Question

Your firm spends $6,500 annually for electricity. Johnson Controls offers to install a new computer-controlled lighting system that will reduce electric bills by $1,000 in each of the next 5 years. The system costs $1,450 to install and $2,750 to dispose of at the end of 5 years. Assume the cost savings are known with certainty and the interest rate is 10%. What are the IRRs of the project? There should be two IRRs even if one of them is not useful.

Answer 1

We have found out the NPV under 3 scenarios:

		Discount rate =			10%	Discount rate =			44.765%	Discount rate =			-23.792%
Year	CF	Discount Factor		DCF		Discount Factor		DCF		Discount Factor		DCF
0	-1450	1/1.10^0=	1	-1450*1=	-1450	1/(1+0.447654405752536)^0=	1	-1450*1=	-1450	1/(1+-0.2379237)^0=	1	-1450*1=	-1450
1	1000	1/1.10^1=	0.909090909	1000*0.909090909090909=	909.0909091	1/(1+0.447654405752536)^1=	0.690772602	1000*0.690772601545166=	690.7726015	1/(1+-0.2379237)^1=	1.312204565	1000*1.31220456534339=	1312.204565
2	1000	1/1.10^2=	0.826446281	1000*0.826446280991735=	826.446281	1/(1+0.447654405752536)^2=	0.477166787	1000*0.477166787045476=	477.166787	1/(1+-0.2379237)^2=	1.721880821	1000*1.72188082130804=	1721.880821
3	1000	1/1.10^3=	0.751314801	1000*0.751314800901578=	751.3148009	1/(1+0.447654405752536)^3=	0.329613743	1000*0.329613742858351=	329.6137429	1/(1+-0.2379237)^3=	2.259459875	1000*2.25945987469764=	2259.459875
4	1000	1/1.10^4=	0.683013455	1000*0.683013455365071=	683.0134554	1/(1+0.447654405752536)^4=	0.227688143	1000*0.227688142659303=	227.6881427	1/(1+-0.2379237)^4=	2.964873563	1000*2.96487356278845=	2964.873563
5	-1750	1/1.10^5=	0.620921323	-1750*0.620921323059155=	-1086.612315	1/(1+0.447654405752536)^5=	0.157280731	-1750*0.157280730645753=	-275.2412786	1/(1+-0.2379237)^5=	3.890520625	-1750*3.89052062475693=	-6808.411093
				NPV = Sum of all DCF	633.253131			NPV = Sum of all DCF	0			NPV = Sum of all DCF	0

• If the discount rate is 10% then the NPV is positive
• If it is 44.765% then NPV = 0
• If it is -23.792% then NPV = 0
• As CFs have multiple sign changes there are multiple IRRs. But -23.792% is not relevant as it is a negative number