Question

How much would the owner of a building be justified in paying for a sprinkler system that will save $1000 a year in insurance premiums if the system has to be replaced every 15 years and has a salvage value equal to 10% of its initial cost? Assume money is worth 5%.

Answer 1

Answer:

The maximum price the buildng owner should pay for this system is $10,903.

Explanation:

The investment of the purchase of this system must be recovered in 15 years, being the positive cash flows the annual savings and the salvage value.

We can express the net present value of the investment as:

$NPV=-P+\sum_{k=1}^{15}\frac{AS}{(1+i)^k}+\frac{SV}{(1+i)^{15}}=0\\\\\\0=-P+1000*\sum_{k=1}^{15}\frac{1}{(1.05)^k}+\frac{0.1P}{(1.05)^{15}} \\\\\\0=-P+1,000*10.38+0.048P\\\\\\0=-P+10,380+0.048P\\\\\\(1-0.048)P=10,380\\\\\\P=\frac{10,380}{0.952}=10,903$

The maximum price the buildng owner should pay for this system is $10,903.