Question

**Dividends discount model:**

The MBS Corporation’s dividends per share are expected to grow indefinitely by 5% per year.

**DDa. ** If
this year-end dividend is $8 and the market capitalization rate is
10% per year, what must the current stock price be according to the
DDM (Dividends Discounting Model)?

**DDb.** If the
expected earnings per share are 12$, what is the implied value of
the ROE on future investment opportunities?

**DDc.** How
much is the market paying per share for growth opportunities (i.e.,
for an ROE on future investments that exceeds the market
capitalization rate)?

The stock of Nogo Corporation is currently selling for $10 per share. Earnings per share in the coming year are expected to be $2. The company has a policy of paying out 50% of its earnings each year in dividends. The rest is retained and invested in projects that earn a 20% rate of return per year. This situation is expected to continue indefinitely.

**DD1.** Assuming
the current market price of the stock reflects its intrinsic value
as computed using the constant-growth DDM (Dividends Discounting
Model), what rate of return do Nogo’s investors require?

**DD2.** By how
much does its value exceed what it would be if all earnings were
paid as dividends and nothing were reinvested?

**DD3.** If
Nogo were to cut its dividend payout ratio to 25%, what would
happen to its stock price? What if Nogo eliminated the
dividend?

Answer #1

Solution:

DDa.)calculation of current stock price(Po)

Po=Next year dividend/(capitalization rate-growth rate)

=$8*(1.05)/10%-5%

**=$168**

DDb)Calculation of implied value of ROE

We know that,

Growth rate=Retention Ratio*ROE

Dividend payou ratio=$8/$12

=2/3

Retention Ratio=1-Dividend payou ratio

=1-2/3

=1/3

Thus,ROE is;

=Growth rate/retention ratio

=5%/(1/3)

**=15%**

DDc)Price of share is;

Po=$12/.10

=$120

Current market price per share=$168

Thus,market is paying $48(168-120) per share for growth opportunities.

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