Question 4 OR (a)
Gordon's model at two payout ratios
8 marks
- Time to write
- About 16 minutes
From an older CBCS paper
Question
Question 4 OR (a) · 8 marksIf the cost of equity is 11%, the rate of return on investment 12% and earnings per share Rs. 15, calculate the price per share by the 'Gordon Model' at dividend pay-out ratio of 10% and of 30%. 8
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
- calculateFormula first, then the working, then the answer with its unit (₹, %, units).
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Formula and conditions 2 marks 4 min
- 2 Price at 10% payout 3 marks 5 min
- 3 Price at 30% payout 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.
Gordon's model. P = E(1 − b) ÷ (ke − br), where b is the retention ratio and g = br; it requires ke > br. E = ₹15; r = 12%; ke = 11%.
1Sunita holds this year's dividend—money in her hand today.
Current dividendsInvestors put a premium on certain returns.
2Verma ji's payout sits inside a half-built project, and he worries.
Retained earningsUncertain future gains.
3At the counter, savers crowd the company that pays now over the one that promises later.
Bird in handInvestors are risk averse and value current dividends more than uncertain future gains.
| Particulars | Payout 10% | Payout 30% |
|---|---|---|
| Dividend per share E(1 − b) (₹) | 1.50 | 4.50 |
| Retention ratio (b) | 0.90 | 0.70 |
| Growth g = br | 10.80% | 8.40% |
| ke − g | 0.20% | 2.60% |
| Price per share (₹) | 750.00 | 173.08 |
- At 10% payout: P = 1.50 ÷ (0.11 − 0.108) = 1.50 ÷ 0.002 = ₹750.
- At 30% payout: P = 4.50 ÷ (0.11 − 0.084) = 4.50 ÷ 0.026 = ₹173.08.
Comment. Since r (12%) exceeds ke (11%), Gordon's model gives a higher price the more the firm retains. The very high price at 10% payout arises because g approaches ke; the model is sensitive when ke − g is small.
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Formula and conditions | 2 |
| 2 | Price at 10% payout | 3 |
| 3 | Price at 30% payout | 3 |
| Total | 8 |
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