# Present Values

#### Giordano Bruno

##### Well-known Member
I have two roofs. One lasts 25 years and the other lasts 50 years. The building lasts only 50 years.

I need a formula to compare the present values of both roofs.

Say roof A costs \$10,000 to build and another \$10,000 in 25 years
Roof B costs \$20,000 to build and last as long as the building.

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What discount rate do you want to use?

Hi Andrew,

A variable rate. Let's say 6% for the purpose of the exercise.

Maybe:

=XNPV(6%,{50000,-50000},{1,18264})
=XNPV(6%,{50000,-25000,-25000},{1,9132,18264})

Hi Andrew.

Many thanks for your time and trouble. In the case in point, as the life of the building is only 50 years, I presume that I could modify the formulas to the following:

=XNPV(6%,{50000},{1})
=XNPV(6%,{50000,-25000},{1,9132})

Thanks again.

The series of values must contain at least one positive value and one negative value.

Thanks Andrew,

In fact the roofs have no value at the end of the 50 years as the building will be demolished. Do you think it perhaps better in this case to establish the present value of the cost of intermediate replacement, discounted by 1/(1 + IntRate)^n where n is 25. If the building life were extended to say 60 years, there would be a second replacement of one roof at 50 years and perhaps still no replacement of the other roof. In this case, the same calculation where n = 50 would be added to the initial cost and the discounted 25 year cost to give the present value/cost of the roof.

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