In case I get a chance to work on this tomorrow...

[sinjun]

Question 6
Investors demand a 15% return on ABC Corp. common shares that currently trade at $30 per share. Dividend payments for the current year are expected to be $1.50 per share.

a) What is the implied long-term average growth rate in dividends that shareholders expect?

R = D1 / P0 + g
0.15 = [1.5 * (1+g)] / 30 + g
g = 0.0952 or 9.52%

The implied long-term average growth rate in dividends that the shareholders expect is 9.52%

b) If, because of changed business conditions, investors adjust their expectations down to a zero growth rate, but still demand a 15% market return on the shares, what will happen to the market price of the shares?

P0 = D/r because the dividend is always the same. The stock can be viewed as an ordinary perpetuity.
P0 = 1.5 / 0.15
= $10.00

The market price of the stock will go down, because the return on investment in a zero-growth stock is less than the return on investment in a growth stock.

c) Conversely, if because of buoyant economy, investors reassess their growth expectations to 15% per year but still demand a 15% rate of return, at what price should the common shares trade?

If the growth rate and the discount rate are equal, the present value of the dividends tends to infinity, and the stock price is infinitely large. We cannot use the dividend growth model in this case, as follows:
D1 = D0 *1.15 = 1.50 * 1.15 = 1.725
R = D1 / P0 + g
D1 / P0 = R – g
D1 = (R-g) * P0
P0 = D1/(R-g)
= 1.725 / (.15 - .15)
= 1.725 / 0

d) What are the economic implications of the mathematical derivation in part c)?
Economically speaking,

Question 7
UVW Inc. expects to earn $1.00 per share for each of the future operating periods if the firm makes no new investments and returns the earnings as dividends to the shareholders. There is, however, an opportunity to retain and invest 50% of the earnings beginning three years from today and this opportunity will continue indefinitely. It is expected that the return will be 20% on this new investment, the return beginning one year after each investment is made. The firm’s equity discount rate is 10% throughout.

a) What is the price per share of UVW Inc. stock now, without making the new investment?
D1 = 1.00 zero-growth model and cash cow
Equity discount rate = 0.10

P0 = D/r = 1.00/0.10 = $10.00

Current price per share of UVW Inc. stock is $10.00

b) If the new investment were to be made, what would the value of the stock be now?
P/E = 1/r + NPVGO/EPS
There is, however, an opportunity to retain and invest 50% of the earnings beginning three years from today and this opportunity will continue indefinitely. It is expected that the return will be 20% on this new investment, the return beginning one year after each investment is made. The firm’s equity discount rate is 10% throughout.
NPVGO = the PV of cash inflows minus the PV of cash outflows
Earnings next year = earnings this year + (retained earnings * return on retained earnings)

g = retention rate * return on retained earnings
= .5 * .2
=0.1

Cash outflows: we have to invest .5 beginning three years from today.
= .2/(0.2 - 0.1) - 0.5
= 1.5 in that year.

Price = EPS/r + NPVGO
=10 + NPVGO
=

c) What is the expected capital gain yield for the second period, assuming the proposed investment is made? What is the expected capital gain yield for the second period, assuming the proposed investment is not made?


d) What is the expected dividend yield for the second period, assuming the proposed investment is made? What is the expected dividend yield for the second period, assuming the proposed investment is not made?