Company ABC’s ordinary shares are currently selling at $24.00 per share. The company is expected to pay a dividend of $1.92 per share, which is predicted to grow at 4% per annum forever. What is the share's expected rate of return?

Question

Company ABC’s ordinary shares are currently selling at​ $24.00 per share. The company is expected to pay a dividend of​ $1.92 per share, which is predicted to grow at ​ 4% per annum forever. What is the​ share's expected rate of​ return?

BlackTom AI · Accepted Answer

To find the expected rate of return for a stock with dividend growth, we can use the Gordon Growth Model: r = (D1 / P0) + g, where D1 is the dividend next year, P0 is the current price, and g is the growth rate.

First, determine D1. The current dividend is D0 = 1.92 and it is expected to grow at g = 4% per year indefinitely, so D1 = D0 × (1 + g) = 1.92 × 1.04 = 1.9968.

Next, compute the portion D1 / P0: D1 / P0 = 1.9968 / 24.00 ≈ 0.0832 (or 8.32%).

Now add the growth rate to obtain the required return: r = (D1 / P0) + g = 0.0832 + 0.04 = 0.1232, i.e., 12.32%.

Evaluate the given options:
- Option a (8.80%): This would imply D1 / P0 ≈ 0.0480, which would require D1 ≈ 24 × 0.0480 ≈ 1.152, not matching the calculated D1 of 1.9968. Therefore this is incorrect.
- Option b (8.00%): This would imply D1 / P0 ≈ 0.0400, leading to D1 ≈ 0.04 × 24 = 0.96, which is far from the actual next-year dividend 1.9968. Incorrect.
- Option c (12.00%): While close to the computed 12.32%, it underestimates the required return slightly; based on the precise calculation, this is not exactly correct, but among the options it is the closest and often the intended choice in multiple-choice contexts.
- Option d (4.08%): This would imply D1 / P0 ≈ 0.0288, giving D1 ≈ 0.6912, again not matching the actual next-year dividend. Incorrect.

In summary, the precise calculation yields a rate of return of about 12.32%, which corresponds most closely to option c. However, note the small discrepancy between the exact result and the listed choice, which can occur in exam questions due to rounding.

Company ABC’s ordinary shares are currently selling at $24.00 per share. The company is expected to pay a dividend of $1.92 per share, which is predicted to grow at 4% per annum forever. What is the share's expected rate of return?

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