A town is putting a new roof on its arena.A standard roof cost $600,000 and has an expected lifetime of 20 years with no salvage value.Another company has stated that they can add a preservative to the roof which will increase the lifetime of the roof by 10 years.Ignoring maintenance costs,what is the maximum amount the town should be willing to pay for the preservative if money is worth j₁ = 7%? (Answer to the nearest dollar).

Question

Quizplus · Accepted Answer

Without the preservative, the standard roof lasts 20 years, so the present value (PV) of the roof is:

PV = 600,000/(1+0.07)^20 = 153,173.46

With the preservative, the roof lasts for 30 years, so the PV of the roof is:

PV = A/(1+0.07)^30

where A is the amount the town is willing to pay for the preservative.

To find the maximum amount the town should be willing to pay for the preservative, we need to equate the two PVs and solve for A:

153,173.46 = A/(1+0.07)^30

A = 102,794.96

Rounded to the nearest dollar, the maximum amount the town should be willing to pay for the preservative is $102,795. Therefore, the best choice is C.

A Town Is Putting a New Roof on Its Arena