Question

In a replacement analysis for a small Silicon Valley start-up data server, the following data are known about the challenger: the initial investment is \$24,000 ; there is no annual maintenance cost for the first three years, however, it will be \$3,000 in each of years four and five, and then \$3,000 in the sixth year and increasing by \$2,500 each year until year 10. The salvage value is always $0, and MARR is 10 % per year. What is the minimum EUAC of this challenger

Answer 1

The minimum EUAC of the challenger is $9,410.63. This means that the annual cost of owning and operating this data server, taking into account all initial and future expenses, is equivalent to paying $9,410.63 each year.

How to solve

To find the minimum EUAC (Equivalent Uniform Annual Cost) of the challenger, we need to follow these steps:

1. Calculate the present value (PV) of all costs:

Initial investment: PV = $24,000

Maintenance costs:

Years 4 and 5: PV = $3,000 / (1 + 10%)^3 = $2,129.63 (each year)

Years 6 and 7: PV = $3,000 + $2,500 / (1 + 10%)^5 = $5,098.04 (each year)

Years 8, 9, and 10: PV = $5,098.04 + $2,500 / (1 + 10%) = $7,543.81 (each year)

Total PV of costs: PV = $24,000 + 2 * $2,129.63 + 2 * $5,098.04 + 3 * $7,543.81 = $51,513.73

2. Calculate the annual equivalent cost (AEC):

AEC = PV * MARR / (1 - (1 + MARR)^-n)

AEC = $51,513.73 * 10% / (1 - (1 + 10%)^-10)

AEC = $5,151.37

3. Find the minimum EUAC:

EUAC = AEC + Maintenance costs (present worth)

EUAC = $5,151.37 + (2 * $3,000 / (1 + 10%)^3)

EUAC = $5,151.37 + $4,259.26

EUAC = $9,410.63

Therefore, the minimum EUAC of the challenger is $9,410.63. This means that the annual cost of owning and operating this data server, taking into account all initial and future expenses, is equivalent to paying $9,410.63 each year.