Question

3. A machine tool costs $10,000 and does not have any salvage value. The manufacturer's warranty covers the maintenance and repair cost for the first year. The maintenance and repair costs for the second year will be $1,000 and will increase for $500 for the subsequent years. The operating costs for the first year will be $400 and will increase for $400 for the subsequent years. Consider an analysis period of 8 years and interest rate of 9%, and find the minimum cost life and minimum EUAC. (25 pts)

Answer 1

Concept: Minimum cost life is the life of the asset over which the minimum equivalent annual cost is lowest. It is advisable to replace the asset after the minimum cost life of the asset Equivalent unfirm annual cost (EUAC) is the annual cost of owning, operating, and maintaining an asset over its entire life. EAC is often used by firms for capital budgeting decisions, as it allows a company to compare the cost-effectiveness of various assets that have unequal lifespans. Particulars Initial cost (A) $10,000 Maintenance and repair cost (B) Operating costs (C) $0 $0 SO Annity factor @ 9% (E) 1.00 1.92 2.76 $400 Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Total Cost (A+B+C) $10,000 $400 $1,800 $2,700 $3,600 $4,500 $5,400 $6,300 $7,200 $1,000 $1,500 $2,000 $2,500 $3,000 $3,500 $4,000 3.53 Year on year Cumulative cost (D) $10,000 $10,400 $12,200 $14,900 $18,500 $23,000 $28,400 $34,700 $41,900 $800 $1,200 $1,600 $2,000 $2,400 $2,800 $3,200 Discounting factor @ 9% (E) 1.00 0.92 0.84 0.77 0.71 0.65 0.60 0.55 0.50 Minimum Cost Life Equivalent Uniform Annual cost (D/E) $10,000 $5,424 $4,422 $4,219 $4,363 $4,704 $5,177 $5,752 $6,412 4.24 4.89 5.49 6.03 6.53 Conclusion: Minimum cost life in the question is 3 years Equivalent uniform annual cost (EUAC) is $6,412 if the life of the asset is 8 years