Question 4 OR (a)
Gordon model: share price at four payouts and three rates of return
12 marks
- Time to write
- About 24 minutes
Question
Question 4 OR (a) · 12 marksA company has a total equity capital of ₹30,00,000 (₹10 per share). Taking the return on investment (ROI) as 10%, 12%, and 15% and the cost of equity as 12%, compute the price of a share using the Gordon model if the dividend payout ratio is 0%, 50%, 75%, and 100%.
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
- computeFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
Earnings per share are not given. They are read as the return on investment times the ₹10 per share of equity capital, the book value per share.
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Gordon's formula and EPS at each ROI 2 marks 3 min
- 2 Prices at each payout and ROI 8 marks 14 min
- 3 Comment, including the 0% payout cases 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Short on time? Step 2 carries 8 of the 12 marks: guard its minutes.
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.
Gordon's formula: P0 = E(1 − b) ÷ (ke − br), where b is the retention ratio, so br is the growth rate. The model assumes ke > br. Here ke = 12%, and EPS = ROI × ₹10 a share (paper note): ₹1.00, ₹1.20 and ₹1.50 for ROI of 10%, 12% and 15%.
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.
| Payout | Retention (b) | ROI 10% (E = ₹1.00) | ROI 12% (E = ₹1.20) | ROI 15% (E = ₹1.50) |
|---|---|---|---|---|
| 0% | 1.00 | nil (no dividend is ever paid) | not defined (br = ke) | not applicable (br > ke) |
| 50% | 0.50 | 0.50 ÷ (0.12 − 0.05) = 7.14 | 0.60 ÷ (0.12 − 0.06) = 10.00 | 0.75 ÷ (0.12 − 0.075) = 16.67 |
| 75% | 0.25 | 0.75 ÷ (0.12 − 0.025) = 7.89 | 0.90 ÷ (0.12 − 0.03) = 10.00 | 1.125 ÷ (0.12 − 0.0375) = 13.64 |
| 100% | 0.00 | 1.00 ÷ 0.12 = 8.33 | 1.20 ÷ 0.12 = 10.00 | 1.50 ÷ 0.12 = 12.50 |
- ROI 10% (r < ke): the price rises as the payout rises, so the firm should distribute its earnings.
- ROI 12% (r = ke): the price is ₹10 at every payout for which the model applies; dividend policy does not matter.
- ROI 15% (r > ke): the price rises as more is retained, so the firm should retain earnings, but only so far as growth (br) stays below ke. At full retention br exceeds ke and the formula no longer applies.
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Gordon's formula and EPS at each ROI | 2 |
| 2 | Prices at each payout and ROI | 8 |
| 3 | Comment, including the 0% payout cases | 2 |
| Total | 12 |
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