Corporate Finance
NPV and IRR
Net present value discounts a project's cash flows and subtracts the outlay to measure value created.
Definition
Net present value is the sum of a project's future cash flows discounted at the opportunity cost of capital, minus the initial investment. A positive NPV means the project is worth more than it costs and adds value; a negative NPV destroys value.
Because it is expressed in currency rather than as a rate, NPV is additive and directly answers the question a decision-maker cares about: how much value does this create?
Intuition
NPV asks one question: after paying for the capital and the project, is there money left over? If yes, take it.
When to use it
- Choosing between mutually exclusive projects.
- As the primary rule in capital budgeting, with IRR and payback as supporting checks.
When not to use it
- As the sole rule when capital is rationed and projects cannot all be funded: the profitability index helps there.
Formula
Net present value
NPV = Σ [CFₜ ÷ (1 + r)ᵗ] − C₀
Value today of the project's cash flows, net of the outlay.
- CFₜ
- Cash flow in period t
- r
- Discount rate (cost of capital)
- C₀
- Initial investment at time zero
Worked example
A three-year project
Invest 100,000 today; receive 40,000 a year for three years; the cost of capital is 10%.
- 1
Annuity factor
[1 − 1.10⁻³] ÷ 0.10 = 2.486852.
- 2
Present value of inflows
40,000 × 2.486852 = 99,474.
- 3
Subtract the outlay
99,474 − 100,000 = −526.
NPV is about −526. The project very nearly breaks even but destroys a little value at a 10% cost of capital.
Common mistakes
- Discounting the year-one cash flow at time zero.
- Including sunk costs, or ignoring the release of working capital at the end.
- Using one discount rate for projects of very different risk.
How it connects
is an advanced form of
The source extends the target once the basics are secure.
- Time value of money: NPV applies time value to a whole project.
requires
Learn the source first; the target assumes it.
- Time value of money: You must be able to discount before you can compute NPV.
relates to
Useful to study together, in either order.
is used in
The source appears as an input to the target.