Problems from page 369 – 375

Problems 369

CHAPTER SUMMARY The breakeven point for a variable for one project is expressed in terms such as units per year or hours per month. At the breakeven amount QBE, there is indifference to accept or reject the proj- ect. Use the following decision guideline:

Single Project (Refer to Figure 13–2.)

Estimated quantity is larger than QBE ? accept project Estimated quantity is smaller than QBE ? reject project

For two or more alternatives, determine the breakeven value of the common variable. Use the following guideline to select an alternative:

Two Alternatives (Refer to Figure 13–5.)

Estimated level is below breakeven ? select alternative with higher variable cost (larger slope)

Estimated level is above breakeven ? select alternative with lower variable cost (smaller slope)

Payback analysis estimates the amount of time, for example, number of years, necessary to re- cover the initial investment plus a stated rate of return. This is a supplemental analysis technique used primarily for initial screening prior to a full evaluation by PW or some other method. The technique has some drawbacks, especially for no-return payback analysis, where i = 0% is the stated return.

PROBLEMS Breakeven Analysis for a Project

13.1 The fixed cost at Harley Motors is $5 million annu- ally. The main product has revenue of $89 per unit and $45 variable cost. Estimate the following: (a) Breakeven quantity per year; and (b) annual profit if 100,000 units are sold, and if 200,000 units are sold.

13.2 A manufacturing process at Simplicity XP has a fixed cost of $40,000 per month. A total of 100 units can be produced in 1 day at a cost of $3000 for materials and labor for the day. If the compa- ny’s MARR is 12% per year, compounded monthly, how many units must be sold each month at $50 per unit for the company to just break even?

13.3 A professional photographer who specializes in wedding-related activities paid $48,000 for equip- ment that will have a $2000 salvage value after 5 years. He estimates that his costs associated with each event amount to $65 per day. If he charges $300 per day for his services, how many days per year must he be employed in order to break even at an interest rate of 8% per year?

13.4 An independent over-the-road (OTR) truck driver- owner paid $68,000 for a used tractor-trailer. The

salvage value of the rig after 5 more years of use is expected to be $36,000. The operating cost is $0.50 per mile and the base mileage rate (i.e., rev- enue) is $0.61 per mile. (a) How many miles per year must the owner

drive just to break even at an interest rate of 10% per year?

(b) If the owner drives 600 miles per day, how many days per year will be required for break even?

13.5 Handheld fiber optic meters with white light polar- ization interferometry are useful for measuring tem- perature, pressure, and strain in electrically noisy environments. The fixed costs associated with man- ufacturing are $800,000 per year. If variable costs are $290 per unit and the company sells 4000 units per year, at what selling price per unit will the com- pany break even?

13.6 The costs and revenue projections for a new prod- uct are estimated. What is the estimated profit at a production rate of 20% above breakeven?

Fixed cost = $500,000 per year Production cost per unit = $200 Revenue per unit = $250

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13.7 Freeport McMoRan engineers estimated that the capital investment necessary for recovering valu- able metals (nickel, silver, gold, etc.) from a cop- per refinery’s wastewater would be $150 million. The equipment is expected to have a useful life of 10 years with no salvage value. The amount of metal currently discharged in the wastewater is 12,500 pounds per year. The recovered metals are expected to have a selling price of $250 per pound. The efficiency relation of the recovery operation is represented by X 0.5, where X represents the effi- ciency in percentage. What value of X is necessary for the company to break even? Assume i = 10% per year.

13.8 A company that manufactures automatic blow- down control valves (for applications where boilers are operated unsupervised for 24 to 36 hours) has fixed cost of $160,000 per year and variable cost of $400 per valve. If the company expects to sell 12,000 valves per year, determine the selling price in order for the com- pany to (a) break even, and (b) make a profit of $400,000 per year.

13.9 If the cost of gasoline is $2.50 per gallon, how far out of your way (one way) could you afford to drive (in miles) to a service station that has gaso- line at $2.25 per gallon if your vehicle gets 30 miles per gallon and you will fill up with 20 gallons of fuel? Consider only the cost of gaso- line in vehicle driving cost. (Hint: Since you are going out of your way, you have to drive back the same distance.)

13.10 The landfill for Wellsburg has an area of 30 acres available for receiving waste from the city of 40,000 people who generate 25,000 tons of mu- nicipal solid waste (MSW) per year. If the fixed cost of the landfill is $300,000 per year and the operating cost is $12 per ton, how much must the landfill charge per ton of MSW to break even?

13.11 A financial services consulting company bought an office building for $900,000. The company has 10 professional staff members. Monthly expenses for salaries, utilities, grounds maintenance, etc. are $1.1 million. The average billing rate per profes- sional is $90 per hour. Use an interest rate of 1% per month and assume the building will have a re- sale value of $1.5 million after 10 years. (a) How many hours per month must be billed in order to make a profit of $15,000 per month? (b) How many hours per professional per month must be billed? (c) There are 260 eight-hour workdays per year. Of the total work hours available per month,

what percentage does the hours per professional in part (b) represent?

13.12 You work for Bellevue Window Products. While performing an analysis for a new window prod- uct, you found a report from last year that pro- vided the following information regarding the manufacture of a similar product: annual produc- tion rate = 40,000 units; selling price = $70 per unit; fixed production cost = $240,000 per year; variable production cost = $1,700,000 per year; variable selling expenses = $96,000 per year. As a first-cut, you decide to use this information to estimate (a) the breakeven production rate per year, (b) the company’s profit last year, and (c) the annual production rate that would generate a profit of $1,000,000 per year. What are your estimates?

13.13 An automobile company is investigating the ad- visability of converting a plant that manufactures economy cars into one that will make retro-sports cars. The initial cost for equipment conversion will be $250 million with a 20% salvage value anytime within a 5-year period. The cost of pro- ducing a car will be $25,000, but it is expected to have a selling price of $43,000 (to dealers). The production capacity for the first year will be 4000 units. At an interest rate of 12% per year, by what uniform amount will production have to in- crease each year in order for the company to recover its investment in 3 years? Assume the production cost and selling price will remain con- stant for the 3-year period. Solve (a) by hand, and (b) using a spreadsheet.

Breakeven Analysis Between Alternatives

13.14 A rotational molding operation has fixed costs of $10,000 per year and variable costs of $50 per unit. If the process is automated via conveyor, its fixed cost will be $22,800 per year but its variable cost will be only $10 per unit. Determine the number of units each year necessary for the two operations to break even.

13.15 A two-lane road surface can be finished with concrete or asphalt. Concrete will cost $2.3 mil- lion per mile (excluding right-of-way, environ- mental mitigation, or soil and site conditions) and will last for 20 years. If signing, mowing, and winter maintenance are not included, the basic maintenance costs for concrete and asphalt roadways average $486 and $774 per mile per year, respectively. The interest rate is 8% per year. (a) What is the maximum amount that can be spent on asphalt if it lasts 10 years? (b) Use a

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Problems 371

spreadsheet to graph the breakeven curve for the cost of asphalt, if different quality levels of as- phalt can be used with expected lives of 5, 8, 10, 12, and 15 years.

13.16 Pure gasoline has an energy density of 115,600 BTU per gallon while ethanol has an energy den- sity of 75,670 BTU per gallon. If gasoline costs $3.50 per gallon, (a) what would the cost of pure ethanol have to be in order for the energy costs of the two fuels to break even? (b) What would the price of E85 (85% ethanol, 15% gasoline) have to be for its energy cost to be the same as that of pure gasoline?

13.17 A construction company can purchase a used backhoe for $90,000 and spend $450 per day in operating costs. The equipment will have a 5-year life with no salvage value. Alternatively, the com- pany can lease the equipment for $800 per day. How many days per year must the company use the equipment in order to justify its purchase at an in- terest rate of 8% per year.

13.18 Process A has a fixed cost of $160,000 per year and a variable cost of $50 per unit. For Process B, 10 units can be produced in 1 day at a cost of $200. If the company’s MARR is 10% per year, what will the annual fixed cost have to be for Process B in order for the two alternatives to have the same an- nual total cost at a production rate of 1000 units per year?

13.19 There are a number of reasons for not paving a rural road, including low traffic volume, property owners who do not want it paved, speed control, and political issues. On the other hand, paved roads have lower road-user operating costs and are less costly to maintain. In Washington County, a report prepared by the county engineer showed that the construction cost for a stabilized gravel road that will last 3 years is $1,025,000, with a maintenance cost of $355,000 per year. A bitumi- nous road will cost $3,525,000, but it will last for 10 years. Use i = 8% per year. (a) At what main- tenance cost per year (for the bituminous road) will the equivalent annual costs of the two roads be the same? (b) If the road is not paved and the annual maintenance cost of the stabilized gravel surface is actually 30% per year higher than esti- mated, how many years must this surface last for the two to break even, assuming the paved road maintenance would be the breakeven value deter- mined above? Answer these questions using man- ual and spreadsheet solution, as your instructor requests.

13.20 A land development company is considering the purchase of earth-moving equipment. This equipment will have an estimated first cost of $190,000, a salvage value of $70,000, a life of 10 years, a maintenance cost of $40,000 per year, and an operating cost of $260 per day. Alternatively, the company can rent the neces- sary equipment for $1100 per day and hire a driver at $180 per day. (a) If the company’s MARR is 10% per year, how many days per year must the company need the equipment in order to justify its purchase? (b) When approached to rent for the breakeven number of days, the equipment owner indicated that the minimum rental is for 100 days per year; however, he might consider a lower daily rental cost. What is the daily rental cost to justify renting over pur- chasing? If the equipment was purchased, as- sume it would be used for the breakeven number of days. Use the Goal Seek or Solver tool to de- termine the required rental cost per day.

13.21 Microsurfacing is part of a pavement restoration and maintenance program that seals the surface of a street that has minor cracking to prevent water from penetrating into the base material. The annual cost of the equipment (truck, tank, valves, etc.) is $109,000 per year and the material cost is $2.75 per square yard. Alternatively, regu- lar street resurfacing requires equipment that has a first cost of $225,000 with a 15-year life and no salvage value. The variable cost for regular resur- facing is $13 per square yard. At an interest rate of 8% per year, how many square yards per year must be resurfaced for the two methods to break even?

13.22 Two membrane systems are under consideration for treating cooling tower blowdown to reduce its volume. A low-pressure seawater reverse osmosis (SWRO) system will operate at 500 psi and pro- duce 720,000 gallons of permeate per day. It will have a fixed cost of $465 per day and an operating cost of $485 per day. A higher-pressure SWRO system operating at 800 psi will produce 950,000 gallons per day at a cost of $1280 per day. The fixed cost of the high-pressure SWRO system will be only $328 per day because fewer membranes will be required. How many gallons of blowdown water will require treatment each day for the two systems to break even?

13.23 Three methods can be used for producing heat sen- sors for high-temperature furnaces. The interest rate for the economic evaluation is 10% per year.

Method A: Fixed cost of $140,000 per year Production cost of $62 per part

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372 Chapter 13 Breakeven and Payback Analysis

Method B: Fixed cost of $210,000 per year Production cost of $28 per part

Method C: Equipment first cost of $500,000 Life of 5 years Salvage value of 25% of first cost Production cost of $53 per part

(a) Determine the breakeven annual production rate between the two lowest-cost methods.

(b) Develop the spreadsheet graph of the an- nual cost for all three methods and estimate the breakeven production rate(s) from the graph.

(c) Use your spreadsheet and graph to deter- mine the required annual fixed cost of method A that forces a breakeven between methods A and C at the rate of 2000 parts per year.

13.24 An online commercial directory service must de- cide between composing the ads for its clients in- house or paying a production company to compose them. To develop the ads in-house, the company will have to purchase computers, printers, and a database management system at an estimated cost of $42,000. This equipment will have a useful life of 3 years, after which it will be sold for $2000. The employee who creates the ads will be paid $55,000 per year. In addition, each ad will have an average cost of $10. Alternatively, the company can outsource development at a flat fee of $21 per ad. At an interest rate of 10% per year, how many ads must the company sell each year for the op- tions to just break even?

13.25 James, the plant manager at Global Foundries (GF), received estimates from two contractors to improve traffic flow and repave the parking areas at his production facility. Proposal A includes new curbs, grading, and paving at an initial cost of $250,000. The expected life of the parking lot surface is 4 years with annual costs for mainte- nance and repainting of strips of $3000. Accord- ing to proposal B, the pavement has a higher quality and an expected life of 12 years. The an- nual maintenance cost will be negligible for the parking area, but the markings will have to be re- painted every 2 years at a cost of $5000. The MARR is 12% per year. (a) How much can GF afford to spend on proposal B for the two propos- als to break even? (b) Proposal B first cost came in at $700,000. Now, what is the breakeven initial cost for proposal A, if all other estimates are correct?

13.26 Alfred Home Construction is considering the purchase of five dumpsters and the transport truck to store and transfer construction debris from building sites. The entire rig is estimated to

have an initial cost of $125,000, a life of 8 years, a $5000 salvage value, an operating cost of $40 per day, and an annual maintenance cost of $2000. Alternatively, Alfred can obtain the same services from the city as needed at each con- struction site for an initial delivery cost of $125 per dumpster per site and a daily charge of $20 per day per dumpster. An estimated 45 construc- tion sites will need debris storage throughout the average year. If the minimum attractive rate of return is 12% per year, how many days per year must the equipment be required to justify its purchase?

13.27 Process X is estimated to have a fixed cost of $40,000 per year and a variable cost of $60 per unit in year 1, decreasing by $5 per unit per year thereafter. Process Y will have a fixed cost of $70,000 per year and a variable cost of $10 per unit in year 1, increasing by $1 per unit per year thereafter. At an interest rate of 12% per year, how many units must be produced in year 3 for the two processes to break even?

13.28 The Ecology Group wishes to purchase a piece of equipment for recycling of various metals. Ma- chine 1 costs $123,000, has a life of 10 years, an annual cost of $5000, and requires one operator at a cost of $24 per hour. It can process 10 tons per hour. Machine 2 costs $70,000, has a life of 6 years, an annual cost of $2500, and requires two operators at a cost of $24 per hour each to process 6 tons per hour. Assume i = 7% per year and 2080 hours per work year. Determine the annual break- even tonnage of scrap metal at i = 7% per year and select the better machine for a processing level of 1500 tons per year.

13.29 Claris Water Company makes and sells filters for water drinking fountains for the public. The filter sells for $50. Recently a make/buy analysis was done based on the need for new manufacturing equipment. The equipment first cost of $200,000 and $25,000 annual operation cost comprise the fixed cost, while Claris’s variable cost is $20 per filter. The equipment has a 5-year life, no salvage value, and the MARR is 6% per year. The deci- sion to make the filter was based on the breakeven point and the historical sales level of 5000 filters per year. (a) Determine the breakeven point. (b) An engineer at Claris learned that an out-

sourcing firm offered to make the filters for $30 each, but this offer was rejected by the president as entirely too expensive. Perform the breakeven analysis of the two options and determine if the “make” decision was correct.

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Problems 373

(c) Develop and use the profit relations for both options to verify the preceding answers.

(d) Use a spreadsheet to verify the answers to parts (b) and (c) above by plotting the profit lines.

Payback Analysis

13.30 State why payback analysis should be used only as a supplemental analysis tool when an economic study is performed.

13.31 Darnell Enterprises constructed an addition to its building at a cost of $70,000. Extra annual ex- penses are expected to be $1850, but extra income will be $14,000 per year. How long will it take for the company to recover its investment at an interest rate of 10% per year? Also, write the spreadsheet function that determines np.

13.32 (a) How long would it take to recover an invest- ment of $245,000 in enhanced CNC controls that include axis control to eight axes on the milling model, if the associated income is $92,000 per year, expense is $38,000 per year, and the salvage value is estimated to be 15% of the first cost? Use a MARR of 15% per year. (b) Also, write the spreadsheet function that determines np.

13.33 Accusoft Systems is offering small business own- ers a software package that keeps track of many ac- counting functions from bank transactions to sales invoices. The site license will cost $39,000 to in- stall and will require a fee of $6000 every 3 months. If your company can save $13,500 every quarter and have the security of managing its books in- house, how long will it take for you to recover the investment at an interest rate of 10% per quarter?

13.34 (a) What is the approximate number of years you would have to sell a mobile phone app to break even if income is estimated to be $50,000 per year, expense is $15,000 per year, your initial invest- ment is $280,000, and your MARR is 10% per year? (b) Find the exact payback period using a spreadsheet function.

13.35 The price of a car you want is $42,000 today. Its price is expected to increase by $1000 each year. You now have $25,000 in an investment account, which is earning 10% per year. How many years will it be before you have enough to buy the car without borrowing any money? Solve by (a) trial and error, and (b) by spreadsheet.

13.36 A process for producing the mosquito repellant Deet has an initial investment of $200,000 with annual costs of $50,000. Income is expected to be $90,000 per year. (a) What is the payback period at

i = 0% per year? A i = 12% per year? (Note: Round your answers to the nearest integer.) (b) What is the annual breakeven production quantity for both payback periods (determined above) if net profit, that is, income minus cost, is $10 per gallon?

13.37 Two machines can be used to produce a part from titanium. The costs and other cash flows associated with each alternative are estimated. The salvage val- ues are constant regardless of when the machines are replaced. Determine which alternative(s) should be selected for further analysis if alternatives must have a payback of 5 years or less. Perform the analy- sis with (a) i = 0%, and (b) i = 10% per year.

Machine Semiautomatic Automatic First cost, $ ?40,000 ?90,000 Net annual income, $ per year 10,000 15,000 Maximum life, years 10 10 Salvage value, $ 0 0

13.38 A manufacturer of diaphragm seals has identified the cash flows shown for manufacturing and sales functions. Determine the no-return payback period.

First cost of equipment, $ ?130,000 Annual expenses, $ per year ?45,000 Annual revenue, $ per year 75,000

13.39 In desalting groundwater that contains a signifi- cant amount of sulfates, the concentrate that is generated during the desalting process can some- times be tough on equipment, so the equipment’s useful life is uncertain. For a treatment train that has an initial cost of $90,000 and an estimated operating cost (OC) between $15,000 and $20,000 per month, use a spreadsheet to deter- mine how many months the equipment must last to recover the investment at i = 0.5% per month at each OC value? Assume the income from the sale of calcium sulfate is $22,000 per month. (Note: Solve using increments of $1000 OC per month.)

13.40 A multinational engineering consulting firm that wants to provide resort accommodations to spe- cial clients is considering the purchase of a three- bedroom lodge in upper Montana that will cost $250,000. The property in that area is rapidly ap- preciating in value because people anxious to get away from urban developments are bidding up the prices. If the company spends an average of $500 per month for utilities and the investment increases at a rate of 0.75% per month, how long would it be before the company could sell the property for $100,000 more than it has invested in it?

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374 Chapter 13 Breakeven and Payback Analysis

13.41 A window frame manufacturer is searching for ways to improve revenue from its triple-insulated sliding windows, sold primarily in the far northern areas of the United States. Alternative A is an in- crease in TV and radio marketing. A total of $300,000 spent now is expected to increase reve- nue by $60,000 per year. Alter na tive B requires the same investment for enhancements to the in-plant manufacturing process that will improve the temper ature retention properties of the seals around each glass pane. New revenues start slowly for this alternative at an estimated $10,000 the first year, with growth of $15,000 per year as the im- proved product gains reputation among builders. The MARR is 8% per year and the maximum pro- jection period is 10 years for either alternative. Use (a) payback analysis, and (b) present worth analy- sis (for 10 years) to select the more economical alternative. State the reason(s) for any difference in the alternative chosen between the two analyses. (c) Find the payback and present worth values using aspreadsheet.

EXERCISES FOR SPREADSHEETS

13.42 Benjamin used regression analysis to fit quadratic relations to monthly revenue, R, and total cost, TC, data with the following results, where Q is quantity.

R = ?0.008Q2 + 32Q TC = 0.005Q2 + 2.2Q + 10

(a) Plot R and TC. Estimate the quantities QBE and Qp, where the maximum profit should occur. Estimate the amount of profit at this quantity.

(b) The profit relation P = R ? TC and calculus can be used to determine the quantity Qp at which the maximum profit will occur and the amount of this profit. The equations are:

Profit = aQ2 + bQ + c Qp = ?b/2a

Maximum profit = ?b2/4a + c

Use these relations to confirm your graphical estimate of QP. (Your instructor may ask you to derive the relations above.)

13.43 The National Potato Cooperative purchased a deskinning machine last year for $150,000. Reve- nue for the first year was $50,000. Over the total estimated life of 8 years, use a spreadsheet to esti- mate the remaining equivalent annual revenues (years 2 through 8) to ensure breakeven by recov- ering the investment and a return of 10% per year. Costs are expected to be constant at $42,000 per year and a salvage value of $10,000 is anticipated.

Problems 13.44 and 13.45 are based upon the following information.

Wilson Partners manufactures thermocouples for remote temperature monitoring of electronics applications. The current system has a fixed cost of $400,000 per year and a variable cost of $10 per unit. Wilson sells the units for $14 each. A newly proposed system will add on-board features that allow the revenue to increase to $16 per unit, but the fixed cost will now be $600,000 per year. The variable cost of the new system will be based on a $48 per hour rate with 0.2 hour dedicated to produce each unit.

13.44 Determine the annual breakeven quantity for the (a) current system, and (b) proposed system.

13.45 Plot the two profit relations and estimate graphi- cally the breakeven quantity between the current and proposed systems. Comment on your estimate.

Problems 13.46 through 13.49 are based on the following information.

Mid-Valley Industrial Extension Service, a state-spon- sored agency, provides water quality sampling services to all business and industrial firms in a 10-county region. Last month, the service purchased all necessary lab equip- ment for full in-house testing and analysis. Now, an out- sourcing company has offered to take over this function on a per-sample basis. Data and quotes for the two options have been collected. The MARR for government projects is 5% per year and a study period of 8 years is chosen.

In-house: Equipment and supplies initially cost $125,000 for a life of 8 years, an AOC of $15,000, and annual salaries of $175,000. Sample costs average $25. There is no significant salvage value for the equipment and supplies cur- rently owned.

Outsourced: Cost averages $100 per sample for the first 5 years, increasing to $125 per sample for years 6 through 8.

13.46 Determine the breakeven number of tests between the two options.

13.47 Use a spreadsheet to graph the AW curves for both options for test loads between 0 and 5000 per year in increments of 1000 tests. What is the estimated breakeven quantity?

13.48 The service director has asked the outsource com- pany to reduce the per sample costs by 25% across

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Additional Problems and FE Exam Review Questions 375

13.50 In linear breakeven analysis, if process A has a variable cost of $45 per unit and process B has a variable cost of $31 per unit, which alternative would be preferred if the breakeven point is 7400 units and production is expected to be 6200 units? (a) Process A (b) Process B (c) Process B if its fixed cost is lower than the

fixed cost of Process A (d) Cannot tell; need more information

13.51 An automobile leasing company has a contract with a new car dealer to do major repairs for $720 per car. The leasing company estimates that for $400,000, it could buy equipment to service their own cars at a cost of $300 per car. If the equipment will have a salvage value of 10% of its first cost after 15 years, the minimum number of cars that must require major servicing each year to justify the equipment at a MARR of 10% per year is closest to: (a) 88 (b) 122 (c) 128 (d) 143

13.52 For the following two AW relations, the breakeven point QBE in miles per year is closest to:

AW1 =?23,000(A/P,10%,10) + 4000(A/F,10%,10) ? 5000 ? 4X

AW2 = ?8,000(A/P,10%,4) ? 2000 ? 6X

(a) 1984 (b) 1224 (c) 1090 (d) 655

13.53 A milling process is accomplished using either method X or Y. Method X has fixed costs of $10,000 per year with a variable cost of $50 per unit. Method Y is an automated process with a fixed cost of $5,000 per year and a variable cost of only $30 per unit. The number of units that must be produced each year in order for method Y to be favored is closest to: (a) Y will be favored for any level of production (b) 125 (c) 375 (d) X will be favored for any level of production

13.54 You saw that there was a gasoline price war going on in a small town 27 miles from where you live (54 miles

round trip), so you are thinking about driving there to fill the tank in your pick-up truck, which gets 18 miles per gallon. You think it will take 22 gallons to fill your tank. If the cost of gasoline at your usual station is $3.60 per gallon, the required price at the out-of-town station to just breakeven is closest to: (a) $3.63 (b) $2.82 (c) $2.95 (d ) $3.11

13.55 Revcon Products has two subcontractor bids to auto- mate a composite winding process. Process A will have fixed costs of $42,000 per year and will require two workers at $80 per day each. Together, these workers can generate 100 units. Process B will have fixed costs of $56,000 per year, but with this pro- cess, three workers will generate 200 units of prod- uct. If x is the number of units, the variable cost (VC) per year for B is best represented as: (a) VC per Year = [2(80)/100]x (b) VC per Year = [3(80)/200]x (c) VC per Year = [3(80)/200]x + 56,000 (d ) VC per Year = [2(80)/100]x + 42,000

13.56 The pieces of equipment required to place 160 cubic yards of concrete in 1 day by experienced workmen are two gasoline engine vibrators and one concrete pump. If the vibrators cost $76 per day and the con- crete pump costs $580 per day, the variable cost of the equipment per cubic yard of concrete is closest to: (a) $0.95 (b) $3.63 (c) $4.10 (d ) $4.60

13.57 A jalapeno canning company is faced with a make/ buy decision. Cardboard shipping cartons can be purchased for $0.60 each or made in-house. If man- ufactured, two machines will be required. Machine X will cost $20,000 and have a life of 6 years with a $2000 salvage value. Machine Y will cost $11,000 and have a life of 4 years with no salvage value. The annual maintenance cost for machines X and Y are $6000 and $5000 per year, respectively. A total of four operators will be required for the two machines at a rate of $22.50 per hour per person. In a normal

ADDITIONAL PROBLEMS AND FE EXAM REVIEW QUESTIONS

the board over the 8 years. Will this increase or decrease the breakeven point? (Hint: Look care- fully at your graph from the previous problem be- fore answering.) Determine the breakeven point by hand and using your spreadsheet.

13.49 Assume the Extension Service can reduce its an- nual salaries from $175,000 to $100,000 per year

and the per sample cost from $25 to $20. Out- sourced samples will cost $100 per sample. What will this do to the breakeven point? (Hint: Again, look carefully at your graph from the previous problems before answering.) Use your spreadsheet and hand solution to estimate the new annual breakeven test quantity.