Question

The risk-free rate is 2.36% and the market risk premium is 7.42%. A stock with a β of 1.04 just paid a dividend of $2.54. The dividend is expected to grow at 22.19% for five years and then grow at 4.45% forever. What is the value of the stock?

The risk-free rate is 3.31% and the market risk premium is 7.71%. A stock with a β of 1.73 just paid a dividend of $2.31. The dividend is expected to grow at 20.72% for three years and then grow at 3.88% forever. What is the value of the stock?

A stock has an expected return of 15.00%. The risk-free rate is 3.48% and the market risk premium is 8.14%. What is the β of the stock?

Answer 1

Answer to Question 1:

Required Return, rs = Risk-free Rate + Beta * Market Risk Premium
Required Return, rs = 2.36% + 1.04 * 7.42%
Required Return, rs = 10.08%

Last Dividend, D0 = $2.54

Growth rate for next 5 years is 22.19% and a constant growth rate (g) of 4.45%

D1 = $2.5400 * 1.2219 = $3.1036
D2 = $3.1036 * 1.2219 = $3.7923
D3 = $3.7923 * 1.2219 = $4.6338
D4 = $4.6338 * 1.2219 = $5.6620
D5 = $5.6620 * 1.2219 = $6.9184
D6 = $6.9184 * 1.0445 = $7.2263

P5 = D6 / (rs - g)
P5 = $7.2263 / (0.1008 - 0.0445)
P5 = $7.2263 / 0.0563
P5 = $128.3535

P0 = $3.1036/1.1008 + $3.7923/1.1008^2 + $4.6338/1.1008^3 + $5.6620/1.1008^4 + $6.9184/1.1008^5 + $128.3535/1.1008^5
P0 = $96.97

Value of stock = $96.97

Answer to Question 2:

Required Return, rs = Risk-free Rate + Beta * Market Risk Premium
Required Return, rs = 3.31% + 1.73 * 7.71%
Required Return, rs = 16.65%

Last Dividend, D0 = $2.31

Growth rate for next 3 years is 20.72% and a constant growth rate (g) of 3.88%

D1 = $2.3100 * 1.2072 = $2.7886
D2 = $2.7886 * 1.2072 = $3.3664
D3 = $3.3664 * 1.2072 = $4.0639
D4 = $4.0639 * 1.0388 = $4.2216

P3 = D4 / (rs - g)
P3 = $4.2216 / (0.1665 - 0.0388)
P3 = $4.2216 / 0.1277
P3 = $33.0587

P0 = $2.7886/1.1665 + $3.3664/1.1665^2 + $4.0639/1.1665^3 + $33.0587/1.1665^3
P0 = $28.25

Value of stock = $28.25

Answer to Question 3:

Required Return = Risk-free Rate + Beta * Market Risk Premium
15.00% = 3.48% + Beta * 8.14%
11.52% = Beta * 8.14%
Beta = 1.42