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 $110, 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 15% on dividends and 10% on capital gains?

b. Suppose that investors pay 50% tax on dividends and 20% tax on capital gains. If stocks are priced to yield an after-tax return of 8%, what would A, B, and C each sell for? Assume the expected dividend is a level perpetuity.

Answer 1

a) We have to calculate expected returns. We can calculate it by the following formula,

Net Return=(Dividend×(1−Dividend Tax ))+(Capital Gain×(1−Capital Gain Tax)) / Price

1) Pension Fund

A = 10 * (1 - 0) / 110 = 9.09%

B = (5 * (1 - 0) + 5 * (1 - 0)) / 110 = 9.09%

C = 10 * (1 - 0) / 110 = 9.09%

2) Corporations

A = (0 * (1 - 0.063) + 10 * (1 - 0.21)) / 110 = 7.18%

B = (5 * (1 - 0.063) + 5 * (1 - 0.21)) / 110 = 7.85%

C = (10 * (1 - 0.063) + 0 * (1 - 0.21)) / 110 = 8.51%

3) Individual

A = (0 * (1 - 0.15) + 10 * (1 - 0.10)) / 110 = 8.18%

B = (5 * (1 - 0.15) + 5 * (1 - 0.10)) / 110 = 7.95%

C = (10 * (1 - 0.15) + 0 * (1 - 0.10)) / 110 = 7.72%

b) Computation of price of the stock

We can calculate the price of the stock by the following formula,

Price = (Dividend×(1−Dividend Tax))+(Capital Gain×(1−Capital Gain Tax)) / Yield

A = (0 * (1 - 0.50) + 10 * (1 - 0.20)) / 0.08 = $100

B = (5 * (1 - 0.50) + 5 * (1 - 0.20)) / 0.08 = $81.25

C = (10 * (1 - 0.50) + 0 * (1 - 0.20)) / 0.08 = $62.5

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