Question 4 (a)

MM: dividend does not affect the value of the firm

12 marks

Time to write: About 24 minutes
Topic: Dividend theories and dividend policy

Question

Question 4 (a) · 12 marks

Using the data given below shows that, under the Modigliani and Miller hypothesis, paying or not paying dividend does not affect the value of the firm:

EPS (Earnings Per Share)	₹28
P/E Ratio	8.33 times
Outstanding equity shares (number)	1,80,000
Expected dividend per share	₹10
Expected total net income	₹24,00,000
New investment	₹36,00,000

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

24 minfor 12 marks

What the paper leaves open

"Using the data given below shows" is printed so. Earnings per share times the number of shares does not equal the expected total net income. The figures are kept as printed, and the net income given is the one used for financing the investment.

Write it in this order

Read the data; note exactly what is asked 2 min
1 P0 and ke from EPS and P/E 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

1234

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.

Basic figures. Current price P0 = EPS × P/E = 28 × 8.33 = ₹233.24. The capitalisation rate is the earnings yield, ke = EPS ÷ P0 = 28 ÷ 233.24 = 1 ÷ 8.33 = 12.0048%. n = 1,80,000 shares; D1 = ₹10; net income E = ₹24,00,000 (as given; the paper note records that it differs from EPS × shares); new investment I = ₹36,00,000.

Picture itMM: dividend does not affect the value of the firm

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 formulas: P1 = P0(1 + ke) − D1; m = [I − (E − nD1)] ÷ P1; nP0 = [(n + m)P1 − (I − E)] ÷ (1 + ke).

1. Price at the end of the year. P0 × (1 + ke) = 233.24 + 28 = 261.24.

Dividend not paid: P1 = ₹261.24.
Dividend paid: P1 = 261.24 − 10 = ₹251.24.

2. New shares to be issued

₹	Dividend not paid	Dividend paid
Net income available (E)	24,00,000	24,00,000
New equity to be raised	12,00,000	30,00,000
Funds needed: investment + dividend (I + nD1)	36,00,000	54,00,000
Price per new share (P1)	261.24	251.24
Number of new shares (m)	4,593.48	11,940.77

3. Value of the firm

Dividend not paid: [(1,80,000 + 4,593.48) × 261.24 − (36,00,000 − 24,00,000)] ÷ 1.120048 = (4,82,23,200 − 12,00,000) ÷ 1.120048 = ₹4,19,83,200.
Dividend paid: [(1,80,000 + 11,940.77) × 251.24 − 12,00,000] ÷ 1.120048 = (4,82,23,200 − 12,00,000) ÷ 1.120048 = ₹4,19,83,200.

Conclusion. The value of the firm is ₹4,19,83,200 (= 1,80,000 × ₹233.24) whether or not the dividend is paid. The dividend shareholders receive is exactly offset by the lower year-end price and the larger number of 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	P0 and ke from EPS and P/E	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

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