Present Value Calculator

What this calculator tells you

Present value is what a future payment is worth today. A sum promised in five years is worth less than the same sum now, because money available today can be invested and earn a return. This calculator discounts a future amount at a chosen rate to show its value in today's terms.

It is one of the most important ideas in finance. It underlies loan and bond pricing, the valuation of investments and the comparison of payments that arrive at different times.

How the discounting works

The present value equals the future amount divided by one plus the discount rate, raised to the number of years until the payment. The discount rate is the return you could earn on an alternative of similar risk. A higher rate or a longer wait reduces the present value, while a lower rate or a shorter wait raises it.

A worked example

Suppose you are promised 1,000 in five years and your alternative return is 5% a year. Five years at 5% multiplies money by about 1.276. Dividing 1,000 by 1.276 gives a present value of about 783.53. Put another way, 783.53 invested at 5% would grow to about 1,000 in five years, so the two are equivalent at that rate.

Choosing the discount rate

The discount rate is the most important assumption. For a payment that is certain, a low-risk rate, such as the yield on a government bond of the same length, is often used. For a payment that is uncertain, such as a business income stream, a higher rate is appropriate to reflect the risk that the payment does not arrive. Test a range of rates, because the result changes noticeably as the rate moves.

Limits of the calculation

The calculator treats the future amount as certain and the discount rate as fixed. It does not model inflation, which reduces the buying power of the future sum, or taxes, which reduce what you keep. If the payment grows or shrinks over time, the result for a single payment will not capture that pattern. For a stream of payments, the annuity present value calculator is more suitable.

Using present value in everyday decisions

Present value is useful for comparing a lump sum offer with payments spread over time, for judging the cost of waiting for a delayed payment, and for checking a contract that offers a discount for early payment. Compare each option at the same discount rate, because changing the rate can reverse the ranking.

It also helps with long-term planning. Working backwards from a future cost to the amount needed today shows whether a goal is affordable now or depends on future saving.

Using the result

Use present value to compare offers that pay at different times, to decide whether a lump sum or a future payment is worth more today, and to check whether an investment's cost is justified by the cash it returns. Compare the present value with the amount on offer today to see which is larger at your chosen rate.

Choosing between a lump sum and instalments

When a choice is between a lump sum now and payments over several years, the present value at your discount rate shows which is worth more in today's terms. Compare the two using the same rate, and consider the security of each payment. A guaranteed stream may be worth more than a larger lump sum that depends on the payer staying solvent, so the rate should reflect the risk of each option.