Question 5 (b)

Walter's model: optimal payout and the neutral P/E ratio

11 marks

Time to write
About 22 minutes

From an older CBCS paper

Question

Question 5 (b) · 11 marks

Bradley International began a year ago, with equity capital of Rs 24,00,000. Its other relevant details are below:

Number of outstanding shares24,000
Earnings of the companyRs. 2,40,000
Dividend paidRs. 1,80,000
P/E ratio12.5

  1. What is the company's dividend payout ratio? At this payout ratio, what is the share's market price? According to Walter's model, is the dividend payout ratio optimal?

  2. At what P/E ratio will the dividend payout ratio have no effect on the value of the share?

  3. If the P/E ratio is 8, what will your decision be?

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

22 minfor 11 marks

Read from the question

  • What is the…?Is…?What…?5 questions in all: answer every one.
  • your decisionEnd with a one-line decision that follows from your figures.

What the paper leaves open

The rate of return is the earnings over the equity capital; the capitalisation rate is the reciprocal of the P/E ratio.

Write it in this order

  1. Read the data; note exactly what is asked 1 min
  2. 1 R, ke, EPS, DPS and payout ratio 2 marks 4 min
  3. 2 Price at the present payout; not optimal, with the optimum 4 marks 7 min
  4. 3 P/E ratio at which payout has no effect 2 marks 4 min
  5. 4 Decision at P/E 8, with prices 3 marks 5 min
  6. Check: arithmetic, units (₹, %), final answer underlined 1 min

Short on time? End with step 4's one-line decision, whatever happens: never leave the figures without it.

Try it first. About 22 minutes for 11 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. EPS = 2,40,000 ÷ 24,000 = ₹10; DPS = 1,80,000 ÷ 24,000 = ₹7.50; r = 2,40,000 ÷ 24,00,000 = 10%; ke = 1 ÷ P/E = 1 ÷ 12.5 = 8% (paper note).

Walter's formula: P = [D + r(E − D) ÷ ke] ÷ ke.

(i) Payout ratio, price and optimality. Payout ratio = 7.50 ÷ 10 = 75%.

P = [7.50 + 0.10 × (10 − 7.50) ÷ 0.08] ÷ 0.08 = (7.50 + 3.125) ÷ 0.08 = ₹132.81.

The payout is not optimal. With r (10%) above ke (8%), the firm is a growth firm: it should retain its earnings, and the optimum payout is zero. At a zero payout, P = [0 + 0.10 × 10 ÷ 0.08] ÷ 0.08 = 12.50 ÷ 0.08 = ₹156.25.

(ii) P/E at which the payout has no effect. For a normal firm, where r = k, the dividend policy does not affect the value of the share. So ke must equal r = 10%, that is, a P/E ratio of 1 ÷ 0.10 = 10. (At ke = 10%, P = E ÷ ke = ₹100 at any payout.)

(iii) If the P/E ratio is 8. Then ke = 1 ÷ 8 = 12.5%, above r = 10%: the firm is a declining firm, and its shareholders gain if it distributes its earnings, so the optimum payout is 100%.

  • At the present 75% payout: P = [7.50 + 0.10 × 2.50 ÷ 0.125] ÷ 0.125 = (7.50 + 2.00) ÷ 0.125 = ₹76.
  • At a 100% payout: P = 10 ÷ 0.125 = ₹80.

Decision: pay out all the earnings as dividend, which raises the price from ₹76 to ₹80.

Where the 11 marks sit

#ComponentMarks
1r, ke, EPS, DPS and payout ratio2
2Price at the present payout; not optimal, with the optimum4
3P/E ratio at which payout has no effect2
4Decision at P/E 8, with prices3
Total11
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