Question

Machine A costs $30,000 to purchase and is worth $9,000 in 5 years. Machine B costs $15,000 to purchase and is worth $2,000 in 2 years. Assume that these machines are needed for 20 years and can be repurchased at the same price in the future. (use 13% interest rate)

Compute the Annual Equivalent Cost of each machine and subtract those values. Record the difference as a POSITIVE if Machine A is best, or a NEGATIVE if Machine B is best.

Answer 1

Machine A:
AW of first cost = 30000*(0.13*1.13^5)/(1.13^5-1) =	$ 8,529.44
[The formula for finding PV of annuity is adapted and used]
AW of Salvage value = 9000*0.13/(1.13^5-1) =	$ 1,388.83
AEC = 8529.44-1388.83 =	$ 7,140.61
Machine B:
AW of first cost = 15000*(0.13*1.13^2)/(1.13^2-1) =	$ 8,992.25
AW of Salvage value = 2000*0.13/(1.13^2-1) =	$     938.97
AEC = 8992.25-938.97 =	$ 8,053.28
Difference in AEC = 7140.61-8053.28 =	$    -912.67
Machine A is best as its AEC is lowest