What is present value?
Present value (PV) is the current value of a future cash flow, discounted at a rate that reflects the time value of money and the risk of the cash flow. PV is the foundation of every modern valuation method — DCF, NPV, IRR, bond pricing, lease accounting — and the lens through which long-dated cash streams are compared on a like-for-like basis.
Formula
Present value of a single future cash flow:
PV = CF ÷ (1 + r)^n
where CF is the cash flow received at time n and r is the periodic discount rate. For a stream of cash flows, PV is the sum of each cash flow discounted to today.
What the discount rate represents
- Time value: a dollar today is worth more than a dollar next year because it can be invested.
- Risk premium: uncertain future cash flows require higher discount rates than certain ones.
- Opportunity cost: the return available on alternative investments of similar risk.
Common discount rates: WACC for corporate cash flows, equity cost of capital for shareholder returns, risk-free rate (government bond yield) for low-risk flows.
PV vs. related concepts
- PV vs. NPV (net present value): NPV is PV of inflows minus PV of outflows — a project’s net economic gain.
- PV vs. future value (FV): FV is what a present amount grows to; PV reverses the calculation.
- PV vs. terminal value: terminal value is the PV at a specific future date of all subsequent cash flows; common in DCF.
Where founders meet PV
In LTV modelling: long-dated customer cash flows should be discounted, not summed nominally — a 60-month LTV undiscounted overstates value by 20–40% depending on rate. In option valuation: stock options are valued using Black-Scholes, which is built on discounted expected payoffs. In lease accounting: IFRS 16 requires lease liabilities to be measured at PV of future lease payments.
Do: apply a sensible discount rate to multi-year cash flow streams in LTV, valuation and capital allocation models; document the rate assumption.
Don’t: use undiscounted future cash flows for any decision involving inter-temporal comparison — it systematically over-rewards distant uncertain returns.