Matilda Industries pays a dividend of $2.10 per share and is expected to pay this amount indefinitely. If Matilda's equity cost of capital is 9%, which of the following would be closest to Matilda's stock price?

Question

BlackTom AI · Accepted Answer

We’re given a perpetuity: Matilda pays a fixed dividend of $2.10 per share forever, and the equity cost of capital is 9%. In a perpetuity, the stock price equals the dividend divided by the cost of capital: P = D / r.

Option 1: $14.00. If the price were $14.00, the implied yield would be D/P = 2.10 / 14.00 ≈ 0.150, or 15.0%. That does not match the stated cost of equity of 9%, so this price is inconsistent with the given data.

Option 2: $29.16. Here, the implied yield would be 2.10 / 29.16 ≈ 0.0720, or 7.20%. This is lower than the given 9% cost of equity, so this price would reflect a lower required return than specified, making it inconsistent.

Option 3: $23.33. Using the perpetuity formula P = D / r with D = 2.10 and r = 0.09 gives P = 2.10 / 0.09 = 23.333..., which rounds to $23.33. This price aligns exactly with the given cost of capital and the fixed dividend.

Option 4: $18.66. The implied yield would be 2.10 / 18.66 ≈ 0.1127, or 11.27%. This is higher than 9%, so it does not match the stated cost of equity.

Overall, you compare each option to the fundamental relationship P = D / r for a perpetuity with constant dividends. Values that yield a percentage different from the given 9% indicate inconsistency with the input data. The option that yields exactly 9% with the provided dividend is the one that matches the perpetuity price formula.

Matilda Industries pays a dividend of $2.10 per share and is expected to pay this amount indefinitely. If Matilda's equity cost of capital is 9%, which of the following would be closest to Matilda's stock price?单项选择题

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