Chapter 11 — Exercises

Thirty-six problems, graduated from recall through applied judgment. Items marked with a dagger (†) have worked solutions in the Answers to Selected Exercises appendix — try them before you look.

This is the arithmetic chapter of the book, so a warning: do these with a calculator and a pencil, not by reading them. Every one of them is a calculation an operator performs for real, and the difference between following a worked example and producing one yourself is the entire difference between this chapter working and not working. Where a problem asks you to check that something foots, actually check it.

A. Recall and definitions (1–7)

1. Write the formula for food cost percentage using inventory. Then state, in one sentence, what the invoice-over-sales shortcut computes instead.

2. † Define as-purchased cost and edible-portion cost, and write the formula that converts one to the other. Explain in one sentence why the conversion makes cost go up.

3. What is a waste allowance? What range is common, and what single piece of evidence would tell you whether yours is set correctly?

4. Define the Q factor and name four things that belong in it.

5. † State the difference between ideal food cost and actual food cost, and list six things that can live in the gap between them.

6. What is target-cost pricing? Write the formula, and then write its inverted form.

7. A cook says the disher is "a twelve." How many fluid ounces does it hold, and how did you work that out?

B. Building cost cards (8–14)

8. † Build the card. A dish has these costed components:

Total the components, add a 3% waste allowance, and state the plate cost. Then price the item to a 30% food cost target.

9. A sauce batch costs \$34.20 and the recipe claims a yield of 52 fluid ounces. The portion spec is 2.5 fl oz. What does the card carry? Now the batch is actually weighed and yields 46 fl oz. What does the card carry now, what is the difference per plate, and what is it worth annually at 140 plates a week?

10. † Compute a Q factor. Bread service is 1.2 oz of bread at \$0.22/oz plus 0.35 oz of butter at \$0.31/oz; condiments and table oil come to \$0.05 a cover. State the Q factor. Then, for a restaurant doing 28,000 covers and \$840,000 of food sales a year, express it as points of food cost.

11. Reproduce the Hearth Chicken card from memory as far as you can, then check it against the chapter. Confirm that the components foot to \$8.35 and the plate cost to \$8.52. Then compute the menu price that would produce exactly a 28.0% food cost.

12. † The waste-allowance sensitivity. Using the Hearth Chicken's \$8.35 of components, compute the plate cost and the food cost percentage at \$29.00 under a 2%, a 4%, and a 5% allowance. State what that range implies about how carefully the allowance deserves to be set.

13. A restaurant's cost cards include no line for cooking oil, salt, or garnish. Estimate the error as a percentage, using the Hearth Chicken as your model, and state what that would do to a menu of thirty items.

14. A dish is costed from a batch recipe written in "bunches" of herbs. The chef rewrites the recipe in "cups of picked leaves." What must change on the cost card, and what error appears if nobody makes the change?

C. AP, EP, and yield (15–21)

15. A 40 lb case of broccoli costs \$1.28 a pound. After trimming, 26.4 lb are usable. Compute the yield percentage and the EP cost per pound, and verify your answer by a second route.

16. † Run a butcher test. A 22.6 lb beef sub-primal costs \$9.85 a pound. Breaking it down produces 3.4 lb of fat and sinew (discarded), 2.8 lb of grind trim (used for burger; you would otherwise buy ground beef at \$5.60/lb), and 16.4 lb of saleable steaks.

• (a) Confirm that the streams reconcile.
• (b) Compute the yield percentage to the steaks.
• (c) Compute the EP cost per pound with and without the by-product credit.
• (d) Compute the cost of an 8 oz portion using the credited EP figure.
• (e) State what the portion would have cost if it had been carded at the AP price, and by how much that understates it.

17. Three yield tests on the same product return: 16.4 lb usable from 22.6 lb; 8.0 lb from 12.0 lb; 17.2 lb from 23.4 lb. Compute the yield each way — total-out ÷ total-in, and the simple average of the three percentages. Which is correct, why, and how much do they differ?

18. † Bellwether's roasted roots go 12.0 lb as purchased → 9.0 lb trimmed → 7.6 lb roasted. Compute the trim yield, the cooking yield, and the overall as-purchased-to-as-served yield. Then explain which of the three belongs on a card whose portion spec reads "5 oz roasted."

19. Your supplier's spec sheet claims a 74% yield on a product. Your three tests average 66%. Write the five questions you would ask before concluding anyone is wrong.

20. A restaurant carries its entire produce program at as-purchased prices. Produce is roughly 18% of its food cost, and its average produce yield is 74%. Estimate the resulting understatement in points of food cost, and state the assumption your estimate depends on.

21. † An operator is considering switching from whole chickens at \$3.20/lb to pre-portioned half birds at \$4.35/lb. The pre-portioned product has no butchery labor. Using the chapter's figure of \$0.79 a portion for butchery and brining, evaluate the switch on plate cost, on labor, and on prime cost. State what additional information would change your answer.

D. Pricing (22–26)

22. † An item has a plate cost of \$4.85. The house target is 29%.

• (a) What price does target-cost pricing produce?
• (b) The menu actually charges \$19.00. What is the item's food cost percentage and contribution margin at that price?
• (c) How much contribution per plate would obeying the formula have given away, and what is that worth annually at 85 plates a week?
• (d) Name the reason this item is a legitimate exception.

23. A market price point of \$26.00 is fixed by the competition. At a 31% target, what is the maximum plate cost you can afford? If your current card is \$8.90, how much headroom do you have and what would you spend it on?

24. † Price these five items to a 30% target and compare each with the price given. For each, state whether you would take the formula's answer or override it, and why.

25. A consultant recommends repricing every item on the menu to exactly 30% food cost, arguing that this guarantees a 30% food cost. Write the two-paragraph rebuttal, using at least one number from the chapter.

26. † A dish's plate cost rises from \$6.10 to \$7.05. Its menu price is \$23.00. Compute:

• (a) the food cost percentage before and after;
• (b) the price that restores the original contribution margin in dollars;
• (c) the price that restores the original food cost percentage;
• (d) the contribution margin each of those two prices produces.

Then state which you would choose and why.

E. Counting, ideal vs. actual, and diagnosis (27–32)

27. † The central problem of the chapter. Two consecutive four-week periods:

• (a) Compute the true food cost percentage for each period.
• (b) Compute the invoices-over-sales figure for each period.
• (c) State what each method reports about the direction of change.
• (d) Verify that the difference between the two methods equals the change in inventory divided by sales, in both periods.
• (e) Compute both figures across the two periods combined and explain why they converge.

28. † Compute the ideal. A four-week period produced these unit counts:

• (a) Compute total ideal cost, total sales, and the ideal food cost percentage.
• (b) Actual usage from the count was \$5,510. Compute the variance in dollars and in points.
• (c) Characterize it against the tolerances in §11.7.

29. A restaurant's ideal food cost rises from 27.9% to 29.4% between two periods while the variance holds at 0.6 points. State what happened, what it does not mean, and what one number you would look at next.

30. † Find the leak. A period shows a 2.8-point ideal-to-actual variance worth \$2,240. You are given four facts: the menu changed twice in the period and ran eleven daily specials; a new prep cook started in week two; a poultry promotion was bought in week one and the walk-in was full; the comp report shows 1.9% of sales comped against a 0.8% standard. Rank the causes you would investigate and, for each, name the single document you would pull.

31. Cost the comps. In a period, 34 entrées were comped at an average plate cost of \$7.90 against food sales of \$71,000. Express the comped product as points of food cost. Then explain why comps appear in the variance rather than in the ideal.

32. † The prime-cost trade. A chef proposes taking bread production in house. Bread currently costs \$310 a week delivered. In-house production would cost \$88 a week in ingredients plus ten hours of prep labor at \$19/hour fully loaded, and would let the restaurant reduce the Q factor by \$0.04 a cover on 700 covers a week.

• (a) Compute the weekly effect on food cost in dollars.
• (b) Compute the weekly effect on labor cost in dollars.
• (c) Compute the net weekly effect on prime cost.
• (d) Name two non-financial factors that could change the decision.

F. Judgment, writing, and the Business Plan (33–36)

33. The ethics problem. Poultry has risen 15%. The chef proposes moving from a 3.5 lb air-chilled bird to a 3.25 lb conventionally chilled bird, holding the \$29.00 price and not changing the menu copy, which reads "air-chilled chicken, wood-fired." Evaluate this proposal on three axes: the arithmetic, the guest relationship, and the legal exposure. State what you would do and what you would tell the staff.

34. † Write the memo. Your ideal-to-actual variance has run above 2 points for two consecutive periods and you have concluded the primary cause is portioning. Write the one-page memo to the kitchen team that introduces scales at two stations and the first-three-plates check. It must (a) not read as an accusation, (b) state what will be measured and how often, (c) explain why it matters in terms a cook cares about, and (d) say what happens if the number does not move.

35. Business Plan extension. Build a cost card for one dish from your own concept — or from the Bellwether menu if you are not working your own — from batch recipes and portion specs. It must foot to the cent, carry a stated waste allowance, and record on the card where each price came from and when. Then compute its food cost percentage and contribution margin at the price you intend to charge, and write one sentence defending that price against the target-cost answer.

36. † Business Plan extension. Reproduce the checkpoint's bridge from theoretical food cost to the plan's line, using your own numbers: blended theoretical, plus Q factor, plus an honest variance allowance. State the resulting range. If it lands above your plan's target, write the three-line commitment that would have to be true for the target to hold — and then say plainly, in one sentence, what the difference costs in prime cost if it doesn't.