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The first option, a straightforward replacement after 4 years, can be described with the following expression:
PW = -P + {t(P-S)/n}(P/A, i%, n) and PW = -$4,577
The second option, a coating with annual maintenance valued at 10% installation, and an installation cost equal to P, can be described as:
PW = -P + {t(P-S)/n}(P/A, i%, n) - (1-t)(X)(P/A, i%, n), where X = 0.1 P
PW = -P + 0.364 P - 0.185 P
PW = -0.821 P
Equating the first option cost to this expression yields the maximum installation cost of the coating:
-0.821 P = -$4,577
P = $5,574 is the answer for the installation cost of the coating
