### Stock price sensitivity to discount rate and dividend growth rate variations

 DDM is extremely useful for quantifying stock price sensitivity to changes in discount or dividend growth rate. Recall the NPV formula where r is the discount rate and g is the dividend growth rate. Deriving Equation (1) with respect to discount rate r give Equation (2) quantifies how sensitive the NPV is to variations in discount rate. Dividing Equation (2) by NPV, we obtain the relative value sensitivity to the discount rate: Equation (3) shows how much the valuation changes if the discount rate changes. Recall that the discount rate is the rate of return that investors demand from investments. This can change as market psychology changes for example due to recession, change in interest rates or unforeseen crisis/war. The historical discount rates for stock market have ranged from 6% to 19%. Currently, the market discount rate is ~7% which is low by historical standards. This does not mean that stock prices will fall – it is possible that investors are so in love with owning stocks that they will continue buying them even with the meager 7% return. But should the interest rates increase from the current historical lows or should the investors get nervous about possible recession, it is almost certain that investors will demand higher returns from stocks which require that the price must come down. Equation (3) tells as how much stock prices much fall so that they are priced to offer higher returns. The results are very revealing. For example, for the stock market (SP500, Y = 2%, g = 5%), Equation (3) shows that if the discount rate changes by just 1 percentage point, then the NPV drops by a whopping -1/(0.07-0.02)=-50%! This type of price action is not unheard of and explains wide variations in the stock market price. On the other hand, same change for a dividend stock (T, Y=6% and g=2%) gives a more modest drop of -1/(0.08-0.02)= -17%. This is why dividend stocks are more much more stable investments.A similar analysis for dividend growth rate gives Equation (4) can be used to analyze what happens if the market changes the assumptions regarding the future dividend growth rate g. For example, if a dividend growth company (Y = 3%, g = 6%, r = Y+g = 9%) suddenly stagnates and the growth rate drops by 2% to 4%, the stock price is pulverized by -42(0.09-0.06)=-67%. In other words, valuation of dividend growth companies is highly sensitive to growth rate assumption. In comparison, similar 2% drop for a dividend stock (for examle T, Y=6% and g=2%) gives a more modest drop of -2/(0.08-0.02)= -34%.Summary: The value of growth stocks is very sensitive to changes in discount rate and dividend growth rate. This makes them volatile investments. One of the most dangerous investment is a dividend growth stock that unexpectedly fails to grow as the stock will take heavy beating. High dividend yield stocks are less volatile investments.