Glenhill Co. is expected to maintain a constant 3.8% growth rate in its dividends indefinitely. If the company has a dividend yield of 5.6%, what is the required return on the company's stock?

Question

BlackTom AI · Accepted Answer

Required return r equals the dividend yield plus the growth rate: r = (D1/P0) + g.

Relevant concepts: The Gordon (constant growth) dividend-discount model gives P0 = D1 / (r − g). Dividing both sides by P0, the dividend yield is D1/P0, so rearranging yields r = (D1/P0) + g. Here the dividend yield is given directly and the growth rate is constant, so add them.

Step-by-step calculation:
1. Dividend yield = 5.6% = 0.056 (in decimal form).
2. Growth rate g = 3.8% = 0.038.
3. Required return r = dividend yield + g = 0.056 + 0.038.
4. r = 0.094 in decimal form.
5. Convert to percent: r = 0.094 × 100% = 9.4%.

Why this is correct: The dividend yield represents the D1/P0 term in the Gordon model; to get the total expected return required by investors you must add the expected growth in dividends. This yields 9.4%, which is the required return that satisfies P0 = D1/(r − g).

Why the other choices are wrong:
- 1.8%: This equals 5.6% − 3.8%, a mistaken subtraction; it confuses yield and required return.
- 1.47%: Not consistent with any correct rearrangement; likely a computational error.
- 21.28%: Far too large; not derived from adding yield and growth and likely a miscalculation.
- 11.2%: This is 2× the dividend yield (or another incorrect manipulation); it does not follow r = yield + g.

Conclusion: Using r = dividend yield + g gives r = 5.6% + 3.8% = 9.4%, which matches the provided correct answer (9.4%).

Glenhill Co. is expected to maintain a constant 3.8% growth rate in its dividends indefinitely. If the company has a dividend yield of 5.6%, what is the required return on the company's stock?单项选择题

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