Chapter 32 — Exercises

Items marked † have worked solutions in the answers appendix. Everything else is yours to defend. Unless a problem says otherwise, use Bellwether's figures from the chapter: fixed cost \$437,635, CM ratio 40.53%, dinner check \$46** at 475 covers a week, brunch check **\$24 at 220 covers a week, plan revenue \$1,550,000**, and debt service **\$69,500. Show your arithmetic. A break-even you cannot reproduce is a break-even you do not own.

A. Recall and definitions (1–8)

1. Define fixed cost, variable cost, and semi-variable cost in one sentence each, and give a restaurant example of each that does not appear in the chapter.

2. † Write the break-even formula. Then write the formula for break-even covers, and state the one piece of information you must name for the second formula to mean anything.

3. What is the contribution margin ratio, and what does a CM ratio of 40.53% mean expressed in cents?

4. Explain the difference between contribution margin per cover and contribution margin ratio, and say which one you use for a covers-per-night calculation.

5. † Define margin of safety and give four different units it can be expressed in.

6. What is the degree of operating leverage, and what does a DOL of 3.30 predict about a 6% revenue decline?

7. Explain the difference between accounting break-even and cash break-even, and name three obligations that appear in the second but not the first.

8. What is the "relevant range," and why does it matter that a break-even chart is a straight line?

B. Applied reasoning (9–16)

9. † A restaurant's owner insists that all labor is variable "because I can send people home." Give three specific counter-examples from a working restaurant, and explain what treating all labor as variable does to the break-even figure — in which direction and why.

10. Chapter 4 estimated Bellwether's labor as \$252,000 fixed plus 16.0% of sales variable, and got \$500,000 at plan volume — the exact plan figure. Explain why a correct total is not evidence of a correct split, and identify the one kind of question for which the split matters and the total does not.

11. Bellwether's occupancy is \$95,200 on a ten-year lease. Under what circumstances would you reclassify occupancy as semi-variable rather than fixed? Name a real lease term from Chapter 6 that would force the reclassification.

12. † Explain why credit-card processing at 2.81% of net sales is a variable cost and not a fixed "bank fee," and compute what it costs Bellwether at plan revenue, at break-even revenue, and at the operating ceiling of about 132 covers a night. (For the third, assume the ceiling sustains \$2.05M of annual revenue.)

13. A consultant tells a client, "Your break-even is \$980,000." List five questions you would ask before writing that number into anything.

14. Bellwether's brunch CM ratio is 34.25% and dinner's is 42.11%. Explain, without arithmetic, why this means the restaurant's break-even in dollars can rise without a single cost line changing.

15. † Explain why a 10% revenue decline is far worse for a restaurant than a 10% decline in profit, using Bellwether's actual numbers. Then explain why the percentage damage from a fixed dollar shortfall falls as revenue rises, even though the dollar damage is identical.

16. Bellwether has a construction contingency and a working-capital reserve (Chapter 1, Chapter 5). Neither appears anywhere in this chapter's fixed-cost schedule. Should they? Argue both sides, then commit.

C. Cost this (17–21)

17. † Split this semi-variable line with the high-low method. A restaurant's paper-and-supplies cost by month, with sales:

Compute the variable rate and the monthly fixed base using the highest and lowest months, then test your split against March. Report the annual split on \$1,380,000 of sales.

18. Cost Bellwether's fixed labor floor from scratch. Three salaried positions at \$55,000, \$48,000, and \$47,000, burdened at 13.0%, plus 26.5 hours a week of open-and-close hourly time at \$14.70, burdened at the same rate. Does your total match the chapter's \$191,895? Explain any difference.

19. † A restaurant's other-operating line is \$186,000 on \$1,240,000 of sales. Sort these components into fixed, variable, and semi-variable, and split each semi-variable line with a defensible assumption you must state: card processing \$34,720 · utilities \$41,000 · supplies \$23,560 · linen \$6,200 · smallwares and breakage \$9,920 · repairs \$16,600 · marketing \$24,800 · technology \$18,600 · insurance \$10,600. Then report total fixed, total variable, and the variable rate on sales.

20. Cost the sous-chef reclassification from Chapter 20. A \$48,000 salary covering a 40-hour week, actual hours 55, burden 13.0%. Compute the regular rate, the overtime rate, the annual overtime premium, and the burdened cost. Then state whether the result is a fixed or a variable cost and defend the answer.

21. † A restaurant is quoted two card-processing offers: (a) 2.60% plus \$0.10 per transaction, or (b) a flat 2.90% with no per-transaction fee. Annual sales are \$1,550,000 across 34,000 transactions averaging \$45.59. Compute the all-in effective rate for each, name the winner, and state the effect on break-even sales given a 40.53% CM ratio before the change.

D. Break-even and covers (22–28)

22. † Compute break-even sales for a restaurant with \$392,000 of fixed cost and a 38.0% CM ratio. Then compute break-even covers at a \$41 average check, and break-even covers per night if it serves six nights a week.

23. Bellwether's break-even at Chapter 19's labor line is \$1,079,815. Recompute it if the landlord's first escalation adds \$4,200 a year to occupancy and the insurance renewal adds \$2,600. State the new break-even in dollars and in dinner covers per night.

24. † Convert \$1,079,815 of break-even sales into dinner covers per night two ways: (a) scaling the whole business proportionally against \$1,550,000, and (b) holding brunch's \$94,037 and the bridge's \$55,696 of contribution constant and flexing dinner alone. Explain in two sentences why the answers differ and when you would use each.

25. An operator divides Bellwether's break-even sales of \$1,079,815 by the blended base check of \$39.04 and reports 27,659 break-even covers. Identify the error precisely, compute the correct figure, and express the size of the error in dinner covers per night.

26. † A 120-seat restaurant does lunch and dinner six days a week. Fixed cost \$610,000. Lunch: 70 covers a service at \$19, CM ratio 31%. Dinner: 130 covers a service at \$44, CM ratio 44%. Compute total contribution, operating profit, the blended CM ratio, break-even sales, and break-even covers per service for each daypart on a fully-allocated basis.

27. Using the restaurant in exercise 26: is lunch carrying itself? Answer twice — once on avoidable cost, assuming closing lunch would save \$46,000 of genuinely avoidable fixed cost, and once fully allocated. Then say which answer you would act on and why.

28. † Bellwether's operating ceiling is about 132 dinner covers a night and its break-even is 66. Express the viable operating band as a percentage of capacity, then state what the band would be at the Chapter 20 labor line plus debt service. What does the narrowing tell you?

E. Operating leverage and margin of safety (29–33)

29. † Compute the degree of operating leverage for each of Bellwether's three labor scenarios (\$500,000 / \$570,461 / \$597,461), then compute the dollar and percentage profit effect of an 8% revenue decline under each. Present it as a table an owner could read in thirty seconds.

30. A restaurant with a DOL of 5.2 and one with a DOL of 1.9 both earn \$140,000 of operating profit. Describe the likely structural differences between them — service style, occupancy, staffing model — and say which you would rather own in a year with an uncertain economy, and why the answer is not automatic.

31. † Bellwether's margin of safety at Chapter 19's labor line is 30.3%. Recompute it in all four units (dollars, percent, dinner covers a night, weeks of trading) for a downside case in which revenue lands at \$1,395,000 rather than \$1,550,000.

32. Model the Chapter 9 ramp. Q1 revenue \$363,100 at 66.6% prime cost; annual fixed cost \$437,635; fixed labor \$191,895; variable other operating 7.29% of sales. Compute Q1's variable prime rate, Q1's CM ratio, Q1's break-even, Q1's operating profit, and Q1's margin of safety. Then state in one sentence what this does to the credibility of an annual-average break-even.

33. Weeks 14–52 must average 58.0% prime cost for Bellwether's year to land on 60.0%. Verify that claim arithmetically, then state what break-even would be for weeks 14–52 alone if the restaurant hit 58.0% exactly.

F. Read this and find the problem (34–36)

34. † A P&L for a 74-seat restaurant, one full year:

The owner reports break-even of \$792,000, computed as fixed costs of \$356,400 (occupancy + G&A + other operating) divided by a CM ratio of 45% (100% − 30% COGS − 25% "the labor I can actually cut"). Find every error, rebuild the analysis with a defensible split — state your assumptions — and report the honest break-even, margin of safety, and DOL.

35. The same restaurant's owner is considering a \$3 menu price increase across the board, expecting to lose "maybe a few covers." Using your rebuilt numbers from exercise 34, compute how many covers they can afford to lose, and express it per night.

36. † A break-even section from a business plan reads: "With fixed costs of \$410,000 and a contribution margin of 62%, we break even at \$661,290 — only 43% of our projected \$1,540,000, giving us an exceptional margin of safety of 57%." Something is badly wrong. Diagnose it, name the most likely cause, and estimate what the honest CM ratio and break-even probably are for a full-service restaurant of this size.

G. Decisions (37–40)

37. † Price the Sunday-dinner decision for a different restaurant: dinner check \$52, dinner CM ratio 44%, new fixed cost \$16,000 a year for a shift lead and utilities, expected Sunday volume 48 covers, estimated cannibalization 25% from Friday and Saturday. Compute break-even Sunday covers with and without the cannibalization adjustment, and the net effect on operating profit at 48 covers.

38. Price an added position. A \$61,000 salary at a 14% burden, in a restaurant with a 39% CM ratio, a \$48 average check, and 300 services a year. Compute the break-even shift in sales and in covers per service. Then write the four-sentence argument you would make for the hire, quantifying at least two sources of return.

39. † Bellwether is offered a catering contract: 40 events a year at \$2,400 each, requiring \$9,000 of new equipment amortized over three years, \$3,000 a year of additional insurance, and event labor at 26% of event revenue with food cost at 24%. Compute the contract's CM ratio, its contribution, the change to Bellwether's fixed base, the new break-even, and the new margin of safety. Then name two costs the arithmetic does not capture.

40. Judgment. A restaurant is running 4% below break-even in a soft quarter. The owner has three options on the desk: (a) cut the Tuesday service, saving \$1,202 a service of allocated fixed cost; (b) cut two hourly shifts a week; (c) raise prices 5%. Using the chapter's arithmetic, evaluate each on what it actually does to break-even — being careful about the difference between allocated and avoidable cost — and then argue which one you would choose and what you would refuse to do. Name at least one non-financial cost of each option.

H. Business Plan extension (41–43)

41. † For your own restaurant concept, build the complete cost-behavior schedule: every line sorted fixed / variable / semi-variable, every semi-variable line split with a stated method, and the two totals. Report total fixed cost, the variable rate, and the CM ratio.

42. Compute your break-even four ways: accounting, cash (including debt service), cash plus a 1.5% capital-replacement reserve, and first-year ramp. Convert all four to covers per night at your own average check and operating pattern. Put them on one ladder like Figure 32.7.

43. Write the one-page Break-Even Analysis section of your business plan. It must contain: the fixed cost schedule, the CM ratio with its derivation, break-even in sales and in covers per night, a sensitivity table with at least three scenarios, the margin of safety in two units, and an honest paragraph naming what the analysis does not settle. No paragraph may contain a number you cannot reproduce.

I. Ethics and honesty (44–45)

44. You are preparing a break-even section for a business plan. Your honest analysis gives \$1,079,815; using the plan's labor target instead gives \$970,915, which reads much better. The labor target is the one in the rest of the document. Write the two sentences you would put in the plan, and say what you would do about the inconsistency in the other sections.

45. † A restaurant group's regional manager asks each general manager for their break-even, and compensation is partly tied to performance above it. Describe three specific ways a GM could produce a lower break-even figure without lying about a single number, and describe the review process you would build to make those three moves visible.