Question

Carnes Cosmetics Co.'s stock price is $52, and it recently paid a $1.50 dividend. This dividend is expected to grow by 29% for the next 3 years, then grow forever at a constant rate, g; and rs = 12%. At what constant rate is the stock expected to grow after Year 3?

Answer 1

Current Price, P0 = $52.00
Last Dividend, D0 = $1.50

Growth rate for next 3 years is 29% and a constant growth rate (g) thereafter

D1 = $1.5000 * 1.29 = $1.9350
D2 = $1.9350 * 1.29 = $2.4962
D3 = $2.4962 * 1.29 = $3.2201

Required Return, rs = 12%

P0 = D1/(1+rs) + D2/(1+rs)^2 + D3/(1+rs)^3 + P3/(1+rs)^3
$52.00 = $1.935/1.12 + $2.4962/1.12^2 + $3.2201/1.12^3 + P3/1.12^3
$52.00 = $6.0096 + P3*0.711780
$45.9904 = P3*0.711780
P3 = $64.6132

D4 = D3 * (1 + g)
D4 = $3.2201 * (1 + g)

P3 = D4 / (rs - g)
$64.6132 = $3.2201 * (1 + g) / (0.12 - g)
20.065588 = (1 + g) / (0.12 - g)
2.407871 - g * 20.065588 = 1 + g
2.407871 - 1 = g + g * 20.065588
1.407871 = g * 21.065588
g = 0.0668 or 6.68%

Therefore, constant growth rate is 6.68%