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Sagot :
Certainly! Let's address the problem step-by-step.
Given:
- Degree of Operating Leverage (DOL) = 4
- Degree of Financial Leverage (DFL) = 2
- Interest expenses = Rs. 200
- Variable Cost Percentage = 75% = 0.75
- Tax rate = 50% = 0.50
To find:
- Total Sales
- Total Variable Cost
- Total Contribution
- Total Fixed Cost
- EBIT (Earnings Before Interest and Taxes)
- EBT (Earnings Before Taxes)
- Profit after tax
## Step-by-Step Solution
1. Finding Total Contribution and EBIT:
We know:
[tex]\[ \text{DOL} = \frac{\text{Total Contribution}}{\text{EBIT}} \][/tex]
[tex]\[ \text{DFL} = \frac{\text{EBIT}}{\text{EBT}} \][/tex]
Also:
[tex]\[ \text{Interest expenses} = 200 \][/tex]
We can define EBIT as some variable [tex]\( \text{EBIT} \)[/tex].
From the degree of financial leverage:
[tex]\[ \text{DFL} = 2 = \frac{\text{EBIT}}{\text{EBT}} \][/tex]
Which gives:
[tex]\[ \text{EBT} = \frac{\text{EBIT}}{2} \][/tex]
Now, considering interest expenses:
[tex]\[ \text{EBT} = EBIT - \text{Interest expenses} \][/tex]
[tex]\[ \frac{\text{EBIT}}{2} = \text{EBIT} - 200 \][/tex]
Solving for EBIT:
[tex]\[ \text{EBIT} - \frac{\text{EBIT}}{2} = 200 \][/tex]
[tex]\[ \frac{\text{EBIT}}{2} = 200 \][/tex]
[tex]\[ \text{EBIT} = 400 \][/tex]
Using DOL:
[tex]\[ \text{DOL} = 4 = \frac{\text{Total Contribution}}{\text{EBIT}} \][/tex]
[tex]\[ \text{Total Contribution} = 4 \times \text{EBIT} = 4 \times 400 = 1600 \][/tex]
2. Calculating Total Sales:
[tex]\[ \text{Total Contribution} = \text{Total Sales} - \text{Total Variable Cost} \][/tex]
Given that:
[tex]\[ \text{Total Variable Cost} = 75\% \text{ of Total Sales} \][/tex]
[tex]\[ \text{Total Contribution} = \text{Total Sales} - 0.75 \times \text{Total Sales} \][/tex]
[tex]\[ \text{Total Contribution} = \text{Total Sales} \times (1 - 0.75) \][/tex]
[tex]\[ \text{Total Contribution} = 0.25 \times \text{Total Sales} \][/tex]
Solving for Total Sales:
[tex]\[ 1600 = 0.25 \times \text{Total Sales} \][/tex]
[tex]\[ \text{Total Sales} = \frac{1600}{0.25} = 6400 \][/tex]
3. Calculating Total Variable Cost:
[tex]\[ \text{Total Variable Cost} = 0.75 \times \text{Total Sales} \][/tex]
[tex]\[ \text{Total Variable Cost} = 0.75 \times 6400 = 4800 \][/tex]
4. Calculating Total Fixed Costs:
[tex]\[ \text{Total Contribution} = \text{Total Fixed Costs} + \text{EBIT} \][/tex]
[tex]\[ 1600 = \text{Total Fixed Costs} + 400 \][/tex]
[tex]\[ \text{Total Fixed Costs} = 1600 - 400 = 1200 \][/tex]
5. Calculating EBT:
[tex]\[ \text{EBT} = \text{EBIT} - \text{Interest expenses} \][/tex]
[tex]\[ \text{EBT} = 400 - 200 = 200 \][/tex]
6. Calculating Profit after tax:
[tex]\[ \text{Profit after tax} = \text{EBT} \times (1 - \text{tax rate}) \][/tex]
[tex]\[ \text{Profit after tax} = 200 \times (1 - 0.50) = 200 \times 0.50 = 100 \][/tex]
## Summary of Results:
1. Total Sales = Rs. 6400
2. Total Variable Cost = Rs. 4800
3. Total Contribution = Rs. 1600
4. Total Fixed Cost = Rs. 1200
5. EBIT = Rs. 400
6. EBT = Rs. 200
7. Profit after tax = Rs. 100
These are the required calculations based on the given data and the given financial leverage and operating leverage values.
Given:
- Degree of Operating Leverage (DOL) = 4
- Degree of Financial Leverage (DFL) = 2
- Interest expenses = Rs. 200
- Variable Cost Percentage = 75% = 0.75
- Tax rate = 50% = 0.50
To find:
- Total Sales
- Total Variable Cost
- Total Contribution
- Total Fixed Cost
- EBIT (Earnings Before Interest and Taxes)
- EBT (Earnings Before Taxes)
- Profit after tax
## Step-by-Step Solution
1. Finding Total Contribution and EBIT:
We know:
[tex]\[ \text{DOL} = \frac{\text{Total Contribution}}{\text{EBIT}} \][/tex]
[tex]\[ \text{DFL} = \frac{\text{EBIT}}{\text{EBT}} \][/tex]
Also:
[tex]\[ \text{Interest expenses} = 200 \][/tex]
We can define EBIT as some variable [tex]\( \text{EBIT} \)[/tex].
From the degree of financial leverage:
[tex]\[ \text{DFL} = 2 = \frac{\text{EBIT}}{\text{EBT}} \][/tex]
Which gives:
[tex]\[ \text{EBT} = \frac{\text{EBIT}}{2} \][/tex]
Now, considering interest expenses:
[tex]\[ \text{EBT} = EBIT - \text{Interest expenses} \][/tex]
[tex]\[ \frac{\text{EBIT}}{2} = \text{EBIT} - 200 \][/tex]
Solving for EBIT:
[tex]\[ \text{EBIT} - \frac{\text{EBIT}}{2} = 200 \][/tex]
[tex]\[ \frac{\text{EBIT}}{2} = 200 \][/tex]
[tex]\[ \text{EBIT} = 400 \][/tex]
Using DOL:
[tex]\[ \text{DOL} = 4 = \frac{\text{Total Contribution}}{\text{EBIT}} \][/tex]
[tex]\[ \text{Total Contribution} = 4 \times \text{EBIT} = 4 \times 400 = 1600 \][/tex]
2. Calculating Total Sales:
[tex]\[ \text{Total Contribution} = \text{Total Sales} - \text{Total Variable Cost} \][/tex]
Given that:
[tex]\[ \text{Total Variable Cost} = 75\% \text{ of Total Sales} \][/tex]
[tex]\[ \text{Total Contribution} = \text{Total Sales} - 0.75 \times \text{Total Sales} \][/tex]
[tex]\[ \text{Total Contribution} = \text{Total Sales} \times (1 - 0.75) \][/tex]
[tex]\[ \text{Total Contribution} = 0.25 \times \text{Total Sales} \][/tex]
Solving for Total Sales:
[tex]\[ 1600 = 0.25 \times \text{Total Sales} \][/tex]
[tex]\[ \text{Total Sales} = \frac{1600}{0.25} = 6400 \][/tex]
3. Calculating Total Variable Cost:
[tex]\[ \text{Total Variable Cost} = 0.75 \times \text{Total Sales} \][/tex]
[tex]\[ \text{Total Variable Cost} = 0.75 \times 6400 = 4800 \][/tex]
4. Calculating Total Fixed Costs:
[tex]\[ \text{Total Contribution} = \text{Total Fixed Costs} + \text{EBIT} \][/tex]
[tex]\[ 1600 = \text{Total Fixed Costs} + 400 \][/tex]
[tex]\[ \text{Total Fixed Costs} = 1600 - 400 = 1200 \][/tex]
5. Calculating EBT:
[tex]\[ \text{EBT} = \text{EBIT} - \text{Interest expenses} \][/tex]
[tex]\[ \text{EBT} = 400 - 200 = 200 \][/tex]
6. Calculating Profit after tax:
[tex]\[ \text{Profit after tax} = \text{EBT} \times (1 - \text{tax rate}) \][/tex]
[tex]\[ \text{Profit after tax} = 200 \times (1 - 0.50) = 200 \times 0.50 = 100 \][/tex]
## Summary of Results:
1. Total Sales = Rs. 6400
2. Total Variable Cost = Rs. 4800
3. Total Contribution = Rs. 1600
4. Total Fixed Cost = Rs. 1200
5. EBIT = Rs. 400
6. EBT = Rs. 200
7. Profit after tax = Rs. 100
These are the required calculations based on the given data and the given financial leverage and operating leverage values.
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