I would like to see a detailed solution of this question that will help me out t

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I would like to see a detailed solution of this question that will help me out to learn the material

Question: A firm earns 1 million in year 0. Thereafter, it continues to earn 1 million a year in perpetuity. The financial manager of the firm is considering two choices regarding dividends i. 11, Paying out all earnings as dividends, or starting from year 0, investing 20% of its earnings each year in projects which earn 10% return Assume that the opportunity cost of capital is 15%. a (10 points) Under choice ii, how much dividends will be paid in year zero, b. (10 points) What will be the value of the firm (year 0's dividends included) c. (10 points) What percentage of the value of the firm under policy ii is due to year one, year two, year T under policies i and i? PVGO? How do you reconcile your answer with your result in part (a) which showed dividends growing over time

Explanation / Answer

Answer:a. One way to estimate the growth rate is by (retained earnings) times the return on those earnings, which can be measured by the ROE (return on equity). That is, g=.2*.1 =.02. Thus under choice ii,

D 1 = 1,000,000* (1-.2) = 800,000

D 2 = D 1 * (1=g) = D 1 (1.02) = 816,000 …. ……

D t = D 1 (1.02) T-1

Answer:b For each policy the value of the firm will be:

Policy i.     V(i) = DIV1 (i)/r

= E/r

= 1,000,000/.15

= 6.67m

Policy ii.    V(ii) = DIV1(ii)/r-g(ii)

= 800,000/.15-.02

= 6.15m

Answer:c P = E/r +PVGO

6.15m = 6.67m +PVGO

PVGO = -.52m

Notice that the new project has a Rate of Return of 10% while the cost of capital is 15%. So the project should not be invested. That is why the PVGO is negative.

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