Cougar Corp. has mapped out four years of dividends and is planning on paying $3.00, $5.00, $7.50, and $10.00 a share over the next four years, respectively. After that the dividend will be a constant $2.50 per share per year. What is the market price of this stock if the market rate of return is 15%?

Question

BlackTom AI · Accepted Answer

We start by listing the cash flows and the timing:
D1 = 3.00, D2 = 5.00, D3 = 7.50, D4 = 10.00, and from year 5 onward the dividend is a constant 2.50 per year (a perpetuity).
The required rate of return is 15% (0.15), so we discount at 1.15 per year accordingly.
Option A examines only the present value of the first four dividends and omits the continuing perpetuity, which is why it yields a too-low price. Specifically, the PVs of D1 to D4 are:
- PV(D1) = 3 / 1.15 ≈ 2.609
- PV(D2) = 5 / (1.15)^2 ≈ 3.783
- PV(D3) = 7.5 / (1.15)^3 ≈ 4.932
- PV(D4) = 10 / (1.15)^4 ≈ 5.719
Sum ≈ 2.609 + 3.783 + 4.932 + 5.719 ≈ 17.04. This matches the figure in option A but misses the value of future dividends.
Option B proposes 22.39, which would require either underestimating the dividends or miscomputing the discounting; note that including only four years of dividends without the perpetuity cannot reach 22.39 given the cash flows.
Option C is 26.57, which aligns with the full present value including the perpetuity tail. The value at year 4 of the perpetuity starting in year 5 is P4 = 2.50 / 0.15 = 16.6667. Discounting this back four years gives PV(P4) = 16.6667 / (1.15)^4 ≈ 16.6667 / 1.749 ≈ 9.525. Adding this to the PV of the first four dividends (≈17.04) yields total ≈ 26.57.
Option D of 29.08 would imply a higher PV either from an overestimated tail value or misapplication of the perpetuity formula, which would conflict with the given cash flows and discount rate.
Putting it together, the correct approach is to sum the PVs of D1–D4 and add the PV of the perpetuity beginning in year 5. The computed total price is about 26.57, matching option C.

MSB-250-300-002 Proctored Midcourse Exam 2

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