The firm is capitalized by 100,000 shares of common stock which trade at the beginning of...

The firm is capitalized by 100,000 shares of common stock which trade at the beginning of the period at 10 per share. The expected net income in period one is 200,000 and the firm has declared a cash dividend of 1 per share, to be paid at the end of the period. The firm's cost of equity is 20%. Ignore personal taxes. Hint: think of a relationship between today's price and next period's price in the dividend discount model.

1. what is the ex-dividend share price? what would have been the end-of-period stock price if the firm skipped the dividend?

2. how many shares of common stock will the firm have to sell at the ex-dividend price in order to undertake an investment project which requires an investment equivalent to I(1)=200,000?

3. what is the value of the firm just after the new issue? what would have been the value of the firm if it skipped the dividend and used the retained earnings to finance the investment?

Solutions

Expert Solution

Given Info-

total shares- 100000

Current market price = 10

Net Income = 200000

Cash Dividend to be paid = 100000

For calculating ex-dividend share price, we first have to calculate the growth rate using the formula

cost of equity = (D₁ / P₀) + g,

where, D₁ = 1 +g%

and P₀= Price of share i.e., 10

By equating it in the above formula we will get g = 19.88%

According to Dividend Discount model, value of share = EPS / (cost of capital equity - Growth rate)

=1/(0.20-0.1988) = 8.33

Answer1. Ex div share price is 8.33, if the firm skipped the dividend, the end of period stock price would be cum-dividend

i.e., 9.33.

Answer2. The firm will have to sell shares equivalent to = Investment required/ Price per share

= 200000 / 8.33

= 24010(approx.)

Answer3. Current Value of firm = (100000+24010)*8.33

= 10,33,003.3

If dividend is skipped, the price will be 9.33, and reamining investment req will be 100000.

So new value of firm is = (100000*9.33)+(100000)

= 10,33,000

jeff jeffy answered 11 months ago

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