Question 3 (a)
The arbitrage process of the MM theory, with an illustration
8 marks
- Time to write
- About 16 minutes
From an older CBCS paper
Question
Question 3 (a) · 8 marksExplain and illustrate the "Arbitrage Process" of the MM theory of capital structure. 8
Reworded from the university paper; 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.
- ProcessA process: the steps in order, one heading each.
Write it in this order
- Read; underline the asks; jot your points 1 min
- 1 The MM hypothesis 1½ marks 3 min
- 2 Arbitrage steps 2½ marks 4 min
- 3 Assumptions 1 mark 2 min
- 4 Illustration 3 marks 5 min
- Check: every ask answered, key terms underlined 1 min
Short on time? Trim steps 1, 2 and 4 evenly rather than skip one: each is capped at its own marks.
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.
The hypothesis. Without taxes, MM hold that the value of a firm and its overall cost of capital do not depend on its capital structure: the cheaper debt is exactly offset by the rise in the cost of equity as leverage increases.
The behavioural justification: arbitrage. Where the NOI approach simply assumes this, MM explain it by how investors behave. Two firms identical in all respects except capital structure cannot have different market values, because if they did, arbitrage would take place:
- Investors in the overvalued firm (usually the levered one) sell their shares.
- They borrow on their own account in proportion to their share of that firm's debt, substituting personal leverage for corporate leverage.
- They buy the shares of the undervalued firm, earning the same income for a smaller outlay and with the same risk.
- The selling depresses the price of the overvalued firm and the buying raises that of the undervalued firm, until the two total values are equal; then no further gain is possible.
Assumptions behind it: no corporate taxes, a perfect market, rational investors, firms in identical risk classes, and all earnings distributed. Personal borrowing must also be possible on the same terms as corporate borrowing.
Illustration. Two firms each earn EBIT of ₹1,00,000. U is all-equity, with equity capitalised at 10%: value ₹10,00,000. L has ₹5,00,000 of 6% debt (interest ₹30,000) and its equity, capitalised at 10%, is worth 70,000 ÷ 0.10 = ₹7,00,000, so L is valued at ₹12,00,000, more than U.
| Investor holding 10% of L's equity | ₹ |
|---|---|
| Present income: 10% of L's equity earnings (70,000) | 7,000 |
| Sells L's shares | 70,000 |
| Borrows 10% of L's debt at 6% | 50,000 |
| Funds available | 1,20,000 |
| Buys 10% of U's shares | 1,00,000 |
| Income from U: 10% of 1,00,000 | 10,000 |
| Less: interest on personal borrowing | 3,000 |
| Net income after switching | 7,000 |
He earns the same ₹7,000 with the same leverage but keeps ₹20,000 uninvested. Such switching continues until the values of L and U are equal (with figures supplied by the answer for illustration).
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | The MM hypothesis | 1.5 |
| 2 | Arbitrage steps | 2.5 |
| 3 | Assumptions | 1 |
| 4 | Illustration | 3 |
| Total | 8 |
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