Problems

1 Two alternative production methods have been proposed: one a manual method, the other an automatic machine. Data are given in the following table.

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Manual Automatic

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First cost $15,000 $95,000

Annual operating cost$30,000 $10,000

Salvage value 0 $15,000

Service life (years) 10 7

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Use rate of return of 10% to select the more economical alternative if the two alternatives are equivalent in terms of capability.

2 Two alternative production methods have been proposed: one a manual method, the other an automatic machine. Data are given in the following table.

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Manual Automatic

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First cost $15,000 $95,000

Annual operating cost$30,000 $10,000

Salvage value 0 $15,000

Service life (years) 10 7

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Use a rate of return of 20% to select the more economical alternative if the two alternatives are equivalent in terms of capability.

Why is the selection of the method different from that of Problem 1?

3 A proposed automatic machine is to be used exclusively to produce one type of workpart. The machine has a first cost of $50,000 and its expected service life is 3 years with a salvage value of $20,000 at the end of the 3 years. The machine will be operated 4000 h/yr (two shifts) at $8.00/h (labour, power, maintenance, etc.). Its production rate is 10 units/h. Excluding raw material costs, compute the production cost per unit using a rate of return of 25%.

4 The following data apply to the operation of a particular automated manufacturing system:

direct labour rate = $10.00/h

number of operators required = 1

applicable labour factory overhead rate = 50%

capital investment in system = $300,000

service life = 10 years

salvage value = $30,000

applicable machine factory overhead rate = 30%

The system is operated one shift (2000 h/yr.). Use a rate of return of 25% to determine the appropriate hourly rate for this worker-machine system.

5 Solve Problem 4 except using three-shift operation (6000 h/yr.). Note the effect of increase machine utilisation on the hourly rate for the system as compared to the results of Problem 4.

6 A piece of automated production equipment has a first cost of $100,000. The service life is 6 years, the anticipated salvage value is $10,000 and the annual maintenance costs are $3000. The equipment will produce at the rate of 10 units/h, each unit worth $2.00 in added revenue. One operator is required full time to tend the machine at a rate of $10.00/h. Assume that no overhead rates are applicable. Raw material costs equal $0.20/unit. Use a rate of return of 20%.

a) Compute the profit break-even point.

b) How many hours of operation are required to produce the number of units indicated by the break-even point?

c) How much profit (or loss) will be made if 50,000 units/yr. are produced?

d)

7 In Problem 6, recompute the break-even point if the applicable overhead rates are 20% for the machine and 40% for the labour.

8 The break-even point is to be determined for two methods of production, a manual method and an automated method. The manual method requires two operators at $9.00/h each. Together, they produce at a rate of 36 units/h. The automated method has an initial cost of $125,000, a 4-year service life, no salvage value, and annual maintenance costs of $3000. No labour (except for maintenance) is required to operate the machine, but the machine consumes energy at the rate of 50kW when running. Cost of electricity is $0.05/kWh. If the production rate for this automated machine is 100 units/h, determine the break-even point for the two methods if a 25% rate of return is required.

9 Determine the unit cost equation as a function of quantity Q for the data given in Problem 6.

10 Determine the unit cost equation as a function of quantity Q for the data given in Problem 7.

11 Determine the unit cost equation as a function of quantity Q for the two production methods in Problem 8.

12 A proposal has been submitted to construct a new warehouse with 16,000 m² of storage floor space. Assume that 80% of the floor space in the warehouse is available for storage purposes. The building will cost $500.000 to build and is expected to have a 20-year life with a salvage value at that time of $100,000. Annual maintenance and operating costs will be $120,000. The rate of return used by the firm in this problem is 25%. This rate applies to investments in building or in inventory.

a) For a given item that costs $125.00 to purchase and requires 5 m² of floor space, how much will it cost the company to store the item in the warehouse for 3 months? Your answer must consider both storage costs and inventory investment costs.

b) If the item indicated in part a) is typical in size and cost of the companys inventory stores in the warehouse, determine a value for h, the holding cost rate.

c) Determine the total costs of inventory in the warehouse on an annual basis, assuming that the warehouse is filled to its capacity throughout the year.

13 A batch of large castings is processed through a machine shop. The batch size is 20. Each raw casting costs $175. There are 22 machining operations performed on each casting at an average operation time of 0.5 h per operation. Setup time per operation averages 5 h. The cost rate for the machine and labour

of $40/h. Non-operation costs (inspection, handling between operations, etc.) average $5 per operation per part. The corresponding non-operation time between each operation averages 2 working days. The shop works five 8-h days per week, 52 weeks per year. The interest rate used by the company is 25% for investing in WIP inventory, and the storage cost rate is 14% of the value of the item held. Both rates are annual rates. Determine the following:

a) Manufacturing lead time for the batch of castings.

b) Total cost of each batch when it is completed, including both production cost and holding cost (MLT cost).

c) The holding cost (MLT cost) for each batch if the manufacturing lead time is reduced by 50%.