1. Breakeven & Payback

2. Fixed and variable costs $ o utput per period total cost fixed cost variable cost

3. “Classical” breakeven analysis (from microeconomics) $ output/period breakeven total revenue total cost

4. To reduce the breakeven quantity Only three variables: reduce fixed cost indirect costs such as rent, advertising, management sometimes called “downsizing” reduce variable cost reduce direct labor (automation or efficiency) reduce energy costs (efficiency or energy conservation) use cheaper materials increase selling price

5. Reduce fixed cost $ output/period bB R tc TC fc FC

6. Reduce variable cost $ output/period bB R tc TC FC

7. Increase selling price $ output/period bB R tc TC FC r

8. Breakeven example A commuter airline has fixed operating costs of $630,000 per month. It flies 320 flights per month with a maximum of 25 passengers per flight. Tickets are sold for $120 and each passenger incurs $20 in variable costs. How many passengers must the airline serve each month to break even? Each passenger covers $120 - 20 = $100 of the fixed cost. (called the “contribution”) Since the capacity is 320 * 25 = 8000 passengers per month, each flight must average 6300/8000 = 78.75% full to break even.

9. Breakeven for comparison between alternatives Total Cost Units per period Alternative A Alternative B Breakeven point

10. Breakeven with other variables Initial cost$120,000 Salvage Value40,000 Annual Revenue36,000 Annual cost20,000 If your MARR is 15% what project life is needed to break even on this project? NPW = 0 = -120,000 + 40,000 (P/F,15%,n) +16,000 (P/A,I%,n) Probably will require interpolation if you do it by hand and need a fractional year answer.

11. Class problem Your trucking company is considering two alternatives for saving fuel costs. Costs per truck are given. Diesel fuel costs $1 per gallon and the trucks get 5 miles per gallon. Use a planning horizon of four years. Your MARR is 10%. Over what range of mileage driven per year do you prefer each alternative? AB Initial cost$1000$400 Fuel savings16%8% Annual maintenance $10$5

12. Solution Use present worth. Current fuel cost is $1 * miles / 5 PW(A) = -1000 + (.16 *.2 * miles)(P/A,10%,4) PW(B) = -400 + (.08 *.2 * miles) (P/A,10%,4)

13. Payback period How long does it take to recover your initial investment?

14. Simple examples If you pay $1000 now for a project which will save you $500 per year what is the “payback period?” $1000/$500 = 2 years If you pay $1000 now for a project which will save you $300 per year what is the payback period? $1000/$300 = 3.33 years

15. Payback is different The only method which ignores time value of money. Assumes continuous cash flows, not end of period cash flows, so that fractional years can be calculated. Ignores all cash flows after payback. Works better for yes-no decisions than for comparisons.

16. According to the textbooks: “Payback period should never be used as the primary measure of worth to select an alternative. Rather it should be determined in order to provide initial screening or supplemental information in conjunction with an analysis performed using present worth or another method.” “It is incorrect to use the no-return payback period to make final alternative selections…….”

17. Payback Very widely used in industry. Easy to compute Easy to understand Measures liquidity Usually used very conservatively typical paybacks are 12, 18 and 24 months Frequently used for small projects often has a dollar limit attached can speed implementation

18. Project balance example Payback period is

19. Using payback for comparison between alternatives Use fractional years or months to compare To select alternative A over alternative B you need to meet three criteria: A must cost less than the company-set maximum cost for use of payback. A must have a payback shorter than the company- set maximum. A must have a shorter payback than B. Requires common sense: don’t select an alternative that “pays back and quits!”

20. Comparison Example Payback = 4 years Payback = 1 2/3 years

21. Another comparison All have the same (2-year) payback period but they are not all equally desirable.