Question

The following information is available in respect of ABC Ltd.

Earning per share (EPS or E) Rs. 10 (Constant)
Cost of Capital, k, .10 (Constant)

Find out the market price of the share under different rate of return, r, of 8%, 10% and 15% for different payout ratios of 0%, 40%, 80%, and 100%.​

Answer 1

Answer:

To calculate the market price of the share under different rates of return and payout ratios, we can use the Gordon Growth Model, which is given by the formula:

$P = \frac{E \times (1 - \text{Payout Ratio})}{k - r}$

Where:

P = Market price of the share

E = Earnings per share (EPS)

Payout Ratio = Percentage of earnings paid out as dividends

k = Cost of Capital

r = Rate of return

Given:

Earnings per share (EPS), E = Rs. 10 (constant)

Cost of Capital, k = 0.10 (constant)

Using the above formula, we can calculate the market price of the share under different rates of return and payout ratios:

For a rate of return (r) of 8%:

- Payout Ratio = 0%

$P = \frac{10 \times (1 - 0)}{0.10 - 0.08} = \frac{10}{0.02} = Rs. 500$

- Payout Ratio = 40%

$P = \frac{10 \times (1 - 0.40)}{0.10 - 0.08} = \frac{6}{0.02} = Rs. 300$

- Payout Ratio = 80%

$P = \frac{10 \times (1 - 0.80)}{0.10 - 0.08} = \frac{2}{0.02} = Rs. 100$

- Payout Ratio = 100%

$P = \frac{10 \times (1 - 1)}{0.10 - 0.08} = \frac{0}{0.02} = Rs. 0$

For a rate of return (r) of 10%:

- Payout Ratio = 0%

$P = \frac{10 \times (1 - 0)}{0.10 - 0.10} = \frac{10}{0} = Undefined$

- Payout Ratio = 40%

$P = \frac{10 \times (1 - 0.40)}{0.10 - 0.10} = \frac{6}{0} = Undefined$

- Payout Ratio = 80%

$P = \frac{10 \times (1 - 0.80)}{0.10 - 0.10} = \frac{2}{0} = Undefined$

- Payout Ratio = 100%

$P = \frac{10 \times (1 - 1)}{0.10 - 0.10} = \frac{0}{0} = Undefined$

For a rate of return (r) of 15%:

- Payout Ratio = 0%

$P = \frac{10 \times (1 - 0)}{0.10 - 0.15} = \frac{10}{-0.05} = -Rs. 200$

- Payout Ratio = 40%

$P = \frac{10 \times (1 - 0.40)}{0.10 - 0.15} = \frac{6}{-0.05} = -Rs. 120$

- Payout Ratio = 80%

$P = \frac{10 \times (1 - 0.80)}{0.10 - 0.15} = \frac{2}{-0.05} = -Rs. 40$

- Payout Ratio = 100%

$P = \frac{10 \times (1 - 1)}{0.10 - 0.15} = \frac{0}{-0.05} = Rs. 0$

Therefore, the market price of the share under different rates of return and payout ratios are as follows:

Rate of Return 8%:

- Payout Ratio 0%: Rs. 500

- Payout Ratio 40%: Rs. 300

- Payout Ratio 80%: Rs. 100

- Payout Ratio 100%: Rs. 0

Rate of Return 10%:

- Payout Ratio 0%: Undefined

- Payout Ratio 40%: Undefined

- Payout Ratio 80%: Undefined

- Payout Ratio 100%: Undefined

Rate of Return 15%:

- Payout Ratio 0%: -Rs. 200

- Payout Ratio 40%: -Rs. 120

- Payout Ratio 80%: -Rs. 40

- Payout Ratio 100%: Rs. 0

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