### Comparison of Alternatives

P1

To sweep the floor of a machine shop a company is considering two alternatives. An automatic broom is available that costs \$35. The broom must be replaced every year. The old broom is thrown away. A vacuum cleaner is available for \$90 with an annual expense of \$10. This machine will last four years with no salvage value. The company's minimum rate of return is 15%. Use the present worth and annual cost methods to analyze these investments.

P2

Two machines are being considered to manufacture some product. The first machine costs \$1100 initially and has a \$100 salvage value after ten years. It costs \$200 a year to operate. The second costs \$1300 initially. It has a salvage value of \$100 after ten years and costs \$152.30 per year to operate. At the minimum rate of return of 15%, which machine should you select? Explain your answer.

P3

As in problem 2, the first machine costs \$1100 initially and has a \$100 salvage value after ten years. The second costs \$1300 initially and has a salvage value of \$100 after ten years. Now assume, however, that the first machine has annual operating costs of \$500. The minimum rate of return is 15%. What operating cost would make the second machine have the same equivalent uniform annual cost? In this case, which machine should you select?

P4

A city agency must install street lamps. Two types are available. Type A cost \$500. The bulb must be replaced in the lamp at an average rate of once per year. It costs \$20 to replace the lamp. A second type cost \$700, but its bulb must be replaced once every two years at a cost of \$30. The lamps will operate indefinitely. If the city's cost of capital is 6%, which type of lamp should be bought?

P5

You are purchasing your first car and considering two models. One has a long life of 10 years, but it costs \$20,000 initially and \$1500 per year to operate. The other costs \$15,000, and has an annual operating cost of \$1000 and lasts 5 years. Which should you select? Both have salvage values of \$500 at the end of their lives. You will finance the entire cost of either car with a 12% loan.

P6

For \$500 you can install extra ceiling insulation in your house which you feel will save you \$100 a year in heating and cooling bills. For \$1250 you can install extra insulation plus cooling fans in your attic which will save you \$250 per year. You plan to keep the house for seven years. The insulation will add nothing to the house's resale value, but the cooling fans will add \$300. Your minimum rate of return on investments is 10%. What should you do?

P7

Compare the two alternatives using 12% compounded annually:

 Investment Salvage Life Expense per year Project A \$50,000 \$10,000 11 years \$5000 Project B \$40,000 0 10 years \$2000

P8

A plant manager is deciding between two machines. Machine A has an initial cost of \$9,000. It has no salvage value at the end of its six year useful life. The annual operating cost of machine A is \$5,000.

Machine B costs \$16,000 new and has a resale value of \$4,000 at the end of its nine year economic life. Its operating costs are \$4,000 per year.

Do a present worth analysis to determine which machine should be purchased. Assume that operating costs are paid at the end of each year and that the annual interest rate is 10%.

P9 A product has a selling price of \$100 per unit. Three manufacturing processes can be used to make it. The processes have cost characteristics as shown below. The First Cost is the investment required to initially setup the production process. The Unit Cost is the cost of manufacturing one unit of product. The Life is the number of years the process will operate before replacement is required. All have 0 salvage value. The MARR is 15%.
 First cost Life Unit cost Manual 0 Forever \$90 Machine Tool \$10,000 3 Years \$80 Automated \$70,000 5 Years \$60

The Marketing Department estimates that 700 units of the product will be produced and sold each year. The demand for the product is expected to last for a long time. Which process should be selected? Use any method of analysis, but show the analysis that justifies your selection.