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
.

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.

类似问题

If the expected ROE on reinvested earnings is equal to k, the multistage DDM reduces to

The constant-growth dividend discount model (DDM) can be used only when the growth rate is __________ blank .

Alibaba just paid an annual dividend of $1.42 a share. The firm plans to pay annual dividends of $1.45, $1.50, and $1.53 over the next 3 years, respectively. After that time, the dividends will be held constant at $1.60 per share. What is this stock worth today at a discount rate of 11.7 percent?

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