Financial Planning
Time Value of Money: A Worked Present-Value Example
The time value of money means that equal cash amounts at different dates are not directly comparable.
What you will learn
- Calculate present and future value using a stated rate and period.
- Check a discounting calculation by reversing it.
- Separate time discounting from uncertainty about receiving cash.
The time value of money means that equal cash amounts at different dates are not directly comparable. A present-value calculation translates a future cash flow to a stated date using an explicit discount rate. It does not prove the future payment will happen or choose the right rate for your situation.
What is meant by the time value of money?
Money available now can be used now or held for a return, while a future receipt arrives later. OpenStax’s time-value-of-money lesson develops the relationship between cash amount, rate and periods. Keep this timing calculation separate from inflation forecasts, default risk, taxes and investment advice.
For a single amount with a constant rate compounded once per period, future value is FV=PV×(1+r)^n. Rearranging gives PV=FV/(1+r)^n. Use a decimal rate and match the period count to the rate. The formulas here assume the payment occurs at the end of the specified periods.
Discount a fictional two-year payment
Assume a certain teaching payment of $12,100 at the end of year 2 and a supplied 10% annual discount rate. These are invented inputs, not an available investment, forecast or recommended personal rate.
Original present-value calculation
| Step | Calculation | Result |
|---|---|---|
| Two-year factor | (1+0.10)² | 1.21 |
| Present value | $12,100/1.21 | $10,000 |
| One-year growth from present value | $10,000×1.10 | $11,000 |
| Second-year reverse check | $11,000×1.10 | $12,100 |
The reverse check matters. If you discount the amount and then compound it forward with the same rate, dates and convention, you should recover the original future payment, aside from rounding. A failure often means the percentage, period or timing convention changed halfway through.
Change one assumption at a time
The same $12,100 payment under supplied assumptions
| Case | Present-value calculation | Present value |
|---|---|---|
| Two years at 10% | $12,100/(1.10)² | $10,000.00 |
| One year at 10% | $12,100/1.10 | $11,000.00 |
| Two years at 5% | $12,100/(1.05)² | $10,975.06 |
A later receipt has a lower present value at the same positive rate. A higher discount rate also reduces present value for the same future receipt. These are properties of the supplied arithmetic, not a prediction that an investment will earn either rate. Compounding more frequently or discounting several payments requires matching the formula to those different assumptions.
Do not use discounting to manufacture an equity value
A hypothetical equity payout may have an uncertain amount, uncertain date, unfulfilled vesting or settlement conditions, restrictions and a possibility of no payout. Discounting a guessed exit number does not establish its fair value or make it comparable with salary. First state whether the amount is a known contractual cash flow or a conditional scenario.
For a private-equity discussion, keep the timing illustration and probability assumptions in separate panels. Do not quietly use a higher rate to conceal every unknown or claim a present-value calculation has resolved personal tax and investment choices.
Copy the calculation check
- Cash-flow amount, currency and date.
- Present date and number of matching periods.
- Rate per period and compounding convention.
- Formula, unrounded result and rounding rule.
- Reverse check and separately stated uncertainty.
Continue with IRR versus MOIC for a different return-measurement job, or use the financial-model lesson to keep inputs traceable. Finta can keep the reviewed scenario, source materials and follow-up questions connected; it does not certify a valuation.
About this lesson. By Finta Editorial Team. Sources checked November 14,2026. Examples and exercise amounts are fictional. General education, not individualized legal, tax, accounting or investment advice. Confirm actual terms with the responsible company team and qualified advisers.