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 $175, 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

Answer :

(a.) Calculation of Expected Return

Expected Return = {[Dividend * (1 - Dividend tax rate)] + [Capital Gain * (1 - Capital Gain tax rate)]} / Current Price

For Pension Fund :

Return on Stock A = {[ 0 * (1 - 0)] + [10 * (1 - 0)]} / 175

= 0.05714285714 or 5.71%

Return on Stock B = {[ 5 * (1 - 0)] + [5 * (1 - 0)]} / 175

= 0.05714285714 or 5.71%

Return on Stock C = {[ 10 * (1 - 0)] + [0 * (1 - 0)]} / 175

=0.05714285714 or 5.71%

For Corporations

Return on Stock A = {[ 0 * (1 - 0.063)] + [10 * (1 - 0.21)]} / 175

= 0.04514285714 or 4.51%

Return on Stock B = {[ 5 * (1 - 0.063)] + [5 * (1 - 0.21)]} / 175

= 0.04934285714 or 4.93%

Return on Stock C = {[ 10 * (1 - 0.063)] + [0 * (1 - 0.21)]} / 175

= 0.05354285714 or 5.35%

For Individual

Return on Stock A = {[ 0 * (1 - 0.10)] + [10 * (1 - 0.05)]} / 175

= 0.05428571428 or 5.43%

Return on Stock B = {[ 5 * (1 - 0.10)] + [5 * (1 - 0.05)]} / 175

= 0.05285714285 or 5.29%

Return on Stock C = {[ 10 * (1 - 0.10)] + [0 * (1 - 0.05)]} / 175

= 0.05142857142 or 5.14%

(b.) Calculation of Stock Price

Stock Price = {[Dividend * (1 - Dividend tax rate)] + [Capital Gain * (1 - Capital Gain tax rate)]} / Yield

Stock Price of Stock A = {[ 0 * (1 - 0.40)] + [10 * (1 - 0.10)]} / 0.10

= 90

Stock Price of Stock B = {[ 5 * (1 - 0.40)] + [5 * (1 - 0.10)]} / 0.10

= 75

Stock Price of Stock C = {[ 10 * (1 - 0.40)] + [0 * (1 - 0.10)]} / 0.10

= 60