Chapter 32 — Self-Check Quiz
Twenty-six questions. Answers are in the collapsed block at the bottom — do the whole thing before you
open it. Bellwether's figures: fixed cost \$437,635, CM ratio 40.53%, plan revenue
\$1,550,000**, debt service **\$69,500.
Multiple choice
1. Which of these is a semi-variable cost in a restaurant?
- a) Base rent
- b) Food cost
- c) Utilities
- d) General liability insurance premium
2. The contribution margin ratio is:
- a) (Sales − fixed costs) ÷ sales
- b) (Sales − variable costs) ÷ sales
- c) Operating profit ÷ sales
- d) Sales ÷ variable costs
3. A restaurant has \$500,000 of fixed costs and a 40% contribution margin ratio. Break-even sales
are:
- a) \$800,000
- b) \$1,000,000
- c) \$1,250,000
- d) \$2,000,000
4. The degree of operating leverage is computed as:
- a) Fixed costs ÷ variable costs
- b) Contribution margin ÷ operating profit
- c) Sales ÷ break-even sales
- d) Operating profit ÷ sales
5. At a 40% CM ratio, adding \$1 of annual fixed cost raises break-even sales by:
- a) \$1.00
- b) \$1.40
- c) \$2.50
- d) \$4.00
6. Which of these raises break-even sales?
- a) A menu price increase with no change in portions
- b) A rent escalation
- c) A reduction in food cost percentage
- d) Cutting two hourly shifts a week
7. Bellwether's break-even sales, computed on Chapter 19's labor line, are:
- a) \$970,915
- b) \$1,030,454
- c) \$1,079,815
- d) \$1,251,298
8. Bellwether's break-even, expressed in dinner covers per night, is approximately:
9. Cash break-even is always:
- a) Lower than accounting break-even
- b) Equal to accounting break-even
- c) Higher than accounting break-even
- d) Unrelated to accounting break-even
10. Which of these is not a fixed cost at Bellwether?
- a) Credit-card processing
- b) Budgeted marketing
- c) The sous chef's salary
- d) Liquor liability insurance
11. A restaurant's DOL is 3.30. Revenue declines 10%. Operating profit declines by approximately:
- a) 3.3%
- b) 10%
- c) 33%
- d) 66%
12. Bellwether's contribution margin per dinner cover is:
- a) \$8.22
- b) \$15.84
- c) \$19.37
- d) \$46.00
13. The high-low method is used to:
- a) Find the highest and lowest sales months of the year
- b) Split a semi-variable cost into a fixed base and a variable rate
- c) Set menu prices from a target food cost
- d) Compute the degree of operating leverage
14. Reclassifying a salaried sous chef as non-exempt, and paying the overtime owed, adds a cost that
is best treated as:
- a) Variable, because it depends on hours worked
- b) Fixed, because the position works the same schedule at any volume
- c) Semi-variable, split evenly
- d) Not a cost at all, since the salary was already budgeted
15. Chapter 4's break-even preview for Bellwether was \$1,030,454. Relative to the honest figure it
was:
- a) Correct
- b) \$49,361 too low
- c) \$49,361 too high
- d) \$93,109 too low
16. Brunch at Bellwether has a CM ratio of 34.25% against dinner's 42.11%. This means:
- a) Brunch loses money and should be closed
- b) Brunch labor is badly scheduled
- c) Every sales dollar shifted from dinner to brunch costs about eight cents of contribution
- d) Brunch's break-even is lower than dinner's
Short answer
17. Chapter 4 split Bellwether's labor as \$252,000 fixed plus 16.0% variable, which totals exactly
\$500,000 at \$1,550,000 of sales. Why did the error go unnoticed for so long, and what kind of question
exposes it?
18. Explain the "phantom \$51 average check" in one short paragraph, and state the rule that prevents
it.
19. A restaurant has \$445,000 of fixed cost and a variable cost ratio of 58%. Compute break-even
sales.
20. For the restaurant in question 19, expected sales are \$1,480,000. Compute margin of safety in
dollars and as a percentage.
21. A restaurant's DOL is 4.2 and its operating profit is \$88,000. Revenue falls 7%. What is the new
operating profit?
22. Bellwether's brunch labor runs 31.5% of brunch revenue while dinner labor runs 22.6% of dinner
revenue. Explain the mechanism, and name the lever that fixes it.
23. Is brunch carrying itself at Bellwether? Give both answers — avoidable-cost and fully-allocated —
with a number for each.
24. Name three cash obligations that appear in a cash break-even but not in an accounting break-even.
25. Explain why break-even sales is mix-dependent, using Bellwether's two readings from §32.3.
26. A restaurant has \$380,000 of fixed cost, a 41% CM ratio, a \$38 average check, and serves dinner
five nights a week. Compute break-even sales, break-even covers, and break-even covers per night.
Answer key
**1. (c) Utilities.** Compressors, hood, lights, and HVAC run at any volume; dish cycles, gas, and hot
water scale with covers. Rent and insurance are fixed; food cost is variable.
**2. (b) (Sales − variable costs) ÷ sales.** Equivalently, 1 − the variable cost ratio.
**3. (c) \$1,250,000.** \$500,000 ÷ 0.40.
**4. (b) Contribution margin ÷ operating profit.**
**5. (c) \$2.50.** \$1 ÷ 0.40. At Bellwether's 40.53% the multiplier is \$2.47.
**6. (b) A rent escalation.** It raises the fixed base with no effect on the CM ratio. The other three
either raise the CM ratio or lower variable cost, both of which lower break-even.
**7. (c) \$1,079,815.** \$437,635 ÷ 0.4053.
**8. (b) 66.** \$1,079,815 ÷ \$1,550,000 = 69.67%; 95 planned covers × 0.6967 = 66.2.
**9. (c) Higher than accounting break-even,** because it adds obligations — debt service, capital
replacement — that leave the bank account without appearing as operating expenses.
**10. (a) Credit-card processing.** At 2.81% of net sales it is one of the purest variable costs in the
building. Operators file it mentally under "bank fees" and get the split wrong.
**11. (c) 33%.** 3.30 × 10%. At Bellwether that is \$62,819 of profit — nine and a half dinner covers a
night.
**12. (c) \$19.37.** \$46 × 42.11%. \$8.22 is brunch; \$15.84 is the blended base figure.
**13. (b) Split a semi-variable cost into a fixed base and a variable rate.**
**14. (b) Fixed.** The sous chef works the same fifty-five hour week at sixty covers or a hundred and
thirty, so reclassification raises the fixed floor — the worse of the two outcomes for break-even, since
it raises the threshold by 1 ÷ CM ratio.
**15. (b) \$49,361 too low.** \$1,079,815 − \$1,030,454. Chapter 4 overstated the fixed floor by \$60,105
*and* understated the variable rate by 8.42 points; the second error dominated, and then the honest labor
line added \$70,461 of cost Chapter 4 did not have at all.
**16. (c) Every sales dollar shifted from dinner to brunch costs about eight cents of contribution.**
Brunch still contributes \$94,037 a year and clears its fully-allocated break-even, so (a) is wrong; the
staffing is appropriate to the service, so (b) is wrong.
**17.** Because the *total* landed on the number the plan wanted, so nobody examined the structure
underneath it. The two errors pointed in opposite directions and cancelled at exactly one volume —
\$1,550,000, the volume the plan was written for. Any question about a *different* volume exposes it
immediately, and break-even is by definition a question about a different volume.
**18.** Take the plan's weekly revenue (\$29,808), subtract brunch at the base level (\$5,280), and divide
the \$24,528 remainder by 475 dinner covers, and you get a \$51.64 average check that the menu cannot
produce and the plan never claimed. It is an artifact of dividing one revenue base by the cover count of a
different one — the extra \$139,240 comes from patio seats, event contracts, and takeout, not from guests
spending more. **The rule: name your revenue base out loud, in the sentence, every time.**
**19.** CM ratio = 1 − 0.58 = 42%. \$445,000 ÷ 0.42 = **\$1,059,524.**
**20.** \$1,480,000 − \$1,059,524 = **\$420,476**, which is **28.4%** of expected sales.
**21.** 4.2 × 7% = 29.4% profit decline. \$88,000 × 0.294 = \$25,872. New operating profit =
**\$62,128.**
**22.** A brunch service needs a nearly complete building — a lead cook and two on the line because eggs
do not hold, a dish body, a host, three servers, a busser, a bartender — against a \$24 check instead of a
\$46 check. Brunch labor is not worse per hour or per cover; it is worse *per dollar*, because the dollars
are smaller. **The lever is the check average, not the schedule.** A \$2 brunch increase is worth \$22,880
of pure contribution and drops break-even \$22,471.
**23.** **Avoidable cost: decisively yes.** Closing brunch gives up \$94,037 of contribution and saves
maybe \$18,000 of genuinely avoidable fixed cost — a net loss of about \$76,000. Its avoidable break-even
is 21 covers a service against 110. **Fully allocated: yes, but thinly.** Brunch's proportional share of
fixed cost is \$77,505, leaving \$16,532 of allocated profit — a 6.0% margin, with its own break-even at
91 covers a service against 110. At Chapter 20's labor line that falls to \$11,750 and 96 covers.
**24.** Any three of: debt service (principal, and interest if it is shown below the operating line);
capital replacement, since Bellwether's plan carries no depreciation; the sales-tax remittance, which was
never the restaurant's money; inventory build as revenue grows; owner distributions beyond salary.
**25.** Because different dayparts have different CM ratios. §32.3 produced two break-even revenue
figures for the same restaurant — \$1,079,815 when everything falls proportionally, \$1,097,498 when only
dinner falls and brunch runs at plan. The second is higher because the mix is weighted toward brunch,
whose CM ratio is nearly eight points worse, so more total revenue is needed to clear the same fixed nut.
A break-even quoted without its mix assumption is incomplete.
**26.** Break-even sales = \$380,000 ÷ 0.41 = **\$926,829.** Break-even covers = \$926,829 ÷ \$38 =
**24,390.** Services = 5 × 52 = 260, so break-even covers per night = 24,390 ÷ 260 = **93.8, call it 94.**