Question

Consider equally risky, all-equity financed firms G and D. Both firms are currently trading at $50 per share. Firm G pays no dividends, but firm D pays all its earnings as dividends. In a year from today, the stock of firm G is expected to be at S65 per share. Firm Dis expected to pay a $15 dividend per share at the year-end and its stock price at the year-end is expected to be $50 per share. Capital gains are taxed at half the 40% regular income tax rate, but the dividend income is taxed at 30%. Required At what share price should the stock of firm D be trading to-day in a competitive stock market? Show calculations to support your answer.

Answer 1

In a competitive stock market, the return of both the stocks of Firm D and G will be the same.

Step 1:

Computation of after tax return on stock of Firm G:

Current Price of Firm G = $50

Price at year end of Firm G = $65

Capital Gain = Price at year end - Current Price = $65-$50 = $15

Capital Gain Tax = half of 40% = 20%

Thus, after tax capital gain = $15*(1-tax rate) = $15*(1-20%) = $15*0.8 = $12

After Tax Return % = After tax capital gain / Current Price of Firm G = $12/$50 = 24%

Step 2:

Computation of after tax dividend of stock of Firm D:

Dividend at year end = $15

Dividend tax = 30%

After tax dividend at year end = $15*(1-tax rate) = $15*(1-30%) = $15*0.7 = $10.5

Step 3:

Computation of current price of stock of Firm D equalling the return of stock of Firm G

After Tax Return % of stock of Firm G = 24%

After tax dividend at year end of stock of Firm D = $10.5

Current price of stock of Firm D = Return of Firm G Stock / Dividend at year end of Firm D stock = $10.5 / 24% = $43.75

Thus, the price of stock of Firm D should be trading to-day at $43.75 in a competitive stock market.