MacLean Inc.currently pays no dividends.Today, the firm announced that it will pay its first dividend of $1 per share in four years, then $1.50 in each of the following three years, after which dividends are expected to grow at a constant rate of 5% per year.What is the share price today if the risk-free rate is 4% and the risk premium associated with this share is 6%?

Question

Quizplus · Accepted Answer

We can use the constant growth dividend discount model to calculate the share price today:
D1 = $1
D2 = $1.50
D3 = $1.50 * 1.05 = $1.575
D4 = $1.575 * 1.05 = $1.654
D5 = $1.654 * 1.05 = $1.7377
Next we can calculate the present value of all future dividends using the formula:
PV = D1/(1+r) + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4 + D5/(1+r)^5
where r = risk-free rate + risk premium = 4% + 6% = 10%
PV = $1/(1+0.10) + $1.50/(1+0.10)^2 + $1.575/(1+0.10)^3 + $1.654/(1+0.10)^4 + $1.7377/(1+0.10)^5
PV = $3.7909
Finally, we can add the present value of all future dividends to the present value of the stock price after 5 years, which is:
PV = D6/(r-g) / (1+r)^5
where D6 = $1.7377 * 1.05 = $1.8246
g = constant growth rate = 5%
PV = $1.8246/(0.10-0.05) / (1+0.10)^5
PV = $16.8142
Total PV = $3.7909 + $16.8142 = $20.6051
Therefore, the share price today is $20.6051, which is closest to option B ($19.45).