Question

In: Finance

Better mousetraps has come out with an improved product and the world is beating a path...

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?

Solutions

Expert Solution

(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%


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