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.

类似问题

ABC, Inc. just paid a dividend of $2. ABC expects dividends to grow at 10% annually forever. The return on shares like ABC, Inc. is typically around 12%. What is the most you would pay for ABC’s share?

ALP’s most recent dividend was $2.00 per share and is selling today for $70. The dividend is expected to grow at 7% per year for the foreseeable future. Should you purchase the share if the market return is 10% on investments with comparable risk?

Using a dividend discount model, find the intrinsic value (price at time zero) for a firm whose expected dividend is $1.92 and growth in dividends for year 2, 3, and 4 is 23.2% and constant growth afterwards is 0.54%. The cost of equity is 9.21%. (Answer in 2 decimal places, 6.21 for $6.21).

Using a dividend discount model, find the intrinsic value (price at time zero) for a firm whose expected dividend is $1.37 and growth in dividends for year 2, 3, and 4 is 13.8% and constant growth afterwards is 1.42%. The cost of equity is 6.67%.

AWSM has just paid a dividend of $1.24 and is expected to increase the future dividends at a rate of 3% per year indefinitely. If you, as a shareholder, require 12% per year, what is the current price per share?

How much should you be willing to pay for one share of stock if the company just paid an $0.80 annual dividend (D0), the dividends increase by 4% annually and you require an 8% rate of return?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单