Question

2. Warren Widgets just purchased a building to use for additional warehouse space for the next 20 years. Warren must replace the roof before the present the building can be put to use. A traditional pitch (tar) and gravel roof will cost $80,000 and last six years. A new rubber membrane roof can be installed that will last nine years. What is the maximum that Warren should be willing to pay for the rubber roof? Use 3%.

Answer 1

As both of these options have unequal project lives, we should not directly compare there net present values. Rather we use the equivalent annual annuity to compare them.

The annuity payment (PMT) for 6 years that has a present value of 80,000 can be calculated as

(Note: you may also use PMT function of any financial calculator or Excel to calculate with same inputs):

r = 3%

n = 6

PV of annuity =

1-((1+5)*) PMTX

80000= PMT * (1- (1 / (1+0.03)^6) ) / 0.03

Solving this for PMT we get

PMT = 14,767.8

This is the equivalent annuity for gravel roof

So, for rubber roof as well, this is the maximum annual equivalent annuity that he should pay.

The present value of such a 9 year annuity of 14,767.8 can be calculated by the same formula as used above by putting n=6 & solving for PV

PV = 14,767.8 * (1- (1 / (1+0.03)^9) ) / 0.03

= $ 114,983.7 is the maximum that he should pay for the rubber roof.