Question 3 (b)
Walter's model: share price, optimum payout and indifference
12 marks
- Time to write
- About 24 minutes
Question
Question 3 (b) · 12 marksThe following information is provided to you about Dhruv Ltd.:
Earnings of the firm ₹43,20,000 No. of equity shares 3,60,000 Amount of dividend paid ₹21,60,000 Return on equity 15% Cost of Equity 10%
Using Walter’s Model, calculate the present price of a share and the value of the firm.
Is this the optimum pay-out ratio? At the optimum pay-out ratio, what is the firm's value?
If the firm wants to keep its share price at ₹160, what should the payout ratio be?
When will the firm be indifferent about the payment of dividend?
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
- Is…?What is the…?What…?4 questions in all: answer every one.
- calculateFormula first, then the working, then the answer with its unit (₹, %, units).
- should theEnd with a one-line decision that follows from your figures.
Write it in this order
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- Read the data; note exactly what is asked 2 min
- 1 EPS, DPS and Walter's formula 2 marks 3 min
- 2 (i) Present price and value of the firm 3 marks 5 min
- 3 (ii) Optimum payout zero r > ke 3 marks 5 min
- 4 (iii) Payout for a price 2 marks 3 min
- 5 (iv) Indifference when r = ke 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 3 min
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Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
Data. EPS (E) = ₹43,20,000 ÷ 3,60,000 = ₹12. DPS (D) = ₹21,60,000 ÷ 3,60,000 = ₹6 (payout 50%). r = 15%, ke = 10%.
P = [D + (r ÷ ke)(E − D)] ÷ ke
(i) Present price and value of the firm
P = [6 + (0.15 ÷ 0.10)(12 − 6)] ÷ 0.10 = (6 + 9) ÷ 0.10 = ₹150.
Value of the firm = ₹150 × 3,60,000 = ₹5,40,00,000.
(ii) Is 50% the optimum payout? No. Since r (15%) > ke (10%), the firm is a growth firm, and retaining earnings earns shareholders more than they require. Under Walter's model the optimum payout for such a firm is zero. At zero payout:
P = [0 + 1.5 × (12 − 0)] ÷ 0.10 = 18 ÷ 0.10 = ₹180.
Value of the firm at the optimum payout = ₹180 × 3,60,000 = ₹6,48,00,000.
(iii) Payout ratio for a price of ₹160
160 = [D + 1.5(12 − D)] ÷ 0.10, so 16 = D + 18 − 1.5D, so 0.5D = 2, and D = ₹4.
Payout ratio = 4 ÷ 12 = 33.33%.
(iv) When the firm will be indifferent. When the rate of return on investment equals the cost of equity (r = ke), the dividend policy does not affect the market value of the share, so there is no optimum payout. For this firm that means r = 10%. Then P = E ÷ ke = 12 ÷ 0.10 = ₹120 at every payout. Equivalently, the firm is indifferent at the price-earnings ratio at which ke equals r.
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | EPS, DPS and Walter's formula | 2 |
| 2 | (i) Present price ₹150 and value of the firm ₹5,40,00,000 | 3 |
| 3 | (ii) Optimum payout zero (r > ke); price ₹180, value ₹6,48,00,000 | 3 |
| 4 | (iii) Payout for a ₹160 price: 33.33% | 2 |
| 5 | (iv) Indifference when r = ke | 2 |
| Total | 12 |
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