Project cash flow n A B -4500 -2900 1 2610 1210 2 2930 1720 3 2300 Example 1: Consider the following two mutually exclusive investment projects. Assume that MARR=12%. Which alternative would be selected by using the PW criterion? Which alternative would be selected by using the net-future-worth criterion? Project cash flow n A B -4500 -2900 1 2610 1210 2 2930 1720 3 2300 1500

Example 2: Consider the following two investment alternatives. The firm’s MARR is 15%. (a) Compute the PW for project A. (b) Compute the unknown cash flow X in years two and three for project B. (c) Compute the project balance for project A at the end of year three. (d) If these two projects are mutually exclusive alternatives, which project would you select? Project cash flow n A B -15000 -25000 1 9500 2 12500 X 3 7500 PW(15%) ? 9300

Example 3: You need to know if the building of a new warehouse is justified under the following conditions: The proposal is for a warehouse costing $100000. The warehouse has an expected useful life of 35 years and a net salvage value of $25000. Annual receipts of $17000 are expected, annual maintenance and administrative costs will be $4000, and annual income taxes are $2000. Given this data, which of the following are correct? (a) The proposal is justified for a MARR of 9%. (b) The proposal has a net present worth of $62730.5, when 6% is used as the interest rate. (c) The proposal is acceptable as long as MARR≤10.77%.

Spray Guns With Overhead Monorail PW = [-22.2(1+(P/F,18%,6)) + 6(P/A,18%,12) + 8((P/F,18%,6)+ (P/F,18%,12))]*1000 = $2,395.92 Spray Guns With Overhead Monorail PW = [-250.9(1+(P/F,18%,6)) + 91(P/A,18%,12) + 44((P/F,18%,6) + (P/F,18%,12))]*1000 = $114,664.04 Paint robot PW = [-510.13 (1+ (P/F,18%,4) + (P/F,18%,8) ) + 154(P/A,18%,12) + 73 ( (P/F,18%,4) + (P/F,18%,8) + (P/F,18%,12) )] * 1000 = -$103,740.634 Answer: Choose Spray Guns With Overhead Monorail

Example 5: Before your company writes the purchase order for the paint system selected in Example 4 it is announced that the production of metal door frames will be discontinued in 4 years. Assuming that the salvage value is constant at any time after the system is installed, which will you now choose? Your MARR is still 18% and you still use present worth analysis. Show your cash flow diagrams. SPRAY GUNS WITH OVERHEAD MONORAIL PAINT ROBOT Initial Cost $22,200 $250,900 $510,130 Annual Savings 6,000 91,000 154,000 Salvage Value 8,000 44,000 73,000 Life 6 yrs. 4 yrs.

Spray Guns PW = [-22.2 + 6(P/A,18%,4) + 8(P/F,18%,4)] * 1000 = -$1933.60 Spray Guns With Overhead Monorail PW = [-250.9 + 91(P/A,18%,4) + 44(P/F,18%,4)] * 1000 = $16,585.20 Paint robot PW = [-510.13 + 154(P/A,18%,4) + 73(P/F,18%,4)] * 1000 = -$58,216.60

Option OK FINE Example 6: For the project described below you have been told that the function will be needed for only 4 years. At an MARR of 15% which will you choose? Salvage value is the same at any time after installation. Show the cash flow diagrams. Option OK FINE Initial cost 40000 55000 Salvage value 4000 6000 Annual benefit 20000 21000 Useful Life 3 4

Example 7: Consider the following cash flows for two types of models. Both models will have no salvage value upon their disposal (at the end of their respective service lives). The firm’s MARR is known to be 15%. (a) Notice that models have different service lives. However, model A will be available in the future with the same cash flows. Model B is available now only. If you select model B now, you will have to replace it with model A at the end of year 2. If your firm uses the present worth as a decision criterion, which model should be selected assuming that your firm will need either model for an indefinite period? (b) Suppose that your firm will need either model for only two years. Determine the salvage value of model A at the end of year two that makes both models indifferent (equally likely). Project cash flow n A B -6000 -15000 1 3500 10000 2 3

Example 8: Susan wants to buy a car that she will keep for the next four years. She can buy a Honda Civic at 15000 and then sell it for 8000 after four years. If she bought this car, what would be her annual ownership cost (capital recovery cost)? Assume that her interest rate is 6%.

Example 9: The following cash flows represent the potential annual savings associated with two different types of production processes, each of which requires an investment of 12000. Assuming an interest rate of 15%, complete the following tasks: (a) Determine the equivalent annual savings for each process. (b) Determine the hourly savings for each process assuming 2000 hours of operation per year. (c) Determine which process should be selected. n A B -12000 1 9120 6350 2 6840 3 4560 4 2280

Example 10: Norton Auto Parts, Inc. is considering two different forklift trucks for use in its assembly plant. Truck A costs 15000 and requires 3000 annually in operating expenses. It will have a 5000 salvage value at the end of its 3-year service life. Truck B costs 20000 and requires 2000 annually in operating expenses. It will have a 8000 salvage value at the end of its 4-year service life. The firm’s MARR is 12%. Assuming that the trucks are needed for 12 years and no significant changes are expected in the future price and functional capacity of both trucks, select the most economical truck based on AE analysis.

Capital Recovery Cost

Example 11: Your company needs a small front loader for handling bulk materials at the plant. It can be leased from the dealer for three years for $4050 per year including all maintenance. It can also be purchased for $14,000. You expect the loader to last for six years and to have a salvage value of $3000. You predict that maintenance will cost $400 the first year and increase by $200 per year in each year after the first. Your MARR is 15%. Use annual equivalence analysis to determine whether to lease or buy the loader. What is the shortest project life for which the annual worths you have calculated are exactly correct?

Present worth