Question 3 OR (b)
Gordon's model: share price at different payout ratios
10 marks
- Time to write
- About 20 minutes
From an older CBCS paper
Question
Question 3 OR (b) · 10 marksRT Ltd. has invested ₹30,00,000 in 3,00,000 shares of ₹10/- each. Its rate of return on investment is 15%, and its retention ratio is 70% of its earnings. If the capitalisation rate appropriate to it is 12%,
What would the price be as per Gordon's Model?
What would the price be if the company's payout ratios are 25% and 75%?
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
- What…?Two asks in one question: answer both.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Gordon's formula and EPS 2 marks 4 min
- 2 Price at 70% retention 3 marks 5 min
- 3 Price at 25% and 75% payout 4 marks 7 min
- 4 Interpretation 1 mark 2 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.
Gordon's model. P = E(1 − b) ÷ (ke − br), where E is earnings per share, b the retention ratio, r the rate of return on investment and ke the capitalisation rate; the growth rate is g = br. The model assumes an all-equity firm financed by retained earnings, constant r and ke, a perpetual life, a constant retention ratio, and ke > br.
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.
EPS = (30,00,000 × 15%) ÷ 3,00,000 shares = 4,50,000 ÷ 3,00,000 = ₹1.50. r = 15%, ke = 12%.
(i) Price with retention of 70% (payout 30%; g = 0.70 × 15% = 10.5%): P = 1.50 × 0.30 ÷ (0.12 − 0.105) = 0.45 ÷ 0.015 = ₹30.00.
(ii) Price at other payout ratios
| Payout ratio | Retention (b) | Growth g = br | Dividend E(1 − b) (₹) | ke − g | Price (₹) |
|---|---|---|---|---|---|
| 25% | 0.75 | 11.25% | 0.375 | 0.0075 | 50.00 |
| 75% | 0.25 | 3.75% | 1.125 | 0.0825 | 13.64 |
Interpretation. RT Ltd. earns more on its investments (15%) than its capitalisation rate (12%), so under Gordon's model the share price rises as the payout falls: ₹50.00 at a 25% payout, ₹30.00 at 30%, and ₹13.64 at 75%.
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Gordon's formula and EPS | 2 |
| 2 | Price at 70% retention | 3 |
| 3 | Price at 25% and 75% payout | 4 |
| 4 | Interpretation | 1 |
| Total | 10 |
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