How this works
Present value (PV) answers a single question: how much is a guaranteed future sum worth right now? The future has uncertainty, alternative uses for capital, and inflation, so a dollar tomorrow is worth less than a dollar today. The discount rate captures all of that — it's the return you could earn elsewhere on equivalently safe capital.
The formula is PV = FV / (1 + r)^n with the appropriate per-period rate and number of periods. Annual compounding is the textbook default and works fine for back-of-the-envelope work; monthly and daily compounding give slightly higher PV (because more frequent compounding accumulates faster, so a smaller PV can grow to the same FV) but the difference is small at common rates.
Use PV when you need to compare options at different points in time. "Win $1M in 20 years vs $400K today, at a 6% discount rate?" — PV of $1M in 20 years at 6% is $311K, so the $400K today is the better deal. The trick is picking a defensible discount rate. For corporate finance, use the firm's weighted average cost of capital (WACC). For personal finance, use the rate of return you could realistically earn on diversified investments — typically 4–6% real (after inflation) for long horizons. Higher rates penalise the future more aggressively; lower rates make future money look more valuable today.
The formula
Choose the compounding frequency that matches the rate quote. APR/APY of "X% compounded monthly" means m=12 and you should use that.
Example calculation
- $10,000 in 5 years, 6% annual compounding.
- PV = 10000 / 1.06^5 ≈ $7,473.
Frequently asked questions
How do I choose the discount rate?
Use the return you could realistically earn elsewhere on equivalently safe money. For corporate decisions, the firm's WACC. For personal long-term planning, 4–6% real (after-inflation) for diversified equities or a balanced portfolio. For very-short-term cash decisions, current Treasury or savings rates. Higher rates make the future look smaller; lower rates make it look bigger — sensitivity-test by trying ±2 percentage points.
Does compounding frequency change the answer much?
A bit, not a lot, at common rates. At 6% / 10 years: annual gives PV factor 0.5584, monthly 0.5510, daily 0.5489 — ~1.7% spread. The frequency matters more at higher rates and longer horizons. For most planning, annual or monthly is fine; daily only matters for cash management or rate arbitrage.
When is PV more useful than NPV?
PV is for a single future cash flow; NPV (net present value) is for a series of cash flows minus the initial investment. Use PV to value a single bond payment, a settlement offer, or a future windfall. Use NPV when you have an upfront cost and a stream of inflows (a project, a rental property, an annuity). Both share the same discount-rate logic.