Question

Carnes Cosmetics Co.'s stock price is $57, and it recently paid a $1.75 dividend. This dividend is expected to grow by 27% 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? Do not round intermediate calculations. Round your answer to two decimal places. 6.62% is the wrong answer by the way

Answer 1

Current share price is the PV of future expected cash flows

Using Gordon Growth Model

P3 = D4 / (Ke – g)

Where,

P3 - Market price at the end of year 3 =?

D4 - Expected dividend in year 4 = 1.75*1.27^3*(1+g)=3.58467025*(1+g)

Ke – Cost of equity = 12%

G – Growth rate in dividend = ?

P3 = (3.58467025*(1+g))/(.12-g)

= (3.58467025+3.58467025g)/(.12-g)

CF1/(1+R)^1+CF2/(1+R)^2+.....+CFn/(1+R)^n

(1.75*1.27)/1.12^1+(1.75*1.27^2)/1.12^2+(1.75*1.27^3)/1.12^3+((3.58467025+3.58467025g)/(.12-g))/1.12^3

1.984375+2.25013950893+2.55149747887+((3.58467025+3.58467025g)/(.12-g))/1.12^3 = 57

((3.58467025+3.58467025g)/(.12-g))/1.12^3 = 57-6.7860119878

= 50.2139880122

((3.58467025+3.58467025g)/(.12-g)) = 50.2139880122*1.12^3

= 70.54703775

3.58467025+3.58467025g =  70.54703775*(.12-g)

= 8.46564453-70.54703775g

70.54703775g+3.58467025g = 8.46564453-3.58467025

74.131708g = 4.88097428

g = 4.88097428/74.131708

= 6.58%