Question

The initial cost of a new machine is 10, 000. the annual maintenance cost is 2000 for the first two years, then increases 1000 every year after that. The machine has 10 years useful life with salvage value of 4000. Calculate EUAC for keeping the machine

Answer 1

MARR is not given. Assuming MARR to be 10%

Equivalent Uniform Annual Cost = Present Value of Cost/PVAF(r%,n)

Present Value of Cost = Initial Cost + Present Value of Annual Maintenance Cost - Present Value of Salvage Value

Since, the annual maintenance cost increases from year 3, we will divide the annual maintenance cost into two parts:

1. Uniform cost of $2,000 for 10 years

2. Arithemetic cost increasing by $1,000 for 8 years from 3rd year and to bring it to zero year we will use PVF for 2 years

P = PUniform series + Parithemetic series

P = Uniform Amount*PVAF(r%,n) + Increased Amount*[( 1- (1+nr)*(1+r)-n)/r2]

PV = 10,000 + 2,000*[(1-1.1-10)/0.1] + 1,000*[(1- (1.8*0.4665))/0.12]*1.1-2 - 4,000*1.1-10

PV = 10,000 + 2,000*6.1445 + 1,000*16.02867*0.82644 - 4,000*0.38554

PV = 10,000 + 12,289 + 13,246 - 1,542

PV = $33,993

EUAC = 33,993/6.1445

EUAC = $5,532