Finance⏱ 6 min read
What Is Net Present Value (NPV) and How Do You Calculate It?
NPV is the most important concept in investment appraisal — it tells you whether a project will create or destroy value in today's money. Here's the formula, worked examples, and when to use it.
Net Present Value is the foundation of rational investment decision-making. It answers a question that sounds simple but is surprisingly deep: "Is this investment worth making?" The answer depends on understanding that money today is worth more than money in the future.
The Time Value of Money
£1,000 today is worth more than £1,000 in three years, for three compounding reasons:
- Opportunity cost: Money today can be invested and grow
- Inflation: Future money has less purchasing power
- Risk: Future cash flows are uncertain; present cash is certain
To compare cash flows at different points in time, we "discount" future values back to present value using a discount rate.
Present Value of a Future Cash Flow
PV = FV ÷ (1 + r)^n
PV = Present Value
FV = Future Value (cash you'll receive/pay)
r = Discount rate per period
n = Number of periods
Example: What is £10,000 received in 3 years worth today at 8% discount rate?
PV = 10,000 ÷ (1.08)³ = 10,000 ÷ 1.2597 = £7,938
The NPV Formula
NPV = -Initial Investment + Σ [Cash Flow_t ÷ (1 + r)^t]
Where t = year of each cash flow
Decision rule:
NPV > 0: Accept the investment (creates value)
NPV < 0: Reject (destroys value)
NPV = 0: Indifferent (exactly meets hurdle rate)
Worked Example: Equipment Purchase
A business considers buying a machine for £50,000. It will generate £15,000/year for 5 years then be worthless. The company's cost of capital (discount rate) is 10%.
Year 0: −£50,000 (initial outlay)
Year 1: £15,000 ÷ 1.10¹ = £13,636
Year 2: £15,000 ÷ 1.10² = £12,397
Year 3: £15,000 ÷ 1.10³ = £11,270
Year 4: £15,000 ÷ 1.10⁴ = £10,245
Year 5: £15,000 ÷ 1.10⁵ = £9,314
Sum of PVs: £56,862
NPV = £56,862 − £50,000 = +£6,862
Positive NPV → accept the investment.
Choosing the Discount Rate
The discount rate is one of the most consequential — and contested — inputs in any NPV calculation.
- For businesses: Typically the Weighted Average Cost of Capital (WACC) — blends the cost of debt and equity financing
- For personal decisions: Your expected investment return, or the interest rate on debt you'd avoid by not making the investment
- For government projects: A social discount rate, often lower, reflecting intergenerational considerations
Small changes in discount rate create large changes in NPV for long-dated cash flows. A project that looks good at 5% may look terrible at 12%. Always test NPV sensitivity to different discount rate assumptions.
NPV vs IRR
Internal Rate of Return (IRR) is the discount rate that makes NPV exactly zero. It's a useful companion metric but has limitations:
- Projects with irregular cash flows (positive then negative then positive) can have multiple IRRs
- IRR implicitly assumes intermediate cash flows are reinvested at the IRR itself — often unrealistic
- For mutually exclusive projects, NPV is the more reliable decision tool
The best approach: calculate both, but when they conflict, trust NPV.