## Example

XYZ Corporation purchases fully automated (no labor) equipment needed for its production line. The cost of purchase, installation, and start-up adds up to \$100,000. The MTBF and MTTR are stated by the manufacturer to be 11.5 months and 15 days, respectively. The cost of operation is \$5,000 per month increasing by \$250 per month per year. The administrative and nondirect expenses allocated to the operation of this machine are \$5,000 per year increasing by \$500 each year. No routine maintenance is required, and the cost of major repair and overhaul is \$3,000 per year. The output produces a gross income of \$10,000 per month reducing by \$200 per month each year due to loss of productivity caused by aging. For a planned life of six years, calculate the LTW of this machine. The company uses straight-line five-year life depreciation, its total tax rate (federal, state, and local) is 40%, and its cost of money is 12%. The equipment has to be scrapped at the end of the sixth year. Its salvage value is equal to the cost of its removal. What is the LTW of this equipment?

Solution:

Depreciation:

First year: Expense:

Direct Operation

Major Maintenance

3,000

5,000

Total

65,000

Income

Years 2 to 6

Increase in expenses per year 250* 11.5 + 500 = 3375

Decrease in income

We can, therefore, construct a table similar to the table of Example 9.5 and develop the after tax cash flow and calculate the lifetime worth.

Yr. Income Expense OP. Depr. Bk. Taxable

100,000 -100000

1 115,000 65,500 49,500

2 112,700 68,875 43,825

3 110,400 72,250 38,150

4 108,100 75,625 32,475

5 105,800 79,000 26,800

6 103,500 82,375 21,125

20,000 80000 29,500 11,800

20,000 60000 23,825 9,530

20,000 40000 18,150 7,260

20,000 20000 12,475 4,990

20,000

21,125 8,4500

IAT -100,000 37,700 34,295 30,890 27,485 24,080 12,675

Fig. 2.5 is the cash flow diagram representing the financial situation of this equipment through its intended life.

Fig. 2.5 is the cash flow diagram representing the financial situation of this equipment through its intended life.

LTW ■ -100000 +37700 (P/F, 12J) +34295 {P/FJ2, 2) +30S90(P,Tst2s 3} +274S5 (P/F.12. 4)

Spreadsheet programs can easily be developed to calculate the LTW. The following spreadsheet will provide us with the same result. The advantage is that we can do a sensitivity analysis using different interest rates or tax rates. The sensitivity analysis allows us to understand the risk involved if actual tax rate or cost of money is not exactly what we estimated.

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