A contractor is evaluating whether to purchase a $180,000 excavator or rent it for $1,200 per day. The project requires the equipment for 180 days over 18 months. Assuming 8% annual cost of capital, what is the approximate present value of rental costs?
Correct Answer
C) $204,000
Total rental cost = 180 days × $1,200 = $216,000. Discounting over 18 months at 8% annual rate (12% for 1.5 years) gives approximately $204,000 present value, making rental more expensive than purchase.
Why This Is the Correct Answer
Option C correctly calculates the present value of rental costs by first determining the total rental cost (180 days × $1,200 = $216,000), then discounting this amount over 18 months using the 8% annual cost of capital. The discount factor for 1.5 years at 8% is approximately 0.944, which when applied to $216,000 gives approximately $204,000. This present value analysis allows for proper comparison with the $180,000 purchase price.
Why the Other Options Are Wrong
Option A: $198,000
Option D ($189,000) applies an excessive discount that doesn't align with the 8% annual rate over 18 months, likely from calculation errors.
Option D: $189,000
Option A ($198,000) underestimates the present value by applying too high of a discount rate or incorrect time period calculation.
Memory Technique
Remember 'PV-FV-Rate-Time' - Present Value equals Future Value discounted by Rate over Time. For equipment decisions, always discount rental payments to compare apples-to-apples with upfront purchase costs.
Reference Hint
Business and Finance for Contractors chapter on Time Value of Money and Equipment Acquisition Analysis
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