Question 3
MM approach: values and the gain from switching (with an inconsistent printed EBIT)
8 marks
- Time to write
- About 16 minutes
From an older CBCS paper
Question
Question 3 · 8 marksTwo companies, 'L Ltd' and 'U Ltd ', are identical in all respects except their capital structure. The information below is available:
| L Ltd. | U Ltd. | |
|---|---|---|
| EBIT (Rs.) | 120,000 | 600,000 |
| 12% debentures (Rs.) | 600,000 | NIL |
| Equity capitalization rate | 20% | 16% |
Calculate the two firms' values and, using the MM approach, illustrate how an investor, holding 10% shares of L Ltd, would be benefitted by switching his investment over from L Ltd. to U Ltd. 8
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
- illustrateExamples are asked for: one short example with each point.
- CalculateFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
The firms are said to be identical apart from capital structure, but the EBIT printed for U Ltd. (Rs 600,000 here) differs from L Ltd.'s (Rs 120,000 here). A handwritten correction on the source copy changes it; the printed figure is kept. The answer works on the figures printed and points out the inconsistency.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Values of L and U 3 marks 5 min
- 2 Switching steps and income 3 marks 5 min
- 3 Gain, and the equal-EBIT case 2 marks 4 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 16 minutes for 8 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.
Values of the two firms (no taxes; equity earnings capitalised at each firm's rate)
| Particulars (₹) | L Ltd. | U Ltd. |
|---|---|---|
| EBIT | 1,20,000 | 6,00,000 |
| Less: interest @ 12% | 72,000 | Nil |
| Earnings for equity | 48,000 | 6,00,000 |
| Equity capitalisation rate | 20% | 16% |
| Value of equity | 2,40,000 | 37,50,000 |
| Value of debt | 6,00,000 | Nil |
| Value of the firm | 8,40,000 | 37,50,000 |
A point to note (paper note). The firms are said to be identical except in capital structure, yet U Ltd.'s printed EBIT (₹6,00,000) is five times L Ltd.'s. The answer works on the printed figures and also shows the case the question evidently intends, with equal EBIT.
Switching under MM. Investors substitute personal leverage for corporate leverage: they sell the shares of the levered firm, borrow on their own account in proportion to its debt, and buy the unlevered firm's shares. An investor with 10% of L's equity has shares worth ₹24,000 and income 10% × 48,000 = ₹4,800.
| Step | ₹ |
|---|---|
| Sell 10% of L's equity | 24,000 |
| Borrow personally 10% of L's debt at 12% | 60,000 |
| Funds available, invested in U's shares | 84,000 |
Income from U's shares = 84,000 × 16% = 13,440 (U pays all its earnings to equity); less interest on the personal loan 12% × 60,000 = 7,200: ₹6,240, against ₹4,800 before. With the same leverage (his own debt replaces his share of L's debt), he gains ₹1,440 a year.
With equal EBIT (₹1,20,000 for U). U would be worth 1,20,000 ÷ 0.16 = ₹7,50,000 and L (₹8,40,000) overvalued. The investor buys 10% of U for ₹75,000 out of his ₹84,000, earning 12,000 − 7,200 = ₹4,800, the same income, and keeps ₹9,000. Either way he is better off, and switching continues until the values are brought into line.
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Values of L and U | 3 |
| 2 | Switching steps and income | 3 |
| 3 | Gain, and the equal-EBIT case | 2 |
| Total | 8 |
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