Question 4 OR (a)
Operating and financial leverage and the change in EPS
10 marks
- Time to write
- About 20 minutes
From an older CBCS paper
Question
Question 4 OR (a) · 10 marksThe capital structure of Kavita Ltd. consists of ordinary share capital of (₹) 12,00,000 (Shares of ₹100 each) and (₹) 12,00,000 of 9% debentures. The selling price is (₹) 10 per unit, while variable costs amount to (₹) 7 per unit and fixed expenses amount to (₹) 1,60,000. The income tax rate is assumed to be 35%. The sales level is expected to increase from 1,50,000 units to 1,80,000 units.
I. You are required to compute:
The percentage increase in the earnings per share:
The degree of financial leverage at 1,50,000 units and 1,80,000 units.
The degree of operating leverage at 1,50,000 units and 1,80,000 units.
- Comment on how operating and financial leverages behave in relation to the increase in production from 1,50,000 units and 1,80,000 units.
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
- Comment onThe comment carries marks too: say what the figures show, in two or three lines.
- computeFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
The paper speaks of the sales level and of production; both are read as the same change from 1,50,000 to 1,80,000 units. The fixed expenses are operating fixed costs, and the debentures carry the only interest.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Income statement at both output levels, with EPS 3 marks 5 min
- 2 I (i) Percentage increase in EPS 1½ marks 3 min
- 3 I (ii) DFL at both levels 1½ marks 3 min
- 4 I (iii) DOL at both levels 1½ marks 3 min
- 5 II Comment on the behaviour of both leverages 2½ marks 4 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.
Number of equity shares = 12,00,000 ÷ 100 = 12,000. Interest on the debentures = 9% of 12,00,000 = ₹1,08,000 (paper note: the only interest). The fixed expenses of ₹1,60,000 are operating fixed costs (paper note). Output rises by 20%, from 1,50,000 to 1,80,000 units.
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.
| Particulars | 1,50,000 units | 1,80,000 units |
|---|---|---|
| Sales @ ₹10 | 15,00,000 | 18,00,000 |
| Less: variable costs @ ₹7 | 10,50,000 | 12,60,000 |
| Contribution | 4,50,000 | 5,40,000 |
| Less: fixed expenses | 1,60,000 | 1,60,000 |
| EBIT | 2,90,000 | 3,80,000 |
| Less: interest on 9% debentures | 1,08,000 | 1,08,000 |
| EBT | 1,82,000 | 2,72,000 |
| Less: tax @ 35% | 63,700 | 95,200 |
| EAT | 1,18,300 | 1,76,800 |
| EPS (EAT ÷ 12,000 shares) | 9.86 | 14.73 |
I (i) Percentage increase in EPS. The number of shares does not change, so EPS rises in the same proportion as EAT: (1,76,800 − 1,18,300) ÷ 1,18,300 × 100 = 49.45% (EPS from ₹9.858 to ₹14.733).
I (ii) Degree of financial leverage = EBIT ÷ EBT:
- at 1,50,000 units: 2,90,000 ÷ 1,82,000 = 1.59;
- at 1,80,000 units: 3,80,000 ÷ 2,72,000 = 1.40.
I (iii) Degree of operating leverage = Contribution ÷ EBIT:
- at 1,50,000 units: 4,50,000 ÷ 2,90,000 = 1.55;
- at 1,80,000 units: 5,40,000 ÷ 3,80,000 = 1.42.
Check. DFL measures the percentage change in EPS for a 1% change in EBIT, and DCL = DOL × DFL measures it for a 1% change in sales. EBIT rises by 90,000 ÷ 2,90,000 = 31.03%, and 1.5934 × 31.03% = 49.45%; equally, DCL at 1,50,000 units = 1.5517 × 1.5934 = 2.4725, and 2.4725 × 20% = 49.45%, the rise in EPS found above.
II Comment. Both leverages fall as output rises from 1,50,000 to 1,80,000 units: operating leverage from 1.55 to 1.42 and financial leverage from 1.59 to 1.40.
- Operating leverage comes from the fixed operating costs. The ₹1,60,000 stays the same while contribution grows, so it is a smaller part of contribution and the firm moves further above its operating break-even point; working well above break-even protects the firm from operating risk.
- Financial leverage comes from the fixed interest of ₹1,08,000, which does not change while EBIT rises from ₹2,90,000 to ₹3,80,000, so interest takes a smaller share of EBIT and financial risk falls.
- Each level of output has its own DOL and each level of EBIT its own DFL; DOL shows business risk and DFL financial risk. Both measures are above 1 at each level, so the 20% rise in output still lifts EPS by much more than 20%, but the magnifying effect, and with it the risk, is weaker at the higher output.
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Income statement at both output levels, with EPS | 3 |
| 2 | I (i) Percentage increase in EPS | 1.5 |
| 3 | I (ii) DFL at both levels | 1.5 |
| 4 | I (iii) DOL at both levels | 1.5 |
| 5 | II Comment on the behaviour of both leverages | 2.5 |
| Total | 10 |
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