Question

You are provided with the following data,

a) Earning per share = kes 10,
b) Dividend per share = kes 6
c) cost of capital = 18%
d) Rate of return = 25%
e) Retention ratio = 45%
Required: calculate the market price of a share of ABC Ltd., under (i) Walter’s formula; (ii) the Dividend growth model.

Answer 1

To calculate the market price of a share of ABC Ltd., we can use Walter's formula and the Dividend growth model. Using Walter's formula, the market price is kes 31.034, and using the Dividend growth model, it is kes 32.

Step-by-step explanation:

There are two formulas that can be used to calculate the market price of a share of ABC Ltd.:

(i) Walter's formula:

1. First, we need to calculate the dividend payout ratio by subtracting the retention ratio from 1. In this case, it would be 1 - 0.45 = 0.55.
2. Next, we can use the formula: P = D / (r - g), where P is the market price per share, D is the dividend per share, r is the required rate of return, and g is the growth rate of dividends. In this case, D = kes 6, r = 0.25, and g = 0.55 * 10 = 5.5.
3. Plugging in the values, we get: P = 6 / (0.25 - 0.055) = kes 31.034.

(ii) The Dividend growth model:

1. First, we need to calculate the expected growth rate of dividends. In this case, it would be the retention ratio multiplied by the rate of return: 0.45 * 0.25 = 0.1125.
2. Next, we can use the formula: P = D / (r - g), where P is the market price per share, D is the dividend per share, r is the required rate of return, and g is the growth rate of dividends. In this case, D = kes 6, r = 0.25, and g = 0.1125.
3. Plugging in the values, we get: P = 6 / (0.25 - 0.1125) = kes 32.

Therefore, the market price of a share of ABC Ltd. using Walter's formula is kes 31.034, and using the Dividend growth model is kes 32.