Present value

Before you rely on it

What to check

State the discount rate and where it came from.

The common error

Where people go wrong with present value

Accepting a lump-sum offer without discounting the alternative stream. The two are only comparable once both sit at the same date, and the offer is usually built assuming nobody does that.

Worked through

Present value in plain numbers

A lottery offers $1,000,000 as $50,000 a year for twenty years, or $600,000 now. Discount the payments at 5%: the present value of the stream is $50,000 × 12.46, about $623,100. At that rate, the annual payments are worth slightly more than the lump sum. At 7% the stream is worth $50,000 × 10.59, about $529,700, and the lump sum wins; the winning choice depends on the discount rate you use, which reflects what you could earn on the money elsewhere and how much you trust the payer. Present value converts a stream over time into a comparable amount today.

Easily confused

Present value and its neighbours

Present value is not the same as future value, net present value or face value. Future value moves money forward in time with growth. Present value moves it back with discounting. NPV subtracts the initial cost from the present value of inflows. Face value is the stated amount on a bond or note, whatever it is worth today. Present value also differs from market value, which is what buyers will pay now, and the two match only if the market uses the same rate and expectations as your calculation.

In real decisions

Where present value turns up

Anyone comparing money at different times uses it: lump sums versus payments, lease versus buy, settlement offers, pensions and structured payouts; companies value projects and acquisitions with it; lenders convert a stream of payments into a loan amount. Investors value bonds and dividends. A calculator does the arithmetic once you supply the amount, rate and time.

Know the edges

Where present value stops being reliable

The result is only as good as the discount rate and the reliability of the cash flows; small changes in the rate move long-dated values a lot. Taxes, inflation and risk of non-payment change the picture, and a present value is a comparison tool, not a market price. Test a few rates, and consider the security of the payments.

Quick answers

What people ask about present value

Why is present value lower than the future amount? Because money today can be invested. You would need less than the future amount now to reach it later. The higher the rate and the longer the wait, the lower the present value.

How do I find the present value of a series of payments? Discount each payment to today and add them, or use the annuity formula for level payments. A calculator does it directly.

What rate do I use for a pension or settlement offer? Think about what you could earn safely on the money and how sure the payments are. Test a few rates to see how the comparison changes.

Is present value the same as market value? No. Market value is what buyers pay. Present value is what the payments are worth under your chosen rate.