Chapter 5, Additional Exercises 1.
A firm sells sells a product product for for $45 $45 per unit. unit. Variabl Variablee costs costs per unit unit are are $33 and and fixed costs equal equal $450,000. $450,000. How many units must must be sold in order order to break even?
Ans. 37,500 units 2. A product product sells sells for for $25 per per unit. unit. Variable Variable costs costs per per unit unit are $12.50 $12.50 and and fixed fixed costs costs are $100,000. $100,000. How many units units must be produced produced in order order to break even? Ans. 8000 units. 3. A produc productt sells sells for $240 $240 per per unit. unit. Variable Variable costs costs per unit unit are are $212.5 $212.50 0 and and fixed costs equal equal $3 million. million. How many units must be be produced in order order to break even? Ans. 109,090.9 units 4. A product product sells sells for for $22 per per unit. unit. Variable Variable costs costs per per unit unit are $17.50 $17.50 and and fixed fixed costs equal $750,000. How many units must be produced and sold in order to (a) break even? (b) to earn a profit of $250,000? Ans. (a) 166,666.67 units, (b) 222,222.22 units 5. A product product sells sells for for $95 per per unit. unit. Variable Variable costs costs per per unit unit are $77.50 $77.50 and and fixed fixed costs equal $2,500,000. $2,500,000. How many units must must be sold in order order to (a) break even (b) earn a profit of $2 million? Ans. (a) 142,857.14 units, (b) 257,142.86 units. 6. A community community health health center center is holdi holding ng a car raffle raffle to raise raise money money for one of its programs. 500 tickets are to be sold and the objective is to earn a profit of $10,000 $10,000.. If the car costs the health health center center $12,000, $12,000, what price should should be charged for each ticket? Ans. $44.00 7. An enterp enterpri risin sing g colle college ge stude student nt has decide decided d to purchas purchasee a local local car wash business. business. The purchase purchase cost cost is $250,000. $250,000. Car washes washes will be priced at at $5.50. Variable cost cost per car wash (soap, (soap, water, labor, etc.) is $1.50. $1.50. How many cars must be washed in order to recover the $250,000 purchase cost? Ans. 62,500 washes
8.
A charitable organization is planning a raffle to raise $25,000. Five hundred tickets will be sold with the winner receiving a new car. The car will cost the organization $20,000. How much should be charged for each raffle ticket for the organization to raise $25,000?
Ans. $90. 9.
A publisher has a fixed cost of $250,000 associated with the production of a college mathematics text. The contribution to fixed cost and profit from the sale of each book is $6.25. (a) Determine the number of books that would have to be sold in order to break even. (b) What is the expected profit if 50,000 copies of the text are sold?
Ans. (a) 40,000 copies, (b) $62,500 10. A local university football team has added a national power to next year’s schedule. The other team has agreed to play the game for a guaranteed fee of $350,000 plus 30 percent of ticket revenues. Assume that all tickets will be sold for $25. (a) How many tickets must be sold in order to recover the $350,000 guarantee? (b) If college official wish to net a profit of $500,000 from the game, how many tickets must be sold? (c) If a sellout of 50,000 fans is assured, what ticket price would allow the university to earn the desired profit of $500,000? (d) Assuming a sellout of 50,000 tickets, what would total profit equal if the tickets are priced at $25? Ans. (a) 20,000 tickets, (b) 48,571.4 tickets, (c) $24.29, (d) $525,000 11. A local civic arena is negotiating a contract with a touring ice-skating show, Icy Blades. Icy Blades charges a flat fee of $60,000 per night plus 40 percent of ticket revenues. The civic arena plans on charging $12.50 for all tickets. (a) How many tickets must be sold each night for the civic arena to break even? (b) If the civic arena has a goal of earning a profit of $15,000 each night, how many tickets must be sold? (c) What would nightly profit equal if average attendance is 7500 persons? Ans. (a) 8000 tickets, (b) 10,000 tickets, (c) -$3750.00 12. In the previous exercise, assume that past experience indicates that average attendance should equal 7500 persons. (a) What ticket price would enable the arena to break even? (b) What ticket price would allow the arena to earn a profit of $15,000? (c) Given the answer in part (b), what factors might cause the arena to earn the $15,000 profit at that price? Ans. (a) $13.33, (b) $16.67
13. A local charity is selling raffle tickets for a new house. The new house and land on which it will be constructed will cost the charity $150,000. If 2500 tickets are going to be sold and the goal is to earn a profit of $100,000 from the raffle, what price should be charged for each ticket? Ans. $100 14. Two professional basketball teams have agreed to play an exhibition game in a civic arena which holds 15,000 spectators. Each team will be guaranteed $100,000 plus 10 percent of ticket revenues. Assume that a sellout is guaranteed and that all tickets are going to be sold for the same price. (a) What price should be charged if the goal is to break even? (b) What price if a profit of $50,000 is desired from the game. Ans. (a) $16.66, (b) $20.83 15. A rock group is booking a large theatre for one show. The theatre seats 5,000 persons and is guaranteed to sell out for the concert. The group is to be paid $60,000 plus 40 percent of ticket revenues. (a) What ticket price should be charged if the goal is to break even? (b) How much would the rock group earn at this price? (c) What price if the promoters want to earn a profit of $40,000? (d) What would the rock group earn at this price? Ans. (a) $20, (b) $100,000, (c) $33.33, (d) $126,666.67 16. Two ice hockey teams have agreed to play an exhibition game in a civic arena that holds 20,000 spectators. Each team will be guaranteed $50,000 plus 20 percent of ticket revenues. Other expenses are expected to equal approximately 10 percent of ticket revenues. If a sell out is guaranteed and all tickets are going to be sold at the same price, (a) what price should be charged if the goal is to break even? (b) How much money would each team earn? (c) What price should be charged if the goal is to earn a profit of $80,000? Ans. (a) $10.00, (b) $90,000, (c) $18.00 17. A broadway show is being scheduled at a theatre for one show. The theatre seats 4,000 persons and is guaranteed to sell out for the performance. The theatrical group is to be paid $100,000 plus 40 percent of the ticket revenues. (a) What price should be charged per ticket if the goal is to break even? (b) How much would the theatrical group earn at this price? (c) What ticket price should be charged if the goal is for the promoters to earn a profit of $50,000? (d) What would the theatrical group earn at this ticket price? Ans. (a) $41.67, (b) $166,666.67, (c) $62.50, (d) $200,000
18. Assume that a manufacturer can purchase a needed component from a supplier at a cost of $9.50 per unit or it can invest $60,000 in a piece of equipment and produce the item at a cost of $7.00 per unit. (a) Determine the quantity for which total costs are equal for the make and buy alternatives, (b) What is the minimum cost alternative if 15,000 units of the component are needed, (c) If 25,000 units of the component are needed, how much money would be saved by making the component as opposed to buying it? (d) Discuss factors that might lead the company to decide to buy the component in part (c) even though it would be more costly. Ans. (a) 24,000 units, (b) Buy, (c) $2,500 19. Assume that a manufacturer can purchase a needed component from a supplier at a cost of $7.50 per unit or it can invest $100,000 in a piece of equipment and produce the item at a cost of $5.50 per unit. (a) Determine the quantity for which total costs are equal for the make and buy alternatives, (b) What is the minimum cost alternative if 60,000 units of the component are needed, (c) If 75,000 units of the component are needed, how much money would be saved by making the component as opposed to buying it? Ans. (a) 50,000 units, (b) Make, (c) $50,000 20. Assume that a manufacturer can purchase a needed component from a supplier at a cost of $22.50 per unit or it can invest $500,000 in a piece of equipment and produce the item at a cost of $17.50 per unit. (a) Determine the quantity for which total costs are equal for the make and buy alternatives, (b) What is the minimum cost alternative if 90,000 units of the component are needed, (c) If 90,000 units of the component are needed, how much money would be saved by buying the component as opposed to buying it? (d) Discuss factors that might lead the company to decide to buy the component in part (c) even though it would be more costly. Ans. (a) 100,000 units, (b) Buy, (c) $50,000 21. A company can purchase a needed part from a supplier at a cost of $25 per unit or it can invest $1,000,000 in a piece of equipment and make the unit. Assume the company needs 200,000 units of the part. What would the cost per unit of making the unit have to be for the make and buy options to be equally costly. Ans. $20 per unit.
22. A company can purchase a needed part from a supplier at a cost of $30 per unit or it can invest $750,000 in a piece of equipment and make the unit. Assume the company needs 150,000 units of the part. What would the cost per unit of making the unit have to be for the make and buy options to be equally costly. Ans. $25 per unit. 23. A company can make a needed component part for $27.50 per unit if it spends $900,000 on a piece of machinery. The company can also purchase the part from a supplier. (a) If the company needs 120,000 units of the part, what would the purchase price per unit have to be for the make and buy options to be equal? (b) What would the costs equal for the two alternatives? Ans. (a) $35 per unit, (b) $4,200,000 24. A company can make a needed component part for $50 per unit if it spends $600,000 on a piece of machinery. The company can also purchase the part from a supplier. (a) If the company needs 60,000 units of the part, what would the purchase price per unit have to be for the make and buy options to be equal? (b) What would the costs equal for the two alternatives? Ans. (a) $60 per unit, (b) $3,600,000 25. A firm has two equipment alternatives that it can choose from in producing a new product. One automated piece of equipment costs $200,000 and produces items at a cost of $4 per unit. Another semi-automated piece of equipment costs $125,000 and produces items at a cost of $5.25 per unit. (a) For what number of units are the costs the same for the two pieces of equipment? (b) If 80,000 units are to be produced, which piece of equipment is less costly? (c) In part (b), what is the minimum cost? Ans. (a) 60,000 units, (b) The automated machine, (c) $520,000 26.
A information technology company has two options for software development. One option is to hire programmers. For this option, overhead costs of supporting a programmer equal $50,000 per year and the average cost per line of computer code is $1.50. The second option is to have software developed by an outside vendor. Under this option, costs are estimated to equal $2.25 per line of computer code. (a) For what number of lines of computer code are the two options equally costly? (b) If the company estimates that it needs 100,000 lines of code developed each year, what would the costs be under the two options?
Ans. (a) 66,666.67 lines, (b) $200,000 for in-house development; $225,000 from the vendor. 27.
A car-leasing agency purchases new cars each year at a cost of $24,000. Cars are leased for a 3-year period, after which they are sold for an average cost of $8000. The maintenance cost on a vehicle is estimated to equal $.15 per mile. Cars are leased at a flat rate of $.55 per mile (gasoline not included). (a) What is the break-even mileage for a three-year lease? (b) What are total revenue, total cost and total profit for a car that is leased for 50,000 miles over three years? (c) What price per mile must be charged for the firm to break even on a car that is leased for 50,000 miles over three years? (d) What price per mile must be charged in order for the firm to earn a profit of $10,000 on a car leased for 50,000 miles over three years? Ans. (a) 40,000 miles, (b) total revenue = $27,500, total cost = $23,500, total profit = $4000, (c) $.47, (d) $.67 28. A company makes three products. The three products sell at prices of $30, $35, and $25, respectively. Variable costs per unit are $18, $24, and $16, respectively, while shared fixed costs total $1.5 million. Sales of the products are such that for each unit sold of product 2, 3 units of product 1 and 2 units of product 3 are sold. How many units of each product must be sold in order to break even? Ans. 69,230.77 units of product 1, 23,076.92 units of product 2 and 46,153.84 units of product 3. 29. A company makes three products. The three products sell at prices of $25, $15, and $40, respectively. Variable costs per unit are $17, $9, and $26, respectively, while shared fixed costs total $2.4 million. Sales of the products are such that for each unit sold of product 1, 4 units of product 2 and 2 units of product 3 are sold. How many units of each product must be sold in order to break even? Ans. 40,000 units of product 1, 160,000 units of product 2 and 80,000 units of product 3. 30. A company makes three products. The three products sell at prices of $14, $9, and $18, respectively. Variable costs per unit are $8, $4, and $9, respectively, while shared fixed costs total $500,000. Sales of the products are such that for each unit sold of product 3, 2 units of product 1 and 2.5 units of product 3 are sold. How many units of each product must be sold in order to break even? Ans. 29,850.75 units of product 1, 37,313.43 units of product 2 and 14,925.37 units of product 3.
31. A company makes three products. The three products sell at prices of $65, $80, and $64, respectively. Variable costs per unit are $47, $72, and $40, respectively, while shared fixed costs total $750,000. Sales of the products are such that for each unit sold of product 1, 3 units of product 2 and 2.5 units of product 3 are sold. How many units of each product must be sold in order to break even? Ans. 7352.94 units of product 1, 22,058.82 units of product 2 and 18,382.35 units of product 3. 32. A company makes four products. The four products sell at prices of $50, $45, $30 and $20, respectively. Variable costs per unit are $20, $15, $10 and $10, respectively, while shared fixed costs total $500,000. Sales of the products are such that for each unit sold of product 4, 1.5 units of product 3, 3 units of product 2 and 2.5 units of product 1 are sold. (a) How many units of each product must be sold in order to break even? (b) How many units of each product must be sold in order to earn a profit of $2,000,000? Ans. (a) 6097.5 units of product 1, 7317 units of product 2, 3658.5 units of product 3 and 2439 units of product 4. (b) 30,487.8 units of product 1, 36,585.36 units of product 2, 18,292.68 units of product 3 and 12,195.12 units of product 4. 33. A company makes three products. The three products sell at prices of $40, $32, and $55, respectively. Variable costs per unit are $20, $24, and $46, respectively, while shared fixed costs total $2,800,000. Sales of the products are such that for each unit sold of product 1, 4 units of product 2 and 2 units of product 3 are sold. (a) How many units of each product must be sold in order to break even? (b) How many units of each product must be sold in order to earn a profit of $3,500,000? Ans. (a) 40,000 units of product 1, 160,000 units of product 2 and 80,000 units of product 3. (b) 90,000 units of product 1, 360,000 units of product 2 and 180,000 units of product 3.
