Question

(a) Aan, an analyst, has made the following assumptions about the stock of A Capital, a financial firm. The earnings per share for the year that has just ended (i.e., at t = 0) is $20. The earnings growth rates will be 25% over the next year, 20% over the second year (i.e., year after the next), 15% over the third year, 10% for the fourth year and thereafter indefinitely. The dividend payout rate is 50% of earnings, and the discount rate is 15%/year. Given the assumptions, what should be Aan’s estimate of the share price of the stock? Show your steps.

(b) Due to a sudden unexpected event, A Capital finds that it must give another institution four annual penalty payments, which happen to be identical (in terms of both the amount and timing) to the dividends D1 through D4 of RSM, for year 1 through year 4, respectively.

Answer 1

To estimate the share price of the A Capital stock, we calculate the present value of expected dividends for four years considering the growth rates and discount them at 15%. The terminal value calculation involves the Gordon Growth Model. After summing all present values, we divide by the total number of shares to arrive at the price per share.

Step-by-step explanation:

To estimate the share price of A Capital stock given Ana's assumptions, we need to calculate the present value of the expected dividends. The earnings per share is $20, and earnings are expected to grow at different rates over the next four years: 25%, 20%, 15%, and 10%. The dividend payout rate is 50% of these earnings. We must calculate the present value (PV) of each dividend payment, discounting them at a 15% yearly discount rate.

Let E(0) be the earnings per share at t=0, which is $20. For the first year, the earnings will be E(1) = E(0) * (1 + 25%) = $20 * 1.25.
Dividend D(1) = E(1) * 50%, and the present value PV(D(1)) = D(1) / (1 + 15%). The calculations for the subsequent years follow the same pattern but with the corresponding growth rates and dividend payout. After calculating the present values of dividends for years 1 through 4, we sum them up to get the total present value of those dividends.

For the terminal value, which represents the constant growth phase starting in year 5, we use the Gordon Growth Model. The terminal value formula is TV = D(5) / (r - g), with D(5) being the dividend at year 5, r the discount rate (15%), and g the perpetual growth rate (10%). The PV of the terminal value is then discounted back to the present.

Finally, we add the PVs of the individual dividends and the terminal value to get the total present value of dividends, which is then divided by the number of shares to find the price per share.