Your company is evaluating whether to purchase or rent a crane. The crane costs $180,000 to purchase with a $120,000 resale value after 2 years. Monthly rental is $3,200. Considering a 6% annual cost of capital, what is the approximate annual equivalent cost of purchasing?
Correct Answer
C) $38,800
Net purchase cost over 2 years: $180,000 - $120,000 = $60,000. Annual equivalent cost with 6% interest: $60,000 ÷ 1.833 (present value factor) ≈ $32,700. Adding opportunity cost on average investment: approximately $38,800 annually.
Why This Is the Correct Answer
Option B correctly calculates the annual equivalent cost by first determining the net cost of ownership ($60,000 depreciation over 2 years), then converting this to an annual equivalent using present value factors for the 6% cost of capital. The calculation also properly includes the opportunity cost of the capital tied up in the equipment investment, which increases the total annual equivalent cost to approximately $38,800.
Why the Other Options Are Wrong
Option A: $41,200
This amount overestimates the annual equivalent cost by not properly applying the present value factors or by incorrectly calculating the opportunity cost component of the investment.
Option D: $44,600
This amount significantly overestimates the annual cost, likely by double-counting some cost components or using incorrect interest calculations in the present value analysis.
Memory Technique
DOIT: Depreciation + Opportunity cost + Interest + Time value = total annual equivalent cost
Reference Hint
Look up 'Present Value Analysis' and 'Equipment Economics' in construction management or engineering economics chapters
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