QF5213 Chap.6 Sensitivity and Break-Even Project Analysis
Sensitivity and Break-Even Project Analysis
Why a single NPV is not the end of the analysis
A discounted cash flow model turns one set of forecasts into one number. That number is only as reliable as the price, cost and volume estimates behind it, and in a new venture those estimates can be wrong by a wide margin. Project analysis sits beside the NPV calculation rather than replacing it.
Its job is to show a decision maker where the forecast is fragile, how much damage a plausible miss would cause, and how far sales could fall before the investment stops earning its cost of capital.
The Capital Budgeting 2 class works through these tools on a single manufacturing project, rebuilding the income statement each time an input changes. That repetition is deliberate.
Every technique in this chapter is the same cash flow equation, revenue less variable cost, fixed cost and tax, plus depreciation added back, solved under a different question.
Sensitivity first, then scenarios
Sensitivity analysis sets each input in turn to a pessimistic value and then an optimistic value, holds every other input at its expectation, and recalculates NPV.
Comparing the spread of results tells you which forecast deserves the most research before money is committed. A convenient summary divides the percentage change in NPV by the percentage change in the input: when that ratio is large, a small forecasting error swamps the base case.
Sensitivity has one weakness that the slides address directly. Real inputs move together.
A weak market lowers volume and pushes prices down at the same time, and a supply shock can raise unit costs across the board. Scenario analysis therefore changes several variables at once, choosing combinations that tell a coherent economic story.
It gives a more realistic picture of a bad year, but it depends on the analyst understanding how the variables interact, and a carelessly built scenario can be less informative than a clean one-variable test.
Break-even: two definitions of losing money
Break-even analysis asks a different question: what is the lowest sales level at which the project still holds up?
Accounting break-even is the volume at which annual profit is zero, so contribution margin just covers fixed cost and depreciation.
It is quick to compute but treats depreciation as full repayment of the investment, ignoring the return that capital could have earned elsewhere.
Financial break-even, also called present value break-even, corrects that by charging the equivalent annual cost of the investment, found by dividing the initial outlay by the annuity factor at the required return.
The after-tax version adds fixed cost net of tax, subtracts the depreciation tax shield, and divides by the after-tax contribution margin. The volume it produces is the point where NPV equals zero, and it is always higher than accounting break-even for any project with a positive discount rate.
Expect multiple choice questions that test whether you can tell the two apart, compute each from a short description, and judge whether a forecast clears the relevant line.
What this chapter covers
- 01
Why one NPV hides forecasting risk
- 02
Running a one-variable-at-a-time sensitivity test
- 03
Measuring NPV response per 1% change in an input
- 04
Building consistent multi-variable scenarios
- 05
Accounting break-even from fixed cost and depreciation
- 06
Financial break-even using equivalent annual cost
- 07
Judging a forecast against the right break-even line
Worked example · free
Accounting and financial break-even for a five-year packaging line
- 2Compute depreciation, the unit contribution margin and accounting break-even.
- 2Find the 5-year annuity factor at 8% and the equivalent annual cost of the outlay.
- 2Combine EAC, after-tax fixed cost and the depreciation tax shield into financial break-even.
- 1Compare the 75,000-unit forecast with both lines and state the decision.
Key terms
- Sensitivity Analysis
- A test that moves one forecast input to its pessimistic or optimistic value while holding all others at expectation, then recalculates NPV.
- Scenario Analysis
- A method that changes several related inputs together so each case describes a coherent economic situation, then values the project under it.
- Forecasting Risk
- The danger that a project is accepted or rejected on cash flow estimates that later prove materially wrong.
- Accounting Break-Even
- The sales volume at which annual accounting profit is zero, equal to fixed cost plus depreciation divided by unit contribution margin.
- Financial Break-Even
- The sales volume at which project NPV equals zero, found by charging the equivalent annual cost of the investment instead of depreciation.
- Equivalent Annual Cost
- A level annual amount whose present value over the project life equals the initial investment, computed as outlay divided by the annuity factor.
- Contribution Margin
- Selling price minus variable cost per unit, the amount each sale contributes toward fixed cost, depreciation and profit.
- Depreciation Tax Shield
- The tax saved each year because depreciation is deductible, equal to annual depreciation multiplied by the tax rate.
Sensitivity and Break-Even Project Analysis FAQ
Why is financial break-even always higher than accounting break-even?
Accounting break-even recovers the investment only through depreciation, which returns the original dollars with no reward for waiting. Financial break-even replaces depreciation with an equivalent annual cost that includes the required return, so more units must be sold each year to cover that extra charge whenever the discount rate is positive.
How do I tell which variable NPV is most sensitive to?
Recalculate NPV with each input at its pessimistic and optimistic values, one input at a time, and compare the spread between the two results. The variable producing the widest spread matters most. Dividing the percentage change in NPV by the percentage change in the input gives a ratio you can compare across inputs.
What is the difference between sensitivity analysis and scenario analysis?
Sensitivity analysis changes one variable while freezing the rest, which isolates its effect but assumes independence. Scenario analysis moves several variables together, such as lower volume with lower prices, to represent a consistent state of the world. It is more realistic, yet only useful if the analyst understands how those inputs are connected.
How do I find break-even sales in dollars when variable cost is a percentage of sales?
Replace the per-unit contribution margin with the contribution ratio, which is one minus the variable cost share. Accounting break-even revenue is fixed cost plus depreciation divided by that ratio. For the financial version, divide EAC plus after-tax fixed cost less the depreciation tax shield by the ratio times one minus the tax rate.
Does tax affect the accounting break-even volume?
No. Profit after tax equals pretax profit multiplied by one minus the tax rate, so setting it to zero simply requires pretax profit to be zero. Tax therefore cancels out. It does matter for financial break-even, where after-tax cash flows, the depreciation tax shield and the after-tax margin all enter the formula.
Exam move
Build one small spreadsheet for a project of your own design with price, variable cost, volume, fixed cost, depreciation, tax and the discount rate as input cells. Add rows that compute annual cash flow, NPV, accounting break-even and financial break-even. Then change each input by plus and minus ten percent, record the NPV, and rank the inputs.
Repeating this until you can predict the ranking before calculating it is the fastest way to master the chapter.
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