Delmo Donuts sells donuts for $1.30 each. Over the past year, the highest monthly sales volume was 5,100 and the lowest monthly sales volume was 3,340. In the month where the highest sales were achieved, total costs were $4,870. In the month where the lowest sales occurred, total costs were $3,814. Delmo Donuts’ estimated variable cost per donut (to the nearest cent) is

Question

BlackTom AI · Accepted Answer

Using the high–low method to separate variable and fixed costs, the variable cost per unit equals the change in total cost divided by the change in units between the highest- and lowest-activity months.

1. Relevant concepts
- Total cost = Fixed cost + (Variable cost per unit × Number of units).
- High–low method: variable cost per unit = (Cost at high activity − Cost at low activity) / (High units − Low units).
This isolates variable cost behavior from total costs when only two activity levels are known.

2. Step-by-step reasoning
- Identify high and low activity points:
  - High: 5,100 donuts, total cost = $4,870.
  - Low: 3,340 donuts, total cost = $3,814.
- Compute changes:
  - Change in cost = $4,870 − $3,814 = $1,056.
  - Change in units = 5,100 − 3,340 = 1,760.

3. Calculations (all intermediate steps)
- Variable cost per donut = 1,056 / 1,760.
- Divide numerator and denominator: 1,056 ÷ 1,760 = 0.6.
- In currency terms: $0.60 per donut.

4. Why this is correct
- The high–low formula directly measures how costs change with activity; the $1,056 cost increase for 1,760 additional donuts implies each additional donut added $0.60 to total cost.
- Verify fixed cost consistency:
  - Using low month: Fixed = 3,814 − (0.60 × 3,340) = 3,814 − 2,004 = $1,810.
  - Using high month: Fixed = 4,870 − (0.60 × 5,100) = 4,870 − 3,060 = $1,810.
  The fixed cost is identical in both months, confirming the calculation.

5. Why other choices would be incorrect
- Any other variable-cost-per-unit value (for example $0.50 or $0.70) would produce inconsistent fixed costs between the two months (the fixed amounts would not match), so they cannot be correct.

6. Conclusion
The estimated variable cost per donut is $0.60, which matches the provided correct answer.

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