A Note on Valuation and Evaluation
Mark Lang
One of the central uses of financial statements is in valuation. Many of the approaches that are used (e.g., price/earnings ratio and market/book ratio) are based on heuristics rather than fundamental finance principles.
To understand valuation, it is useful to consider a simple example based on a mutual fund. A mutual fund is like a very simple company. A deposit into a mutual fund is analogous to contributed capital and a withdrawal is analogous to a dividend.
The first fundamental in valuation is the notion that one only invests in anticipation of future cash flow. In terms of a mutual fund, that implies that the value is determined by expected future withdrawals. That fact is clear if you consider the alternative. Suppose that a mutual fund was formed from which money could never be retrieved. Clearly, it would have no value. Similarly, suppose a company was formed that investors knew would never pay any dividends-it was formed, earned just enough to fund its operations and ultimately was liquidated with no payments to equity holders. The value of the firm would be zero since no one would pay for an investment which they knew would never provide them with any cash flows.[1]
1.The Dividend Discount Model
The basic dividend discount approach is:
Vt=E (Dividendt+1)/(1+r)+E(Dividendt+2)/(1+r)2+E(Dividendt+3)/(1+r)3+…
where Vt is the value per share (the amount an investor would be willing to pay for one share) at time t, E() denotes the expected value and r is the appropriate discount rate given the firm’s risk. The discount rate, which will be discussed in more detail in finance is often referred to as the cost of capital. Conceptually, it can be viewed in one of two ways-either as the amount that investors expect to earn from investments with similar risk, or as the amount investors such as lenders charge you for using their capital.[2]
To illustrate, suppose you invest in a mutual fund containing bonds earning 10% interest and that you plan to withdraw the full amount in one year. Assume that the discount rate is also 10% (i.e., you can borrow at 10% and can find other investments with similar risk returning 10%). The amount available in one year is then $100 + ($100 x 10%) = $110. The value of the fund is
$110/(1+10%)=$100. It is only worth $100 because there are a variety of other mutual funds you could have invested in also earning 10%.
Now, suppose that the savings account has locked in a 12% return for one year (because, for example, it purchased bonds when interest rates were higher) and you plan to withdraw at the end of one year. Then, the price is $112/(1+10%)=$102. It is worth a little more than $100 because it returns more than the market rate of interest.
Exactly the same approach would work in valuing a stock-one could forecast all future dividends, discount them back, and that would give the value of the stock.
3.The Free Cash Flow Approach
A problem with the dividend discount approach is that dividend distributions can be arbitrary and difficult to estimate. Conceptually, the ability to pay dividends derives from value creation through profitable operations, but the dividend discount approach does not look to operations.
Therefore, most valuation professionals rely on an approach based on cash flows, typically a discounted free cash flow approach. Under certain fairly simple assumptions, the value of the firm can be expressed as the present value of “free cash flows,” defined as the sum of cash from operations (generally positive) and cash from investing (generally negative). This captures the notion that dividends must ultimately be financed by internally-generated cash flows.
The discounted cash flow approach is typically implemented by valuing the cash flows expected to be received from the assets and subtracting off the existing interest-bearing debt. The basic idea is that we can use the expected cash flows from assets to value the assets and the book value of existing debt captures the present value of cash flows on that debt (any additional debt to be issued in the future is zero net present value.
Vt=E(AFCFt+1)/(1+r)+E(AFCFt+2)/(1+r)2+E(AFCFt+3)/(1+r)3+… - Existing Interest-Bearing Debt
where AFCF denotes free cash flow per share, adjusted by adding back after-tax interest (analogous to the add back for interest in return on assets).[3]
To illustrate the free cash flow approach, consider the earlier numerical example. If the investment return is 10%, the free cash flows are $10 from interest plus $100 from sale of the investment (i.e., cashing out of the bonds). Since both occur at the end of the period, the value of the investment is $10 (1+10%)+$100/(1+10%)=$100 as before. Similarly, if the investment returned 12%, the computation would be $12/(1+10%)+$100/(1+10%)=$102.[4]
Exactly the same approach could be applied in valuing a stock. Often in valuation analysts estimate free cash flows going forward and then discount them back to estimate the value of a stock. A problem with this approach is that free cash flow forecasts are generally not readily available because analysts focus most effort on forecasting earnings. Forecasting free cash flows from earnings requires a balance sheet forecast as well. Further, the free cash flow approach is quite sensitive to assumptions about free cash flows far into the future that are difficult to forecast.
3.The Balance Sheet Approach
A second approach is to base value on the market value of the underlying assets. Underlying this approach is the assumption that a market has correctly done the work of computing the present value of cash flows from the assets. In terms of a mutual fund, you generally would not bother to forecast the cash flows explicitly but rather would use the market valuation of the stocks relying on the market’s valuation of the cash flows.
The problem with this approach is that many assets of corporations, especially intangibles, do not have observable market prices.
4.Implications
The preceding illustrates several important points for understanding financial statements. First, valuation is fundamentally about the forecasting the future. That is why there is such divergence in opinion on over- and under- valuation of individual stocks and of the market as a whole. Given the difficulty in predicting the future for individual companies and the economy as a whole, one can justify a wide range of valuations based on what one assumes about firms’ future profitability. Similarly, share prices can fluctuate wildly in vale based on factors like macroeconomic news, the Asian crisis and FDA drug approvals because each can have important implications for future profitability. Analysts devote a great deal of attention to forecasting earnings because future earnings are fundamental to valuation; the most accurate forecasters tend to be the best stock pickers.
Second, each of the financial statements is potentially important to valuation. The income statement helps us understand current net income, which is useful to predicting future net income. The balance sheet provides the book value of shareholders’ equity and information on the assets and liabilities of the firm are useful in predicting future earnings. The statement of cash flows illustrates the relation between current net income and cash flows which is useful in predicting future cash flows.
Finally, an understanding of the fundamental valuation relations is important in interpreting financial statements. Investors often use ratios like market/book, price/earnings and price/cash from operations to assess mis-valuation. These approaches may be useful as heuristics, but are incomplete. For example, one may be tempted to argue that market/book ratios are unrealistically high relative to past levels. However, that alone ignores the fact that profit expectations for the future may be unusually high or interest rates unusually low. Similarly, one might argue that one company is overvalued relative to another because its price earnings ratio is higher. However, that may reflect differences in future earnings expectations. The point is that it is important to understand the underlying valuation model and be complete and consistent in the analysis.
[1] One might argue that could purchase it anticipating a sale to someone else. However, that presumes you could find someone else to pay for an investment which would provide them with no payback.
[2] There is an implicit assumption here that investors can borrow and lend at the same rate. In practice, of course, there is a spread between the rate you pay when you borrow money from the bank and the rate you receive when you lend to (deposit money in) the bank. However, ignoring that difference is generally small and ignoring it does not affect the analysis in any material way.
[3] The basic idea is that we value the assets of the firm (by using cash flows before interest) and subtract off debt’s claim against the assets. Another approach would go directly to valuing the cash flows available to equity, but that is more difficult to implement because it requires assumptions about debt issuance.
[4] In this example, the computation was basically the same for the dividend discount and free cash flow approaches since all free cash flows were immediately paid out in dividends. More generally that will not be the case, but both approaches will give the same answer. Examples will be provided later when we talk more about free cash flows.