A bank offers a perpetuity that pays $1,000 per year, with the first payment occurring at Year 1 and identical payments each year thereafter.

The interest rate is 10% APR, compounded annually.

What is the perpetuity’s present value today?

Round your final answer to the nearest cent. Enter two decimals, without punctuation e.g. enter 2500.35 for $2,500.3531

Question

A bank offers a perpetuity that pays $1,000 per year, with the first payment occurring at Year 1 and identical payments each year thereafter.

The interest rate is 10% APR, compounded annually.

What is the perpetuity’s present value today?

Round your final answer to the nearest cent. Enter two decimals, without punctuation e.g. enter 2500.35 for $2,500.3531

BlackTom AI · Accepted Answer

Step 1: Identify the cash flow pattern. This is a perpetuity paying a fixed amount of 1,000 every year starting at Year 1 and continuing forever. Step 2: Recall the present value formula for a perpetuity. For a perpetuity with payment PMT and interest rate r (per period), the present value today is PV = PMT / r, provided payments occur at the end of each period and the rate is per period. Step 3: Confirm the rate period alignment. The problem states an APR of 10% compounded annually, which means the effective annual rate is 10% per year, i.e., r = 0.10 per year. Step 4: Apply the formula. Substitute PMT = 1,000 and r = 0.10 into PV = PMT / r, giving PV = 1,000 / 0.10. Step 5: Compute the value. 1,000 divided by 0.10 equals 10,000. Step 6: Consider rounding instruction. Since the result is 10,000.00 exactly, the final rounded value is 10,000.00. Step 7: Final check. The calculation is consistent with perpetuity theory: the present value is the payment amount displaced by the discount rate over an infinite horizon, which yields 10,000 in this case.

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

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