Question 3
MM approach: critical appraisal and the arbitrage process
18.75 marks
- Time to write
- About 38 minutes
From an older CBCS paper
Question
Question 3 · 18.75 marksQ3. Critically appraise the Modigliani and Miller Approach to the theory of capital structure.
Two companies, U and L, are in the same risk class. They are alike in every respect, except that firm L has 12% debentures of Rs. 12,00,000. Given below is the information about the two firms:
| Particulars | Firm U | Firm L |
|---|---|---|
| Net operating income(EBIT) | Rs. 4,80,000 | Rs. 4,80,000 |
| 12% Debentures | - | Rs. 12,00,000 |
| Equity capitalization rate(ke) | 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 holdings 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
- Critically…Compute…Explain…3 questions in all: answer every one.
- CriticallyBoth sides: the strengths, the limits, then your own view.
- ComputeFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
No mark is printed for the question; the paper asks for any four of six, equal marks.
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 MM propositions, merits and criticism 8 marks 14 min
- 2 Values of the two firms 3.8 marks 7 min
- 3 Arbitrage steps, income and gain 5 marks 9 min
- 4 When arbitrage ends 2 marks 4 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 38 minutes for 18.75 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.
Part 1: critical appraisal of the MM approach.
The propositions. Without taxes, MM hold that the value of a firm and its overall cost of capital are independent of its capital structure: the cheaper debt is offset by a rise in the cost of equity. Two firms alike except in capital structure cannot have different values, because arbitrage would restore equality: investors substitute personal for corporate leverage. With corporate taxes (1963), the value of the levered firm exceeds that of the unlevered firm by debt × tax rate, VL = VU + tD.
Merits. It gives a behavioural basis (arbitrage) for the irrelevance view, instead of merely assuming it as the NOI approach does, and it identifies the tax shield as the real advantage of debt.
Criticism. The arbitrage process fails to work because of imperfections in capital markets, transaction costs and corporate income taxes. Further: personal borrowing is riskier and dearer than corporate borrowing; institutional investors may not be allowed to borrow for personal leverage; and with taxes the model implies 100% debt, ignoring bankruptcy costs. Its assumptions (perfect markets, rational investors, identical risk classes, no taxes) do not hold in practice, so capital structure does matter.
| Particulars (₹) | Firm U | Firm L |
|---|---|---|
| Net operating income (EBIT) | 4,80,000 | 4,80,000 |
| Less: interest @ 12% | Nil | 1,44,000 |
| Earnings for equity | 4,80,000 | 3,36,000 |
| Equity capitalisation rate | 0.15 | 0.16 |
| Value of equity | 32,00,000 | 21,00,000 |
| Value of debt | Nil | 12,00,000 |
| Value of the firm | 32,00,000 | 33,00,000 |
L is overvalued. An investor with 10% of L's equity (worth ₹2,10,000, earning 10% × 3,36,000 = ₹33,600) switches:
| Step | ₹ |
|---|---|
| Sell 10% of L's equity | 2,10,000 |
| Borrow personally 10% of L's debt at 12% | 1,20,000 |
| Funds available | 3,30,000 |
| Use of funds | ₹ |
|---|---|
| Buy 10% of U's equity | 3,20,000 |
| Left over | 10,000 |
| Funds used | 3,30,000 |
Income after switching = 10% of 4,80,000 − 12% × 1,20,000 = 48,000 − 14,400 = ₹33,600: the same income and the same risk, with ₹10,000 left over, so he is better off.
When arbitrage ends. Selling depresses L's share price and buying raises U's, until the two firms' total values are equal; then no further gain is possible and switching stops.
Where the 18.75 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | MM propositions, merits and criticism | 8 |
| 2 | Values of the two firms | 3.75 |
| 3 | Arbitrage steps, income and gain | 5 |
| 4 | When arbitrage ends | 2 |
| Total | 18.75 |
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