the formulae Po= D1 / R-g  to find the growth rate

Where Po= current price of stock at $50

D1= Dividend at $6 at end of year

R = Expected return = 0.18

50= 6/ 0.18-g

50(0.18-g) =6

9-50g=6

50g=9-6

g= 3/50

g=0.06 = 6%

Now that we have gotten the growth rate and expected return, we can now determine the price the investors are expected to sell the stock at the end of year.

Price of stock = D( 1-g) / R-g

= 6( 1+0.06)/ 0.18 -0.06

=6+0.36/0.12

=6.36/0.12=  $53