Question

A company has a beta of 1.5. The risk-free rate of return is 5 percent and the market risk premium is 6 percent. Find the required rate of return on the stock (i.e., the cost of equity capital).

b) The firm will pay a dividend of $4.00 per share next year. The firm will increase the dividend payment by $0.50 a share every year for the next 5 years (i.e., years 2 to 6). Thereafter, the dividends are expected to grow at 5 percent per year forever. What is the firm’s current stock value? Use the required rate of return on the stock from (a).

Answer 1

a) We can find the required rate of return using Capital asset pricing method (CAPM).

Required rate of return = Risk free rate + (Beta * Market risk premium)

= 5% + 1.5(6%)

= 5% + 9%

= 14%.

b)

Step 1: Find D1, D2, D3, D4, D5, D6 and D7

D1 = $4.00

D2 = $4.00 + $0.50 = $4.50

D3 = $4.5 + $0.50 = $5.00

D4 = $5.00 + $0.50 = $5.50

D5 = $5.50 + $0.50 = $6.00

D6 = $6.00 + $0.50 = $6.50

D7 = $6.50 + 5% of $6.50 = $6.825

Step 2: Find the value of stock at Year 7

V7 = Value of stock at year 7
D7 = Expected dividend in year 7
R = Required rate
g = dividend growth rate

Step 3: Find the present value of D1, D2, D3, D4, D5, D6 and V7. Sum of these present value will be the firm's current value.

Here, i = Required rate of return i.e 14% or 0.14

Therefore, firm’s current stock value is $54.23