Question

Better mousetraps has come out with an improved product and the world is beating a path to its door. As a result, the company projects a 20% growth for 4 years. By then the other firms will copy its technology and drive down profit margins and the sustainable growth rate will fall to 5%. The most recent annual dividend was $1 per share.

1. What are the expected dividends for the next 5 years?
2. What is the expected stock price 4 years from now? The discount rate is 10%
3. What is the stock price today?
4. What is the current dividend yield?
5. What is the expected return to an investor who buys and sells the stock in 1 year?
6. What is the before tax expected rate of return?
7. After tax expected rate of return?

Answer 1

(a)
Calculation of Dividend paid every year
Last paid dividend (D0) =			$1.00
Next 4 years growth rate in dividend is 20% a year and 5 % per year thereafter
To calculate D1 to D5, growth rate of 14% is added. To calculate D6, Growth rate of 8% is added to D5.
D1 = D0 + (D0 * growth rate)
(D0 = 1.0)	20%%		1.200000
D2 = D1 + (D1 * growth rate)			1.440000
	20%
D3 = D2 + (D2 * growth rate)			1.728000
	20%
D4 = D3 + (D3 * growth rate)			2.073600
	20%
D5 = D4 + (D4 * growth rate)			2.177280
	5%
So, expected dividend in 1 year			$1.20
2 year			$1.44
3year			$1.73
4 year			$2.07
5 year			$2.18
(b)
growth rate after 4 years = 5% or			0.05
Discount rate =			10%
P4 = D5/(ke-g)
2.17728/(0.10-0.05)
43.5456
so, stock price 4 years from now is $43.55.
(c)
Calculation of P0
Year		Cash flows	P.V.F.@10%	cash flows * P.V.F.
1	D1	1.200000	0.9090909091	1.090909091
2	D2	1.440000	0.826446281	1.190082645
3	D3	1.728000	0.7513148009	1.298271976
4	D4	2.073600	0.6830134554	1.416296701
4	P4	43.5456	0.6209213231	27.03839157
				__________
				32.03395198
So, present value of stock is $32.03.
(d)
Current Dividend yield = D1/ P0
1.2/32.03395
0.0374602547	or 3.75%
So, Dividend yield is 3.75%