Question 3 OR (a)
Value of two firms and the MM arbitrage process
12 marks
- Time to write
- About 24 minutes
Question
Question 3 OR (a) · 12 marksSuppose there are two firms, L and U, in the market. The two firms are alike in all respects, except that firm L has 10%, ₹12,00,000 Debentures. Each of the firms has an operating profit of ₹2,40,000. The equity capitalization rate (k_e) is 16% for firm L and 12.5% for firm U.
Calculate the value of each firm and explain how, under the Modigliani-Miller Approach, an investor Ishaan Verma who own 10% equity shares of the firm that is overvalued will be better off by moving his holding to the other firm. Also explain at what point this process will end.
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
- Calculate…Explain…Two asks in one question: answer both.
- CalculateFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
"Who own" is printed so and kept.
Write it in this order
A step that gives the answer away stays hidden: tap it to see it.
- Read the data; note exactly what is asked 2 min
- 1 Value of each firm; overvalued firm identified 3 marks 5 min
- 2 Arbitrage: sale, personal borrowing, purchase of U, income compared 6 marks 10 min
- 3 Point at which the process ends 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Short on time? Step 2 carries 6 of the 12 marks: guard its minutes.
Try it first. About 24 minutes for 12 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.
1. Value of each firm (no taxes; equity value = earnings for equity ÷ ke)
| ₹ | Firm U | Firm L |
|---|---|---|
| Operating profit (EBIT) | 2,40,000 | 2,40,000 |
| Less: interest (10% × 12,00,000) | — | 1,20,000 |
| Earnings for equity | 2,40,000 | 1,20,000 |
| Equity capitalisation rate (ke) | 12.5% | 16% |
| Value of equity (E) | 19,20,000 | 7,50,000 |
| Value of debt (D) | — | 12,00,000 |
| Value of the firm (V) | 19,20,000 | 19,50,000 |
Under MM (no taxes) two firms alike in every respect but capital structure must have the same value. Firm L, at ₹19,50,000, is overvalued against U at ₹19,20,000.
2. How Ishaan Verma gains by switching (arbitrage)
Present position: 10% of L's equity, worth ₹75,000, earning 10% × ₹1,20,000 = ₹12,000.
He sells his L shares and borrows personally in the same proportion as L's debt, 10% × ₹12,00,000 = ₹1,20,000 at 10%, so his personal leverage replaces L's corporate leverage:
| ₹ | |
|---|---|
| Sale of 10% of L's shares | 75,000 |
| Personal borrowing at 10% | 1,20,000 |
| Funds available | 1,95,000 |
He invests the whole ₹1,95,000 in U's shares:
| ₹ | |
|---|---|
| Income from U: 1,95,000 × 12.5% | 24,375 |
| Less: interest on personal borrowing: 1,20,000 × 10% | 12,000 |
| Net income | 12,375 |
His income rises from ₹12,000 to ₹12,375, a gain of ₹375, with the same financial risk, since he has simply replaced L's corporate debt with an equal personal debt. (Equally, he could buy 10% of U for ₹1,92,000, earn the same ₹12,000 net, and keep ₹3,000 of his funds free.)
3. When the process ends. Other investors in L do the same. Selling L's shares lowers L's share price, raising its ke; buying U's shares raises U's share price, lowering its ke. The arbitrage goes on until the two firms have the same total value (and the same overall cost of capital), when no investor can gain by switching. If U's value stayed at ₹19,20,000, L's equity would fall to ₹7,20,000, at which L's ke would be 1,20,000 ÷ 7,20,000 = 16.67%.
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Value of each firm; overvalued firm identified | 3 |
| 2 | Arbitrage: sale, personal borrowing, purchase of U, income compared | 6 |
| 3 | Point at which the process ends | 3 |
| Total | 12 |
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