Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period. It is the gold-standard method for capital budgeting — a positive NPV means a project adds value.
The NPV Formula
NPV = Σ [Ct / (1 + r)^t] − C₀
Where:
- Ct = Cash flow at time t
- r = Discount rate (cost of capital / required return)
- t = Time period
- C₀ = Initial investment (at t=0)
Worked Example
You are considering a project costing £100,000 upfront, with the following expected cash flows and a 10% discount rate:
| Year | Cash flow | Discount factor (10%) | Present value |
|---|---|---|---|
| 0 | −£100,000 | 1.000 | −£100,000 |
| 1 | £30,000 | 0.909 | £27,273 |
| 2 | £35,000 | 0.826 | £28,926 |
| 3 | £40,000 | 0.751 | £30,052 |
| 4 | £35,000 | 0.683 | £23,905 |
| 5 | £25,000 | 0.621 | £15,523 |
| NPV | +£25,679 |
Decision: NPV is positive → accept the project (it adds £25,679 of value above the required return).
Discount Factor Formula
Discount factor = 1 / (1 + r)^t
| Year | r = 8% | r = 10% | r = 12% |
|---|---|---|---|
| 1 | 0.926 | 0.909 | 0.893 |
| 2 | 0.857 | 0.826 | 0.797 |
| 3 | 0.794 | 0.751 | 0.712 |
| 5 | 0.681 | 0.621 | 0.567 |
| 10 | 0.463 | 0.386 | 0.322 |
NPV Decision Rule
| NPV | Decision |
|---|---|
| > 0 | Accept (adds value) |
| = 0 | Neutral (earns exactly required return) |
| < 0 | Reject (destroys value) |
When comparing mutually exclusive projects, choose the one with the highest positive NPV.
Choosing the Discount Rate
The discount rate should reflect the opportunity cost of capital — typically:
- Company's WACC
- Required rate of return on similar-risk investments
- Hurdle rate set by management
A higher discount rate makes future cash flows worth less today, making long-term projects less attractive.
NPV vs IRR
| Metric | What it gives | Weakness |
|---|---|---|
| NPV | Absolute value added | Doesn't compare scale |
| IRR | Return as a percentage | Can give multiple answers for non-conventional flows |
Use NPV as the primary decision tool; use IRR for communication.
Sensitivity Analysis
Test how NPV changes when inputs vary:
| Scenario | Discount rate | NPV |
|---|---|---|
| Optimistic | 8% | £34,200 |
| Base case | 10% | £25,679 |
| Pessimistic | 12% | £17,400 |
If NPV stays positive across reasonable scenarios, the project is robust.