Question 4 (a)
MM: values, the switch from L to U, and the limits of arbitrage
8 marks
- Time to write
- About 16 minutes
From an older CBCS paper
Question
Question 4 (a) · 8 marks- U and L are alike in all respects, except that Firm U is unlevered, whereas L has 10% debentures of ₹ 36,00,000.
Calculate the firms' value, assuming that EBIT = Rs. 9,00,000, that cost of equity of L = 20%, and that cost of equity of U = 15%
Under the MM approach, explain how, if an investor holds 10% equity shares of L Ltd. will be better off switching to U.
Is the arbitrage process limited in any way?
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
- (i)–(iii)3 items, each marked on its own: give each its share.
- assuming that EBIT = RsThe paper fixes this: use it as given, and say so in your answer.
- CalculateFormula 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 U and L 2½ marks 4 min
- 2 The switch and the gain 3 marks 5 min
- 3 Limits of arbitrage 2½ marks 4 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
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.
(i) Values of the firms (no taxes)
| Particulars (₹) | U (unlevered) | L (levered) |
|---|---|---|
| EBIT | 9,00,000 | 9,00,000 |
| Less: interest @ 10% on 36,00,000 | — | 3,60,000 |
| Earnings for equity | 9,00,000 | 5,40,000 |
| Cost of equity | 15% | 20% |
| Value of equity | 60,00,000 | 27,00,000 |
| Value of debt | — | 36,00,000 |
| Value of the firm | 60,00,000 | 63,00,000 |
L is valued ₹3,00,000 above U although the firms differ only in capital structure, so under MM L is overvalued.
(ii) The switch. An investor holding 10% of L's equity (worth ₹2,70,000) earns 10% × 5,40,000 = ₹54,000. He substitutes personal for corporate leverage:
| Step | ₹ |
|---|---|
| Sell 10% of L's shares | 2,70,000 |
| Borrow personally 10% of L's debt at 10% | 3,60,000 |
| Funds available | 6,30,000 |
- Buy 10% of U for ₹6,00,000: income 10% × 9,00,000 = 90,000 less interest 36,000 = ₹54,000, the same income with the same leverage, and ₹30,000 is left over.
- Or invest all ₹6,30,000 in U: income 6,30,000 × 15% − 36,000 = ₹58,500, a gain of ₹4,500 a year.
Either way he is better off; such switching continues until the two values are equal.
(iii) Limits of the arbitrage process. It works only under MM's assumptions, and it fails to work where the capital market is imperfect, transactions cost money and corporate income taxes exist:
- Personal and corporate leverage are not perfect substitutes: individuals usually borrow at higher rates than firms, and lenders may not lend to them on the same terms.
- Limited liability: shareholders of a levered firm have limited liability, but personal borrowing carries unlimited personal liability, so investors may not see the two positions as equally risky.
- Transaction costs (brokerage, issue costs) reduce or remove the gain from switching.
- Corporate taxes: interest is tax-deductible for the firm, so a levered firm genuinely is worth more.
- Institutional restrictions: many institutional investors cannot borrow to buy shares.
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Values of U and L | 2.5 |
| 2 | The switch and the gain | 3 |
| 3 | Limits of arbitrage | 2.5 |
| Total | 8 |
Report a problemopens an email to admin@getkunji.com with the question ID2516-Q4aalready filled in.