Question

You feel that Stock X will be able to grow its dividend by 10% per year for the next two years, after which time the growth rate will drop to 3% and then stay at that rate forever. You feel that a discount rate of 10% is fair, given the company’s risk. Earlier today, Stock X paid a dividend of $0.72 per share. According to your expectations, what should be Stock X’s current price? Write your answer out to the nearest penny.

Answer 1

>>>

r = discount rate = 10%

g = 10% for 2 years and 3% from 3 year to forever

Current Dividend = D0 = $0.72

Dividend in Year 1 = D1 = D0 * (1+g) = $0.72 * (1+10%) = $0.792

Dividend in Year 2 = D2 = D1 * (1+g) = $0.792 * (1+10%) = $0.8712

Dividend in Year 3 = D3 = D2 *(1+g) = $0.8712 *(1+3%) = $0.897336

>>>

Horizon value at year 2 for years 3 to forever = D3 / (r - g)

= $0.897336 / (10% - 3%)

= $0.897336 / 0.07

= $12.8190857

>>>

Stock X's current Price = Prsent value of future dividends

= [D1 /(1+r)^1] + [D2 /(1+r)^2] + [H /(1+r)^2]

= [ $0.792 / (1+10%)^1] + [ $0.8712 / (1+10%)^2] + [ $12.8190857 / (1+10%)^2]

= [ $0.792 / 1.1] + [ $0.8712 / 1.21] + [ $12.8190857 / 1.21]

= $0.72 + $0.722479339 + $10.5942857

= $12.036765

Therefore, Stock X's Current Price is $12.04