## 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

Expected Growth Rate

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.

## Retirement Planning For The Golden Years

If mutual funds seem boring to you, there are other higher risk investment opportunities in the form of stocks. I seriously recommend studying the market carefully and completely before making the leap into stock trading but this can be quite the short-term quick profit rush that you are looking for if you am willing to risk your retirement investment for the sake of increasing your net worth. If you do choose to invest in the stock market please take the time to learn the proper procedures, the risks, and the process before diving in. If you have a financial planner and you definitely should then he or she may prove to be an exceptional resource when it comes to the practice of 'playing' the stock market.

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