Question

Carnes Cosmetics Co.'s stock price is $40, and it recently paid a $1.25 dividend. This dividend is expected to grow by 18% for the next 3 years, then grow forever at a constant rate, g; and r_s = 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.

Answer 1

Year	Dividend	PVF@12%	Dividend*PVF
1	1.25(1+.18)= 1.475	.89286	1.31697
2	1.475(1+.18)=1.7405	.79719	1.38751
3	1.7405(1+.18)= 2.0538	.71178	1.46185
3(Horizon value)	X	.71178	.71178 X
Current stock price	40

Now,

current stock price = sum of present value of dividend

40 = 1.31697+1.38751+1.46185 +.71178x

40 = 4.16633+.71178X

40-4.16633= .71178X

X= 35.83367/.71178

= $ 50.34374

Horizon value at year 3 =50.34374

###working :Find PVF using present value table or using the formula 1/(1+i))^n where i = 12%,n=1,2,3

Step 2:

Horizon value = D3(1+g)/(rs-g)

50.34374 = 2.0538(1+g)/(.12-g)

50.34374/2.0538 = (1+g)/(.12-g)

24.51249 (.12-g) = 1+g

2.94150 -24.51249 g= 1+g

2.94150-1 = g+ 24.51249g

1.94150 = 25.51249 g

g =1.94150/25.51249

= .0761 or 7.61%

constant growth = 7.61%