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 $34.5 million. However, the investment is also estimated to save the City $7.32 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

%

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 45.5% of the interest rate.

Yes, the City should make the investment because the IRR of the investment in LEDs is 45.5% of the interest rate.

No, the City should not make the investment because the IRR of the investment in LEDs is 220% of the interest rate.

Yes, the City should make the investment because the IRR of the investment in LEDs is 220% of the interest rate.

Answer 1

a.
	Cash Outflows
Year 0	34500000
	Cash Inflows	Payback Period
Year 1	7320000	7320000
Year 2	7320000	14640000
Year 3	7320000	21960000
Year 4	7320000	29280000
Year 5	7320000	36600000
Usually 4 Years Cost Covered is 29280000
Difference is 34500000 - 29280000 = 5220000
So, 7320000 savings in 12 months then 5220000 in how mnay months
Simply i.e 12 X 5220000/ 7320000 = 8.55 months
Hence Pay Back Period is 4 years 8.55 Months

b.
	Cash Outflows
Year 0	34500000
	Cash Inflows	PV Factor @ 5%	PV Value @ 5 %	PV @ 12.387%	PV Value @ 12.387 %	PV @ 11%	PV Value @ 11%
Year 1	7320000	0.9524	6971429	0.8897	6512456	0.9009	6595555
Year 2	7320000	0.9070	6639456	0.7915	5794000	0.8116	5942036
Year 3	7320000	0.8638	6323291	0.7042	5154804	0.7312	5353281
Year 4	7320000	0.8227	6022182	0.6265	4586124	0.6587	4822871
Year 5	7320000	0.7835	5735412	0.5574	4080182	0.5935	4345024
Year 6	7320000	0.7462	5462297	0.4959	3630055	0.5346	3914531
Year 7	7320000	0.7107	5202187	0.4412	3229586	0.4817	3526703
PV of Cash Inflows		42356253		32987207		34500000
Cash Outflows		34500000		34500000		34500000
			7856253		-1512793		0
1
Here Using the Interpolation and Expolation to Determine the IRR
Diffrence in 5 % and 12.387 % NPV is 7856253 -( 1512793) = 9369046
Difference in % % and 12.387 % = 7.378 %
Difference between 7856253 - 0 ( IRR point) = 7856253
IRR = 11 % approx
2
Here the Interest rate is 11 % approx it means
5 % /11% = 220 % of the Interest Rate.
Because Financing the Investment rate is 5%
Whereas Earning is 11 %
Hence they can finace at 5% as IRR is greater than Financing Cost
Hence Correct Option is Yes, the City should make the investment because the IRR of the investment in LEDs is 220% of the interest rate