Stock Valuation Based on Earnings The PV approach to stock valuation discounts dividends Dt not earnings Et X P0 t Dt 1 r t X Et 1 r t instead we would overestimate X Et Dt the value of the stock by the PV of retained earnings 1 r t If we were to discount earnings t t Of course if X the entire earnings are distributed as dividends each year Et Et In this case the firm does not invest any of its own Dt then P0 1 r t t capital to grow it is thus plausible to assume that dividends earnings stay constant over time Call this SCENARIO A Then applying the perpetuity formula E1 D1 P0 r r Thus in this case the Price Earnings ratio is given by P0 1 E1 r 1 Yardeni s Fed Model is similar as it says P0 1 E1 r10 where r10 is the interest rate on 10 year government bonds SCENARIO B Now assume that the firm retains some earnings but invests them at the required rate of return r in other words the firm invests its earnings in 0NPV investments Clearly this cannot change the value of stock that is the PV of the dividends Thus the formulas P0 and P0 E1 1 r E1 r 2 still apply Of course now both earnings and dividends will grow 1 Example E1 10 r 0 1 I am using always per share values In scenario A P0 10 0 1 100 In scenario B applying the formula 2 once again P0 10 0 1 100 Magically this will be true however much the firm retains and whatever the resulting dividend pattern is For example suppose the firm retains always 50 of its earnings and pays out 50 as its dividends Thus D1 5 Then one can show that if retained earnings make a return of r 10 as assumed and if dividends grow at a constant rate g g 0 5 0 1 0 05 3 Of course the stock price must again be equal to the PV of future dividends Indeed applying the Gordon growth formula we get P0 5 D1 100 r g 0 1 0 05 Equation 3 is a special case of the following formula g 1 4 t where D Et is the payout ratio assumed constant over time and 1 Et Dt is the retention ratio and is the return on retained earnings See Et section 5 5 of the textbook for further explanation equation 4 is the same as equation 5 8 there Assuming that the firm s investments have zero NPV is the same as assuming that r You don t need to understand equation 4 fully but you should understand the basic intuition behind it earnings and hence dividends will grow the more rapidly the more the firm invests here for simplicity all investment is assumed to come from retained earnings and the more profitable those investments are 2 SCENARIO C Suppose now that the firm keeps reinvesting its earnings in positive NPV projects Specifically suppose that the return on its retained earnings is 12 rather than 10 as in B Then its stock price will be accordingly higher Indeed the constant growth rate will now be g 0 5 0 12 0 06 hence P0 5 D1 125 r g 0 1 0 06 The di erence P0 Er1 125 100 25 is the Net Present Value of Growth Opportunities NPVGO SCENARIO D If the firm keeps making bad investments the NPVGO may be negative For example if the return on its investments is only 8 less than investor s required rate of return of 10 it destroys value Indeed the constant growth rate will now be g 0 5 0 08 0 04 hence P0 5 D1 83 33 r g 0 1 0 04 yielding an NPVGO of 16 67 Scenarios C and D contain an important general lesson earnings growth justifies higher P E ratios only if it is based on genuinely profitable i e positive NPV investments A firm s growth is however often profit neutral zero NPV for example this is typically the case if the firm grows by acquiring other companies 3