Comparing Alternatives that have Perpetual Lives

# Comparing Alternatives that have Perpetual Lives -...

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/ Comparing Alternatives that have Perpetual Lives In many long-lived projects, costs and benefits are computed as if the expected life were 50 years. This is common in both public and private projects. Often capital projects are considered as if they will have perpetual lives. Where the compounding of interest rates is involved, a project lasting, say, 100 years is for all intents and purposes one that will be around for ever. As the number of periods approaches infinity, the capital recovery factor approaches the interest rate assumed in its calculation. That is, . [i(l + on] . 1 1m = 1- n~oo (l + i)n - 1 The difference between 100 years and forever is very small. For example, at 8% interest the capital recovery factor for 100 years is 0.08004. Increasing the interest rate from 8% to 8.004% would have the same effect on annual cost, then, as reducing the estimated life of a structure from forever to 100 years. Even with an interest rate as low as 3%, the difference between 100 years and forever has the same influence on annual cost as a difference of 1/6 of 1% in the interest rate: 0.03165 - 0.03 = 0.00165. [1/6 = .16667] *' So often in the case of a long lived project the interest rate assumed will be substituted for the crfin performing calculations. Let's consider an example where that is the case.

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Comparing Alternatives that have Perpetual Lives -...

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