An investor has a 38 percent ordinary income tax rate and a 20 percent long-term capital gains tax rate. The investor holds stock in a firm that could pay its usual $1 per share dividend or reinvest the cash in the firm. The stock price is currently $30 per share. If the firm does not pay the dividend,the share price will rise. If it pays the dividend,the share price will stay the same. By how much must the share price rise if the dividend is not paid in order to make the investor indifferent between receiving the dividend or not?

Question

Quizplus · Accepted Answer

If the investor chooses to receive the dividend, they will have to pay a 38% tax on the $1 per share, leaving them with only $0.62 ($1 x (1 - 0.38)) per share.

If the investor chooses not to receive the dividend, the share price will rise by an amount that will enable them to sell the shares at the same after-tax price as if they had received the dividend. Therefore, the investor should receive $0.62 after taxes whether they receive the dividend or not.

Assume the original price per share is $p. If the firm does not pay the dividend, the new price per share would be $p'. If the firm pays the dividend, the new price per share would remain at $p.

To find p', we can set up the following equation:

$p' x (1 - 0.20) = (p + 1) x (1 - 0.38)$

Simplifying this equation:

$p' = \frac{0.62p + 0.38}{0.80}$

$p' = 0.775p + 0.475$

Therefore, the share price must rise by $0.775p - p = $0.775 x $30 -$30 = $0.325 to make the investor indifferent between receiving the dividend or not.

Alternatively, we can solve for p' using the present value of the after-tax dividend:

$p' x (1 - 0.20) = (p + 1) x (1 - 0.38) x (1 - 0.20)$

Simplifying this equation:

$p' = 0.78p + 0.60$

Therefore, the share price must rise by $0.78p - p = $0.78 x $30 -$30 = $0.40 to make the investor indifferent between receiving the dividend or not.

Taking the average of the two calculations gives us an estimated share price increase of ($0.325 + $0.40)/2 = $0.3625, which is closest to answer choice C ($0.78).

An Investor Has a 38 Percent Ordinary Income Tax Rate