A contractor is evaluating two equipment options: Option A costs $85,000 to purchase with $1,200 monthly operating costs, or Option B can be rented for $3,800 monthly. At what point (in months) do the total costs become equal?
Correct Answer
B) 33 months
Set up equation: $85,000 + $1,200x = $3,800x, where x is months. Solving: $85,000 = $2,600x, so x = 32.7 months, approximately 33 months.
Why This Is the Correct Answer
Option A is correct because this is a break-even analysis problem where we need to find when the total cost of purchasing equals the total cost of renting. Setting up the equation $85,000 + $1,200x = $3,800x and solving for x gives us the point where costs are equal. The calculation yields 32.7 months, which rounds to 33 months. This represents the break-even point where both options have identical total costs.
Why the Other Options Are Wrong
Option A: 22 months
18 months is significantly too early - at this point, purchasing costs $106,600 while renting costs only $68,400, making the rental option much more economical.
Option C: 18 months
28 months falls short of the break-even point - the purchase option would cost $118,600 while renting would cost $106,400, so renting remains the better financial choice.
Option D: 28 months
22 months is too early - at this point, the purchase option would cost $111,400 ($85,000 + 22 × $1,200) while renting would cost $83,600 (22 × $3,800), making renting still cheaper.
Memory Technique
Remember 'BEEF' - Break-Even Equation Format: Fixed costs plus variables on one side, total variables on the other side, then solve for time.
Reference Hint
Business and Finance chapter - Equipment Cost Analysis and Break-Even Calculations section
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