Breakeven Analysis for the FE Exam
Breakeven analysis determines the point at which two alternatives are equally economical, or the point at which a project becomes profitable. These problems appear regularly on the FE exam and combine engineering economics fundamentals with practical decision-making.
What Is Breakeven Analysis?
Breakeven analysis finds the value of a variable (such as production volume, interest rate, usage hours, or project life) at which two alternatives have equal costs or at which revenues equal costs. Below the breakeven point, one alternative is preferred; above it, the other is preferred.
Simple Breakeven: Revenue vs. Cost
The most basic breakeven analysis compares total revenue to total cost:
Total Revenue = Total Cost
Price * Q = Fixed Cost + Variable Cost per Unit * Q
Solving for Q (the breakeven quantity):
Q_breakeven = Fixed Cost / (Price - Variable Cost per Unit)
Where (Price - Variable Cost per Unit) is the contribution margin per unit. Above Q_breakeven, the project is profitable; below it, the project operates at a loss.
Breakeven Between Two Alternatives
When comparing two alternatives that have different fixed and variable costs, the breakeven point is where the total costs are equal:
Fixed Cost_A + Variable Cost_A * Q = Fixed Cost_B + Variable Cost_B * Q
Solving for Q:
Q_breakeven = (Fixed Cost_A - Fixed Cost_B) / (Variable Cost_B - Variable Cost_A)
Below Q_breakeven, the alternative with lower fixed cost is preferred. Above Q_breakeven, the alternative with lower variable cost is preferred.
Make-or-Buy Decisions
A common engineering economics problem: should a company make a component in-house or buy it from a supplier?
- Make option: Higher fixed cost (equipment, setup) but lower variable cost per unit.
- Buy option: Lower fixed cost (no equipment needed) but higher variable cost per unit (purchase price).
Find the breakeven quantity. Below it, buy. Above it, make. Consider also qualitative factors like quality control, delivery reliability, and intellectual property.
Breakeven with Time Value of Money
For more complex problems involving cash flows over time, set the present worth (or annual worth) of two alternatives equal and solve for the unknown variable:
PW_A = PW_B or AW_A = AW_B
The unknown variable might be the annual usage, the interest rate (which gives the rate of return on the incremental investment), or the project life.
Example: Equipment Selection
Machine A costs $50,000, has annual operating costs of $12,000, and lasts 10 years with $5,000 salvage value. Machine B costs $30,000, has annual operating costs of $18,000, and lasts 10 years with $3,000 salvage value. At what interest rate are they equivalent?
Set AW_A = AW_B and solve for the interest rate. This is an incremental rate of return problem.
Sensitivity Analysis
Sensitivity analysis examines how the economic decision changes when input variables change. It answers questions like:
- How much can the initial cost increase before the project becomes uneconomical?
- What is the minimum annual revenue needed to justify the investment?
- How sensitive is the decision to changes in the interest rate?
The approach: vary one input at a time while holding others constant, and observe the effect on the economic measure (PW, AW, ROR, or B/C ratio).
Multiple Alternatives
When comparing three or more alternatives, the breakeven analysis becomes more complex. The approach:
- Compare alternatives pairwise
- Find breakeven points between each pair
- The preferred alternative depends on the value of the variable relative to the breakeven points
- Graphically: plot the total cost of each alternative vs. the variable; the lowest curve at any given value represents the best choice
Payback Period
The payback period is a simplified breakeven analysis that finds how long it takes for an investment to pay for itself:
Payback period = Initial investment / Annual net savings (or revenue)
For uneven cash flows, find the year when cumulative cash flows equal the initial investment.
Limitations of payback period:
- Ignores the time value of money (simple payback)
- Ignores cash flows after the payback period
- Does not measure profitability, only how quickly the investment is recovered
Discounted payback period addresses the first limitation by using present values.
Common FE Exam Problem Types
- Finding the breakeven production volume between two manufacturing methods
- Determining the breakeven interest rate (incremental ROR) between two alternatives
- Make-or-buy decision with given fixed and variable costs
- Finding the minimum usage hours to justify purchasing equipment vs. renting
- Payback period calculations
Problem-Solving Strategy
- Identify the two alternatives being compared
- Identify the variable that determines which alternative is better
- Set the total costs (or economic measures) of the two alternatives equal
- Solve for the breakeven value of the variable
- Determine which alternative is preferred on each side of the breakeven point
Breakeven analysis is a practical application of engineering economics that comes up frequently on the FE exam. The problems are algebraic and follow consistent patterns, making them reliable points with practice.