Question 3 (b)
MM approach: values of two firms and the arbitrage process
11 marks
- Time to write
- About 22 minutes
From an older CBCS paper
Question
Question 3 (b) · 11 marksTwo companies, X and Y, are in the same risk class. They are alike in everything, except that firm Y has 12.5% debentures of Rs. 14,40,000. The information below about the two firms is available:
| Particulars | X | Y |
|---|---|---|
| Net operating income | Rs. 3,60,000 | Rs. 3,60,000 |
| 12.5% Debentures | – | Rs. 14,40,000 |
| Equity Capitalization Rate | 0.15 | 0.16 |
Compute the value of the two firms, and explain how, under the Modigliani-Miller approach, an investor who holds 10% of the equity shares of the overvalued firm will gain by switching his holding to the other firm. Also explain when the arbitrage process will come to an 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
- Compute…Explain…Two asks in one question: answer both.
- ComputeFormula first, then the working, then the answer with its unit (₹, %, units).
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Values of X and Y 4 marks 7 min
- 2 The arbitrage steps for a 10% holder of Y 4 marks 7 min
- 3 Income before and after; gain 2 marks 4 min
- 4 When the arbitrage ends 1 mark 2 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 22 minutes for 11 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 (equity earnings capitalised at each firm's equity rate; no taxes)
| Particulars (₹) | X | Y |
|---|---|---|
| Net operating income | 3,60,000 | 3,60,000 |
| Less: interest @ 12.5% | Nil | 1,80,000 |
| Earnings for equity shareholders | 3,60,000 | 1,80,000 |
| Equity capitalisation rate | 0.15 | 0.16 |
| Market value of equity | 24,00,000 | 11,25,000 |
| Market value of debt | Nil | 14,40,000 |
| Value of the firm | 24,00,000 | 25,65,000 |
Firm Y, the levered firm, is valued higher: it is the overvalued firm.
Arbitrage under MM. Two firms identical except in capital structure cannot have different values: investors in the overvalued firm sell, substitute personal borrowing ("personal leverage") for the firm's borrowing, and buy the undervalued firm, until the two values are equal. They earn the same return at a lower outlay with the same risk.
An investor holding 10% of Y's equity has shares worth 10% × 11,25,000 = ₹1,12,500 and income of 10% × 1,80,000 = ₹18,000. He switches:
| Step | ₹ |
|---|---|
| Sell 10% of Y's equity | 1,12,500 |
| Borrow personally 10% of Y's debt at 12.5% | 1,44,000 |
| Funds available | 2,56,500 |
| Use of funds | ₹ |
|---|---|
| Buy 10% of X's equity | 2,40,000 |
| Left over | 16,500 |
| Funds used | 2,56,500 |
Income after switching = 10% of X's earnings 36,000 − interest on the personal loan (12.5% × 1,44,000) 18,000 = ₹18,000, the same as before. He keeps the same income and the same financial risk (his personal debt replaces his share of Y's debt) and has ₹16,500 left over, so he is better off.
When arbitrage ends. Selling by Y's shareholders lowers the price of Y's shares, and buying raises the price of X's shares. The switching goes on until the two firms' total values are equal; then no investor can gain by switching and the arbitrage stops.
Where the 11 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Values of X and Y | 4 |
| 2 | The arbitrage steps for a 10% holder of Y | 4 |
| 3 | Income before and after; gain | 2 |
| 4 | When the arbitrage ends | 1 |
| Total | 11 |
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