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Answer :
Final answer:
Joyce needs to drive approximately 1,431 miles to break even. The effect of a decrease in sales on her profit cannot be calculated with the given information.
Explanation:
To determine how many miles Joyce needs to drive to break even, we can use the cost equation derived from the high-low method. The cost equation is given as:
total monthly cost = $415 + $0.17 per mile driven
Let's denote the number of miles driven as 'x'. To break even, Joyce's total monthly cost should be equal to her total revenue. Since she charges $0.46 per mile driven, her total revenue can be calculated as:
total revenue = $0.46 * x
Setting the total monthly cost equal to the total revenue, we have:
$415 + $0.17x = $0.46x
Simplifying the equation, we get:
$415 = $0.29x
Dividing both sides by $0.29, we find:
x = $415 / $0.29
Therefore, Joyce needs to drive approximately 1,431 miles to break even.
To calculate Joyce's degree of operating leverage when she drives 4,300 miles, we need to determine the percentage change in operating profit and the percentage change in sales. The formula for calculating the degree of operating leverage is:
degree of operating leverage = percentage change in operating profit / percentage change in sales
Since we don't have the operating profit and sales figures for 4,300 miles, we cannot calculate the degree of operating leverage.
Suppose Joyce took a week off and her sales for the month decreased by 22 percent. Using the degree of operating leverage, we can calculate the effect this will have on her profit for that month. Let's denote the original profit as 'P'.
The percentage change in sales is -22 percent, and the degree of operating leverage is not provided. Therefore, we cannot calculate the effect on profit using the given information.
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Rewritten by : Barada
1. Joyce needs to drive approximately 1431 miles to break even.
2. The degree of operating leverage is 1.084 if she drives 4100 miles.
3. If Joyce's sales decrease by 22% and she drives 4300 miles, her profit will decrease by approximately $4756.74.
1. Break-even Point:
To determine the break-even point, we need to set the total monthly cost equal to the revenue. Let's assume the number of miles Joyce needs to drive to break even is x.
Total monthly cost = Revenue
$415 + $0.17x = $0.46x
Solving the equation: $415 = $0.29x
Dividing both sides by $0.29: x = $415 ÷ $0.29 = 1431.03 miles
So, Joyce needs to drive approximately 1431 miles to break even.
2. Degree of Operating Leverage:
The degree of operating leverage can be calculated using the formula: Degree of Operating Leverage = Contribution Margin / Net Operating Income
Contribution Margin is given by: Contribution Margin = Revenue - Variable Cost
Net Operating Income can be calculated by subtracting Total Monthly Cost from Revenue.
For Joyce's case, if she drives 4100 miles:
Contribution Margin = $0.46 * 4100 - $415 = $1895
Net Operating Income = Revenue - Total Monthly Cost = $0.46 * 4100 - $1193 = $1747
Therefore, the Degree of Operating Leverage = $1895 / $1747 ≈ 1.084
3. Effect on Profit:
To calculate the effect on profit, we need to use the formula: Effect on Profit = Degree of Operating Leverage × Change in Sales
Change in Sales is given as a percentage, so we need to multiply it by Revenue to find the actual change in sales.
If Joyce's sales for the month decreased by 22%, and she drives 4300 miles:
Change in Sales = 22% × $0.46 * 4300 = $4383.60
The Effect on Profit = 1.084 × $4383.60 = $4756.74
So, the decrease in sales will negatively affect Joyce's profit by approximately $4756.74.
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