Question 2 OR (b)
MM approach: values of two firms and the arbitrage process
10 marks
- Time to write
- About 20 minutes
From an older CBCS paper
Question
Question 2 OR (b) · 10 marksTwo firms are identical in all respects except their capital structure, as seen from the details below:
| Item | Levered company (L Ltd.) | Unlevered company (U Ltd.) |
|---|---|---|
| EBIT | Rs. 1,20,000 | Rs. 1,20,000 |
| Debt @ 10% | Rs.6,00,000 | - |
| Equity capitalization rate(Ke) | 16 % | 12.5 % |
Find the value of the two firms, and explain how, according to the MM Approach of capital structure, an arbitrage process would be initiated. When will the process stop? (5,10)
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
- Find…When…?Two asks in one question: answer both.
- FindFormula 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 L and U 3 marks 5 min
- 2 Arbitrage steps 4 marks 7 min
- 3 Income before and after; gain 2 marks 4 min
- 4 When arbitrage ends 1 mark 2 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.
Values of the two firms (no taxes, as MM assume; equity earnings capitalised at each firm's ke)
| Particulars (₹) | L Ltd. | U Ltd. |
|---|---|---|
| EBIT | 1,20,000 | 1,20,000 |
| Less: interest @ 10% | 60,000 | Nil |
| Earnings for equity | 60,000 | 1,20,000 |
| ke | 16% | 12.5% |
| Value of equity | 3,75,000 | 9,60,000 |
| Value of debt | 6,00,000 | Nil |
| Value of the firm | 9,75,000 | 9,60,000 |
L Ltd., the levered firm, is overvalued: under MM the value of a levered firm can be neither greater nor lower than that of an unlevered one.
Arbitrage. Under MM, two firms identical except in capital structure cannot have different values; investors in the overvalued firm sell, borrow personally in place of the firm's borrowing, and buy the other firm's shares, until values are equal. They earn the same return with a lower outlay and the same risk.
The investor holds 10% of L's equity, worth ₹37,500, earning 10% × 60,000 = ₹6,000.
| Step | ₹ |
|---|---|
| Sell 10% of L's equity | 37,500 |
| Borrow personally 10% of L's debt at 10% | 60,000 |
| Funds available | 97,500 |
| Use of funds | ₹ |
|---|---|
| Buy 10% of U's equity | 96,000 |
| Left over | 1,500 |
| Funds used | 97,500 |
Income after switching = 10% of U's earnings 12,000 − interest on the personal loan 6,000 = ₹6,000, the same as before, with the same financial risk (his personal debt replaces his share of L's debt) and ₹1,500 left over. He is better off by switching.
When the arbitrage ends. Selling lowers the price of L's shares and buying raises U's; the process continues until the total values of the two firms are equal, when no further gain is possible.
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Values of L and U | 3 |
| 2 | Arbitrage steps | 4 |
| 3 | Income before and after; gain | 2 |
| 4 | When arbitrage ends | 1 |
| Total | 10 |
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