Question

Four years ago, Thomas bought an industrial-grade snowblower and started a business clearing sidewalks for churches, parks, and for the city government. Because of increasing maintenance costs for the snowblower, he is considering replacing it with a new machine. The defender was originally purchased for $1,000 and could be sold now for $700. Maintenance costs for the defender were $60 in year one (four years ago) and have increased by a uniform gradient of $15 per year ever since. In five years, the defender will only have a MV of $100. The challenger could be purchased for $1,300 and would have a MV of $400 in five years. Maintenance for the challenger would be $10 per year, for all five years. Assume a MARR of 12% and a planning horizon of five years. Report the difference between the EUAC of the challenger and the defender (in terms of the challenger’s EUAC minus the defender’s, so that your value would be positive if the challenger has a higher EUAC than the defender). These are cost alternatives, so consider costs to be positive.

Answer 1

MARR = 12%

Current MV of defender = 700

first maint cost = 60 + 15*4 = 120

MV after 5 yr = 100

EUAC of defender = 700*(A/P,12%,5) + 120 + 15*(A/G,12%,5) - 100*(A/F,12%,5)

= 700*0.277409 + 120 + 15*1.77459 - 100*0.157409

= 325.06

initial cost of challenger = 1300

Maint cost = 10

Salvage value = 400

EUAC of challenger = 1300*(A/P,12%,5) + 10 - 400*(A/F,12%,5)

= 1300 * 0.277409 + 10 - 400*0.157409

= 307.67

Diff in EUAC = EUAC of challenger - EUAC of defender

= 307.67 - 325.06 = -17.39

As EUAC of challenger is less it should be selected