GM is expected to pay a dividend of $2.00 in the coming year. Dividends are expected to grow at the rate of 2% per year. The risk-free rate is 4% and the market risk premium is 5%. GM has a beta of 1.2. The value of the stock should be:

Question

BlackTom AI · Accepted Answer

Using the Gordon Growth Model (constant-growth dividend discount model) together with the CAPM for the required return gives the stock value.

1) Relevant knowledge points and formulas
- CAPM: required return on equity r = r_f + β × (market risk premium).
- Gordon Growth Model: intrinsic value P0 = D1 / (r - g), valid when r > g.
Given: D1 = $2.00, g = 2% = 0.02, r_f = 4% = 0.04, market risk premium = 5% = 0.05, β = 1.2.

2) Step-by-step reasoning and calculations
Step A — compute required return via CAPM:
- β × market risk premium = 1.2 × 0.05 = 0.06 (6.0%).
- r = r_f + β × (market risk premium) = 0.04 + 0.06 = 0.10 (10.0%).

Step B — apply the Gordon Growth Model:
- Ensure r > g: 0.10 > 0.02, so model applies.
- P0 = D1 / (r - g) = $2.00 / (0.10 − 0.02) = $2.00 / 0.08.

Step C — compute the value:
- $2.00 / 0.08 = $25.00.

3) Intermediate arithmetic shown
- 1.2 × 0.05 = 0.06
- 0.04 + 0.06 = 0.10
- 0.10 − 0.02 = 0.08
- 2.00 ÷ 0.08 = 25.00

4) Why this answer is correct
The CAPM gives the appropriate discount rate reflecting the stock’s systematic risk (β = 1.2). Plugging that required return and the constant growth rate into the Gordon formula yields $25.00 as the present value of all future dividends.

5) Why the other multiple-choice options are incorrect
- $40.00 would imply r − g = 2/40 = 0.05 → r = 0.07 (7%), which contradicts the CAPM-implied 10% required return.
- $20.00 implies r − g = 2/20 = 0.10 → r = 0.12 (12%), higher than the CAPM rate.
- $30.00 implies r − g = 2/30 ≈ 0.06667 → r ≈ 8.667%, also inconsistent with CAPM’s 10%.
All three give discount rates inconsistent with the required return derived from the given β and market risk premium.

Conclusion: The correct stock value is $25.00, which matches the provided answer.

GM is expected to pay a dividend of $2.00 in the coming year. Dividends are expected to grow at the rate of 2% per year. The risk-free rate is 4% and the market risk premium is 5%. GM has a beta of 1.2. The value of the stock should be:单项选择题

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