Question 4 OR (b)
MM: how arbitrage makes dividend policy irrelevant
9 marks
- Time to write
- About 18 minutes
Question
Question 4 OR (b) · 9 marksDescribe how, in the Modigliani-Miller Model, the arbitrage process shows that dividend policy does not affect the value of the firm.
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
- 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 proposition 2 marks 4 min
- 2 Arbitrage process step by step 5 marks 9 min
- 3 Conclusion and assumptions 2 marks 3 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.
Try it first. About 18 minutes for 9 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 proposition. Modigliani and Miller hold that, given the firm's investment policy, the value of the firm depends on its earning power and investment decisions, not on how its earnings are split between dividends and retained earnings.
1The dividend goes out one window, fresh shares are issued at the other—the firm's value stands still.
Paying the dividend is balanced by the new issueShareholders receive cash, but the issue of additional shares lowers the terminal value of their existing shares.
2The old investor counts it out: the share sits lower today by exactly the coins in his hand.
The price falls by the amount of the dividendThe year-end share price falls by exactly the dividend paid
3No dividend declared? He sells a few shares at the counter and makes his own.
Shareholders can make their own dividendsA shareholder who wants cash when no dividend is paid can sell some shares
The arbitrage process. Arbitrage means entering into two transactions at once that exactly balance each other. For a firm whose investment programme is fixed:
- The firm can retain or distribute. It can finance its investment from retained earnings, or pay the earnings out as dividends and raise an equal amount from outside by issuing new shares.
- Paying the dividend is balanced by the new issue. If it pays the dividend, it must sell new shares to replace the cash. The two transactions offset: shareholders receive cash, but the issue of additional shares lowers the terminal value of their existing shares.
- The price falls by the amount of the dividend. The year-end share price falls by exactly the dividend paid, so P0 = (D1 + P1) ÷ (1 + ke) is the same whatever D1 is. The shareholder's wealth, the dividend plus the ex-dividend price, is therefore the same whether or not the dividend is paid; this is what the DU text means when it says the price before and after the payment is identical.
- Shareholders can make their own dividends. A shareholder who wants cash when no dividend is paid can sell some shares; one who receives an unwanted dividend can buy more shares. These personal transactions reproduce any dividend pattern at no cost under MM's assumptions.
Conclusion. Because the effect of a dividend on shareholders' wealth is exactly offset by the effect of raising the replacement capital, investors are indifferent between dividends and capital gains, and dividend policy does not affect the value of the firm. The result rests on MM's assumptions (perfect markets, no taxes or flotation costs, a fixed investment policy), which critics point out do not hold fully in practice.
Where the 9 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | MM proposition | 2 |
| 2 | Arbitrage process step by step | 5 |
| 3 | Conclusion and assumptions | 2 |
| Total | 9 |
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