Question

AAA firm’s required return = 12.00%, the price of the stock = $40 per share. D₀ = $1. Dividend will grow by 30% for the next four years. After the fourth year, the dividend will grow at the rate of g forever. Find g. (hint: D₄ = $1.00(1.30)⁴.

a.   5.17%

b.   6.34%

c.   5.72%

d.   6.02%

Answer 1

Given about AAA Firm,

Required return rs = 12%

Stock price today P0 = $40

D0 = $1

growth rate for next 4 years = 30%

So, D1 = 1*1.3 = $1.3

D2 = 1.3*1.3 = $1.69

D3 = 1.69*1.3 = $2.197

D4 = 2.197*1.3 = $2.8561

let growth rate thereafter is g

So, Stock price at year 4 using constant dividend growth rate is

P4 = D4*(1+g)/(rs-g) = 2.8561*(1+g)/(0.12-g)

Stock price today is sum of PV of all dividends and P4 discounted at rs

So, P0 = D1/(1+rs) + D2/(1+rs)^2 + D3/(1+rs)^3 + D4/(1+rs)^4 + P4/(1+rs)^4

=> 40 = 1.3/1.12 + 1.69/1.12^2 + 2.197/1.12^3 + 2.8561/1.12^4 + P4/1.12^4

=> P4/1.12^4 = 40 - (1.1607 + 1.3473 + 1.5638 + 1.8151)

=> P4 = (1.12^4)*(34.1131) = 53.6777

So, 2.8561*(1+g)/(0.12-g) = 53.6777

=> g = 6.34%

Option b is correct.