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?单项选择题
A
A. $12.39
B
B. $12.79
C
C. $13.30
D
D. $13.41

Question

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?单项选择题

A

A. $12.39

B

B. $12.79

C

C. $13.30

D

D. $13.41

BlackTom AI · Accepted Answer

Dividend valuation with a terminal perpetuity applies: value = present value of the explicit dividends for years 1–3 plus the present value at t=0 of the perpetuity that begins in year 4.

1) Relevant concepts
- Dividend Discount Model (DDM) for nonconstant dividends: price = sum of discounted future dividends.
- For a constant dividend starting in year 4 (perpetuity), value at t=3 = D4 / r, then discount that back to t=0.
- Discount rate r = 11.7% = 0.117; discount factor (1 + r) = 1.117.

2) Step-by-step reasoning and calculations
- Dividends: D1 = $1.45, D2 = $1.50, D3 = $1.53, from year 4 onward D = $1.60.
- Compute discount factors: (1.117)^1 = 1.117; (1.117)^2 = 1.247689; (1.117)^3 = 1.3936696.

Present values of explicit dividends:
- PV(D1) = 1.45 / 1.117 = 1.298 (rounded)
- PV(D2) = 1.50 / 1.247689 = 1.202 (rounded)
- PV(D3) = 1.53 / 1.3936696 = 1.098 (rounded)

Terminal (perpetuity) value at t=3:
- Value at t=3 = D4 / r = 1.60 / 0.117 = 13.67521368
- Discount this to t=0: PV(terminal) = 13.67521368 / 1.3936696 = 9.813 (rounded)

3) Sum all present values:
- Total PV = PV(D1) + PV(D2) + PV(D3) + PV(terminal)
- Total PV ≈ 1.298 + 1.202 + 1.098 + 9.813 = 13.411 ≈ $13.41

4) Why this answer is correct
The calculation exactly applies the DDM: individually discounting the known near-term dividends and converting the constant later dividends into a perpetuity at t=3, then discounting back. Each arithmetic step follows standard present-value formulas.

5) Why the other options are incorrect
- A ($12.39), B ($12.79), and C ($13.30) are close but result from miscalculation or rounding errors (for example, discounting the perpetuity incorrectly or using an incorrect discount factor). The correct consistent application yields $13.41.