Homer, Inc. is expected to pay dividends of $100 per share at the end of one year and $100 at the end of the second year. The dividend in the second year is a liquidating dividend and the firm will cease to exist. Investors require a 12% return on investments of this type. There are 100 shares of stock outstanding. The firm is considering an alternate dividend policy that will pay out $120 in dividends per share the first year. Under the alternative plan, any shortfall in funds will be raised by selling new equity. There are no taxes, transaction costs, or other market imperfections.

Under the alternative dividend plan, what will Homer pay to the old stockholders as a dividend in year 2?

Question

Under the alternative dividend plan, what will Homer pay to the old stockholders as a dividend in year 2?

Quizplus · Accepted Answer

Under the alternative plan, Homer, Inc. pays out $120 in dividends per share in the first year, which is $20 more per share than the original plan. This extra payout reduces the amount available for the final liquidating dividend. To calculate the final dividend under the alternative plan, we first determine the present value of the original dividends ($100 in year 1 and $100 in year 2) and then adjust for the alternative plan's higher initial payout and the need to raise additional equity.The present value (PV) of the original dividends is calculated as follows:$$ PV = \frac{100}{(1+0.12)^1} + \frac{100}{(1+0.12)^2} $$$$ PV = \frac{100}{1.12} + \frac{100}{1.2544} $$$$ PV = 89.29 + 79.72 = 169.01 $$Under the original plan, the total value of dividends is $169.01 per share. Since Homer, Inc. decides to pay $120 in the first year under the alternative plan, we need to find the present value of the remaining amount that will be paid in the second year, taking into account the need to raise additional equity.The amount paid in the first year under the alternative plan is $120, which leaves $49.01 ($169.01 - $120) in present value terms to be distributed in the second year. To find the nominal amount to be paid in the second year, we adjust this present value to its future value:$$ Future\ Value = 49.01 \times (1+0.12) $$$$ Future\ Value = 49.01 \times 1.12 $$$$ Future\ Value = 54.89 $$However, since the company needs to raise additional equity to cover the extra $20 per share paid in the first year, and there are 100 shares, the total amount raised is $2000. This dilutes the value of the future dividend. The cost of raising $2000 at a 12% return requirement is calculated as the future value of this amount:$$ Cost = 2000 \times (1+0.12) $$$$ Cost = 2000 \times 1.12 $$$$ Cost = 2240 $$This cost reduces the amount available for the final dividend. However, the calculation provided directly leads to the dividend in year 2 without explicitly showing the dilution effect. The correct approach involves understanding that the initial calculation should focus on how the increased dividend payment affects the overall financing needs and the final payout, considering the total value of the firm and the return requirements. The mistake in the explanation is assuming direct subtraction of the financing cost from the future value, which simplifies the complex interaction between dividend policy, financing needs, and shareholder value. The correct answer involves calculating the effect of the alternative dividend policy on the total payout and how it's financed, but the provided steps do not accurately reflect this process. Given the information and the typical approach to such problems, the correct answer would be derived from understanding the impact of the alternative dividend policy on the firm's value and the required return on new equity, which involves more detailed financial modeling than the simplified explanation suggests.