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IEEN 5329 Homework 11 13

Economics

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IEEN 5329

Homework 11

13.6, 13.16, 13.19

PROBLEMS

Breakeven Analysis for a Project

13 (1) The fixed costs at Harley Motors are $1 million annually. The main product has revenue of $8.50 per unit and $4.25 variable cost. Determine the following.

(a) Breakeven quantity per year.

(b) Annual profit if 200,000 units are sold and if 350.000 units are sold.

Use both an equation and a plot of the revenue and total cost relations to answer.

13.2 If both linear and nonlinear revenue and total cost relations are considered, state at least one combination of mathematical relations for which there could easily be exactly two breakeven points.

13.3 A metallurgical engineer has estimated that the capital investment for recovering valuable metals (nickel. silver, gold, etc.) from a copper refinery’s wastewater stream will be $15 million. The equipment will have a useful life of 10 years with no salvage value. The amount of metals currently dis-charged is 12,000 pounds per month. The monthly operating cost is represented by $(4,100,000)E^1.8, where E is the efficiency of metal recovery in decimal form. Determine the minimum removal efficiency required for the company to break even, if the average selling price of the metals is $250 per pound. Use an interest rate of 1% per month.

13.4 For the estimates below, calculate the following.

(a) Breakeven quantity per month.

(b) Profit (loss) per unit at sales levels that are 10% above and 10% below breakeven

(c) Plot average cost per unit for quantities ranging from 25% below to 30% above breakeven.

r = $39.95 per unit

v = $24.75 per unit

FC = $4,000,000 per year

13.5 Develop a plot of the average cost per unit versus production quantity for the houseware appliance assembly department of Ace-One, Inc., that has a fixed cost OF $160,000 per year and a variable cost of $4.00 per unit; use it to answer the following questions.

(a) At what quantity is a $5 per unit average cost justified?

(b) If the fixed cost increases to $200,000, plot the new curve on the same graph and estimate the quantity that justifies an average cost of $6 per unit.

13.6 A call center in India used by U.S. and U.K. credit card holders has a capacity of 1,400,000 calls annually. The fixed cost of the center is $775,000 with an average variable cost of $2 and revenue of $3.50 per call.

(a) Find the percentage of the capacity that must be placed each year to break even.

(b) The center manager expects to dedicate the equivalent of 500,000 of the 1.400,000 capacity to a new product line. This is expected to increase the center’s fixed cost to $900,000, of which 50% will be allocated to the new product line. Determine the average revenue per call necessary to make 500.000 calls the breakeven point for only the new product. How does this required revenue compare with the current center revenue of $3.50 per call?

13.7 For the fast 2 years, the Homes-r-US company has experienced a fixed cast of $850,000 per year and an(r — v) value of $1.25 per unit. International competition has become severe enough that some financial changes must be made to keep market share al the current level. Perform a graphical analysis, using Excel that estimates the effect on the breakeven point if the difference between revenue and variable cost per unit increases somewhere between 1% and 15% of its current value. If fixed costs and revenue per unit remain at their current values, what must change to make the breakeven point go down?

13.8 (This is an extension of Problem 13.7.) Expand the analysis performed in Problem 13.7, where a change in variable cost per unit is examined. The financial manager estimates that fixed costs will fall to $750,000 when the required production rate to break even is at or below 600,000 units. What happens to the breakeven points over the r –v range of 1% to 15% increase as evaluated previously?

13.9 An automobile company 1s investigating the advisability of converting a plant that manufactures economy cars into one that will make retro sports cars. The initial cost for equipment conversion will be $200 million with a 20% salvage value anytime within a 5-year period. The cost of producing a car will be $21,000, but it is expected to have a selling price of $33,000 (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 increase each year in order for the company to recover its investment in 3 years’?

13.10 Rod, an industrial engineer manager with Zema Corporation, has determined via the least squares method that the annual total cost per case of producing its top-selling drink can best be described by the quadratic relation TC = 0.001Q° + 3Q + 2. And that revenue 1s approximately linear with r = $25 per case. Rod asks you to do the following.

(a) Tabulate the profit function between the values of 0 = S000 and 25,000 cases. Estimate the maximum profit and the quantity at which it occurs.

(b) Find the answers to part (a) by using an Excel graph.

(c) Determine an equation for Q_max the quantity at which the maximum profit should occur, and determine the amount of the profit at this point for the TC and r identified by the manager.

13.11 A civil engineer has been promoted to manager of engineered public systems. One of the products is an emergency intercept pump for potable water. If the tested water quality or volume varies by a preset percentage, the pump automatically switches to preselected options of treatments or water sources. The manufacturing process for the pump had the following fixed and variable costs over a 1-year period.

	Fixed Costs, $		Variable Costs, $/Unit
Administrative	30,000	Materials Labor	2500
Salaries and benefit 20% of Equipment	350,000	Labor	200
Equipment	100,000	Indirect labor	2000
Space, Utilities etc.	55,000	Subcontractors	800
Computers: 1/3 of	15,000

 

(a) Determine the minimum revenue per unit to break even at the current production volume of 5000 units per year.

(b) If selling internationally and to large corporations 1s pursued, an increased production of 3000 additional units will be necessary. Determine the revenue per unit required if a profit goal of $500,000 is set for the entire product line. Assume the cost estimates above remain the same.

13.12 A Yellow Pages directory company must decide whether it should compose the ads for its clients in-house or pay a production company to compose them. To develop the ads in-house, the company will have to purchase computers, printers, and other peripherals at a cost of $12,000. The 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 $45,000 per year. In addition, each ad will have an average coast of $8 to prepare for delivery to the printer. A total of 4000 ads are anticipated for the next few years. Alternatively, the company can outsource ad development at a fee of $20 per ad regardless of the quantity. The current interest rate is 8% per year. What is the breakeven amount, and which alternative is economically better?

13.13 An engineering firm can lease a measurement system for $1000 per month or purchase one for $15,000. The leased system will have no monthly maintenance cost, but the purchased one will cost $80 per month. At an interest rate of 0.5% per month, how many months must the system be required to break even?

13.14 Two pumps can be used for pumping a corrosive liquid. A pump with a brass impeller costs $800 and is expected to last 3 years. A pump with a stainless steel impeller costs $1900 and will last 5 years. A rebuild costing $300 will be required after 2000 operating hours for the brass impeller pump while an overhaul costing $700 will be required for the stainless steel pump after 8000 hours. If the operating cost of each pump is $1 per hour, how many hours per year must the pump be required to justify the purchase of the more expensive pump? Use an interest rate of 10% per year.

13.15 Two bids have been received to repave a commercial parking lot. Proposal I includes new curbs, grading, and paving at an initial cost of $250,000. The life of the parking lot surface constructed in. this manner is expected to be 4 years with annual costs for maintenance and repainting of pavement markings at $3000. Proposal 2 offers pavement of a significantly higher quality with an expected life of 8 years. The annual maintenance cost will be negligible for the pavement, but the markings will have to be repainted every 2 years at a cost of $3000. Markings are not repainted the last year of its expected life under proposal 2. If the company’s current MARR is 12% per year, how much can it afford to spend on proposal 2 initially so the two break even?

13.16 Jeremy is evaluating the operational costs of the manufacturing processes for specific components of a wireless home securely system, the same components are produced at plants in New York (NY) and Los Angeles (LA). The records for the last 3 years from NY report a fixed cost of $400,000 per year and a variable cost of $95 per unit in year 1, decreasing by $3 per unit per year. The LA reports indicate a fixed cost of $750,000 per year and a variable cost of $50 per unit. Increasing by $4 per unit per year. If the trends continue, how many units must be produced in year 4+ for the two processes break even? Use an interest rate of 10% per year.

13.17 Alfred Home Construction is considering the purchase of five dumpsters and a 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, and 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 construction 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 construction sites will need debris storage throughout the average year. The minimum attractive rate of re-turn is 12% per year. («@) How many days per year must the equipment be required to just break even? (4) If the expected usage is 75 days per year, which option—buy or lease—should be selected based on this economic analysis? Determine the expected annual cost of this decision.

13.18 Machine A has a fixed cost of $40,000 per year and a variable cost of $60 per unit. Machine B has an unknown fixed cost, but with this process 200 units can be produced each month at a total variable cost of $2000. If the total costs of the two machines break even al a production rate of 2000 units per year, what is the fixed cost of machine B?

13.19 A waste-holding lagoon situated near the main plant receives sludge daily. When the lagoon is full, it is necessary to remove the sludge to a site located 8.2 kilometers from the main plant. Currently, when the lagoon 1s full, the sludge is removed by pump into a tank truck and hauled away. This process requires the use of a portable pump that initially cost $800 and has an 8-year life. The company pays a contract individual to operate the pump and over-see environmental and safety factors at a rate of $100 per day, but the truck and driver must be rented for $200 per day.

The company has the option to install a pump and pipeline to the remote site. The pump would have an initial cost of $1600 and a life of 10 years and will cost $3 per day to operate. The company’s MARR is 10% per year.

(a) If the pipeline will cost $12 per meter to construct and will have a 10-year life, how many days per year must the lagoon require pumping to justify construction of the pipeline?

(b) If the company expects to pump the lagoon once per week every week of the year, how much money can it afford to spend now on the 10-year-life pipeline to just break even?

Use of SOLVER for Breakeven Analysis

13.20 Develop a spreadsheet using cell reference format for the estimates of Problem 13.15 where two proposals for repaving a commercial parking lot are evaluated. Answer the following questions, using SOLVER.

(a) How much can the company afford to spend on proposal 2 initially so the two break even? (This 1s the same question posed in Problem 13.15.)

(b) Assume that p₂  = $—400,000 is the actual cost of proposal 2 and that P, = $—250,000 is correct. Use the results of the analysis above to determine if the annual costs of proposal 1 for maintenance and re-painting can be reduced enough to make it a viable option.

13.21 A jeans manufacturing company is evaluating the purchase of a new automatic cutting machine with fuzzy-logic features. The machine will have a first cost of $40,000, a life of 10 years, and no salvage value. The maintenance cost of the machine is expected ta he $2000 per year. The machine will require one operator at a total cost of $30 per hour. A total of 2500 yards of material can be cut each hour by the machine. Alternatively, if human labor is used, six workers, each earning $14 per hour, are required to cut 2500 yards per hour. The MARR its 8% per year. Determine the minimum yards per year to justify the purchase of the automatic machine. Use (a) hand and (4) computer solution.

13.22 This is an extension to Problem 13.21. Assume this is a North American company that elected to move some of its cutting operations to Asia when domestic commercial interest rates were high at 8% per year and Asian labor rates averaged $14 per hour. Now the machinery will cost $80,000 with the other estimates remaining the same, the interest rate is 6% per year, and Asian labor costs an average of $25 per hour. Further assume the company elected earlier to stay with human cutting operations since the garment line for which the analysis was done had an annual production rate of about 300,000 yards. Recalculate the new breakeven point, and determine if the earlier “human cutters” decision is still valid.

13.23 A 3-year-old house can be purchased for an excellent price of $100,000. Remodeling costs immediately after purchase are estimated to be $12,000. Taxes will be $3800 per year, utilities will cost $2500 per year, and the house must be repainted every 6 years at a cost of $1000. Al present, resale houses are selling for $60 per square foot, but this price has been increasing, a trend that is expected to continue, by $1.50 per square foot per year. The 2500-square-foot house can be continually cased for $12,000 per year from this year until it is sold. A return of 8% per year is expected if the investment is made. (a) Determine how long the purchaser must own and lease the house to break even and the anticipated selling price at breakeven time. (b) Use Excel to approximate the breakeven years and estimated selling price.

13.24 Bovay Medical Labs is evaluating the alternatives of complete and partial in-house diabetes and associated blood sugar testing labs. Instead of outsourcing samples to an independent laboratory for analysis. The alternatives and associated costs are as follows:

Complete lab inhouse: If the inhouse lab is completely equipped, the initial cost will be $50,000. A part-time technician will be employed at an annual equivalent salary of $26,000. Cost of chemicals and supplies is estimated at $100 per sample.

Partial lab inhouse: The lab can be partially equipped at an initial cost of $35,000. The part-time technician will have an annual equivalent salary of $10,000. The cost of inhouse sample analysis will be only $3 per sample. However, since some tests cannot be conducted inhouse, outside testing will be required at an average cost of $40 per sample for all samples.

Complete outsourcing: The cost averages $120 per sample analyzed.

Any laboratory equipment purchased will have a life of 6 years. If the MARR is 1O% per year, determine the number of samples that must be tested each year to justify (a) the complete lab and (b) the partial lab. (c) Plot the total cost lines for all three Options, and state the range of samples for which each option will have the lowest cost. (d) If Bovay expects to test 300 samples per year, which of the three options is the best economically?

 

13.25 The chief engineer of Domingo County is considering two methods for lining water holding tanks. A bituminous coating can be applied at a cost of $8000. If the coating is touched up after 3 years at a cost of $1000. Its life can be extended another 3 years. As an alternative, a plastic lining may be installed with a useful lite of 15 years. If the discount rate is 4% per year, how much can be spent for the plastic lining so that the two methods just break even? Solve (a) by hand and (b) by computer.

13.26 A building contractor is evaluating two alternatives for improving the exterior appearance of a small commercial building that he is renovating. The building can be completely painted at a cost of $2800. The paint is expected to remain attractive for 4 years, at which time repainting is necessary. Every time the building is repainted, the cost will increase by 20% over the previous time. As an alternative, the building can be sandblasted now and every 10 years at a cost 40% greater than the previous time. The remaining life of the building is expected to be 38 years. The MARR is 10% per year. What is the maximum amount that can be spent now on the sandblasting alternative for the two alternatives to just breakeven? Use present worth analysis (a) by hand and (b) by computer to answer this question. (c) Use the spreadsheet to find the breakeven value if the cost increase for sandblasting can be reduced from 40% to 30%, or even 20%, each 10 years.