Question

Contec Systems has the opportunity to invest in one of two mutually exclusive machines that will produce a product it will need for the foreseeable future. Machine A costs $2.5 million and realizes after-tax inflows of $900,000 per year for 5 years. Machine B costs $3.4 million and realizes after-tax inflows of $800,000 per year for 9 years. Assume that machine prices are not expected to rise because inflation will be offset by cheaper components used in the machines. The cost of capital is 12%.
i. What is the NPV of each machine? Is it correct to make choice on the basis of NPV in this case?   
ii. Compute equivalent annual annuity-EAA for each machine?
iii. Compute payback period of both machine.                             
iv. Which machine should be accepted finally?

Answer 1

Answer:

i) MACHINE A

Year	Cash Flows	PV @ 12%	Present Value
1	900000	0.8929	803610
2	900000	0.7972	717480
3	900000	0.7118	640620
4	900000	0.6355	571950
5	900000	0.5674	510660
			3244320
		Initial Investment	2500000
		NPV	744320

MACHINE B

Year	Cash Flows	PV @ 12%	Present Value
1	800000	0.8929	714320
2	800000	0.7972	637760
3	800000	0.7118	569440
4	800000	0.6355	508400
5	800000	0.5674	453920
6	800000	0.5066	405280
7	800000	0.4523	361840
8	800000	0.4039	323120
9	800000	0.3606	288480
			4262560
		Initial Investment	3400000
		NPV	862560

Based on NPV, Machine B is preferred as it has a higher NPV than Machine A.
NPV is a useful in evaluating projects which have same length. However, for projects having different time lengths, NPV is less preferred.

ii) Equivalent Annual Annuity (EAA) = (r x NPV) / (1 - (1 + r)-n )
where r is the discount rate, n is the number of period

MACHINE A
EAA = (0.12 * 744320) / (1- (1.12)-5 )
EAA = 206481.60

MACHINE B
EAA = (0.12 * 862560) / (1- (1.12)-9 )
EAA = 161884.30

On the basis of EAA, Machine A is preferred since it has a higher EAA.

iii) Payback Period = A + (B/C)

Where,
A is the last period number with a negative cumulative cash flow;
B is the absolute value (i.e. value without negative sign) of cumulative net cash flow at the end of the period A; and
C is the total cash inflow during the period following period A

MACHINE A

Year	Cash Flows	Cumulative CF
0	-2500000	-2500000
1	900000	-1600000
2	900000	-700000
3	900000	200000
4	900000	1100000
5	900000	2000000

= 2 + (700000/900000) = 2.78 years

MACHINE B

Year	Cash Flows	Cumulative CF
0	-3400000	-3400000
1	800000	-2600000
2	800000	-1800000
3	800000	-1000000
4	800000	-200000
5	800000	600000
6	800000	1400000
7	800000	2200000
8	800000	3000000
9	800000	3800000

= 4 + (200000/800000) = 4.25 years

Shorter paybacks attract more investments. Therefore, on the basis of payback Machine A is better.

iv) Since, NPV is less preferred for projects with different time lengths, therefore, considering payback period and EAA, Machine A is preferred and Contec systems should invest in Machine A.