Payback Period and IRR of a Cost Reduction Proposal$-$Differential Analysis

A light$-$emitting diode $($LED$)$ is a semiconductor diode that emits narrow$-$spectrum light. Although relatively expensive when compared to incandescent bulbs, they use significantly less energy and last six to ten times longer, with a slow decline in performance rather than an abrupt failure.

Metropolitan City currently has $80,000$ incandescent bulbs in traffic lights at approximately $12,000$ intersections. It is estimated that replacing all the incandescent bulbs with LED will cost $$46\mathrm{.}02$ million. However, the investment is also estimated to save the City $$8\mathrm{.}85$ million per year in energy costs.

a$.$ Determine the payback period of converting Metropolitan City traffic lights to LEDs.

Round answer to one decimal place.

Answer $1$

years

b$.$ If the average life of an incandescent streetlight is one year and the average life of an LED streetlight is seven years, should the City finance the investment in LED's at an interest rate of five percent per year? Justify your answer.

$1.$ Compute the internal rate of return on the project. Round to the nearest whole percent.

Answer $2$

$\%$

$2.$ Select the most appropariate answer based on computation.

No$,$ the City should not make the investment because the IRR of the investment in LEDs is $62\mathrm{.}5\%$ of the interest rate.

Yes, the City should make the investment because the IRR of the investment in LEDs is $62\mathrm{.}5\%$ of the interest rate.

No$,$ the City should not make the investment because the IRR of the investment in LEDs is $160\%$ of the interest rate.

Yes, the City should make the investment because the IRR of the investment in LEDs is $160\%$ of the interest rate.