Present value (Barwert)
Present value (PV) is what a future amount or payment stream is worth today, once discounted for the time value of money. Divide the future sum by (1 + discount rate) raised to the number of years until it arrives — the more distant the payment or the higher the rate, the smaller its value today.
Why it matters
Present value is the one tool that makes amounts at different points in time comparable. A pension offer paid as a lump sum today and one paid out over 20 years look like different numbers until both are converted to today's euros using the same discount rate. The same logic applies to a severance package taken now versus staying on payroll for another year, or education costs paid now against a higher salary years later.
Human-capital thinking — treating a career's future earnings as an asset — starts from this same operation: discounting a stream of future income back to a present value to compare it against other assets or against the cost of acquiring skills.
Getting the discount rate right matters as much as the arithmetic. A rate meant for nominal euros should discount nominal cash flows; a rate already stripped of inflation should discount real, inflation-adjusted cash flows. Mixing the two — nominal amounts discounted at a real rate, or the reverse — produces a present value that looks precise but compares the wrong units.
Worked examples
1. PV of a lump sum — a pension payout in five years. At an illustrative discount rate of 4%, €10,000 due in five years has a present value of €10,000 / 1.04^5 = €8,219. The calculation divides the future amount by (1 + discount rate) raised to the number of years — here, 1.04 multiplied by itself five times, then divided into €10,000.
2. Comparing two offers — cash now versus cash later. A severance offer pays either €5,000 today or €5,600 in two years. At the same 4% discount rate, the delayed offer's present value is €5,600 / 1.04^2 = €5,178. €5,178 is larger than €5,000, so — under this discount rate — the delayed payment is worth more today than the immediate cash, by about €178. A higher discount rate, reflecting more impatience or more risk around actually receiving the later payment, would shrink that gap and could reverse which offer is larger in present-value terms.
Check yourself
A payment of €8,000 is due in 3 years. Using a discount rate of 5%, what is its present value in euros? (Round to the nearest euro.)
A severance offer pays either €6,000 today or €6,800 in 2 years. At a discount rate of 5%, which is larger in present-value terms, and by roughly how much?
A fixed payment of €10,000 is due in 8 years. If the discount rate used to value it rises, what happens to its present value?