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 $185, 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 Net % return on each stock for :

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

(i) Pension Fund (pension fund does not pay taxes)

Expected Return on Stock A = { 0 + 10 } / 185

  = 0.05405405405 or 5.41%

Expected Return on Stock B = { 5 + 5 } / 185

  = 0.05405405405 or 5.41%

Expected Return on Stock C = { 10 + 0 } / 185

  = 0.05405405405 or 5.41%

(ii) A corporation paying 21%(0.21) tax on capital gain and tax rate on dividend is 6.3% (0.063)

Expected Return on Stock A = { [0 * (1- 0.063)]+ [10 * (1-0.21) } / 185

  = { 0 + 7.9} / 185

= 0.0427027027 or 4.27%

Expected Return on Stock B = { [5 * (1 - 0.063) + [5 * (1 - 0.21)] } / 185

  = {4.685 + 3.95 } / 185

= 0.04667567567 or 4.67%

Expected Return on Stock C = { [10 * (1 - 0.063)] +[ 0 * (1 - 0.21)]} / 185

  = { 9.37 + 0 } / 185

= 0.05064864864 or 5.06%

(iii) An individual with an effective tax rate of 10% (0.10) on dividends and 5% (0.05) on capital gains

Expected Return on Stock A = { [0 * (1- 0.10)]+ [10 * (1-0.05) } / 185

  = { 0 + 9.5} / 185

= 0.05135135135 or 5.14%

Expected Return on Stock B = { [5 * (1 - 0.10) + [5 * (1 - 0.05)] } / 185

  = {4.5 + 4.75 } / 185

= 0.05 or 5%

Expected Return on Stock C = { [10 * (1 - 0.10)] +[ 0 * (1 - 0.05)]} / 185

  = { 9 + 0 } / 185

= 0.04864864864 or 4.86%

(b.) Calculation of Price of A,B and C

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

Expected Price Stock A = { [0 * (1- 0.40)]+ [10 * (1-0.10) } / 185

= { 0 + 9} / 0.10

= 90

Expected Price Stock B = { [5 * (1- 0.40)]+ [5 * (1-0.10) } / 185

= { 3 + 4.5} / 0.10

= 75

Expected Price Stock C = { [10 * (1- 0.40)]+ [0 * (1-0.10) } / 185

= { 6 + 0} / 0.10

= 60