The fi corporation's dividends per share are expected to grow indefinitely by 5% per year.

a. if this year's 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? current stock price $

b. if the expected earnings per share are $12, what is the implied value of the roe on future investment opportunities? (do not round intermediate calculations. round your answer to the nearest whole percent.) value of roe %

c. how much is the market paying per share for growth opportunities (that is, for an roe on future investments that exceeds the market capitalization rate) ? amount per share

a.)

Dividend discount model (DDM) is used to determine the price of a stock.

The formula is as follows;

Price; P0 = D1 / (r-g)

D1 = Dividend in year 1

r = capitalization rate or required rate of return

g = dividend growth rate

P0 = 8 / (0.10-0.05)

P0 = 160.

The price of the Fi corporation's stock is therefore $160.

b.)

Use the formula that shows the relationship between ROE, retention rate and growth rate. It's as follows;

g = ROE * b

g = growth rate

b = retention rate

Given Earnings per Share (EPS) = $12 and dividend = $8, find dividend payout ratio first.

retention ratio = (1 - dividend payout ratio)

dividend payout ratio = 8/12 = 0.667 or 66.7%

retention ratio; b = (1 - 0.667)

b = 0.333 or 33.3%

Plug it in the formula;

0.05 = ROE * 0.333

ROE = 0.05/0.333

ROE = 0.15 or 15%

c.)

This question is asking for the Present Value of Growth Opportunity (PVGO)

The formula is as follows;

PVGO = Price - EPS1 / r

Price = $160 (from part a)

Expected earnings per share (EPS) = $12

required rate of return (capitalization rate); r = 10% or 0.10 as a decimal

PVGO = 160 - 12/0.10

PVGO = 160 - 120

PVGO = $40

Therefore, the market is paying $40 per share for growth opportunities.