Question

Annual maintenance cost for a particular section of highway pavement are $3,000.The placement of a new surface would reduce the annual maintenance cost to $400 per year for the first 5 years, and to $800 per year for the next 5 years. After 10 years, the annual maintenance cost would again be $3,000. If the maintenance costs are the only saving, how much investment can be justified for the new surface, by assuming interest at 6%

Answer 1

$17,877

Step-by-step explanation:

initial outlay = ?

net cash flows years 1 to 5 = $3,000 - $400 = $2,600

net cash flows years 6 to 10 = $3,000 - $800 = $2,200

assuming that the discount rate is 6%, we need to determine the maximum amount of initial investment that would result in the NPV = 0

in order to do this we have to calculate the present value of the future cash flows:

PV = $2,600/1.06 + $2,600/1.06² + $2,600/1.06³ + $2,600/1.06⁴ + $2,600/1.06⁵ + $2,200/1.06⁶ + $2,200/1.06⁷ + $2,200/1.06⁸ + $2,200/1.06⁹ + $2,200/1.06¹⁰ = $17,877

that means that the maximum amount that can be invested = $17,877, and that way the NPV = 0