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Present Value

General

Present Value (PV)

The current worth of a future sum of money, discounted at a given rate of return ā€” the foundation of all time-value-of-money calculations.

Definition

Present Value (PV) is the current worth of a future sum of money or stream of cash flows, given a specified rate of return (the discount rate). It answers a fundamental question of time value of money: how much is a future payment worth today?

The core insight is that money today is worth more than the same amount of money in the future, because today's money can be invested and grown. Present value quantifies exactly how much less a future amount is worth today, based on when it will be received and what return could be earned on money invested now.

Present value is the inverse of future value: if future value tells you what money grows to, present value tells you what future money is worth now. Together, PV and FV form the foundation of all financial analysis, loan pricing, bond valuation, investment appraisal, insurance pricing, and retirement planning.

Formula

PV = FV / (1 + r)^t

Where:

  • FV = Future Value (the amount to be received in the future)
  • r = Discount rate per period
  • t = Number of periods

PV of Annuity (fixed equal payments):

PV = PMT Ɨ [1 āˆ’ (1 + r)^(āˆ’n)] / r

Where PMT = periodic payment, n = number of periods

PV of Perpetuity: PV = PMT / r

Worked Example

You are promised ā‚¹5,00,000 in 5 years. If you can earn 10% per annum on alternative investments, what is this promise worth today?

PV = ā‚¹5,00,000 / (1.10)^5 = ā‚¹5,00,000 / 1.6105 = ā‚¹3,10,461

The ā‚¹5 lakh in 5 years is worth only ā‚¹3.10 lakh today at a 10% discount rate.

Verification: ā‚¹3,10,461 invested at 10% per year for 5 years grows to: ā‚¹3,10,461 Ɨ (1.10)^5 = ā‚¹5,00,000 āœ“

Loan application: A 5-year loan of ā‚¹5 lakh at 10% interest has monthly EMIs of ā‚¹10,624. The present value of 60 payments of ā‚¹10,624 discounted at 10%/12 per month equals exactly ā‚¹5 lakh, the loan amount. Use the present value calculator to compute PV for any future cash flow.

Key Things to Know

  • PV is the foundation of bond pricing: A bond's market price = PV of all future coupon payments + PV of the face value repayment at maturity. When interest rates rise, the discount rate increases, PV falls, and bond prices fall, explaining the inverse relationship between interest rates and bond prices.
  • Discount rate sensitivity: Small changes in the discount rate cause large changes in PV for long-dated cash flows. A ā‚¹10 lakh cash flow 20 years from now discounted at 8% = ā‚¹2.15 lakh. At 10% discount rate = ā‚¹1.49 lakh. A 2% change in discount rate cuts the PV by 30%. This sensitivity is why terminal value dominates DCF valuations and why the choice of discount rate is so consequential.
  • Real vs nominal PV: If the future cash flow is expressed in nominal terms (not inflation-adjusted), use a nominal discount rate. If expressed in real terms (inflation-adjusted), use a real discount rate (approximately nominal rate minus inflation rate). Mixing nominal cash flows with a real discount rate, or vice versa, produces incorrect PV estimates.
  • Future value is PV's mirror: PV and FV use the same formula rearranged. FV = PV Ɨ (1 + r)^t discounts PV forward; PV = FV / (1 + r)^t discounts FV backward. The process of calculating PV is called "discounting"; the process of calculating FV is called "compounding." Understanding both is essential for all financial planning.
  • Lump sum vs annuity PV: Calculating the PV of a single lump sum uses the basic PV formula. Calculating the PV of a series of equal payments (like loan EMIs or pension income) uses the annuity PV formula. For irregular cash flows (like project cash flows), calculate PV for each period separately and sum them, this is the basis of NPV analysis.

Related Calculators

Present Value Calculator ā†’Calculate the present value of a future sum. Find what tomorrow's money is worth today using discounted cash flow, for investments and FDs instantly.
Compound Interest Calculator ā†’Calculate how your investment grows with compound interest. Get future value and see the impact of regular contributions ā€” free and instant.
Annuity Calculator ā†’Calculate how much monthly pension your retirement corpus will generate. Enter corpus, interest rate, and duration to see periodic payout and total returns.

Related Terms

Future ValueFuture Value (FV)NPVNet Present ValueIRRInternal Rate of ReturnCompound InterestCompound Interest

Frequently Asked Questions

Present Value (PV) is the current value of a single future cash flow, discounted at a given rate. Net Present Value (NPV) is the sum of the present values of all future cash flows from an investment (both inflows and outflows), including the initial investment as a negative cash flow. NPV = Ī£ PV of inflows āˆ’ Initial Investment. PV is a building block; NPV is the decision metric built from multiple PVs.
The discount rate should reflect the opportunity cost of capital, what return you could earn on the money in an alternative investment of similar risk. Common choices: risk-free rate (10-year G-sec yield, ~7% in India) for zero-risk cash flows; inflation rate (~5ā€“6%) to compute real purchasing-power value; equity required return (10ā€“15%) for evaluating equity investments; WACC for corporate project evaluation. The higher the discount rate, the lower the present value.
A higher discount rate means you expect higher returns from alternative investments. So a future rupee is worth less today, you need less today to grow it to that future amount at the higher rate. Example: ā‚¹1 lakh in 10 years discounted at 8% = ā‚¹46,319 today. Discounted at 12% = ā‚¹32,197 today. The higher discount rate reflects a better alternative, making the future cash flow worth less in present terms.
A perpetuity is a series of equal payments that continue indefinitely (like a preference share dividend or rental income expected to continue indefinitely). PV of Perpetuity = Payment / Discount Rate. A perpetuity paying ā‚¹10,000 per year with an 8% discount rate has a PV of ā‚¹10,000 / 0.08 = ā‚¹1,25,000. This formula also underpins the terminal value calculation in DCF models.
PV analysis compares the cost of buying (PV of all future ownership costs, EMIs, maintenance, taxes) vs renting (PV of all future rent payments). If the PV of renting is lower than the PV of buying, renting may be financially superior. The challenge is choosing the right discount rate and forecasting future rent/property costs accurately. The rent-vs-buy decision also involves non-financial factors (flexibility, security) that PV analysis doesn't capture.