## A1 The Gordon model with two dividend growth rates

The Gordon model discussed in Chapter 16 (and previously in Chapter 5) assumes that there equity payouts of the firm will grow at an anticipated future growth rate g. Based on this assumption we showed that the cost of equity is:

where Div0 is the firm's current equity payout (defined as the sum of its total dividends and stock repurchases), g is the growth rate of the equity payout, and P0 is the firm's current equity value (that is, number of shares times the current share price).

The assumption of a single future growth rate may, however, be problematic. Just as for the FCF examples in section 16.2 we concluded that there might be 2 FCF growth rates, it is often plausible to assume that there are 2 dividend growth rates. Typically, we assume that an initial period of high dividend growth is followed by normal dividend growth. In the equation below we've assume that dividends grow at a high growth rate for 5 years and that afterwards the growth rate slows down to a normal dividend growth rate. In this case the basic Gordon model equation becomes:

P Div0* (1 + ghigh ) ^ DiV0 * (1 + ghigh ) * (1 + g norma, ) ^

The present value of the first five years of dividend growth, assumed to grow at a high growth rate, ghigh •

The present value of the rest of the dividends, assumed to grow at a lower rate gnormal •

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