Question 4 OR (b)
MM approach: dividend irrelevance shown, and how realistic it is
11 marks
- Time to write
- About 22 minutes
From an older CBCS paper
Question
Question 4 OR (b) · 11 marksX Ltd. is in a risk class whose appropriate capitalisation rate is 10%. It currently has 30000 shares outstanding, selling at ₹ 100 each. It is contemplating declaring a dividend of ₹ 5 per share at the close of the current financial year. The company expects a net income of ₹ 3 lakh, and has a proposal for new investments of ₹ 5 lakh.
Show that, under the MM assumption, paying a dividend does not affect the firm's value. Do you think the MM model is realistic as regards valuation ? 11
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
- Do you think…?A yes-or-no question: answer it in your first line, then explain why.
- Show thatThe result is given: the marks are for the steps that reach it.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Year-end price with and without the dividend 2 marks 4 min
- 2 New shares in each case 3 marks 6 min
- 3 Value of the firm in each case 3 marks 5 min
- 4 Realism of the MM model 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 22 minutes for 11 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.
Inputs. n = 30,000; P0 = ₹100; ke = 10%; D1 = ₹5; E = ₹3,00,000; I = ₹5,00,000.
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
MM relations. P1 = P0(1 + ke) − D1; new shares m = [I − (E − nD1)] ÷ P1; value of the firm nP0 = [(n + m)P1 − I + E] ÷ (1 + ke).
Year-end price: dividend paid, 100 × 1.10 − 5 = ₹105; not paid, ₹110.
| Particulars | Dividend paid | Dividend not paid |
|---|---|---|
| Retained earnings (E − nD1) | 1,50,000 | 3,00,000 |
| Raised by new shares (balancing) | 3,50,000 | 2,00,000 |
| Investment | 5,00,000 | 5,00,000 |
| New shares (amount ÷ P1) | 3,333.33 | 1,818.18 |
- Paid: [(30,000 + 3,333.33) × 105 − 5,00,000 + 3,00,000] ÷ 1.10 = (35,00,000 − 2,00,000) ÷ 1.10 = ₹30,00,000.
- Not paid: [(30,000 + 1,818.18) × 110 − 5,00,000 + 3,00,000] ÷ 1.10 = (35,00,000 − 2,00,000) ÷ 1.10 = ₹30,00,000.
Both equal 30,000 × ₹100: the dividend does not affect the value of the firm.
Is the MM model realistic? Not fully. It rests on assumptions that do not hold in practice:
- capital markets are not perfect, and information is not free to everyone;
- firms incur flotation costs on new issues, so retained earnings are cheaper than new equity;
- investors pay transaction costs to sell shares for "home-made" dividends, and taxes on dividends and capital gains differ;
- under uncertainty, investors may prefer a certain dividend now to an uncertain future gain, and dividends carry information about the firm's prospects.
So the irrelevance result is a useful benchmark rather than a description of how share prices actually respond to dividends.
Where the 11 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Year-end price with and without the dividend | 2 |
| 2 | New shares in each case | 3 |
| 3 | Value of the firm in each case | 3 |
| 4 | Realism of the MM model | 3 |
| Total | 11 |
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