Stock Valuation Calculator The "Investor workshop" column of the October 1985 AAII Journal described two alternative approaches to the question of stock valuation: the dividend valuation model and the earnings valuation model. The dividend valuation approach stems from the notion that the value of a stock should equal the present value of all expected future cash dividends. Simplifying some of the assumptions and manipulating the present value equation results in the following formula: d (1+g) 0 P = ------- 0 r - g where P is the current value, d is current dividends, g is the 0 0 dividend growth rate, and r is the required rate of return. (Refer to the Journal article for a more detailed description of the model and for precise meanings of all the variables.) The earnings valuation approach entails calculating the expected price/earnings ratio and multiplying that times the expected earnings: P = p/e X e 0 1 1 where P is again current value, p/e is the expected price/earnings 0 1 ratio, and e is expected earnings. 1 Note that with a constant payout ratio (d/e), the earnings growth rate must equal the dividend growth rate, and the two approaches as described in the article are essentially the same: d /e d (1+g) 0 0 0 P = p/e X e = ----- X e (1+g) = ------- 0 1 1 r - g 0 r - g "Stock Valuation Calculator" ("STKVAL") implements these two approaches in a single easy-to-use computer program. (The more involved approach of valuating stocks by computation of the present value of an explicit expected dividend stream was taken up in the "IRR&NPV" program from the last issue of CI.) When you run "STKVAL," you are asked to supply six different data items (following the example given in the Journal article, we will estimate the value of the DJIA, although ordinarily you will want to valuate individual stocks): STOCK PRICE ($)? 1266.78 CURRENT DIVIDENDS ($)? 61.56 CURRENT EARNINGS ($)? 107.87 STOCK BETA? 1.0 EQUITY RISK PREMIUM (%)? 6.2 T-BILL RATE (%)? 7.3 In the case of stocks with both zero current dividends and zero current earnings, enter instead nonzero historical averages of dividends and earnings over, say, the last three years. Beta values, which measure a stock's risk relative to the market as a whole, are available from Value Line or brokerage house reports; or you can estimate beta yourself using the AAII Program #3, "Stock Statistics" ("STATS"). For the equity risk premium, the amount by which equity return should exceed riskless return in order to compensate for the extra riskiness of equities, it is best to use the historical average, 6.2%, although you can substitute a figure conforming to your own expectations if you wish. The current Treasury bill rate is a simple, recommended measure of the expected return on risk-free assets. After you enter those six items, the program performs some calculations, then displays the following information: STOCK VALUATION CALCULATOR 1> STOCK PRICE ($): 1266.78 2> CURRENT DIVIDENDS ($): 61.56 3> CURRENT EARNINGS ($): 107.87 4> STOCK BETA: 1 5> EQUITY RISK PREMIUM (%): 6.2 6> T-BILL RATE (%): 7.3 7> PAYOUT RATIO (%): 57.07 8> REQUIRED RETURN (%): 13.5 9> DIVIDEND GROWTH (%): 8.64 10> DIVIDEND YIELD (%): 4.86 11> PRICE/EARNINGS RATIO: 11.74 --> STOCK VALUATION ($): 1376.23 ENTER 1-11 TO MODIFY THAT VARIABLE, 12 TO REFIGURE ALL DATA, OR 0 TO QUIT? (The above valuation figure and the ones below differ slightly from the figures given in the Journal article due to rounding error. Note that for stocks with zero current dividends, the expected price/earnings ratio is assumed to equal the current p/e ratio.) At this point, if you are dissatisfied with the answer or wish to see the effect on the stock valuation results of changing one or more variables, enter 1 through 11 to change the variable(s) in question. To give an example from the Journal article, enter 9, substitute 4.1% as the new dividend growth rate, then enter 10, and substitute 5.6% as the new dividend yield. The stock valuation changes to $1,144.35. As another example from the article, now substitute the values 10% and 5% for the variables 9 and 10. The revised valuation is $1,354.32. Note that if you want to modify more than one variable, you should modify lower numbered variables before higher numbered variables (ignore any intermediate results). Thus, if you want to find the combined effect of changing the equity risk premium, payout ratio, and dividend yield, you should modify variables 5, 7, and 10 in that order. The reason that care must be taken to modify variables in the correct order is that higher-numbered variables are more or less dependent on lower-numbered variables (excepting the first six variables, which are all independent and therefore separated from the dependent variables below them). If you substitute a different p/e ratio, for example, in terms of the model, the p/e ratio is made inconsistent with several of the variables listed above it. If you subsequently modify the payout ratio (thus breaking the link with the indicated current dividends and current earnings), that will affect the p/e ratio, which depends on the payout ratio for its derivation. Since variables 4 through 11 all involve expectations about the future, there is nothing at all wrong with substituting values arrived at from outside the model (whether by formal analysis, educated guess, or gut feeling); but such action might render one or more of the displayed figures inconsistent with the underlying model, and in that case one should disregard variables that are outside the scope of current analysis. (If ever you want to ensure that all of the figures displayed on the screen are completely consistent with the underlying model, then select option 12 to refigure all the data.) In the final analysis, you must decide how much faith to place in the program and the method. Robert Osterlund