Suppose that there are only three types of investors with the following tax rate

Question

Suppose that there are only three types of investors with the following tax rates:
Individuals Corporations Institutions
Dividends 50% 5% 0%
Capital gains 15 35 0
Individuals invest a total of $80 billion in stocks and corporations invest $10 billion. The
remaining stocks are held by the institutions. All three groups simply seek to maximize
their after tax income. These investors can choose from three types of stocks offering the
following pretax payouts:
Low Payout Medium Payout High Payout
Dividends $5 $5 $30
Capital gains 15 5 0
These payoffs are expected to persist in perpetuity. The low-payout stocks have a total
market value of $100 billion, the medium-payout stocks have a value of $50 billion, and
the high-payout stocks have a value of $120 billion.
a) Who are the marginal investors that determine the prices of the stocks?
b) Suppose that this marginal group of investors requires a 12 percent after-tax return.
What are the prices of the low-, medium-, and high-payout stocks?
c) Calculate the after-tax returns of the three types of stocks for each investor group.
d) What are the dollar amounts of the three types of stocks held by each investor group?

Explanation / Answer

a) The marginal investors are the institutions. They set prices on the market because they can switch between available investments. After-tax rate of return for them must be equal regardless which stock they buy. To see why that must be the case, observe that the total value of stocks held by the institutions is $180 billion. Then suppose that the expected rate of return for some class of stocks is higher than 12%. In such situation the institutions would buy only these class of stocks. Because the value of their portfolio is higher then the value of each single class of stocks, the institutions would compete with each other and bid the price of stocks to the level corresponding with 12% rate of return. On the other hand suppose that the expected rate of return for some class of stocks is lower than 12%. If these stocks are low-payout or high-payout that means that their price must fall, because the institutions refuse to participate in such low-yielding investment (market value of these stocks is higher then the value of combined portfolio of individuals and corporations). If these stocks were medium-payout that means that in principle they could have been bought by individuals (they are worth only $50 billion whereas individuals have $80 billion portfolio). But individuals prefer low-payout stocks, which give them higher after-tax rate of return. Without individuals and institutions the price of medium-payout stocks must fall to the level corresponding with 12% rate of return required by the institutions. We see thus that the expected before-tax rate of return from each stock must be 12%. b) Price of low-payout stock: $20/0.12 = $166.67 Price of medium-payout stock: $10/0.12 = $83.33 Price of high-payout stock: $30/0.12 = $250.00 c) For corporations, after-tax return is 12% for each type of stock. For individuals, aftertax returns are: 9.15%, 8.10%, 6.00%. For corporations: 8.70%, 9.60%, 11.40%. d) Individuals hold $80 billion of low-payout stocks, Corporation $10 billion of highpayout. The rest (20:50:110) is held by the institutions.

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