Question 4 (b)
MM: paying a dividend does not change the value of the firm
12 marks
- Time to write
- About 24 minutes
Question
Question 4 (b) · 12 marksAccording to the MM approach, paying a dividend does not affect the value of firm. Prove this statement with the data given below.
| Outstanding shares (number) | 60,000 |
| Per-share earnings | Rs. 10 |
| Kₑ | 10% |
| P0 | Rs. 100 |
| Dividend per share expected | Rs. 5 |
| New Investment | Rs. 12,00,000 |
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 2 min
- 1 MM formulas 2 marks 3 min
- 2 Year-end price in both cases 2 marks 3 min
- 3 New shares to be issued 4 marks 7 min
- 4 Value of the firm; conclusion 4 marks 7 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Short on time? End with step 4's one-line conclusion, whatever happens: never leave the figures without it.
Try it first. About 24 minutes for 12 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.
MM formulas: P1 = P0(1 + ke) − D1; m = [I − (E − nD1)] ÷ P1; nP0 = [(n + m)P1 − (I − E)] ÷ (1 + ke).
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
Here n = 60,000, P0 = ₹100, ke = 10%, D1 = ₹5, E = 60,000 × ₹10 = ₹6,00,000 and I = ₹12,00,000.
1. Price at the end of the year
- Dividend not paid: P1 = 100 × 1.10 − 0 = ₹110.
- Dividend paid: P1 = 100 × 1.10 − 5 = ₹105.
| ₹ | Dividend not paid | Dividend paid |
|---|---|---|
| Earnings available (E) | 6,00,000 | 6,00,000 |
| New equity to be raised | 6,00,000 | 9,00,000 |
| Funds needed: investment + dividend (I + nD1) | 12,00,000 | 15,00,000 |
| Price per new share (P1) | 110 | 105 |
| Number of new shares (m) | 5,454.55 | 8,571.43 |
- Dividend not paid: [(60,000 + 5,454.55) × 110 − (12,00,000 − 6,00,000)] ÷ 1.10 = (72,00,000 − 6,00,000) ÷ 1.10 = ₹60,00,000.
- Dividend paid: [(60,000 + 8,571.43) × 105 − 6,00,000] ÷ 1.10 = (72,00,000 − 6,00,000) ÷ 1.10 = ₹60,00,000.
Conclusion. The value of the firm is ₹60,00,000 (= 60,000 × ₹100) in both cases. The ₹5 dividend is exactly offset by the lower year-end price and the extra shares issued, so paying a dividend does not affect the value of the firm, as MM state.
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | MM formulas | 2 |
| 2 | Year-end price in both cases | 2 |
| 3 | New shares to be issued | 4 |
| 4 | Value of the firm; conclusion | 4 |
| Total | 12 |
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