Question

You are considering two mutually exclusive projects which can be repeated. A costs $15 million but will provide inflows of $5.5 million per year for 4 years. If Machine A was replaced, its cost would be $18 million and its cash inflows would increase to $7.2 million due to production efficiencies. Machine B costs $16 million and will provide after-tax inflows of $6.5 million per year for 8 years. If the WACC is 9%, which machine should be acquired? Use the EAA method. Kindly show working and formula on every step?

Answer 1

EAA Method

Given :

WACC =9%

We shall consider the NPV for Machine A

over 8 years , to maintain uniformity .

Machine A

Details

Year=n	Investment	Cash inflow	Net Cash Flow	PV factor @9%=1/1.09^n	PV of Net cash flow
0	(15,000,000)	-	(15,000,000)	1.0000	(15,000,000)
1		5,500,000	5,500,000	0.9174	5,045,700
2		5,500,000	5,500,000	0.8417	4,629,350
3		5,500,000	5,500,000	0.7722	4,247,100
4	(18,000,000)	5,500,000	(12,500,000)	0.7084	(8,855,000)
5		7,200,000	7,200,000	0.6499	4,679,280
6		7,200,000	7,200,000	0.5963	4,293,360
7		7,200,000	7,200,000	0.5470	3,938,400
8		7,200,000	7,200,000	0.5019	3,613,680
				NPV =	6,591,870.00

PV annuity factor at 9% for 8 years =(1-1.09^-8)8%=	5.53482
NPV of Machine A =	6,591,870
EAA =6591870/5.53482=	1,190,982.0

Machine B

Details

Year=n	Investment	Cash inflow	Net Cash Flow	PV factor @9%=1/1.09^n	PV of Net cash flow
0	(16,000,000)	-	(16,000,000)	1.0000	(16,000,000)
1		6,500,000	6,500,000	0.9174	5,963,100
2		6,500,000	6,500,000	0.8417	5,471,050
3		6,500,000	6,500,000	0.7722	5,019,300
4		6,500,000	6,500,000	0.7084	4,604,600
5		6,500,000	6,500,000	0.6499	4,224,350
6		6,500,000	6,500,000	0.5963	3,875,950
7		6,500,000	6,500,000	0.5470	3,555,500
8		6,500,000	6,500,000	0.5019	3,262,350
				NPV =	19,976,200.00

PV annuity factor at 9% for 8 years =(1-1.09^-8)8%=	5.53482
NPV of Machine A =	19,976,200
EAA =19,976,200/5.53482	3,609,187.5

As the Equivent Annual annuity of Machine B is higher , Machine B should be acquired.