What Is the Present Value of a $10,000 Perpetuity Discoutned Back to the Present at 11%
What is Perpetuity?
Perpetuity in the financial system is a situation where a stream of cash flow Valuation Free valuation guides to learn the most important concepts at your own pace. These articles will teach you business valuation best practices and how to value a company using comparable company analysis, discounted cash flow (DCF) modeling, and precedent transactions, as used in investment banking, equity research, payments continues indefinitely or is an annuity that has no end. In valuation analysis Valuation Methods When valuing a company as a going concern there are three main valuation methods used: DCF analysis, comparable companies, and precedent transactions , perpetuities are used to find the present value of a company's future projected cash flow stream and the company's terminal value Terminal Value Terminal Value (TV) is the estimated present value of a business beyond the explicit forecast period. TV is used in various financial tools . Essentially, a perpetuity is a series of cash flows that keep paying outforever.
Finite Present Value of Perpetuity
Although the total value of a perpetuity is infinite, it comes with a limited present value Net Present Value (NPV) Net Present Value (NPV) is the value of all future cash flows (positive and negative) over the entire life of an investment discounted to the present. . The present value of an infinite stream of cash flow is calculated by adding up the discounted values of each annuity and the decrease of the discounted annuity value in each period until it reaches close to zero.
An analyst uses the finite present value of perpetuity to determine the exact value of a company if it continues to perform at the same rate.
Real-life Examples
Although perpetuity is somewhat theoretical (can anything really last forever?), classic examples include businesses, real estate, and certain types of bonds.
One example of a perpetuity is the UK's government bond known as a Consol. Bondholders will receive annual fixed coupons (interest payments) as long as they hold the amount and the government does not discontinue the Consol.
The second example is in the real-estate sector when an owner purchases a property and then rents it out. The owner is entitled to an infinite stream of cash flow from the renter as long as the property continues to exist (assuming the renter continues to rent).
Another real-life example is preferred stock, where the perpetuity calculation assumes the company will continue to exist indefinitely in the market and keep paying dividends.
Present Value of Perpetuity Formula
Here is the formula:
PV = C / R
Where:
- PV = Present value
- C = Amount of continuous cash payment
- r = Interest rate or yield
Example – Calculate the PV of a Constant Perpetuity
Company "Rich" pays $2 in dividends annually and estimates that they will pay the dividends indefinitely. How much are investors willing to pay for the dividend with a required rate of return of 5%?
PV = 2/5% = $40
An investor will consider investing in the company if the stock price is $40 or less.
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Perpetuity with Growth Formula
Formula:
PV = C / (r – g)
Where:
- PV = Present value
- C = Amount of continuous cash payment
- r = Interest rate or yield
- g = Growth Rate
Sample Calculation
Taking the above example, imagine if the $2 dividend is expected to grow annually by 2%.
PV = $2 / (5 – 2%) = $66.67
Importance of a Growth Rate
The growth model is important for some terminal value calculations in the discounted cash flow model. The last, or terminal year, in the DCF model DCF Analysis Infographic How discounted cash flow (DCF) really works. This DCF analysis infographic walks through the various steps involved in building a DCF model in Excel. , will be assumed to grow at a constant rate forever. This, in essence, means that the terminal year cash flow is a continuous stream of cash flow.
Additional Resources
Thank you for reading this guide to perpetuities. CFI is the official provider of the Financial Modeling and Valuation Analyst (FMVA)® Become a Certified Financial Modeling & Valuation Analyst (FMVA)® CFI's Financial Modeling and Valuation Analyst (FMVA)® certification will help you gain the confidence you need in your finance career. Enroll today! certification, designed to transform anyone into a world-class financial analyst. To help on your journey, these additional CFI resources will be helpful:
- Valuation Methods Valuation Methods When valuing a company as a going concern there are three main valuation methods used: DCF analysis, comparable companies, and precedent transactions
- Cost of Preferred Stock Cost of Preferred Stock The cost of preferred stock to a company is effectively the price it pays in return for the income it gets from issuing and selling the stock. They calculate the cost of preferred stock by dividing the annual preferred dividend by the market price per share.
- Market Risk Premium Market Risk Premium The market risk premium is the additional return an investor expects from holding a risky market portfolio instead of risk-free assets.
- Debt Schedule Debt Schedule A debt schedule lays out all of the debt a business has in a schedule based on its maturity and interest rate. In financial modeling, interest expense flows
What Is the Present Value of a $10,000 Perpetuity Discoutned Back to the Present at 11%
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