Question

A stock just paid an annual dividend of $2.9. The dividend is expected to grow by 8% per year for the next 4 years. The growth rate of dividends will then fall steadily by 1.5% per year, from 8% in year 4 to 2% in year 8 and stay at that level forever. The required rate of return is 12%.1. What is the stock price if the dividend growth rate will stay 0.05 (5%) forever after 6 years?2. In 6 years, the P/E ratio is expected to be 25 and the payout ratio to be 80%. What is the stock price when using the P/E ratio?

Answer 1

1)

Div₀ = $2.90

Div₁ = $3.132

Div₂ = $3.38256

Div₃ = $3.65316

Div₄ = $3.94542

Div₅ = $4.20187

Div₆ = $4.41196 (an then g = 5% forever)

rrr = 12%

terminal value at end of year 5 = $4.41196 / (12% - 5%) = $63.03

current stock price P₀ = $3.132/1.12 + $3.38256/1.12² + $3.65316/1.12³ + $3.94542/1.12⁴ + $4.20187/1.12⁵ + $63.03/1.12⁵ = $2.796 + $2.697 + $2.600 + $2.507 + $2.384 + $35.765 = $48.749

P₀ = $48.749

2) following question 1, if the payout ratio is 80%, then total earnings per share (EPS) = $4.41196 / 0.8 = $5.51495 per share

if P/E ratio = 25, then the price of each stock in 6 years = 25 x $5.51495 = $137.87