Question 5 OR (b)
MM approach: dividend irrelevance before and after the new issue
11 marks
- Time to write
- About 22 minutes
From an older CBCS paper
Question
Question 5 OR (b) · 11 marksDelta International is in a risk class with an appropriate capitalization rate of 10%. It currently has 1,20,000 equity shares of ₹ 80 each, and it is thinking of declaring a ₹ 4 per share dividend at the year's end. It is expecting a net income of ₹ 9.6 lakh and an investment proposal requiring an investment of ₹ 18 lakh. Show that, under MM assumptions, paying a dividend does not affect the firm's value, either now or after the issue of new shares. 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
- 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 Funds to be raised and new shares 3 marks 5 min
- 3 Value of the firm now in both cases 4 marks 7 min
- 4 Value after the new issue 2 marks 4 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 = 1,20,000; P0 = ₹80; ke = 10%; D1 = ₹4; E = ₹9,60,000; I = ₹18,00,000.
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: under MM the present price equals the year-end dividend plus price, discounted at ke; so with the dividend paid, 80 × 1.10 − 4 = ₹84; not paid, 80 × 1.10 = ₹88.
| Particulars | Dividend paid | Dividend not paid |
|---|---|---|
| Retained earnings (E − nD1) | 4,80,000 | 9,60,000 |
| Raised by new shares (balancing) | 13,20,000 | 8,40,000 |
| Investment | 18,00,000 | 18,00,000 |
| New shares (amount ÷ P1) | 15,714.29 | 9,545.45 |
- Paid: [(1,20,000 + 15,714.29) × 84 − 18,00,000 + 9,60,000] ÷ 1.10 = (1,14,00,000 − 8,40,000) ÷ 1.10 = ₹96,00,000.
- Not paid: [(1,20,000 + 9,545.45) × 88 − 18,00,000 + 9,60,000] ÷ 1.10 = (1,14,00,000 − 8,40,000) ÷ 1.10 = ₹96,00,000.
Value after the issue of new shares (at the year end): paid, 1,35,714.29 × 84 = ₹1,14,00,000; not paid, 1,29,545.45 × 88 = ₹1,14,00,000.
The value is the same both now (₹96,00,000 = 1,20,000 × ₹80) and after the new issue, whether or not the dividend is paid: the dividend is offset by the lower price and the larger number of shares needed to finance the investment, as MM hold.
Where the 11 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Year-end price with and without the dividend | 2 |
| 2 | Funds to be raised and new shares | 3 |
| 3 | Value of the firm now in both cases | 4 |
| 4 | Value after the new issue | 2 |
| Total | 11 |
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