Question 4 (a)
MM: paying or not paying a dividend does not change the value of the firm
12 marks
- Time to write
- About 24 minutes
Question
Question 4 (a) · 12 marksArjun Limited is in a risk class whose approximate capitalization rate is 10%. It currently has 90,000 shares outstanding, selling at ₹100 each. The firm is considering declaring a dividend of ₹15 per share at the close of the current financial year. It expects a net income of ₹6,00,000 and has a proposal to make new investments of ₹10,80,000. Show that, under the Modigliani-Miller assumptions, paying or not paying a dividend does not affect the value of the Arjun Limited.
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
- 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 2 min
- 1 MM formulas 2 marks 3 min
- 2 Year-end price with and without the dividend 2 marks 3 min
- 3 New shares to be issued in each case 4 marks 7 min
- 4 Value of the firm in each case; 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.
- P0 = (D1 + P1) ÷ (1 + ke), so P1 = P0(1 + ke) − D1;
- new shares to be issued, m = [I − (E − nD1)] ÷ P1;
- value of the firm, nP0 = [(n + m)P1 − (I − E)] ÷ (1 + ke).
Here n = 90,000 shares, P0 = ₹100, ke = 10%, D1 = ₹15, E = ₹6,00,000 and I = ₹10,80,000.
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
1. Price of the share at the end of the year
- Dividend not paid: P1 = 100 × 1.10 − 0 = ₹110.
- Dividend paid: P1 = 100 × 1.10 − 15 = ₹95.
| ₹ | Dividend not paid | Dividend paid |
|---|---|---|
| Earnings available (E) | 6,00,000 | 6,00,000 |
| New equity to be raised | 4,80,000 | 18,30,000 |
| Funds needed: investment + dividend (I + nD1) | 10,80,000 | 24,30,000 |
| Price per new share (P1) | 110 | 95 |
| Number of new shares (m) | 4,363.64 | 19,263.16 |
With the dividend, nD1 = 90,000 × ₹15 = ₹13,50,000 is paid out, more than the year's earnings, so the whole investment and ₹7,50,000 of the dividend must be met from new shares.
- Dividend not paid: [(90,000 + 4,363.64) × 110 − (10,80,000 − 6,00,000)] ÷ 1.10 = (1,03,80,000 − 4,80,000) ÷ 1.10 = ₹90,00,000.
- Dividend paid: [(90,000 + 19,263.16) × 95 − 4,80,000] ÷ 1.10 = (1,03,80,000 − 4,80,000) ÷ 1.10 = ₹90,00,000.
Conclusion. The value of Arjun Limited is ₹90,00,000 (= 90,000 × ₹100) whether or not the dividend is paid. The dividend received by shareholders is exactly offset by the lower year-end price (₹95 against ₹110) and the extra shares issued to finance the investment, so under the MM assumptions dividend policy does not affect the value of the firm.
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | MM formulas | 2 |
| 2 | Year-end price with and without the dividend | 2 |
| 3 | New shares to be issued in each case | 4 |
| 4 | Value of the firm in each case; conclusion | 4 |
| Total | 12 |
Report a problemopens an email to admin@getkunji.com with the question ID835-Q4aalready filled in.