Question 4 (b)
Walter's model: share price and optimum payout
10 marks
- Time to write
- About 20 minutes
From an older CBCS paper
Question
Question 4 (b) · 10 marksVWX Limited started a year ago, with paid-up equity capital of rupees 24 lakh. Its other details are below:
| Earnings of the company | Rs 240000 |
| Dividend paid | Rs 192000 |
| Price earnings ratio | 12.5 |
| Number of shares | 48000 |
Using walter's model, find the market price of the company's share at this payout ratio. As per walter's model, is the company's dividend payout ratio optimum? Why?
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
- WhyReasons, not a description: each reason explained in a line or two.
- findFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
The rate of return is earnings over paid-up equity capital; the capitalisation rate is the reciprocal of the price-earnings ratio.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 R, ke, EPS and DPS 3 marks 5 min
- 2 Walter's formula and the price at the present payout 4 marks 7 min
- 3 Optimum payout, with reason and the price at it 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 2 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.
Inputs. Rate of return r = earnings ÷ paid-up capital = 2,40,000 ÷ 24,00,000 = 10%; capitalisation rate ke = 1 ÷ P/E = 1 ÷ 12.5 = 8% (paper note). EPS = 2,40,000 ÷ 48,000 = ₹5; DPS = 1,92,000 ÷ 48,000 = ₹4 (payout 80%).
Walter's formula. P = [D + r(E − D) ÷ ke] ÷ ke.
Market price at the present payout (80%): P = [4 + 0.10 × (5 − 4) ÷ 0.08] ÷ 0.08 = (4 + 1.25) ÷ 0.08 = ₹65.63 (65.625).
Is the payout optimum? No. When r > k the firm is a growth firm: it should retain its earnings, and the optimum payout is zero, which maximises the value of the share. Here r = 10% exceeds ke = 8%, so every rupee retained earns more than shareholders require. At a 0% payout:
P = [0 + 0.10 × 5 ÷ 0.08] ÷ 0.08 = 6.25 ÷ 0.08 = ₹78.13 (78.125).
The present payout of 80% therefore depresses the price, from ₹78.13 to ₹65.63. Under Walter's model only a declining firm (r < k) should pay out everything, and for a normal firm (r = k) the payout does not matter.
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | r, ke, EPS and DPS | 3 |
| 2 | Walter's formula and the price at the present payout | 4 |
| 3 | Optimum payout, with reason and the price at it | 3 |
| Total | 10 |
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