Question

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 $39.8 million. However, the investment is also estimated to save the City $7.65 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

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 1

a calculation of Payback periud Years cash flows Per Year in millions Cumulative cash flows 7.65 7.65 7.65765 765 7.65 7.65 15.3 22.95 30.6 38.25 45.9 olion Initial cost Payback period id the time required to collect the initial cash flows cash flows collected 38.25 in 5 years balance amount ! 139.08- to be collected in 38.25 5th year 0.83 time required to colled the cash 0-1084 flows in year 6 Payback period is 5yearst 10.1084 15 - 108 years b) calculation of net present value 1 Years 1 2 3 4 5 6 7 cash flows per years 7-65 7.65 7.65 7.65 7.65 7.65 7.65 in millions 3 PURF at 5% 10.9134 0-8761/0.8407 0.8103/0.7725/6. 7469047255 4. Present value cash 6.987 6.702 6.431 6.198 5.909 5.713/5.550 flows (23) 5. total present value 143.40 •cash flows 6. initial outlay Net Present value 15.24 (5-6)

The city should finance the investments as the net Present value is positive. 1) Calculation of the internal rate of return 1. Years 6 7.65 7 7.657 raf 3 4 5 7.65 7.65 7.65 7.65 7.65 o I 2. cash flows per Year in millions |-38.25 internal rate of siert return using excel cash flows from Year o Ho 7). 8%.