Question 3 OR (b)
MM approach: share price and new shares with and without a dividend
12 marks
- Time to write
- About 24 minutes
Question
Question 3 OR (b) · 12 marksSuvarna Fabrics currently has 1,20,000 shares outstanding, selling @₹100 each. The firm is considering declaring a dividend of ₹8 per share at the close of the current fiscal year, which has just begun. The opportunity cost of capital of the firm is 10%. Given the assumptions of the M-M approach, answer the following questions:
What will the price of the share be at the end of the year if (i) no dividend is declared, (ii) dividend is declared?
In case the firm has net profits of ₹12,00,000 and makes new investments of ₹24,00,000 in the period, how many new shares must be issued in each of the two situations?
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
- What…?Has…?Two asks in one question: answer both.
- how manyFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
Part (i) numbers its two cases (i) and (ii) inside the part, as printed. "Each of the two situations" in part (ii) refers to those two cases (dividend not declared; dividend declared).
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 MM formulas stated 2 marks 3 min
- 2 (i) Year-end price without and with the dividend 3 marks 5 min
- 3 (ii) Funds to be raised and new shares 5 marks 9 min
- 4 Value of the firm the same either way; conclusion 2 marks 3 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 = 1,20,000 shares, P0 = ₹100, D1 = ₹8, ke = 10%, E = ₹12,00,000 and I = ₹24,00,000.
(i) Price of the share at the end of the year
- No dividend declared: P1 = 100 × 1.10 − 0 = ₹110.
- Dividend declared: P1 = 100 × 1.10 − 8 = ₹102.
| ₹ | Dividend not declared | Dividend declared |
|---|---|---|
| Earnings retained (E − nD1) | 12,00,000 | 2,40,000 |
| New equity to be raised | 12,00,000 | 21,60,000 |
| Investment required (I) | 24,00,000 | 24,00,000 |
| Price per new share (P1) | 110 | 102 |
| Number of new shares (m) | 10,909.09 | 21,176.47 |
With the dividend, nD1 = 1,20,000 × ₹8 = ₹9,60,000 is paid out, so only ₹2,40,000 of the earnings is retained.
Check: the value of the firm is the same either way
- No dividend: [(1,20,000 + 10,909.09) × 110 − (24,00,000 − 12,00,000)] ÷ 1.10 = (1,44,00,000 − 12,00,000) ÷ 1.10 = ₹1,20,00,000.
- Dividend: [(1,20,000 + 21,176.47) × 102 − 12,00,000] ÷ 1.10 = (1,44,00,000 − 12,00,000) ÷ 1.10 = ₹1,20,00,000.
Both equal nP0 = 1,20,000 × ₹100. As MM argue, whatever shareholders receive as dividend is offset by the lower year-end price and the larger number of shares issued to finance the investment; the dividend decision does not change the value of the firm. (In practice the new shares would be rounded up to 10,910 and 21,177.)
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | MM formulas stated | 2 |
| 2 | (i) Year-end price: ₹110 without and ₹102 with the dividend | 3 |
| 3 | (ii) Funds to be raised and new shares: 10,909.09 and 21,176.47 | 5 |
| 4 | Value of the firm the same either way; conclusion | 2 |
| Total | 12 |
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