ABC Corp has just paid its annual dividend of $1.50 per share, and it is expected that these dividend payments will continue indefinitely. If ABC’s equity cost of capital is 12%, then the value of a share of ABC’s stock is closest to:

Question

BlackTom AI · Accepted Answer

For a stock that pays a constant dividend forever (a perpetuity), the present value equals the constant dividend divided by the required return: P0 = D / r.

Relevant concepts:
- Perpetuity: an infinite stream of identical cash flows.
- Equity cost of capital r is the required return used to discount future dividends.
- If a dividend of $1.50 has just been paid and dividends “will continue indefinitely” at the same amount, the next dividend (D1) is also $1.50. The standard formula uses D1: P0 = D1 / r.

Step-by-step reasoning and calculation:
1. Identify the next dividend: D1 = $1.50 (since the dividend just paid equals the ongoing perpetual dividend).
2. Use the perpetuity formula: P0 = D1 / r.
3. Substitute values: P0 = 1.50 / 0.12.
4. Compute: 1.50 / 0.12 = (150 / 12) cents = 12.5 dollars.

Intermediate arithmetic shown: 1.50 ÷ 0.12 = (1.50 × 100) ÷ (0.12 × 100) = 150 ÷ 12 = 12.5.

Why this is correct:
- The Gordon Growth Model with growth g = 0 reduces to the perpetuity formula P0 = D / r. Because dividends are constant and perpetual, discounting each future $1.50 at 12% yields a sum equal to $1.50/0.12 = $12.50.

Why the other options are incorrect:
- $18.50, $16.50, and $14.50 do not equal the correct perpetuity value 1.50/0.12 = $12.50. They would imply either using an incorrect discount rate, adding extraneous terms, or assuming dividend growth—none of which match the problem’s conditions of a constant $1.50 perpetual dividend and a 12% cost of equity.

Conclusion: The calculated share value is $12.50, which matches the provided correct answer.

ABC Corp has just paid its annual dividend of $1.50 per share, and it is expected that these dividend payments will continue indefinitely. If ABC’s equity cost of capital is 12%, then the value of a share of ABC’s stock is closest to:单项选择题

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