## Cf

PV of Growing Perpetuity = 1

where CF1 is the expected cash flow next year, g is the constant growth rate and r is the discount rate. While a growing perpetuity and a growing annuity share several features, the fact that a growing perpetuity lasts forever puts constraints on the growth rate. It has to be less than the discount rate for this formula to work.

Growing perpetuities are especially useful when valuing equity in publicly traded firms, since they could potentially have perpetual lives. Consider a simple example. In 1992, Southwestern Bell paid dividends per share of $2.73. Its earnings and dividends had grown at 6% a year between 1988 and 1992 and were expected to grow at the same rate in the long term. The rate of return required by investors on stocks of equivalent risk was 12.23%.

Current Dividends per share = $2.73 Expected Growth Rate in Earnings and Dividends = 6% Discount Rate = 12.23% With these inputs, we can value the stock using a perpetual growth model:

Value of Stock = $2.73 *1.06 / (. 1223 -.06) = $46.45 As an aside, the stock was actually trading at $70 per share. This price could be justified by using a higher growth rate. The value of the stock is graphed in figure 7 as a function of the expected growth rate.

Figure 3.7: SW Bell -Value versus Expected Growth

Figure 3.7: SW Bell -Value versus Expected Growth

The growth rate would have to be approximately 8% to justify a price of $70. This growth rate is often referred to as an implied growth rate.

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