Solutions Breakeven Analysis PDF

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Solutions to Breakeven Analysis Practice Problems

1. The O’Neill Shoe Manufacturing Company will produce a special-style shoe if the order size is large enough to provide a reasonable profit. For each special-style order, the company incurs a cost of $1,000 for the production setup. There is an additional cost of $30 per pair, and each pair sells for $40. a. Develop a mathematical model for the total cost of producing x pairs of shoes. C = 30x + 1000 b. Develop a mathematical model for the total profit realized from an order for x pairs of shoes. P = 40x – (30x + 1000) = 10x – 1000 c. How large must the shoe order be before O’Neill will break even? P = 0  10x – 1000 = 0 so x = 100 d. Perform an analysis of the following scenarios:  Base case: Costs and revenues as given in the problem statement, with 900 pairs of shoes. C = $28,000 R = $36,000 P = $8000 30(900)+1000 40(900) R-C=  Optimistic case: Variable costs can be decreased to $25 and selling price can be increased to $42 per pair. C = $23,500 R = $37,800 P = $14,300 25(900)+1000 42(900) R-C=  Pessimistic case: Fixed costs increase to $1,100; variable costs increase to $33 and selling price is unchanged at $40 per pair. C = $30,800 R = $36,000 P = $5200 33(900)+1100 40(900) R-C= Compute the total cost, total revenue, and net profit for each scenario. Then calculate the new breakeven points for the optimistic and pessimistic cases. How is the breakeven point you found in item c affected by the assumptions in these two cases? In the optimistic case, the breakeven point decreases from 100 to 58.82 (or 59). 42x-(25x+1000)=17x-1000= In the pessimistic case, the breakeven point increases from 100 to 157.14 (or 158). 40x-(33x+1100)=7x-1000=

2. Eastman Publishing Company is considering publishing a paperback textbook on spreadsheet applications for business. The fixed cost of manuscript preparation, textbook design, and production setup is estimated to be $80,000. Variable production and material costs are estimated to be $3 per book. Demand over the life of the book is estimated to be about 4,000 copies. The publisher plans to sell the text to college and university bookstores for $20 each.   Based on Introduction to Management Science, Anderson, Sweeney, and Williams, 10th edition, 2003.

a. What is the break-even point? C = 3x + 80,000 R = 20x P = 20x – (3x + 80,000) P = 0  17x – 80,000 = 0 so x = 4705.88 or 4706 b. What profit or loss can be anticipated with a demand of 4,000 copies? P = 17(4000) – 80,000 = –12,000 (loss of $12,000) c. With a demand of 4,000 copies, what is the minimum price per copy that the publisher must charge to break even? Let S = selling price (in $) P = 0  4000S – (3(4000) + 80,000) = 0 so S = $23 d. Write a general equation for the breakeven selling price given the quantity sold. Let x = # sold, FC = fixed cost, V = variable cost, and S = selling price. Then the computations for item c can be written in general as Sx – (Vx + FC) = 0. Now solve for S:

Sx = Vx + FC →

S = V + FC/x

You can check the equation by plugging in the values from item c.

e. Management believes that if the price of the book is increased to $25.95, the lowest demand will be 3,500 books. By considering values for demand ranging from 3,500 books to 4,500 books, in increments of 100 books, investigate the effect that the increased price may have on profits. Do you think that Eastman should increase the price to $25.95? Demand 3500 3600 3700 3800 3900 4000 4100 4200 4300 4400 4500

Profit $325 $2,620 $4,915 $7,210 $9,505 $11,800 $14,095 $16,390 $18,685 $20,980 $23,275

Notice that the profit function is linear, so every additional 100 books in demand increases profit by $2,295. In the worst case, Eastman will make a very small profit of $325. The final decision about price should depend on how likely Eastman believes the different demand amounts are to occur. If the probability of a low demand is considered to be small, then Eastman should go ahead and raise the price.

3. Ponderosa Development Corporation (PDC) is a small real estate developer operating in the Rivertree Valley. It has seven permanent employees whose monthly salaries are given below. PDC leases a building for $2,000 per month. The cost of supplies, utilities, and leased equipment runs another $3,000 per month. PDC builds only one style house in the valley. Land for each house costs $55,000 and lumber, supplies, etc. run another $28,000 per house. Total labor costs are figured at $20,000 per house. The one sales representative of PDC is paid a commission of $2,000 on the sale of each house. The selling price of the house is $115,000. Employee Monthly Salary President $10,000 VP, Development $6,000 VP, Marketing $4,500 Project Manager $5,500 Controller $4,000 Office Manager $3,000 Receptionist $2,000 a. Compute the marginal cost and marginal revenue for each house. Variable costs: land, supplies, labor, sales commission Variable cost per house = 55,000 + 28,000 + 20,000 + 2000 = $105,000 Revenue per house = $115,000 b. Develop mathematical models for total monthly cost, revenue, and profit. Fixed costs: salaries, lease, supplies Fixed cost = 35,000 + 2000 + 3000 = $40,000 Cost = 105,000x + 40,000 Revenue = 115,000x Profit = 115,000x – (105,000x + 40,000) = 10,000x – 40,000 c. What is the breakeven point for monthly sales of houses? P = 0  10,000x – 40,000 = 0 so x = 4 d. What is the monthly profit if 12 houses are built and sold in a particular month? Profit = 10,000(12)  40,000 = $80,000 e. Suppose that 12 houses are built and sold in a month but the marginal cost for each house has increased by 5%. What is the corresponding percentage change in monthly profit, assuming the selling price is unchanged? Variable cost per house = 105,000 + 0.05(105,000) = $110,250 Profit = 115,000x – (110,250x + 40,000) = 4,750x – 40,000 so when x = 12 the profit is $17,000 So a 5% increase in marginal cost results in a 78.75% decrease in profit! (based on the change in profit of −$63,000, divided by the original profit of $80,000)

4. You are thinking of opening a new Broadway play. It will cost an estimated $5 million to develop the show. There are 8 shows per week (one every night and two on Sunday), and you project the show will run for 100 weeks. It costs $1,000 to open the theater each night. Tickets sell for $50.00, and you earn an average of $1.50 profit per ticket holder from concessions. The theater holds 800, and you expect 80% of the seats to be full. a. Based on these assumptions, what is your estimated net profit? Total cost consists of development cost and the cost of opening the theater every night C = 5,000,000 + 7(1000)(100) = 5,700,000 Total revenue consists of ticket and concession sales # of tickets sold = 8(100)(0.80)(800) = 512,000 R = (50 + 1.50)(512,000) = 26,368,000 Net profit P = R – C = 26,368,000 – 5,700,000 = 20,668,000

b. How many seats must be filled for the show to break even? Let x = fraction of seats filled # of tickets sold = 8(100)(800)x = 640,000x R = (50 + 1.50)(640,000)x = 32,960,000x Note that total cost is still 5,700,000 since it does not depend on how many tickets are sold P = 0 → 32,960,000x – 5,700,000 = 0 so x = 0.1729 800x = 800 (0.1729) = 138.35 so 139 seats must be filled to break even

c. How many weeks will the play have to run for you earn a 100% return on the play’s development cost? Let w = # of weeks the play runs C = 5,000,000 + 7(1000)w R = (50 + 1.50)(0.80)(800)(8)w = 263,680w

(assuming 80% of seats are filled)

To get a 100% return, the play must have a net profit of $5,000,000 P = 5,000,000 → 263,680w – (5,000,000 + 7000w) = 5,000,000 so w = 38.96 or 39 weeks

5. Suppose that you have been asked to evaluate three possible alternatives for new tanning beds for a local tanning salon. The beds vary substantially in purchase price, but also vary in the projected cost per customer because of different life expectancy for the lights and different labor requirements for cleaning: Alternativ e A B C

Purchase price Cost per user $11,000 $0.14 $9,200 $0.88 $7,800 $1.68

Perform a breakeven analysis of the three alternatives to determine the ranges of users that make each alternative the minimum cost option. Determine the intersection points for each pair of alternatives and compute the corresponding total costs: For A and B 11,000 + 0.14x = 9,200 + 0.88x 1,800 = 0.74x x = 2,432.5 A cost = B cost = $11,341 C cost = $11,886 For A and C 11,000 + 0.14x = 7,800 + 1.68x 3,200 = 1.54x x = 2,077.9 A cost = C cost = $11,291 B cost = $11,029 Notice that this intersection point is not relevant since B has a lower cost than A and C! For C and B 7,800 + 1.68x = 9,200 + 0.88x −1,400 = −0.8x x = 1,750 C cost = B cost = $10,740 A cost = $11,245 Conclusions: For a volume of users at or below 1,750, Alternative C is the lowest cost option. For volumes between 1,750 and 2,432, Alternative B is the lowest cost. For volumes greater than 2,432, Alternative A is the lowest cost. A graph is shown on the next page.

Tanning Bed Alternatives 16,000 14,000 12,000

Alternative A Alternative B Alternative C

8,000 6,000 4,000 2,000 0 0 20 0 40 0 60 0 80 0 1, 00 1, 0 20 1, 0 40 1, 0 60 1, 0 80 2, 0 00 2, 0 20 2, 0 40 2, 0 60 2, 0 80 3, 0 00 3, 0 20 3, 0 40 3, 0 60 3, 0 80 4, 0 00 0

Total cost

10,000

Number of users...