Question

Installing an automated production system costing $300,000 is initially expected to save Zia Corpo- ration $52,000 in expenses annually. If the system needs $7500 in operating and maintenance costs each year and has a salvage value of $30,000 at Year 10, what is the IRR of this system? If the company wants to earn at least 12% on all investments, should this system be purchased? Contributed by Paul R. McCright, University of South Florida

Answer 1

• IRR is the rate at which NPV = 0
• IRR can be calculated using either a financial calculator or excel or through hit and trial:
• Using Excel we get the IRR = 8.87% rounded to two decimal places
• The CFs in years 1-10 apart from the salvage value = 52000-7500 = 44500

Year	CF	Discount Factor		Discounted CF
0	$ -3,00,000.00	1/(1+0.0887372825928295)^0=	1	1*-300000=	-3,00,000.00
1	$       44,500.00	1/(1+0.0887372825928295)^1=	0.918495229	0.918495229279279*44500=	40,873.04
2	$       44,500.00	1/(1+0.0887372825928295)^2=	0.843633486	0.843633486208795*44500=	37,541.69
3	$       44,500.00	1/(1+0.0887372825928295)^3=	0.774873332	0.774873332343025*44500=	34,481.86
4	$       44,500.00	1/(1+0.0887372825928295)^4=	0.711717459	0.711717459052806*44500=	31,671.43
5	$       44,500.00	1/(1+0.0887372825928295)^5=	0.653709091	0.653709090734772*44500=	29,090.05
6	$       44,500.00	1/(1+0.0887372825928295)^6=	0.600428681	0.600428681176384*44500=	26,719.08
7	$       44,500.00	1/(1+0.0887372825928295)^7=	0.551490879	0.551490879182958*44500=	24,541.34
8	$       44,500.00	1/(1+0.0887372825928295)^8=	0.506541742	0.506541741520582*44500=	22,541.11
9	$       44,500.00	1/(1+0.0887372825928295)^9=	0.465256173	0.465256173017472*44500=	20,703.90
10	$       44,500.00	1/(1+0.0887372825928295)^10=	0.427335575	0.427335575309283*44500=	19,016.43
10	$       30,000.00	1/(1+0.0887372825928295)^10=	0.427335575	0.427335575309283*30000=	12,820.07
				NPV = Sum of all Discounted CF	0.00

Year	CF	Discount Factor		Discounted CF
0	$ -3,00,000.00	1/(1+0.12)^0=	1	1*-300000=	-3,00,000.00
1	$       44,500.00	1/(1+0.12)^1=	0.892857143	0.892857142857143*44500=	39,732.14
2	$       44,500.00	1/(1+0.12)^2=	0.797193878	0.79719387755102*44500=	35,475.13
3	$       44,500.00	1/(1+0.12)^3=	0.711780248	0.711780247813411*44500=	31,674.22
4	$       44,500.00	1/(1+0.12)^4=	0.635518078	0.635518078404831*44500=	28,280.55
5	$       44,500.00	1/(1+0.12)^5=	0.567426856	0.567426855718599*44500=	25,250.50
6	$       44,500.00	1/(1+0.12)^6=	0.506631121	0.506631121177321*44500=	22,545.08
7	$       44,500.00	1/(1+0.12)^7=	0.452349215	0.452349215336893*44500=	20,129.54
8	$       44,500.00	1/(1+0.12)^8=	0.403883228	0.403883227979369*44500=	17,972.80
9	$       44,500.00	1/(1+0.12)^9=	0.360610025	0.36061002498158*44500=	16,047.15
10	$       44,500.00	1/(1+0.12)^10=	0.321973237	0.321973236590696*44500=	14,327.81
10	$       30,000.00	1/(1+0.12)^10=	0.321973237	0.321973236590696*30000=	9,659.20
				NPV = Sum of all Discounted CF	-38,905.88

As the NPV is negative at 12% so this equipment should not be purchased.