Question

A machine that costs $20,000 today has annual operating costs of $1,500, $1,600, $1,700 and $1,800 in each of the next four years. The discount rate is 10 percent. The PV of costs is ________ and the equivalent annual annuity is _______.

Answer 1

The PV of costs is ($25,192.61) and the equivalent annual annuity is ($7,947.53).

Step-by-step explanation:

PV Formula = $20,000 + OC 1 / (1 + interest rate) ∧1 + OC 2 / (1 + interest rate)∧ 2 + OC 3 / (1 + interest rate)∧ 3 + OC 4 / (1 + interest rate)∧ 4

where:

PV = Present Value

OP = Opertaiing Cost

PV = $20,000 + 1500/1.1∧1 + 1600/1.1∧2 + 1700/1.1∧3+ 1800/1.1∧2+ 1800/1.1∧4

PV = $20,000 + 1,363.63 + 1,322.31 + 1,277.23 + 1,229.42

PV = $25,192.61

Equivalent Annual Annuity = r (NPV)/1-(1+r)∧-n

EAA = 0.1 X $25,192.61/0.31699

EAA = $7,947.53