Why Later Money Is Worth Less
A dollar today can be invested; a dollar next year cannot. That single fact — not inflation, though inflation compounds it — is why future amounts must be discounted before they can be compared with present ones:
PV = FV / (1 + r)n
Present value is the mirror image of compounding. Where future value multiplies forward, present value divides back.
Present Value Chart
What $100,000 received in the future is worth today:
| Years away | 3% | 5% | 6% | 8% | 10% |
|---|---|---|---|---|---|
| 1 | $97,087 | $95,238 | $94,340 | $92,593 | $90,909 |
| 5 | $86,261 | $78,353 | $74,726 | $68,058 | $62,092 |
| 10 | $74,409 | $61,391 | $55,839 | $46,319 | $38,554 |
| 20 | $55,368 | $37,689 | $31,180 | $21,455 | $14,864 |
| 30 | $41,199 | $23,138 | $17,411 | $9,938 | $5,731 |
Read the bottom-right corner: at a 10% discount rate, $100,000 promised in thirty years is worth under $6,000 today. This is why long-dated promises — pensions, structured settlements, lottery annuities — are worth so much less than their advertised totals.
The Discount Rate Is the Judgement Call
Everything in a present value calculation is arithmetic except the rate, which is an opinion about opportunity cost and risk. Common choices:
- Risk-free rate (Treasury yield) for certain cash flows such as government payments.
- Your borrowing rate when the alternative use of the money is repaying debt.
- Expected portfolio return when the alternative is investing.
- Weighted average cost of capital for corporate projects.
Because the rate is exponentiated, small differences matter enormously over long periods. Two analysts using 6% and 8% will value a thirty-year stream almost twice apart.
Annuities: a Stream Rather Than a Sum
When the money arrives as a series of equal payments, each is discounted by its own period and summed. An ordinary annuity pays at the end of each period; an annuity due pays at the beginning, which is worth exactly one period's interest more. Rent and insurance premiums are annuities due; loan payments and most bond coupons are ordinary annuities.
Where It Is Used
Lump-sum-versus-payments decisions in pensions and lottery wins, bond pricing, lease-versus-buy analysis, legal settlement valuation, and every discounted cash flow model in corporate finance. In each case the question is the same: what is this future money worth in terms I can compare with money I have now?
Frequently Asked Questions
What discount rate should I use?
The return you could reliably earn on the money instead. For a household decision, that is usually the rate on debt you could repay, or a conservative long-run portfolio return of 5–7%.
Is present value the same as net present value?
No. Present value discounts inflows. Net present value subtracts the initial cost from that figure, so a positive NPV means the investment beats the discount rate.
Does present value account for inflation?
Only if you build it into the rate. Discount nominal cash flows at a nominal rate, or real (inflation-adjusted) cash flows at a real rate — never mix the two.