An indefinite cash flow payment Show
What is Perpetuity?Perpetuity in the financial system is a situation where a stream of cash flow payments continues indefinitely or is an annuity that has no end. In valuation analysis, perpetuities are used to find the present value of a company’s future projected cash flow stream and the company’s terminal value. Essentially, a perpetuity is a series of cash flows that keep paying out forever. Finite Present Value of PerpetuityAlthough the total value of a perpetuity is infinite, it comes with a limited present value. 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 ExamplesAlthough 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 FormulaHere is the formula: PV = C / RWhere:
Example – Calculate the PV of a Constant PerpetuityCompany “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. Download the Free TemplateEnter your name and email in the form below and download the free template now! Perpetuity CalculatorDownload the free Excel template now to advance your finance knowledge! Perpetuity with Growth FormulaFormula: PV = C / (r – g)Where:
Sample CalculationTaking 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 RateThe growth model is important for some terminal value calculations in the discounted cash flow model. The last, or terminal year, in the DCF model, 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 ResourcesThank you for reading this guide to perpetuities. To help on your journey, these additional CFI resources will be helpful:
What is the present value of $2000 per year perpetuity at an interest rate of 10 %?Answer and Explanation: The calculated present value of the perpetuity is $200,000.
How do you calculate the present value of a perpetuity?The present value of a perpetuity is determined by simply dividing the amount of the regular cash flows by the discount rate. A growing perpetuity includes a growth rate that increases the cash flows received each period going forward.
What is the present value of a perpetuity that pays $100 per year?Using the formula, we get PV of Perpetuity = D / r = $100 / 0.08 = $1250.
What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5 %?present value of perpetuity = annual payment / discount rate. present value of perpetuity = 250 / 5% present value of perpetuity = 5,000.
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