Question

1. Better Mousetraps has come out with an improved product, and the world is beating a path to its door. As a result, the firm projects growth of 25% per year for 3 years. By then, other firms will have copy technology, and competition will drive down profit margins. However, because of industry barriers and huge capital input, Better Mousetraps is still at advantage, but the growth rate will fall to 10% per year for 2 years. Finally, the competition will drive the sustainable growth rate to a permanent 3%. The most recent annual dividend was DIV0=$1 per share.

1. What are the expected values of (i) DIV1, (ii) DIV2, (iii) DIV3, (iv) DIV4, (v) DIV5, (vi) DIV6?
2. What is the expected stock price 5 years from now? The discount rate is 15%
3. What is the stock price today?
4. Find the dividend yield
5. What will next year’s stock price be?
6. What is the expected rate of return to an investor who buys the stock now and sells it in 1 year?

Answer 1

D1 = D0*(1+g)

= 1*(1+25%)

= $1.25

D2 = 1.25*(1+25%) = $1.5625 i.e. $1.56

D3 = 1.95

D4 = $2.15

D5 = $2.36

D6 = $2.43

b.Price after 5 years = D6/(Required return – growth rate)

= 2.43/(15%-3%)

= $20.25

c.Price today is equal to the present value of all future dividends

= 1.25/(1.15) + 1.56/(1.15)^2 + 1.95/(1.15)^3 + 2.15/(1.15)^4 + 2.36/(1.15)^5 +20.25/(1.15)^5

= $16.02

d.Dividend yield = Expected Dividend/Current price

= 1.25/16.02

= 7.80%

e.Capital gain = 15%-7.80% = 7.2%

Stock price next year = 16.02*(1+7.2%) = $17.17

f.Equal to rate of return i.e. 15%