Question

Problem 9-17 Assume that the risk-free rate of interest is 4% and the expected rate of return on the market is 14%. A share of stock sells for $55 today. It will pay a dividend of $6 per share at the end of the year. Its beta is 1.5. What do investors expect the stock to sell for at the end of the year? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

The stock price at year end is $59.45

Step-by-step explanation:

Given that:

risk-free rate of interest (
`r_f`)= 4% = 0.04,

expected rate of return on the market
`E(r_m)` = 14% = 0.14

Beta (
`\beta`) = 1.5

Dividends (D) = $6

Current price of stock
`P_o` = $55

Therefore, the expected rate of return (
`E(r)`) is given as:

`E(r) = r_f +\beta (E(r_m)-r_f) = 0.04+1.5(0.14-0.04)=0.04+1.5(0.1)=0.19`

The price of the stock at the end of the year (
`P_1`) is given as:

`E(r)=(D+P_1-P_o)/(P_o) \\0.19=(6+P_1-55)/(55) \\10.45=6+P_1-55\\P_1=10.45+55-6=59.45`

P₁ = $59.45