 The dividend discount model takes a simple assumption that the growth rate or the G will be constant forever whereas a firm across its life cycle stages passes through with different dividend profiles at each of the stage. Now these life cycle stages for the firm includes its early stage, its maturity stage and its terminal or declining stage. So far as the firm's early stage is concerned during this period there are ample profitable reinvestment opportunities in the firm itself but there are lower payouts for the shareholders by the firm correspondingly there are rapid growth in the firm. So far as the firm's later stage is concerned during this particular period of time the firm matures it has sufficient production capacity to meet the current market demand. Competitors are entering into the market it is harder for the firm to find attractive reinvestment opportunities so the company goes for higher dividend payout ratios and that reduces the dividend growth rate. Now during this scenario we can say that the multi-stage dividend discount model can be used to value a higher growth company. In multi-stage dividend discount models the simplest model is the two-stage model. This model works under two steps to value a particular firm and first step the present value of all dividends in the initial growth period is determined and in the second stage the constant dividend growth dividend discount model is used to value the remaining dividend stream of the dividends projected for a steady growth phase. Now to understand the application of two-stage growth model we have an example where we have dividend per share for four years from 2017 to 2020. Now we have forecast for 2020 in terms of dividend payout ratio that is 0.53 and ROE that is 19.5%. This means that we have a long term growth rate or the G here in this particular case and that G is equal to 9%. Now to determine the intrinsic value for 2016 we need to capitalize the dividend for 2017, dividend for 2018, dividend for 2019, dividend for 2020 and the sale price of the stock for the year 2020. We have four years cash flows here we need to capitalize these cash flows at the discount rate of the company's opportunity cost of capital but in our example the K or the discount rate is missing so we have to find it out. Now before finding the K we need to determine the stock price for the year 2020 which is not palatable in the question to determine the stock price for the year 2020. We need to use the constant growth dividend discount model. The formula is dividend for 2020 or D2020 over K minus G, D2020 we can find it out by multiplying the D2020 with the growth rate. But for K again we have no value but for G we have the value of 9% we have determined earlier. Now to determine the value of K we can use the KPM model. For KPM we have certain variables with us where risk free rate on long term tree rebonds which is equal to 2.5% market risk premium we have forecast it for 8%. The company's beta is 1.10 now using these values into the KPM model we have the value of K and that is equal to 11.3% now we will be using this K value in P 2020 to determine the stock price for the year 2020 and that comes to 75.83. Now we have determined the stock price at the end of year 2020 we can use this value into our dividend discount formula to determine the stock price for the year 2016 and that comes to 53.74 so with a little reverse calculation we have come to year 2016 and the price at this particular time of 2016 we have determined which is equal to 53.74 now assume actual stock price in year 2016 as 30.98 this means that now the stock is underpriced but if the actual growth rate in post 2020 period is 7% then the V0 for 2016 will be 29.93 and for that value the stock is overpriced so what we can conclude from these two computations we see that stock valuation needs to go for sensitivity analysis because the assumptions used to determine these inputs must be carefully examined by the investment analyst any small change in the input may yield intrinsic value substantially different from what it would be now we have multi-stage growth models such models allow a dividend purchase to grow at many rates as the firm matures many analysts under this particular case use three stage growth models assuming an initial period of high dividend growth a final period of sustainable growth and a transitional period between during which the dividend growth rates taper from initial high rate to the ultimate sustainable rate now to understand the multi-stage growth model we have an extended example here and in this extended example we have certain inputs for the company in the form of beta market risk premium risk rate cost of equity and the growth rate we have yearly data from 2017 to 2032 and the accompanied dividend per share we have here then we use the growth rate we see that the growth for initial phase is till 2021 which is 15.44 percent and the growth for the terminal year is only 6 percent and between these two growth rates the growth rate is declining during that transitional period now using these values we can determine the value of the dividend for the year 2032 and that is 103.57 dollars then we need to convert these values into the cash flows and we have the accompanied cash flows from 2017 to 2032 and the present value of these cash flows is equal to 35.7 dollars and this is basically V naught or the stock price of the company's stock for year 2017 and this we have computed using the constant dividend discount model