Question 5 (b)
MM approach: dividend does not affect the value of the firm
10 marks
- Time to write
- About 20 minutes
From an older CBCS paper
Question
Question 5 (b) · 10 marksAs per the MM approach, paying a dividend does not affect the firm's value. Prove this statement from the data below.
| Outstanding shares (number) | 30,000 |
| Earnings per share | Rs.10 |
| Ke (given) | 10% |
| P/E ratio | 10 |
| Dividend per share expected | Rs.5 |
| New Investments | Rs.6,00,000 |
(5,10)
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
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 P0 and the MM relations 2 marks 4 min
- 2 Year-end price with and without the dividend 2 marks 4 min
- 3 Funds to be raised and new shares in each case 3 marks 5 min
- 4 Value of the firm in each case; conclusion 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Short on time? End with step 4's one-line conclusion, whatever happens: never leave the figures without it.
Try it first. About 20 minutes for 10 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. P0 = EPS × P/E = 10 × 10 = ₹100; ke = 10%; n = 30,000 shares; earnings E = 30,000 × ₹10 = ₹3,00,000; investment I = ₹6,00,000; expected dividend D1 = ₹5.
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's 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 (under MM the present price equals the year-end dividend plus price, discounted at ke)
- Dividend paid: P1 = 100 × 1.10 − 5 = ₹105.
- Dividend not paid: P1 = 100 × 1.10 − 0 = ₹110.
| Particulars | Dividend paid | Dividend not paid |
|---|---|---|
| Earnings retained (E − nD1) | 1,50,000 | 3,00,000 |
| New shares to be issued (balancing) | 4,50,000 | 3,00,000 |
| Investment | 6,00,000 | 6,00,000 |
| Number of new shares (amount ÷ P1) | 4,285.71 | 2,727.27 |
- Dividend paid: [(30,000 + 4,285.71) × 105 − 6,00,000 + 3,00,000] ÷ 1.10 = (36,00,000 − 3,00,000) ÷ 1.10 = ₹30,00,000.
- Dividend not paid: [(30,000 + 2,727.27) × 110 − 6,00,000 + 3,00,000] ÷ 1.10 = (36,00,000 − 3,00,000) ÷ 1.10 = ₹30,00,000.
Both equal nP0 = 30,000 × ₹100. The statement is proved: the dividend shareholders receive is exactly offset by the lower year-end price, as the extra shares needed to replace the funds paid out dilute the holding, so the value of the firm is the same whether or not the dividend is paid.
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | P0 and the MM relations | 2 |
| 2 | Year-end price with and without the dividend | 2 |
| 3 | Funds to be raised and new shares in each case | 3 |
| 4 | Value of the firm in each case; conclusion | 3 |
| Total | 10 |
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