FinanceLesson 2 of 3

NPV, IRR, and payback period

Formulas

Net present value

NPV=Σ [CFt÷(1+r)^t]−C₀

Accept the project if NPV > 0.

CFt: Cash flow in period t
r: Discount rate (usually WACC)
C₀: Initial investment (at t = 0)

IRR decision rule

Accept if IRR>Required Rate of Return

IRR is the discount rate at which NPV = 0.

IRR: Internal Rate of Return

Part 1 of 1

Net Present Value (NPV)

NPV is the gold standard for investment decisions. It answers: "Does this project create or destroy value?"

NPV = Σ [CFt ÷ (1 + r)^t] − C₀

Discount every future cash flow back to today using the cost of capital (r).
Subtract the upfront investment (C₀).
Decision rule: accept if NPV > 0. A positive NPV means the project earns more than the minimum required return — it creates value.

Why NPV wins over other methods: it accounts for the time value of money, uses all cash flows across the project's life, and produces a result in euros (absolute value created), not just a percentage. When choosing between mutually exclusive projects, always pick the one with the higher NPV — not the higher return percentage.

Worked example

1A project requires €10,000 upfront and returns €6,000 at end of year 1 and €7,000 at end of year 2.
2Discount rate = 10%.
3PV of CF1 = 6,000 ÷ 1.10 = €5,454.55.
4PV of CF2 = 7,000 ÷ 1.21 = €5,785.12.
5NPV = €5,454.55 + €5,785.12 − €10,000 = **+€1,239.67**.
6Accept — the project creates €1,240 of value.

For the exam

Decision Rule: Accept if NPV > 0 (adds absolute monetary value to the firm)
TVM Handling: Fully accounts for time value of money by discounting all future cash flows at WACC
Exam Status: Gold standard criterion; always superior when ranking mutually exclusive projects

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The three financial decisions every firm makes Cost of capital, WACC, and risk