Question

Sue was presented with a capital expenditure for a new air conditioning unit which costs $12,000 today and would generate the following savings:

Year	Amount
1	$2,000
2	$3,000
3	$2,000
4	$4,000
5	$5,000
6	$7,500
7	$5,000
8	$2,500

If the appropriate discount rate is 8 percent, what is the NPV and the IRR for this outlay? (Updated Answer with step by step solution).

Answer 1

Initial Investment P=$12000

discount rate r=8%

for NPV=Sum of PV of All cash flow - Initial investment

PV =CF/(1+r)^n

CF=Cash flow

n=year in which cash flow occur

Year	Cash flow	PV
1	2000	1851.85
2	3000	2572.02
3	2000	1587.66
4	4000	2940.12
5	5000	3402.92
6	7500	4726.27
7	5000	2917.45
8	2500	1350.67
Total		21348.96

NPV=21348.96-12000=$9348.96

Let x be the IRR so at IRR NPV=0

Sum of PV of Cash flow = Initial Investment

2000/(1+x)^1+3000/(1+x)^2+2000/(1+x)^3+4000/(1+x)^4+5000/(1+x)^5+7500/(1+x)^6+5000/(1+x)^7+2500/(1+x)^8=12000

So solving for x we get

x=23.06%