IDNLearn.com provides a seamless experience for finding accurate answers. Find accurate and detailed answers to your questions from our experienced and dedicated community members.
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.
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.
