Deluxe Motors owns a Bobcat skid steer that they bought for $38,000 years ago. Today it is currently worth $21,000. Looking to the future they believe it will go down in value by 15% every year. Their operating and maintenance costs for the skid steer will be $1,800 this year and they will increase by $500 every year. Use an interest rate of 10%/yr. What is their marginal cost for year 3? NOTE: Marginal Costs are year-by-year estimates of the costs to own an asset for that year. A. $5,950 B. $6,763 C. $6,593 D. $6,524
To calculate the marginal cost for year 3, we need to consider the change in value, operating and maintenance costs, and interest rate.
First, let's calculate the change in value from year 2 to year 3:
Value in year 2 = $21,000
Decrease in value = 15%
Value in year 3 = Value in year 2 * (1 - 0.15) = $21,000 * 0.85 = $17,850
Next, let's calculate the operating and maintenance costs for year 3:
Operating and maintenance costs for year 2 = $1,800
Increase in costs = $500
Operating and maintenance costs for year 3 = Operating and maintenance costs for year 2 + Increase in costs = $1,800 + $500 = $2,300
Now, let's calculate the present value of the marginal cost for year 3:
Future value of the change in value = $17,850
Interest rate = 10%
Number of years = 3
Present value of the change in value = Future value of the change in value / (1 + Interest rate)^Number of years = $17,850 / (1 + 0.10)^3 = $17,850 / 1.331 = $13,398.50
Present value of the operating and maintenance costs for year 3 = $2,300 / (1 + 0.10)^3 = $2,300 / 1.331 = $1,727.92
Marginal cost for year 3 = Present value of the change in value + Present value of the operating and maintenance costs for year 3 = $13,398.50 + $1,727.92 = $15,126.42
Therefore, the marginal cost for year 3 is $15,126.42.
The closest option is A. $5,950.
To calculate the marginal cost for year 3, we need to calculate the total cost for that year and subtract the total cost for year 2.
First, let's calculate the total cost for year 2:
Original value = $38,000
Value after 2 years of depreciation (15% per year): $38,000 - (2 * 0.15 * $38,000) = $38,000 - $11,400 = $26,600
Operating and maintenance costs for year 2: $1,800 + ($500 * 2) = $1,800 + $1,000 = $2,800
Total cost for year 2: $26,600 + $2,800 = $29,400
Now, let's calculate the total cost for year 3:
Value after 3 years of depreciation: $26,600 - (3 * 0.15 * $26,600) = $26,600 - $11,970 = $14,630
Operating and maintenance costs for year 3: $1,800 + ($500 * 3) = $1,800 + $1,500 = $3,300
Total cost for year 3: $14,630 + $3,300 = $17,930
Finally, to calculate the marginal cost for year 3, we subtract the total cost for year 2 ($29,400) from the total cost for year 3 ($17,930):
Marginal cost for year 3 = $17,930 - $29,400 = -$11,470
From the given answer choices, none of them match the calculated marginal cost. Please check your calculations or provide additional information if necessary.