Question

Suppose that there are just three types of investors with the following tax rates:

	Individuals				Corporations				Institutions
Dividends	35%				20%				0%
Capital gains	18				8				0

Individuals invest a total of $81.5 billion in stock and corporations invest $11.80 billion. The remaining stock is held by the institutions. All three groups simply seek to maximize their after-tax income.

These investors can choose from three types of stock offering the following pretax payouts per share:

	Low Payout				Medium Payout				High Payout
Dividends	$8			$8					$35
Capital gains	18			8					0

These payoffs are expected to persist in perpetuity. The low-payout stocks have a total market value of $101.5 billion, the medium-payout stocks have a value of $51.5 billion, and the high-payout stocks have a value of $121.5 billion.

a. Suppose that this marginal group of investors requires an after-tax return of 12%. What are the prices of the low-, medium-, and high-payout stocks? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Price of low-payout stock	$
Price of medium-payout stock	$
Price of high-payout stock	$

b. Calculate the after-tax returns of the three types of stock for each investor group. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

	Institutions	Individuals	Corporations
Low-payout stock	%	%	%
Medium-payout stock	%	%	%
High-payout stock	%	%	%

c. What are the dollar amounts of the three types of stock held by each investor group? (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.)

	Institutions	Individuals	Corporations
Low-payout stock	$	$	$
Medium-payout stock	$	$	$
High-payout stock	$	$	$

Answer 1

Answer:

a. Suppose that this marginal group of investors requires an after-tax return of 12%. then ,  the prices of the low-, medium-, and high-payout stocks be calculated as follows :

It is given that the payoffs are expected to persist in perpetuity , and expected return after tax is 12 %

Hence, market price per share calculated as = Dividend + capital gain Payoff / expected return

Note : As the tax rate varies as per investor and there is no common or marginal tax rate is given Hence, we do not consider tax on the returns and therefore we does not deduct tax in the calculation

Particulars	Calculations	Amount $
Price of low-payout stock	= $(8 +18) / 12%	$ 216.67
Price of medium-payout stock	= $( 8 +8 ) / 12%	$ 133.33
Price of high-payout stock	= $(35 +0) / 12%	$ 291.67

b. after-tax returns of the three types of stock for each investor group :

after-tax returns = (after tax Dividend + after tax capital gain ) / price per share x 100

Particulars	Institutions	Individuals	Corporations
Low-payout stock	= [ ( $ 8 x ( 1 - 0% ) ) + ( $18 x (1 - 0% ) ) ] /  $ 216.67 x 100 = $ 26 /  $ 216.67 x 100 = 12.00 %	= [ ( $ 8 x ( 1 - 35% ) ) + ( $18 x (1 - 18% ) ) ] / $ 216.67 x 100 = $ 19.96 /  $ 216.67 x 100 = 9.21%	= [ ( $ 8 x ( 1 - 20% ) ) + ( $18 x (1 - 8% ) ) ] / $ 216.67 x 100 = $ 22.96 / $ 216.67 x 100 = 10.60%
Medium-payout stock	= [ ( $ 8 x ( 1 - 0% ) ) + ( $8 x (1 - 0% ) ) ] / $ 133.33 x 100 = $ 16 / $ 133.33 x 100 = 12.00%	= [ ( $ 8 x ( 1 - 35% ) ) + ( $8 x (1 - 18% ) ) ] /  $ 133.33 x 100 = $ 11.76 /  $ 133.33 x 100 = 8.82%	= [ ( $ 8 x ( 1 - 20% ) ) + ( $8 x (1 - 8% ) ) ] / $ 133.33 x 100 = $ 13.76 / $ 133.33 x 100 = 10.32%
High-payout stock	= [ ( $ 35 x ( 1 - 0% ) ) + ( $0 x (1 - 0% ) ) ]  /$ 291.67 x 100 = $ 35 /  $ 291.67 x 100 = 12%	= [ ( $ 35 x ( 1 - 35% ) ) + ( $ 0 x (1 - 18% ) ) ] /  $ 291.67 x 100 = $ 22.75 /  $ 291.67 x 100 = 7.80%	= [ ( $ 35 x ( 1 - 20% ) ) + ( $0 x (1 - 8% ) ) ] / $ 291.67 x 100 = $ 28.00 / $ 291.67 x 100 = 9.60%

c. the dollar amounts of the three types of stock held by each investor group are :

dollar amounts of the three types of stock held by each investor group = Total Market cap x percentage of shares held by investor group

Particulars	Institutions	Individuals	Corporations
Low-payout stock	= $101.50 billion x 6.70 % = $ 6.80 billion	= $101.50 billion x 81.50% = $ 82.72 billion	= $101.50 billion x 11.80 % = $ 11.98 billion
Medium-payout stock	= $51.50 billion x 6.70 % = $ 3.45 billion	= $51.50 billion x 81.50  % = $ 41.97 billion	= $51.50 billion x 11.80 % = $ 6.08 billion
High-payout stock	= $121.50 billion x 6.70 % = $ 8.14 billion	= $121.50 billion x 81.50 % = $ 99.02 billion	= $121.50 billion x 11.80 % = $ 14.34 billion

Working :

1. percentage of holding :

Total Capital $ 100 billion

percentage of share : Investment in stock / Total Capital x 100

Individual = ( $ 81.50 billion / $ 100 billion ) x 100 = 81.50 %

Corporations = ($ 11.80 billion / $ 100 billion ) x 100 = 11.80 %

Institutions = ( $ 100 billion - $ 81.50 billion - $ 11.80 billion ) / $ 100 billion x 100 = 6.70%