Question 3 (b)
MM dividend irrelevance: share price and new shares
10 marks
- Time to write
- About 20 minutes
From an older CBCS paper
Question
Question 3 (b) · 10 marksJayKay Ltd. has 18,000 equity shares, selling at ₹15 per share. The company expects to make a net income of ₹3,60,000 in the year ended 31st March 2024. It is considering a dividend of ₹3 per share at the current year's end. The company is in a risk class whose appropriate capitalization rate is 12%. Assuming there are no taxes, answer these questions:
What will the share's price be at the end of 31st March 2024, in case
The dividend is paid
The dividend is not paid
- If the company pays the dividend and has net profits of ₹3,60,000 in the period, how many new shares must be issued to meet an investment requirement of ₹6,00,000 Apply the MM approach in your calculations.
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
- Assuming there are no taxes, answer…The paper fixes this: use it as given, and say so in your answer.
- how manyFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
"At the end of 31st March 2024" is read as the end of the current year, when the dividend is paid.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 MM price formula 1 mark 2 min
- 2 Year-end price with and without the dividend 4 marks 7 min
- 3 Retained earnings and the amount to be raised 2 marks 4 min
- 4 Number of new shares 2 marks 3 min
- 5 Value of the firm unchanged 1 mark 2 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
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.
Under the MM hypothesis the price at the start of the year is P0 = (D1 + P1) ÷ (1 + ke), so the year-end price is P1 = P0(1 + ke) − D1. Here P0 = ₹15, ke = 12%, D1 = ₹3, n = 18,000 shares; the year end is 31st March 2024 (paper note).
(i) Price of the share at the end of the year
Dividend paid: P1 = 15 × 1.12 − 3 = 16.80 − 3 = ₹13.80.
Dividend not paid: P1 = 15 × 1.12 − 0 = ₹16.80.
(ii) New shares to be issued if the dividend is paid
The investment not covered by retained earnings is raised by issuing new shares at P1: m = [I − (E − nD1)] ÷ P1.
| Particulars | ₹ |
|---|---|
| Net income (E) | 3,60,000 |
| Less: dividend paid (18,000 × ₹3) | 54,000 |
| Retained earnings available | 3,06,000 |
| Amount to be raised by new shares (balancing) | 2,94,000 |
| Investment required (I) | 6,00,000 |
m = 2,94,000 ÷ 13.80 = 21,304.35 shares (21,305 shares in whole numbers).
Check: the value of the firm is the same either way. nP0 = [(n + m)P1 − I + E] ÷ (1 + ke):
- dividend paid: [(18,000 + 21,304.35) × 13.80 − 6,00,000 + 3,60,000] ÷ 1.12 = ₹2,70,000;
- dividend not paid: new shares = (6,00,000 − 3,60,000) ÷ 16.80 = 14,285.71, and [(18,000 + 14,285.71) × 16.80 − 6,00,000 + 3,60,000] ÷ 1.12 = ₹2,70,000.
Both equal 18,000 × ₹15 = ₹2,70,000: what the shareholders gain in dividend they lose in the lower share price, so the dividend decision does not affect the value of the firm.
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | MM price formula | 1 |
| 2 | Year-end price with and without the dividend | 4 |
| 3 | Retained earnings and the amount to be raised | 2 |
| 4 | Number of new shares | 2 |
| 5 | Value of the firm unchanged | 1 |
| Total | 10 |
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