Capital budgeting
Sensitivity and break-even analysis
Find the volume and price at which a project's NPV falls to zero, and see which assumptions matter most.
Learning objectives
- Run a one-at-a-time sensitivity analysis on a project's NPV
- Distinguish cash, accounting and NPV break-even points
- Calculate the break-even volume and price at which NPV is zero
An NPV is built on forecasts, and forecasts are wrong. Before approving a project, ask two questions: which assumptions move the answer most, and how far can they fall before the project destroys value?
Sensitivity analysis changes one assumption at a time and records the NPV. Break-even analysis turns the question around: it finds the value of an assumption (usually volume or price) at which NPV is exactly zero. The gap between the forecast and that break-even is the project's margin of safety.
Q* = [ (EAC − t × D) ÷ (1 − t) + F ] ÷ (P − V), EAC = I ÷ annuity factor
- I
- initial investment; EAC is the annual amount that repays it with a return at r
- D
- annual depreciation (I ÷ life)
- F
- fixed cash costs per year
- P − V
- contribution per unit: price − variable cost
- t
- tax rate
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