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# Stock Price- Dividends, Taxes, Capital Gain

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Dividends and Taxes:

Investors require an after-tax rate of return of 10 percent on their stock investments. Assume that the tax rate on dividends is 30 percent while capital gains escape taxation.
A firm will pay a \$2 per share dividend 1 year from now, after which it is expected to sell at a price of \$20.

a. Find the current price of the stock.
b. Find the expected before-tax rate of return for a 1-year holding period.
c. Now suppose that the dividend will be \$3 per share. If the expected after-tax rate of return is still 10 percent, and investors still expect the stock to sell at \$20 in 1 year, at what price must the stock now sell?
d. What is the before-tax rate of return? Why is it now higher than in part (b)?

#### Solution Preview

Investors require an after-tax rate of return of 10 percent on their stock investments. Assume that the tax rate on dividends is 30 percent while capital gains escape taxation.

A firm will pay a \$2 per share dividend 1 year from now, after which it is expected to sell at a price of \$20.

a. Find the current price of the stock.

Let the current price be Po
Capital gains= \$20-Po
Dividends= \$2.00
Tax on capital gains= 0%
Tax on dividends= 30%

Thus after tax returns= (\$20-Po) + (1-0.3)x \$2= (\$20-Po) + \$ 1.40=
The investors demand 10% return on their stock investment
Therefore 10% x Po = (\$20-Po) + \$ 1.40
or 1.1 Po = \$ 21.40
or Po= \$21.40 / 1.1 = \$19.45