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

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 $46.02 million. However, the investment is also estimated to save the City $8.85 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 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 %

Explanation / Answer

a calculation of payback period years 1 2 3 4 5 6 cash flows per year in millions 8.85 8.85 8.85 8.85 8.85 8.85 cumulative cash flows 8.85 17.7 26.55 35.4 44.25 53.1 initial cost 46.02 millions payback period id the time required to collect the initial cash flows cash flows collected in 5 years 44.25 balance amount to be collected in 5 th year 46.02-44.25 1.77 time required to collect the cash flows in year 6 1.77 / 8.85 0.20 payback period is 5 years + 0.20 years payback period is 5.20 years b calculation of net present value 1 years 1 2 3 4 5 6 7 2 cash flows per year in millions 8.85 8.85 8.85 8.85 8.85 8.85 8.85 3 PVRF at 5 % 0.9524 0.9070 0.8638 0.8227 0.7835 0.7462 0.7107 4 present value cash flows ( 2 * 3 ) 8.43 8.03 7.64 7.28 6.93 6.60 6.29 5 total present value cash flows 51.21 6 initial outlay 44.25 7 net present value ( 5 - 6 ) 6.96 the city should finance the investments as the net present value is positive 1 calculation of the internal rate of return 1 years 0 1 2 3 4 5 6 7 2 cash flows per year in millions -44.25 8.85 8.85 8.85 8.85 8.85 8.85 8.85 internal rate of return using excel .=irr(cash flows from year 0 to 7 ) 9%

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