Each of two stocks, A and B, is expected to pay a dividend of $7 in the upcoming year. The expected growth rate of dividends is 6% for both stocks. You require a return of 10% on stock A and a return of 12% on stock B. Using the constant-growth DDM, the intrinsic value of stock A __________
blank
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Question

BlackTom AI · Accepted Answer

Using the Gordon (constant-growth) dividend discount model: P0 = D1 / (r − g). Here D1 = $7 and g = 6% for both stocks, so the only difference is the required return r.

1. Relevant knowledge points and concepts
- Constant-growth DDM (Gordon growth model): intrinsic price equals next year’s dividend divided by the difference between required return and growth rate, P0 = D1/(r − g).
- For fixed D1 and g, P0 is inversely related to the required return r: a higher r yields a smaller P0, all else equal.

2. Complete reasoning process step by step
- Compute P0 for stock A using rA = 10% (0.10) and g = 6% (0.06).
- Compute P0 for stock B using rB = 12% (0.12) and g = 6% (0.06).
- Compare the two prices.

3. Calculations with intermediate steps
- For stock A: P_A = 7 / (0.10 − 0.06) = 7 / 0.04.
- 7 / 0.04 = 7 ÷ 0.04 = 175.00.
- For stock B: P_B = 7 / (0.12 − 0.06) = 7 / 0.06.
- 7 / 0.06 = 7 ÷ 0.06 ≈ 116.6667.
- Difference: P_A − P_B = 175.00 − 116.6667 ≈ 58.3333.

4. Why the correct answer is correct
- Because both stocks have identical next-year dividends and identical growth rates, the model shows the stock with the lower required return (stock A at 10%) has a larger present value. Mathematically, a smaller denominator (r − g) produces a larger price. Therefore, stock A’s intrinsic value is higher than stock B’s.

5. Why the other options are incorrect
- “The same as” is wrong because different required returns produce different denominators (0.04 vs. 0.06), so prices differ.
- “Will be less than” is wrong because stock A has the lower required return, which increases its DDM price.
- “Cannot be determined” is wrong because all necessary inputs (D1, g, r for both stocks) are provided and the DDM gives unique prices.

6. Conclusion confirming the provided answer
- Calculations show P_A = $175.00 and P_B ≈ $116.67, so the intrinsic value of stock A will be higher than the intrinsic value of stock B, confirming the provided answer.

Similar Questions

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