Chapter 24 — Exercises

Revenue Management: Covers, Seat Turns, RevPASH, and Pricing the Room

Items marked † have worked solutions in the answers appendix. Everything else is yours to defend in class, in a study group, or on the page. Where an exercise asks for a number, show the arithmetic; where it asks for a decision, state what would have to be true for you to change your mind.

Unless told otherwise, use Bellwether's frozen figures: 68 seats (56 dining across 8 two-tops, 7 four-tops, and 2 six-tops, plus 12 at the bar), dinner 5:00–10:00 Tuesday through Saturday at 62 / 78 / 92 / 120 / 123 covers, brunch 10:00–2:00 Saturday and Sunday at 110 covers each, a \$46 dinner check and a \$24 brunch check, a 95-minute dinner dine time and a 70-minute brunch dine time.

A. Recall and definitions (1–7)

1.† Define a seat-hour in one sentence, and state why neither "seats" nor "hours" alone is an adequate measure of a dining room's capacity.

2. Write the RevPASH formula. Then write the decomposition of RevPASH into three levers, and name one concrete technique that moves each lever.

3. Distinguish seat turns from capacity utilization. Give one situation in which two restaurants have identical seat turns and very different capacity utilization.

4.† What is a fence, in the revenue-management sense? Name the three kinds of fence available to a restaurant and give an example of each.

5. Explain, in two sentences, why yield management transferred from airlines to hotels more easily than it transferred to restaurants. Name at least two structural differences.

6. What are shoulder hours? Identify Bellwether's, and say why the 5:00–6:00 hour is a different kind of problem from the 9:00–10:00 hour.

7. State the four effects a prix fixe menu has on a restaurant's economics, and identify which one is the price you pay for the other three.

B. Compute this (8–17)

8.† How many seat-hours does Bellwether manufacture in a week? In a year? Show both.

9. A 46-seat bistro serves dinner 5:30–10:30, six nights a week, at an average of 71 covers a night and a \$52 check. Compute: covers per week, seat turns per service, seat-hours per week, weekly revenue, and RevPASH.

10.† Compute RevPASH and capacity utilization for each of Bellwether's five dinner services, for the dinner week as a whole, and for a brunch service. Then find the pair of services where the ranking reverses — where one fills a larger share of its own capacity than the other and still returns less per available seat-hour — and explain exactly which term of the decomposition causes the reversal.

11. A restaurant reports 1.9 seat turns and is very pleased. Its service window is eleven hours (11:00 a.m. to 10:00 p.m.), it has 84 seats, and its average check is \$21. Compute RevPASH. Then compute RevPASH for a 40-seat dinner-only room doing 1.2 turns across four hours at a \$68 check. Which restaurant is using its capacity harder, and by how much?

12.† Using the decomposition $\text{RevPASH} = \text{utilization} \times (\text{check} \div \text{dine time})$, verify Bellwether's Friday dinner RevPASH from first principles. Show every intermediate figure.

13. Bellwether's operator proposes cutting the average dinner dine time from 95 minutes to 82 minutes through service-leg discipline and a faster table reset. Compute the new revenue per occupied seat-hour. Then state, night by night, how much of that gain actually converts into revenue, and why.

14.† A four-top seated with two guests on a Saturday at 7:10 destroys how many seat-hours? Price the loss two ways — as foregone covers and as foregone contribution — and state the condition under which the loss is zero.

15. Bellwether's plan books 100 patio dinner services at 12 incremental covers and 40 patio brunch services at 10 covers. Compute total patio revenue, total patio seat-hours (16 seats, 5 dinner hours, 4 brunch hours), and patio RevPASH by daypart and blended. Then explain why adding the patio lowers the restaurant's on-premise RevPASH.

16. A company offers \$3,600 for a four-hour Friday buyout of Bellwether's dining room. Compute the revenue floor below which the restaurant should decline, and say whether \$3,600 clears it. Then compute the same floor for a Monday, when the restaurant is dark.

17.† Bellwether's dinner labor is planned at 32.3% of sales. Compute the budgeted labor dollars for Tuesday and for Saturday, and the budgeted labor per cover for each. Then explain why the second number is nearly identical on both nights and why that is the problem.

C. Price this / engineer this (18–24)

18. Design a fenced early prix fixe for Bellwether. Specify the price, the courses, and all three fences. Then cost it: build a three-course plate cost using the Hearth Chicken at a quarter portion (\$5.66) plus a salad and a dessert of your own costing, and state the food cost percentage.

19.† Bellwether's à la carte cover contributes \$33.23 at a \$46 check and 27.8% blended cost of goods. Your prix fixe from Exercise 18 will have a lower check. Compute the prix fixe cover's contribution per occupied seat-hour at a 75-minute dine time, and compare it with the à la carte cover's. State the two very different conclusions this comparison supports at 5:15 on a Tuesday and at 7:30 on a Saturday.

20. An operator proposes "20% off all entrées in February" to fix a soft month. Quantify the cost of leakage to guests who were already coming, using Bellwether's Thursday, Friday, and Saturday cover counts and a \$33.12 food component of the check. Then rewrite the promotion as a properly fenced instrument and estimate what it would cost instead.

21.† Bellwether has 8 two-tops, 7 four-tops, and 2 six-tops against a demand mix of 17 seatings for parties of one or two, 10 for parties of three or four, and 2 for parties of five or six (at 1.71 seatings per table per night). Identify the mismatch quantitatively. Then propose a furniture specification that fixes it, and say what the specification costs at build-out versus in year three.

22. Bellwether's bar runs 15 covers a night on 12 seats. Design a shoulder-hour bar program for the 5:00–6:00 window. State the offer, the price ladder, the fence, and the target covers, and compute what your target is worth annually on Friday and Saturday only.

23. A brunch service does 110 covers at \$24 in four hours. Redesign the brunch check to reach \$29 without raising a single menu price. Name three specific mechanisms and estimate the annual revenue effect if all three work.

24.† Bellwether's Saturday fires an estimated 32 hearth items an hour between 7:00 and 9:00 against a rated 28. Build a revised reservation grid that keeps every hour at or below 28 while raising the night's total covers. State how many covers your grid produces and what has to be true at the host stand for it to happen.

D. Read this and find the problem (25–29)

25. A restaurant's monthly report shows covers up 8% year over year and revenue up 1.4%. State what has happened, name the two numbers you would ask for next, and describe the two most likely underlying causes.

26.† Here is a week from a 90-seat restaurant open 5:00–11:00, six nights:

Compute RevPASH and average check for each night and for the week. Identify the two nights with a problem, say what kind of problem each one has, and state what you would do about each.

27. A reservation report shows a 9% no-show rate on Tuesday bookings and a 3% no-show rate on Saturday bookings. The owner proposes a deposit requirement on Tuesdays. Explain why this is probably backwards, and what the report is more likely telling you.

28. An operator computes RevPASH monthly on total revenue and is pleased that it has risen from \$11.40 to \$13.10 over a year in which the dining room's cover count fell. What has almost certainly happened, and how would you restate the metric?

29.† A 60-seat restaurant runs 2.4 seat turns on a Saturday — a number the owner quotes constantly — with a 55-minute average dine time across a five-hour service. Compute capacity utilization. Then explain what those two numbers together tell you about the guest experience, and what you would want to check before congratulating anyone.

E. Write this (30–33)

30. Write the no-show and deposit policy that appears on Bellwether's booking page. Maximum 150 words. It must cover which bookings are affected, what is charged, when, what is not charged, and how to cancel. Write it so a guest reads it once and is not annoyed.

31.† Write the pre-shift briefing for the first Tuesday the early prix fixe runs. Two minutes of speaking. Cover what the menu is, who it is for, what the fences are, what a server says if a guest at 7:15 asks for it, and why the restaurant is doing this at all.

32. Write a one-page memo to a business partner arguing against a proposal to add a \$5 "weekend seating fee" on Friday and Saturday reservations. Make the commercial case, not the moral one, and propose the alternative instrument that achieves the same economics.

33. Write the section of an operations manual that tells a host how to decide, in eleven seconds, where to seat a party of two on a Saturday at 7:10. Include a release rule with a time on it.

F. Judgment and ethics (34–37)

34. A reservation platform offers to raise your Friday and Saturday prices automatically based on booking velocity, with the guest seeing only the final price. Argue both sides, then state your decision and the principle behind it. Your answer must engage with the fact that this is economically identical to a discount you would accept without hesitation.

35.† The chapter proposes a test for fair demand-based pricing: can the guest see the rule and choose the cheaper side of it? Apply the test to four instruments — an early prix fixe, a holiday prix fixe at a premium, a mandatory 4% "kitchen fee," and a loyalty-app price that varies by user. Then identify the case the test handles badly and explain why.

36. A guest with a \$20-per-seat deposit on a six-top calls at 5:50 p.m. to cancel a 7:00 reservation because a child is sick. The policy says the charge applies inside 48 hours. What do you do, what do you log, and what — if anything — does the answer change about the policy?

37. A restaurant discovers that its early-bird menu is being used almost exclusively by guests on fixed incomes, and that raising its price by \$4 would raise contribution by an estimated \$9,000 a year with modest attrition. Is there a decision here beyond the arithmetic? Argue it.

G. Business Plan extensions (38–40)

38.† Rebuild Bellwether's revenue bridge choosing Bridge B instead of Bridge A. Show the arithmetic, distribute the additional covers across the week explicitly, and then write the three strongest objections a careful reader would raise. State whether you would still choose it.

39. Bellwether's bridge assumes 100 weather-available patio services. Model a bad year at 72 services. Compute the revenue shortfall, and write the half-page contingency section the plan should carry — naming the specific levers, their values, and who is accountable for each.

40. Extend the plan's Revenue Model with a Year 2 view. Year 2's headline is \$1,720,000 against Year 1's \$1,550,000 — a \$170,000 increase. Build it from the three RevPASH levers rather than from a growth percentage, state which of the three carries the most weight, and identify the one assumption in your build that you would most want to be wrong about early.