Question 4 (a)
Walter's model: payout ratio, share price and the optimal payout
10 marks
- Time to write
- About 20 minutes
From an older CBCS paper
Question
Question 4 (a) · 10 marksRST Ltd. commenced business a year ago with a paid-up equity capital of (₹) 60,00,000. The remaining particulars are as follows:
Earnings of the Company: (₹) 7,20,000
Dividend Paid: (₹) 5,40,000
Price-earnings Ratio: 10
Number of Shares: 60,000
Find the dividend payout ratio of the company. Then, using Walter's model, find the market price of one share of the company at this payout ratio.
As per the Walter's model, is the Company's dividend payout ratio optimal? Why?
As per the Walter's model, what is the market price of a share of the company when the dividend payout ratio is optimal?
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
- Find…Is…?What is the…?3 questions in all: answer every one. Where it asks why, give reasons, not a description.
- FindFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
The paper gives neither the rate of return on investment nor the cost of equity. They are read from the data: the rate of return is the earnings divided by the equity capital (the company started with that capital a year ago), and the cost of equity is the reciprocal of the price-earnings ratio.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 EPS, DPS, r and ke from the data 3 marks 5 min
- 2 (i) Payout ratio and the price at 75% 3 marks 5 min
- 3 (ii) Optimality, with the r against ke reason 2 marks 4 min
- 4 (iii) Price at the optimal payout 2 marks 4 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.
Data. Earnings per share (E) = 7,20,000 ÷ 60,000 = ₹12; dividend per share (D) = 5,40,000 ÷ 60,000 = ₹9.
- Rate of return on investment (r) = earnings ÷ equity capital = 7,20,000 ÷ 60,00,000 = 12% (paper note: the company has worked one year on the capital it started with).
- Cost of equity (ke) = the reciprocal of the price-earnings ratio = 1 ÷ 10 = 10%. (The present market price on that ratio is 10 × ₹12 = ₹120.)
(i) Dividend payout ratio = DPS ÷ EPS × 100 = 9 ÷ 12 × 100 = 75%.
Walter's formula: P = [D + r(E − D) ÷ ke] ÷ ke, with D the dividend per share, E the earnings per share, r the internal rate of return and ke the cost of equity.
Price at the 75% payout: P = [9 + 0.12 × (12 − 9) ÷ 0.10] ÷ 0.10 = (9 + 3.60) ÷ 0.10 = ₹126.
(ii) Is the 75% payout optimal? No. The company earns 12% on what it invests, more than the 10% its shareholders require (r > ke): it is a growth firm. Under Walter's model such a firm should keep its earnings, and its optimum payout is zero, which gives the highest share price. By paying out 75% the company hands back money that would have earned more inside the business than shareholders can earn on it elsewhere, so the share is worth less than it could be.
(iii) Price at the optimal payout (0%): with D = 0, P = [0 + 0.12 × (12 − 0) ÷ 0.10] ÷ 0.10 = 14.40 ÷ 0.10 = ₹144.
Conclusion. Payout ratio 75%, price ₹126 under Walter's model; the payout is not optimal because r (12%) exceeds ke (10%); at the optimal nil payout the price rises to ₹144.
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | EPS, DPS, r and ke from the data | 3 |
| 2 | (i) Payout ratio and the price at 75% | 3 |
| 3 | (ii) Optimality, with the r against ke reason | 2 |
| 4 | (iii) Price at the optimal payout | 2 |
| Total | 10 |
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