We have seen that time value formulas can be invoked in setting publicly traded bond prices when prevailing interest rates change from the rates set on the original bond issue. The price of the bond was deemed to be the present value of all future interest income and principal repayments discounted by the now prevailing interest rates.

It might be hoped that time value formulas will prove useful in setting a rational value on the equity share prices of publicly traded firms as well. If we could project the future expected cash flows from owning a share of publicly traded stock and we could use an appropriate discount rate we might have a rational and systematic way of assigning a value to that share of stock.

Alas we must acknowledge the enormous practical difficulties in applying such a pricing model. Unless you are assigning a value to a share of a company that issues a predictable and consistent cash dividend, we are essentially modeling the price of a share as if it were a zero-coupon bond. Of course, in valuing a zero-coupon bond we know the redemption amount and the redemption date. We have no such information in the case of equity.

Now many of the largest and most secure publicly traded firms do in fact issue regular dividends annually, quarterly or monthly. But over 50% of publicly traded companies do not issue regular dividends. However, even the companies that do issue dividends have no legal obligation to do so, and there historically has been wide variation in dividend levels. All this makes the task of cash flow projection a very tricky business.

Suppose we were to try to model the share price of a dividend issuing company on a perpetuity model. Recall that the perpetuity value is given by this formula:

.

This assumes a constant cash flow forever. That’s what a perpetuity is. But there is absolutely no reason to think that any company currently issuing dividends will issue them forever. In fact, there is no reason to believe that any company listed on a publicly traded exchange will be around forever.

Did I say forever? In the 1950s the average life span of an S & P company was about 60 years. Today it is under 20 years. So, the moral of the story is, do not treat your dividend yielding equity as a perpetuity and do not use a perpetuity formula to value the price of a share.

Now there is another possibly more plausible approach to valuing the share prices of publicly traded firms. Instead of confining our attention to the future cash flows distributed to the shareholders in the form of dividends and capital gains, let’s instead focus on the underlying cash flows earned by the company in operating its core business activities. This makes intuitive sense in that a firm’s stock prices ought to be directly related to its underlying profitability. The more profitable the firm, the higher the share value and vice versa.

Since there is a lot of historical and current information about publicly traded companies past performance and in many cases a number of industry analysts attempting to accurately assess at least the near-term earnings forecasts of these firms, it may be possible to develop plausible cash flow projections.

Suppose we have a publicly traded company that has three-year earnings forecast that looks like this.

Now while we know that this publicly traded company might not last much over twenty years it probably will survive more than three years. Furthermore, while short term forecasts are likely to be more accurate than longer term forecasts it may be still reasonable to attempt to stretch the forecasts out beyond this limited term. To do otherwise is to perhaps understate the value of the company and hence the value of its share prices.

So, let’s suppose we have a reasonably plausible forecast of cash flows for three years like the one above. A typical approach suggests that for years four and later we apply a suitable adjustment based on year 3 and apply the perpetuity formula to this adjusted year 4 projection. Let’s assume that year 4 is projected to be 3% higher than year 3, or about $17 million. We could divide this number by an appropriate discount rate and convert this to a lump sum. Let’s say we use 10% as a discount rate. In effect we would be assigning a present value to all future years’ earnings starting at year 4 to be about $170 million($17million/.10). We could then take the present value of all four years at 10% and assign a value to the company as a whole to be about $156 million. Divide that number by the number of outstanding shares of stock and you seemingly have a rational basis for assigning a per share value.

But as we have just seen such a model makes no economic sense. Because a perpetuity model applied at year four makes no more sense than a perpetuity model at year one. Even if we accept the irrational proposition that the company will generate steady cash flows into the indefinite future, we have another conundrum in choosing the discount rate. Recall we faced a similar question when evaluating capital budgeting decisions. In that chapter I suggested using a firm’s borrowing rate as the appropriate discount rate. But this does not seem to the correct approach for valuing share prices.

It would seem that an appropriate discount rate should be[b1] higher than the borrowing rate. Why? Because the returns for investing in equities ought to be higher than the cost of borrowing as equity returns are riskier than debt returns. But how much higher should the discount rate be?

While over long periods of time average equity yields have been higher than debt yields, there have been periods of time when equity yields have been negative, or certainly less than debt yields. Also, not all equity returns have been or will be equal. Various techniques have been developed to measure the volatility of specific share prices relative to the equity market as a whole. But reliable and stable measures are unobtainable and choosing the precisely correct discount rate involves a fair amount of judgment.

The reliance on the perpetuity formula and the difficulty in selecting an appropriate discount rate make the discounted cash flow approach to valuing publicly traded equity shares useless. Despite the uselessness of this approach in modeling the share prices of publicly traded companies, many business appraisers use the model to appraise the equity of closely held non publicly traded firms. This model is even more inappropriate for those businesses.

Copyright 2018 Michael Sack Elmaleh