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Calculate the following, given that the Total Variable Cost is 75% of Sales, Degree of Operating Leverage (DOL) is 4, Degree of Financial Leverage (DFL) is 2, and interest expenses are Rs. 200. Assume a tax rate of 50%.

(i) Total Sales
(ii) Total Variable Cost
(iii) Total Contribution
(iv) Total Fixed Cost
(v) EBIT (Earnings Before Interest and Taxes)
(vi) EBT (Earnings Before Taxes)
(vii) Profit after tax



Answer :

GinnyAnswer
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.

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