Question 4 OR (a)
MM: dividend payment does not affect value
8 marks
- Time to write
- About 16 minutes
From an older CBCS paper
Question
Question 4 OR (a) · 8 marks- Using the data below:
| EPS | ₹7 |
| P/E | 10 |
| Cost of equity | 12% |
| Outstanding shares (number) | 90,000 |
| Expected dividend | ₹5 |
| Expected net income | ₹6,00,000 |
| New investment | ₹9,60,000 |
Using MM's hypothesis, show that paying a dividend does not affect the firm's value.
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.
What the paper leaves open
EPS × shares (₹7 × 90,000 = ₹6,30,000) differs from the expected net income given (₹6,00,000); the paper's figures differ in the same way. The answer uses the net income given for the financing and the P/E for the share price, and states this (C8).
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Current price and year-end prices 2 marks 4 min
- 2 New funds and new shares under each option 3 marks 5 min
- 3 Value of the firm under each option 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 16 minutes for 8 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.
Data (paper note). P0 = EPS × P/E = 7 × 10 = ₹70; ke = 12%; n = 90,000 shares; D1 = ₹5. EPS × shares (₹6,30,000) differs from the expected net income given (₹6,00,000); the net income given is used for the financing.
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 formulae: P1 = P0(1 + ke) − D1; new shares m = [I − (E − nD1)] ÷ P1; value of the firm today = [(n + m)P1 − I + E] ÷ (1 + ke).
| Particulars | Dividend paid | No dividend |
|---|---|---|
| Price at the year end, P1 (₹) | 70 × 1.12 − 5 = 73.40 | 70 × 1.12 = 78.40 |
| Net income, E (₹) | 6,00,000 | 6,00,000 |
| Dividends, nD1 (₹) | 4,50,000 | — |
| Retained earnings (₹) | 1,50,000 | 6,00,000 |
| Add: new funds needed (₹) | 8,10,000 | 3,60,000 |
| New investment, I (₹) | 9,60,000 | 9,60,000 |
| New shares, m | 11,035.42 | 4,591.84 |
| Value of the firm (₹) | Dividend paid | No dividend |
|---|---|---|
| (n + m) × P1 | 74,16,000 | 74,16,000 |
| Less: investment | 9,60,000 | 9,60,000 |
| Add: net income | 6,00,000 | 6,00,000 |
| Total at the year end | 70,56,000 | 70,56,000 |
| Value today (÷ 1.12) | 63,00,000 | 63,00,000 |
The value of the firm is ₹63,00,000 either way, equal to 90,000 × ₹70. Paying the dividend lowers the year-end price by exactly the dividend, and the extra shares sold to replace the cash paid out offset it: under MM, dividend policy does not affect the value of the firm.
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Current price and year-end prices | 2 |
| 2 | New funds and new shares under each option | 3 |
| 3 | Value of the firm under each option | 3 |
| Total | 8 |
Report a problemopens an email to admin@getkunji.com with the question ID2516-Q4aORalready filled in.