will not be accepted. Thanks for your understanding. Question I Firm A has expec

Question

will not be accepted. Thanks for your understanding. Question I Firm A has expected earnings per share of S15 each year, and pays out all its earnings. Its required rate of return is 15%, what is the price per share of Firm A? a) b) Firm B also has expected earnings per share of $15 next year, and the same required rate of return as Firm A ( 15%). Firm B pays out 40% of its earnings every year. The remaining 60% of Firm B's earnings is invested into positive NPV projects which earn a 20% return. Note that the growth rate of earnings of the firm is givern Ean The term Inv/Earn is the retention rate (the proportion the firm retains of its earnings, or plowback ratio), and Earninv is the reinvestment rate of return which the company is able to earn on projects where it directs the reinvested earnings Inv. What is the price per share of Firm B? c) Compute the growth opportunity component (PVGO term) in Firm B's share price. d Firm C also has expected earnings per share of $15 next year, a required rate of return of 15% and like Firm B pays out 40% of its earnings every year. However, Firm C's retained earnings are invested in projects that earn exactly the same rate of return as the expected return on Firm C equity i. What is the growth rate of earnings of Firm C? ii. Using the DDM, what is the price per share of Firm C? ii Compute the growth opportunity component (PVGO term) in Firm C's share price. Can you explain (in words) why Firm C is growing faster than Firm A in part (a), but has the same equity price as Firm A? Does growth per se add value? e) Compute the expected dividend yield and expected capital gain components to an investor making an investment in each of these firms. That is, for each firm compute the: i Expected dividend yield E[Div(t+1)ypo) ii Expected capital gain E[P(t+D)yP(0)-1 Question 2

Explanation / Answer

According to Dividend Discount Model

Price of share = Dividend per share/ (Discount Rate - Dividend Growth Rate)

P = D/ (rE - g)            ………..Eqn. 1

(a)

In this case, D = $15, rE = 0.15, g = 0

So, price per share = $15/0.15 = $100

(b)

Dividend growth rate g = Retention Rate X Reinvestment rate of return    ……….Eqn. 2

Retention rate = 0.6

Reinvestment rate = 0.2

So, g = 0.6 x 0.2 = 0.12

Hence, share price = $15/(0.15-0.12) = $500

(c )

Present Value of Growth Opportunities, PVGO = Stock Price - Earnings/ Cost of Equity

          = $500 - $15/0.15 = $400

(d)

(i)

From Eqn. 2

Growth rate of earnings = 0.6 x 0.15 = 0.09

(ii)

Price per share = $15/ (0.15 - 0.09) = $250

(iii)

PVGO = $250 - $15/0.15 = $150

(e )

An investor will be better off if the retained earnings are invested in a project that has a better return than the return on equity. He might as well be paid the whole earnings as dividends, which he may reinvest at a better rate than 15% if available in the market.

(f)

From Eqn. 1 we get that

rE = D/P + g

D/P = Dividend Yield

g = Capital gains yield

So,

Expected Dividend Yield

Expected Capital gain

Firm A

15%

0%

Firm B

3%

12%

Firm C

6%

9%

Expected Dividend Yield

Expected Capital gain

Firm A

15%

0%

Firm B

3%

12%

Firm C

6%

9%

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