Final answer:
The use of Gordon's Model in determining the share price requires calculating the expected dividend per share and considering the growth rate and discount rate. A change in the payout ratio impacts the dividend amount and consequently the share price.
Step-by-step explanation:
To determine the price of a share using Gordon's Model, we need to calculate the expected dividend per share and then divide it by the difference between the required rate of return (discount rate) and the growth rate of dividends. In this case, the company earns a 12% rate on its investment, which is Kes. 600,000, so the total earnings are 0.12 × 600,000 = Kes. 72,000. With a retention ratio of 40%, the payout ratio is 60%, hence the dividends will be 0.6 × 72,000 = Kes. 43,200. Divided by 600,000 outstanding shares, the dividend per share is 0.072. The growth rate (g) can be found by multiplying the retention ratio (b) by the return on investment (ROI), so g = b × ROI = 0.4 × 0.12 = 0.048 or 4.8%. Using Gordon's Model, P = D/(k-g), where P is the price, D is the dividend per share, k is the discount rate, and g is the growth rate. Thus, P = 0.072/(0.10 - 0.048) = Kes. 1.71 per share. If the payout ratio changes to 60%, dividends will increase, leading to a higher share price, and vice versa for a 20% payout ratio.