Ace Frisbee Corporation produces a good that is very mature in the firm's product life cycles. Ace Frisbee Corporation is expected to pay a dividend in year 1 of $3, a dividend in year 2 of $2, and a dividend in year 3 of $1. After year 3, dividends are expected to decline at the rate of 2% per year. An appropriate required return for the stock is 8%. Using the multistage DDM, the stock should be worth __________
blank
today.

Question

Ace Frisbee Corporation produces a good that is very mature in the firm's product life cycles. Ace Frisbee Corporation is expected to pay a dividend in year 1 of $3, a dividend in year 2 of $2, and a dividend in year 3 of $1. After year 3, dividends are expected to decline at the rate of 2% per year. An appropriate required return for the stock is 8%. Using the multistage DDM, the stock should be worth __________
blank
 today.

BlackTom AI · Accepted Answer

The dividend discount model (DDM) values a stock as the present value of all expected future dividends. For a multistage case, discount the explicit dividends in early years and add a terminal (perpetuity) value for dividends after the explicit period using the Gordon growth formula.

1) Relevant concepts
- Present value (PV) of expected dividends using required return r.
- Terminal (horizon) value at the end of the explicit period: P3 = D4 / (r − g), where D4 is the dividend in year 4 and g is the perpetual growth rate (here g = −2% = −0.02).

2) Step-by-step reasoning and 3) intermediate calculations
Given: D1 = 3, D2 = 2, D3 = 1, g = −0.02, r = 0.08.
Compute D4 = D3 × (1 + g) = 1 × 0.98 = 0.98.
Terminal value at t = 3: P3 = D4 / (r − g) = 0.98 / (0.08 − (−0.02)) = 0.98 / 0.10 = 9.8.

Discount factors: (1.08)^1 = 1.08; (1.08)^2 = 1.1664; (1.08)^3 = 1.259712.

PV of individual items:
- PV(D1) = 3 / 1.08 = 2.7777778
- PV(D2) = 2 / 1.1664 = 1.715049
- PV(D3) = 1 / 1.259712 = 0.793832
- PV(P3) = 9.8 / 1.259712 = 7.779717

Sum: 2.7777778 + 1.715049 + 0.793832 + 7.779717 = 13.066376 ≈ $13.07.

4) Why this answer is correct
The calculation explicitly discounts each known dividend and the correct terminal value using the negative long-term growth rate (−2%). The terminal value formula uses r − g = 0.08 − (−0.02) = 0.10, producing P3 = 9.8; discounting that and the three dividends yields the present value $13.07.

5) Why the other options are incorrect
- $18.78: Matches the result if one mistakenly used a +2% long-term growth instead of −2%, producing a much larger terminal value (D4 = 1.02, P3 = 17) and thus a much higher total.
- $18.25: Likely arises from arithmetic or discounting errors (e.g., miscomputing discount factors or failing to discount the terminal value correctly).
- $13.58: Close but too high; indicates a small rounding or arithmetic mistake in discounting one of the components.

6) Conclusion
The correct present value, computed by discounting D1–D3 and the properly computed terminal value with g = −2%, is $13.07, which matches the provided answer.

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