How much are you willing to pay for one share of stock if the company just paid (at t=0) an annual dividend of $1.53, the dividends increase by 5 percent annually, and you require a rate of return of 12 percent?

Question

BlackTom AI · Accepted Answer

Use the Gordon Growth Model (constant-growth dividend discount model): P0 = D1 / (r − g). This model applies when dividends grow at a constant rate g forever and r > g.

Relevant knowledge points:
- D0 is the most recently paid dividend (at t = 0).
- D1 = D0 × (1 + g) is the dividend expected at t = 1.
- For a perpetuity of growing dividends, P0 = D1 / (r − g), provided r > g.

Step-by-step reasoning and calculations:
1. Identify given values: D0 = $1.53, growth rate g = 5% = 0.05, required return r = 12% = 0.12.
2. Compute the next-year dividend: D1 = D0 × (1 + g) = 1.53 × 1.05 = 1.6065.
3. Compute the denominator: r − g = 0.12 − 0.05 = 0.07.
4. Compute the price: P0 = D1 / (r − g) = 1.6065 / 0.07 = 22.95.

Intermediate arithmetic shown: 1.53 × 1.05 = 1.6065; 1.6065 ÷ 0.07 = 22.95.

Why this answer is correct:
- The Gordon Growth formula requires using D1 (the dividend at t = 1). Plugging D1 and the correct r − g gives P0 = $22.95. The assumption r > g (0.12 > 0.05) holds, so the model is valid.

Why the other choices are incorrect:
- $21.86 equals 1.53 / 0.07 (i.e., using D0 instead of D1). That mis-treats timing of the just-paid dividend and underestimates the price.
- $25.74 and $30.45 do not match the correct application of the constant-growth model with these inputs; they would require different r or g assumptions and thus are not consistent with the given data.

Conclusion: The correct value to pay for one share is $22.95, matching the provided answer.

How much are you willing to pay for one share of stock if the company just paid (at t=0) an annual dividend of $1.53, the dividends increase by 5 percent annually, and you require a rate of return of 12 percent?单项选择题

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