The present value (PV) of a perpetuity refers to the current worth of an infinite stream of uniform payments. In economics and finance, it is closely related to several entities: interest rate, cash flow, duration, and annuity. The PV of a perpetuity represents the initial capital required to generate a constant stream of income over an indefinite period, assuming a constant interest rate and no growth in cash flow.
Structure of the Present Value of a Perpetuity
The present value (PV) of a perpetuity is the current value of a stream of cash flows that will continue forever. It is calculated as the present value of an infinite geometric series. The formula for the PV of a perpetuity is:
PV = C / r
where:
- C is the annual cash flow
- r is the annual interest rate
For example, if you have a perpetuity that pays $100 per year and the annual interest rate is 5%, the PV of the perpetuity would be:
PV = $100 / 0.05 = $2,000
Considerations
- The PV of a perpetuity is inversely proportional to the interest rate. This means that the higher the interest rate, the lower the PV of the perpetuity.
- The PV of a perpetuity is directly proportional to the annual cash flow. This means that the higher the annual cash flow, the higher the PV of the perpetuity.
Table of Present Value Factors
The present value factor is a multiplier that is used to calculate the PV of a perpetuity. The present value factor for a given interest rate can be found in a table of present value factors.
The following table shows the present value factors for different interest rates:
| Interest Rate | Present Value Factor |
|---|---|
| 5% | 20 |
| 10% | 10 |
| 15% | 6.67 |
| 20% | 5 |
Example
Let’s say you are considering purchasing a perpetuity that pays $1,000 per year. The interest rate is 10%. The PV of the perpetuity would be:
PV = $1,000 x 10 = $10,000
The present value factor for an interest rate of 10% is 10. This means that you would be willing to pay $10,000 for the perpetuity.
Question 1:
What is the present value of a perpetuity?
Answer:
The present value of a perpetuity is the current worth of an infinite stream of equal payments made at regular intervals.
Question 2:
How is the present value of a perpetuity calculated?
Answer:
The present value of a perpetuity is calculated by dividing the annual payment by the discount rate.
Question 3:
What factors affect the present value of a perpetuity?
Answer:
The present value of a perpetuity is affected by the annual payment, the discount rate, and the length of time for which the payments will be made.
So, there it is – a quick and dirty intro to the PV of a perpetuity. Hopefully, it’s given you a better understanding of this important financial concept. If you’re still feeling a bit confused, don’t worry – there are plenty of resources available online that can help you learn more. And be sure to check back in with us later for more finance-related articles. We’ll be here when you need us. Thanks for reading!