Which of the following is true about perpetuities?

Question

BlackTom AI · Accepted Answer

We start by restating the question: Which of the following is true about perpetuities? The options are as follows:
Option a: 'All of the above are true statements.'
Option b: 'All else equal, the value of a perpetuity is higher when the periodic cash flow is higher.'
Option c: 'If two perpetuities have the same present value and the same interest rate, they must have the same cash flows.'
Option d: 'All else equal, the value of a perpetuity is higher when the interest rate is lower.'

Now, evaluate each option.

Option b analysis: For a perpetuity, the present value formula is PV = CF / r, where CF is the periodic cash flow and r is the interest rate per period. If r is held constant and CF increases, PV increases linearly. Therefore, all else equal, a higher cash flow yields a higher value. This statement is true.

Option c analysis: If two perpetuities share the same PV and the same r, then their cash flows must satisfy CF = PV × r for each perpetuity. Since PV and r are identical for both, their CF must also be identical. Hence, they must have the same cash flows. This statement is true.

Option d analysis: Again using PV = CF / r, if CF is held constant and r decreases, PV increases. Therefore, all else equal, a lower interest rate leads to a higher value. This statement is true.

Option a analysis: Since options b, c, and d are all true, option a claims that all the above statements are true. Given the conclusions for b, c, and d, this is also a true statement. However, we treat this as part of analysis rather than declaring the final answer directly, per the question’s structure.

Overall, each of the statements b, c, and d is individually true, and the compound option a correctly encompasses them as all being true.

MCD2170 - T2 - 2025 Key Concept 4 Video Quiz

Which of the following is true about perpetuities?

查看解析

登录即可查看完整答案

类似问题

A project generates $100 forever with certainty and cash flows grow at the inflation rate. The nominal interest rate is 4% (real interest rate = 2% and inflation = 2%). Ignore taxes. What is the project’s value?

A bond with unlimited maturity (a perpetuity bond) has a face value of $1,000, and a coupon rate of 5%. If the market interest rate is 10%, what is the current market price of this bond?

You are evaluating a perpetuity that pays $5,000 annually. If the discount rate is 8%, what is the present value of this perpetuity?

The cost of preferred stock is equivalent to the:

A preferred stock pays a dividend of $3.50 in perpetuity. If the return required by shareholders is 11%, what is the price per share for this preferred stock?

National Trucking has paid an annual dividend of $1 per share on its common stock for the past 15 years and is expected to continue paying a dollar per share long into the future. Given this, one share of the firm's stock is:

The Asian Tiger pays a constant annual dividend of $1.18 per share. How much are you willing to pay for one share if you require a 15 percent rate of return?

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