Problem 16-30 Dividends and taxes

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

Individuals Corporations Institutions
Dividends 50 % 15 % 0 %
Capital gains 15 45 0

Individuals invest a total of $81.8 billion in stock and corporations invest $12.16 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:

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Low Payout Medium Payout High Payout
Dividends $ 5 $ 5 $ 34
Capital gains 15 5 0

These payoffs are expected to persist in perpetuity. The low-payout stocks have a total market value of $101.8 billion, the medium-payout stocks have a value of $51.8 billion, and the high-payout stocks have a value of $121.8 billion.

  1. Who are the marginal investors that determine the prices of the stocks?
  2. Suppose that this marginal group of investors requires an after-tax return of 15%. What are the prices of the low-, medium-, and high-payout stocks?
  3. Calculate the after-tax returns of the three types of stock for each investor group.
  4. What are the dollar amounts of the three types of stock held by each investor group?

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