Question 1 OR (b)
Operating, financial and combined leverage; sales fall that wipes out EPS
10 marks
- Time to write
- About 20 minutes
From an older CBCS paper
Question
Question 1 OR (b) · 10 marksCalculate, from the data below
The Operating, Financial and Combined leverage
The percentage drop in sales that would make the earnings per share zero
| EBIT | 7200000 |
| Profit after tax | 1152000 |
| Fixed Cost | 1800000 |
| Tax rate | 40% |
| Preference dividend | 288000 |
Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Read from the question
- CalculateFormula first, then the working, then the answer with its unit (₹, %, units).
Write it in this order
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- Read the data; note exactly what is asked 1 min
- 1 EBT, interest and contribution worked back 3 marks 5 min
- 2 Operating leverage 1½ marks 3 min
- 3 Financial leverage with the preference dividend grossed up 2 marks 4 min
- 4 Combined leverage 1½ marks 3 min
- 5 Sales fall that makes EPS zero, with check 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 20 minutes for 10 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
Working back from profit after tax (₹)
| Particulars | ₹ |
|---|---|
| Profit after tax | 11,52,000 |
| Add: tax (40% of EBT; PAT is 60% of EBT) | 7,68,000 |
| Earnings before tax (EBT = 11,52,000 ÷ 0.60) | 19,20,000 |
| Add: interest (balancing figure) | 52,80,000 |
| EBIT | 72,00,000 |
| Add: fixed cost | 18,00,000 |
| Contribution | 90,00,000 |
- Operating leverage = Contribution ÷ EBIT = 90,00,000 ÷ 72,00,000 = 1.25.
- Financial leverage. Preference dividend is paid out of profit after tax, so it is grossed up for tax: 2,88,000 ÷ (1 − 0.40) = ₹4,80,000 of pre-tax earnings; the financial break-even EBIT is interest + preference dividend ÷ (1 − t). DFL = EBIT ÷ [EBT − PD ÷ (1 − t)] = 72,00,000 ÷ (19,20,000 − 4,80,000) = 72,00,000 ÷ 14,40,000 = 5.00.
- Combined leverage = DOL × DFL = 1.25 × 5.00 = 6.25. It measures the % change in EPS that results from a 1% change in sales.
(ii) Fall in sales that makes EPS zero. EPS falls to zero when it falls by 100%. With a combined leverage of 6.25:
1The baker signs for the bank's money at a fixed interest.
Financial leverageThe use of fixed-charge funds (debt, preference shares) in the capital structure.
2The ovens run full, the queue is long—the loan earns more than it costs, and the owner's share swells.
FavourableThe fixed-charge funds earn more than they cost, so EPS rises.
3The same counter empty: the interest envelope still goes out, from a thinner cash box.
UnfavourableWhen ROI is below the cost of debt: EPS falls.
% fall in sales = 100% ÷ 6.25 = 16%.
Check. EPS is zero at the financial break-even EBIT of 52,80,000 + 4,80,000 = ₹57,60,000, a fall in EBIT of ₹14,40,000. With fixed costs unchanged, contribution must fall by the same ₹14,40,000, which is 16% of ₹90,00,000; since contribution moves in proportion to sales, sales must fall by 16%.
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | EBT, interest and contribution worked back | 3 |
| 2 | Operating leverage | 1.5 |
| 3 | Financial leverage with the preference dividend grossed up | 2 |
| 4 | Combined leverage | 1.5 |
| 5 | Sales fall that makes EPS zero, with check | 2 |
| Total | 10 |
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