Question

The expected pretax return on three stocks is divided between dividends and capital gains in the following way:

Stock	Expected Dividend	Expected Capital Gain
A	$0	$10
B	5	5
C	10	0

Required:

a. If each stock is priced at $135, what are the expected net percentage returns on each stock to (i) a pension fund that does not pay taxes, (ii) a corporation paying tax at 21% (the effective tax rate on dividends received by corporations is 6.3%), and (iii) an individual with an effective tax rate of 10% on dividends and 5% on capital gains?

b. Suppose that investors pay 40% tax on dividends and 10% tax on capital gains. If stocks are priced to yield an after-tax return of 10%, what would A, B, and C each sell for? Assume the expected dividend is a level perpetuity.

Answer 1

From the given information we can calculated the desired results as below

Stock	Expected Dividend	Expected Capital Gain	Stock Price
A	$ 0	$ 10	$ 135
B	$ 5	$ 5	$ 135
C	$ 10	$ 0	$ 135

A i) In the first case we have Pension funds on which no tax is paid , so we can calculated the expected net percentage returns on each stock as follows

Expected net percentage returns = (Net Income / Stock price) * 100

Net Income = Expected Dividend + Expected Capital Gain

Stock	Net Income (Expected Dividend + Expected Capital Gain)	Stock Price	Net Percentage Return    (Net Income / Stock price) * 100
A	$ 10	$ 135	7.41%
B	$ 10	$ 135	7.41%
C	$ 10	$ 135	7.41%

As the Net Income from each stock is same and no tax is deducted, so return from each stock is 7.41%.

A ii) In the second case we have corporation which pays 21% tax and 6.3% tax on dividend income , so we can calculated the expected net percentage returns on each stock as follows

Stock	Net Income (Expected Dividend + Expected Capital Gain)	Stock Price	Net Percentage Return    (Net Income / Stock price) * 100
A	$ 0*(1-6.3%) + 10*(1-21%) = 7.9	$ 135	5.85%
B	$ 5*(1-6.3%) + 5*(1-21%) = 8.64	$ 135	6.40%
C	$ 10*(1-6.3%) + 0*(1-21%) = 9.37	$ 135	6.94%

So as per the tax deducted on capital gain which is 21% and on dividend 6.3%, the stock which includes whole dividend income that is stock C has greater net percentage return as against other stocks.

A iii) In the second case we have individual who pays 10% tax on dividend and 5% tax on capital gains , so we can calculated the expected net percentage returns on each stock as follows

Stock	Net Income (Expected Dividend - tax rate) + (Expected Capital Gain - tax rate)	Stock Price	Net Percentage Return    (Net Income / Stock price) * 100
A	$ 0*(1-10%) + 10*(1-5%) = 9.5	$ 135	7.04%
B	$ 5*(1-10%) + 5*(1-5%) = 9.25	$ 135	6.85%
C	$ 10*(1-10%) + 0*(1-5%) = 9.00	$ 135	6.66%

As in case of individual, tax rate is less on capital gain and stock A has only capital gains, so returns from stock A are high from prospective of individual.

B) In this case as the investors pay 40% tax on dividends and 10% tax on capital gains, also return on stock after tax is 10% , We can use the formula used to calculate expected net percentage returns, to find the price of stock A, B and C as follows

Stock Price = (Net Income / Expected returns)

Stock	Net Income (Expected Dividend - tax rate) + (Expected Capital Gain - tax rate)	Net Percentage Return	Stock Price (Net Income / Expected returns)
A	$ 0*(1-40%) + 10*(1-10%) = 9.00	10%	$ 90
B	$ 5*(1-40%) + 5*(1-10%) = 7.50	10%	$ 75
C	$ 10*(1-40%) + 0*(1-10%) = 6.00	10%	$ 60

So, the price of the Stocks A, B and C are $ 90, $ 75 and $ 60.

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