Question 3 (a)
Arbitrage process in the MM approach and the equilibrium level
7 marks
- Time to write
- About 14 minutes
From an older CBCS paper
Question
Question 3 (a) · 7 marksExplain, with a suitable example, the arbitrage process of the MM approach in reaching the equilibrium level.
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
- suitable exampleExamples 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 MM position and its assumptions 2 marks 3 min
- 2 The arbitrage process, step by step 1½ marks 3 min
- 3 Illustration with figures 2½ marks 4 min
- 4 Equilibrium and limitation 1 mark 2 min
- Check: every ask answered, key terms underlined 1 min
Short on time? Trim steps 1–3 evenly rather than skip one: each is capped at its own marks. End with step 4 in a line or two.
Try it first. About 14 minutes for 7 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 MM position. In a perfect capital market without taxes, Modigliani and Miller hold that the total market value of a firm equals its net operating income divided by the rate suited to its risk class, so the mix of debt and equity does not change that value. A levered firm's cost of equity is higher, Ke = Ko + (Ko - Kd) x D/E, which exactly offsets the cheaper debt and leaves the overall cost of capital unchanged. The approach assumes no corporate taxes, a perfect market, rational investors, firms of the same business risk, and distribution of all earnings.
The arbitrage process. Arbitrage means buying a security where it is cheap and selling where it is dear, and it is what the MM argument uses to show that the two values must meet. Take two firms identical in everything except capital structure, one levered and one unlevered:
- If their values differ, holders of the dearer firm sell their shares and buy shares of the cheaper firm. They obtain the same return for a smaller outlay, with the same or lower risk, and so are better off.
- Where the levered firm is the dearer one, the investor replaces the firm's borrowing with his own, personal leverage in place of corporate leverage: he sells his shares, borrows his proportionate share of the firm's debt, and buys the unlevered firm's shares.
- The selling pushes the price of the dearer firm down and the buying pushes the price of the cheaper firm up, and this continues until the two total values are the same.
Illustration (our own figures). Two firms, U (no debt) and L (debt of ₹10,00,000 at 8%), each earn an operating income (EBIT) of ₹4,00,000. The market capitalises U's earnings at 16% and L's equity earnings at 20%.
| Firm U | Firm L | |
|---|---|---|
| EBIT (₹) | 4,00,000 | 4,00,000 |
| Interest at 8% on ₹10,00,000 (₹) | nil | 80,000 |
| Earnings for equity (₹) | 4,00,000 | 3,20,000 |
| Market value of equity (₹) | 25,00,000 | 16,00,000 |
| Debt (₹) | nil | 10,00,000 |
| Total value of the firm (₹) | 25,00,000 | 26,00,000 |
L is the dearer firm by ₹1,00,000. An investor holds 5% of L's shares and acts as follows (he can borrow at the same 8% as L pays).
| Step | ₹ |
|---|---|
| Sell 5% of L's equity (5% of 16,00,000) | 80,000 |
| Borrow 5% of L's debt (5% of 10,00,000) | 50,000 |
| Money in hand | 1,30,000 |
| Buy 5% of U's equity (5% of 25,00,000) | 1,25,000 |
| Surplus cash | 5,000 |
| Income comparison | Before: holding 5% of L (₹) | After: holding 5% of U (₹) |
|---|---|---|
| Share of earnings | 16,000 (5% of 3,20,000) | 20,000 (5% of 4,00,000) |
| Less interest on personal loan at 8% of 50,000 | nil | 4,000 |
| Net income | 16,000 | 16,000 |
His income is unchanged, his risk is no higher because the personal loan replaces L's own debt, and he is left with ₹5,000. Every holder of L has the same incentive, so L's shares are sold and U's are bought.
Equilibrium. The fall in L's price and the rise in U's price stop when the total values are equal. Taking the common value as ₹25,00,000, L's equity is worth ₹15,00,000. The same investor then needs 5% of 15,00,000 = ₹75,000 plus ₹50,000 borrowed = ₹1,25,000, exactly the price of 5% of U, so the surplus is nil and no gain remains. L's cost of equity is now 3,20,000 / 15,00,000 = 21.33%, which agrees with Ke = Ko + (Ko - Kd) x D/E = 16% + 8% x (10,00,000 / 15,00,000) = 21.33%. If instead the unlevered firm were the dearer one, the process runs the other way: its holders sell and buy a share of the levered firm's equity and debt, until the values meet.
Limitation. The argument fails in practice where the market is imperfect, there are transaction costs, or corporate income tax exists.
Where the 7 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | MM position and its assumptions | 2 |
| 2 | The arbitrage process, step by step | 1.5 |
| 3 | Illustration with figures | 2.5 |
| 4 | Equilibrium and limitation | 1 |
| Total | 7 |
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