Question

A company plans to purchase a new machine. There are two choices. The following are the cash flows from two machines:  

     Machine A:    The machine’s initial purchase price is $99,718, and it has a singlemaintenance fee of $6,000 at the end of year 4. The machine would last for 7 years. Assume that the discount rate is 8% for this machine.

     Machine B:    The machine’s initial purchase price is $10,000, and it has annualmaintenance cost of $10,000 at the end of each year for 5 years. The machine would last for 5 years. Assume that the discount rate is 10% for this machine.

    As a financial analyst assistant, you have been asked to compute Equivalent Annual Annuity (EAA), also called Equivalent Annual Cost (EAC). How much are the EAA of these two machines?

Answer 1

Machine A
Year	Cost	Present Value @8% (Cost/1.08^year)
0	99,718.00	99,718.00
1	-	-
2	-	-
3	-	-
4	6,000.00	4,410.18
5	-	-
6	-	-
7	-	-
	Total (PW)	104,128.18

For machine A

Similarly for Machine B

Machine B
Year	Cost	Present Value @10% (cost/1.1^year)
0	10,000.00	10,000.00
1	10,000.00	9,090.91
2	10,000.00	8,264.46
3	10,000.00	7,513.15
4	10,000.00	6,830.13
5	10,000.00	6,209.21
	Total (PW)	47,907.87

PV	(47,907.87)
rate	10%
nper	5
PMT	$12,637.97

EAC for machine A is $20000.15 and for machine B it is $12637.97. As the EAC is lower for machine B, machine B should be choosen.