If the current risk free-rate is 6%, what should the current price of a stock be if its price and dividend next year are forecast to be $122 and $7, respectively, and its risk premium is 4%.

Question

BlackTom AI · Accepted Answer

The question asks for the present price of a stock given the next-year price, the dividend next year, and the total required return. Keep in mind that the stock’s current price today should be the present value of the next-year cash flow (price plus dividend) discounted at the required return.

Option 1: $70.00
This value would imply a very large discount or a much higher discount rate than the given 10% (6% risk-free plus 4% risk premium). If we discount 129 by 10%, we get 117.27, not 70.00. In other words, this price would underprice the stock relative to the provided forecast cash flows and required return.

Option 2: $110.91
At first glance, this looks like a plausible discounted value, but it corresponds to a discount factor slightly different from 10%. If we solve 129 ÷ (1 + r) = 110.91, we'd get (1 + r) ≈ 1.162, i.e., r ≈ 16.2%, which is not the stated 10% (6% + 4%). Therefore this option mismatches the given risk premium.

Option 3: $117.27
This is the value you get when you apply the correct discounting: price today equals (P1 + D1) divided by (1 + required return). Here, P1 = 122 and D1 = 7, so (122 + 7) = 129. With a required return of 6% + 4% = 10%, the present value is 129 / 1.10 = 117.27. This aligns with the provided inputs.

Option 4: $129.00
This would correspond to not discounting at all, i.e., treating the next-year cash flow as if it were received today. That ignores the time value of money and the required return, so it is inconsistent with the given risk premium and risk-free rate.

2025Fall-ECN3615-01 Final Exam Practice Quiz

If the current risk free-rate is 6%, what should the current price of a stock be if its price and dividend next year are forecast to be $122 and $7, respectively, and its risk premium is 4%.

查看解析

登录即可查看完整答案

类似问题

Which of the following are reasons that you should care about stock valuation (according to the text)?

Assume that your valuations lead to an estimated share price of $39.80. Quizzer’s actual current share price is $37.90. Would you recommend buying or selling shares in Quizzer?

Part 1Compute the price of a share of stock that pays a $5.005.00 per year dividend and that you expect to be able to sell in one year for $3030, assuming you require a 1010% return. The price of the share is $[input]enter your response here . (Round your response to the nearest penny.)

Select the correct alternative regarding stock valuation:

更多留学生实用工具

考试浏览器助手

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