Question

Carnes Cosmetics Co.'s stock price is $74.30, and it recently paid a $2.25 dividend. This dividend is expected to grow by 28% for the next 3 years, then grow forever at a constant rate, g; and rs = 13%. At what constant rate is the stock expected to grow after Year 3? Round your answer to two decimal places. Do not round your intermediate calculations.

Answer 1

D₀ = $2.25

g = 28%

rs = 13%

P₀ = PV (D1) + PV (D2) + PV (D3) + PV (TV₃)

D1 = 2.25 * (1+0.28) = 2.88

D2 = D1 * (1+0.28) = 3.69

D3 = D2 * (1+0.28) = 4.72

PV (D1) = D1 / (1 + rs) = 2.88 / (1 + 0.13) = 2.59

PV (D2) = D2 / (1 + rs) = 3.69 / (1 + 0.13)² = 2.89

PV (D3) = D3 / (1 + rs) = 4.72 / (1 + 0.13)³ = 3.27

PV (TV₃) = P₀ - PV (D1) + PV (D2) + PV (D3)

                = $74.30 - $2.59 - $2.89 - $3.27

                = $65.55

TV₃    = PV (TV₃) * (1+0.13)³ = $65.55 * (1+0.13)³ = $94.58

TV₃   = D3 (1+g) / (rs – g)

$94.58 = 4.72 (1+g) / (0.13 – g)

12.29 – 94.58g = 4.72 + 4.72g

99.3 g = 7.57

g = 7.57 / 99.3

= 7.62%

The Constant rate that the stock is expected to grow after Year 3 = 7.62%