Question

A stock index stands at 1806 at the end of the year. Next year's earnings for the firms included in the index are forecasted to be 146. The current book value of equity for the same firms is 902. Use a required rate of return of 9% and compute the long-term growth rate that is implied by the index level. You can assume that the long-term growth rate is constantt from next year and onwards.

Answer 1

To find the implied long-term growth rate, use the Gordon Growth Model with the stock index level, forecasted earnings, and required rate of return. Rearrange for the growth rate and substitute the given values to calculate the growth rate.

Step-by-step explanation:

To calculate the implied long-term growth rate given the stock index level, the forecasted earnings, the book value of equity, and the required rate of return, you can use the Gordon Growth Model (GGM). The GGM assumes that dividends grow at a constant rate indefinitely. The formula for the GGM is P = D / (k - g), where P is the price (index level), D is the dividends (here we can use earnings as a proxy), k is the required rate of return, and g is the growth rate. Rearranging for g, we get g = k - (D / P). Using the provided index level of 1806, forecasted earnings of 146, and a required rate of return of 9%, we find the implied growth rate. It is important to note that dividends are not explicitly provided but can be estimated from earnings and past trends of dividends, which have been between 1% to 2% recently.

Thus, the final formula with the given numbers plugged in would look like this: g = 0.09 - (146 / 1806). After calculating, you will get the final answer for the implied long-term growth rate.