I have been looking to understand the H-model in finance, that is used for stock price valuation. In particular, I wanted to formally derive the final formula: PV=Dr−g2[1+g2+H2(g1−g2)]PV=\frac{D}{r-g_2}\left[1+g_2+\frac{H}{2}(g_1-g_2)\right] Here PV>0PV>0 is the present value (price) of the stock, D>0D>0 is the constant dividend payment that is paid forever, r∈(0;1)r\in(0;1) is the required rate of return on the stock and the growth rate of the stock follows a pattern: it starts with a growth rate of g1∈(0;1)g_1\in(0;1) and at time H≥0H\ge0 the growth rate switches to g2<g1g_2<g_1 , g2∈(0;1)g_2\in(0;1) . When H=0H=0 the model is equivalent to the Gordon growth model, where we simply evaluate a perpetuity (perpetual stream of discounted and growing dividends). In general the present value should be PV=D1+g11+r+D(1+g11+r)2+...+D(1+g11+r)H−1+D(1+g11+r)H+D(1+g1)H(1+g2)(1+r)H+1+D(1+g1)H(1+g2)2(1+r)H+2+...=D∑i=1H(1+g11+r)i+D(1+g11+g2)H∑i=H+1∞(1+g21+r)iPV=D\frac{1+g_1}{1+r}+D\left(\frac{1+g_1}{1+r}\right)^2+...+D\left(\frac{1+g_1}{1+r}\right)^{H-1}+D\left(\frac{1+g_1}{1+r}\right)^{H}+D\frac{(1+g_1)^{H}(1+g_2)}{(1+r)^{H+1}}+D\frac{(1+g_1)^{H}(1+g_2)^2}{(1+r)^{H+2}}+...=D\sum_{i=1}^{H}{\left(\frac{1+g_1}{1+r}\right)^i}+{D\left(\frac{1+g_1}{1+g_2}\right)^{H}\sum_{i=H+1}^{\infty}{\left(\frac{1+g_2}{1+r}\right)^i}} I evaluated it to be PV=D1+g1r−g1(1−(1+g11+r)H−1⋅g1−g2r−g2)PV=D\frac{1+g_1}{r-g_1}\left(1-\left(\frac{1+g_1}{1+r}\right)^{H-1}\cdot\frac{g_1-g_2}{r-g_2}\right) The paper I found on https://wenku.baidu.com/view/07ef434ae45c3b3567ec8b84.html agrees with me, and it states that the expression I computed can be approximated using the formula of the H-model I showed at the beginning, but does not give a derivation. The paper only gives a strange footnote 'The formal derivation of the H-model ... is available from the authors', but no further elaboration is given. I would be glad to receive any hints as to what technique one should use in order to arrive at the final result