Question

A. 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 $145, 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.

Stock	Pension	Investor Corporation	Individual
A	%	%	%
B	%	%	%
C	%	%	%

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. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Stock	Price
A	$
B	$
C	$

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 ) / 145 = 0.0689655 = 6.90%

Expected Return on Stock B = ( 5 + 5 ) / 145 = 0.0689655 = 6.90%

Expected Return on Stock C = ( 10 + 0 ) / 145 = 0.0689655 = 6.90%

(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 ) } ] / 145

  = [ 0 + 7.9 ] / 145 = 5.45%

Expected Return on Stock B = [ { 5 * ( 1 - 0.063 ) } + { 5 * ( 1 - 0.21 ) } ] / 145

  = [ 4.685 + 3.95 ] / 145 = 5.96%

Expected Return on Stock C = [ { 10 * ( 1 - 0.063 ) } + { 0 * ( 1 - 0.21 ) } ] / 145

  = [ 9.37 + 0 ] / 145 = 6.46%

(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 ) } ] / 145

  = [ 0 + 9.5 ] / 145 = 6.55%

Expected Return on Stock B = [ { 5 * ( 1 - 0.10 ) + { 5 * ( 1 - 0.05 ) } ] / 145

  = [ 4.5 + 4.75 ] / 145 = 6.38%

Expected Return on Stock C = [ { 10 * ( 1 - 0.10 ) } + { 0 * ( 1 - 0.05 ) } ] / 145

  = [ 9 + 0 ] / 145 = 6.21%

Stock	Pension	Investor Corporation	Individual
A	6.90%	5.45%	6.55%
B	6.90%	5.96%	6.38%
C	6.90%	6.46%	6.21%

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 ) } ] / 0.10

= [ 0 + 9 ] / 0.10 = 90

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

= [ 3 + 4.5 ] / 0.10 = 75

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

= [ 6 + 0 ] / 0.10 = 60

Stock	Price
A	$ 90
B	$ 75
C	$ 60