Carnes Cosmetics Co.'s stock price is $46, and it recently paid a $1.75 dividend. This dividend...

Carnes Cosmetics Co.'s stock price is $46, and it recently paid a $1.75 dividend. This dividend is expected to grow by 25% for the next 3 years, then grow forever at a constant rate, g; and r_s = 14%. 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.

Expert Solution

Year	Growth rate	Dividend computation	Dividend	PV factor @14%, 1/(1+r)^time	Dividend * PV factor
1	25.00%	1.75*(1+25%)	$ 2.19	0.8772	$ 1.92
2	25.00%	2.19*(1+25%)	$ 2.73	0.7695	$ 2.10
3	25.00%	2.73*(1+25%)	$ 3.42	0.6750	$ 2.31
				PV of dividends	$ 6.33

Current share price=	$ 46.00
Less PV of dividends (T1-T3)=	$ (6.33)
PV of share price at T3=	$ 39.67
PV factor from T3 to T0	0.6750
Share price at T3=	39.67/0.6750
Share price at T3=	$ 58.77


Current Dividend	$ 3.42
Rate of return	14.00%
Growth Rate	g

Share price at T3=	=Current Dividend*(1+Growth rate)/(Rate of return-Growth Rate)
$ 58.77	=3.42*(1+g)/(0.14-g)
58.77*(14%-g)=	=3.42*(1+g)
8.2278-58.77*g=	3.42+3.42*g)
8.2278-3.42=	=58.77g+3.42g
4.8078	=58.77g+3.42g
4.8078	=62.19*g
g=	4.8078/62.19
g=	7.73%

So the dividends will grow @ 7.73% beyond 3 years

jeff jeffy answered 1 year ago

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