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Hence car A should be selected because its cost has the lower present value over the common time horizon

Example 2.8 (Machine replacement) A specialized machine essential for a company's operations costs \$10,000 and has operating costs of \$2,000 the first year. The operating cost increases by \$1,000 each year thereafter. We assume that these operating costs occur at the end of each year. The interest rate is 10%. How long should the machine be kept until it is replaced by a new identical machine? Assume that due to its specialized nature the machine has no salvage value

This is an example where the cash flow stream is not fixed in advance because of the unknown replacement time We must also account for the cash flows of the replacement machines. This can be done by writing an equation having PV on both sides. For example, suppose that the machine is replaced every year. Then the cash flow (in thousands) is (-10, -2) followed by (0, -10, -2) and then (0,0, -10, -2), and so forth However, we can write the total PV of the costs compactly as because after the first machine is replaced, the stream from that point looks identical to the original one, except that this continuing stream starts 1 year later and hence must be discounted by the effect of 1 year's interest. The solution to this equation is PV = 130 or, in our original units, \$130,000.

We may do the same thing assuming 2-year replacement, then .3 years, and so forth. The general approach is based on the equation where k is the length of the basic cycle. This leads easily to Table 2 3

From the table we see that the smallest present value of cost occurs when the machine is replaced after 5 years, Hence that is the best replacement policy.

Taxes can complicate a cash flow value analysis No new conceptual issues arise; it is just that taxes can obscure the true definition of cash flow. If a uniform tax rate were applied to all revenues and expenses as taxes and credits, respectively, then recommendations from before-tax and after-tax analyses would be identical. The