It is common practice in security analysis to modify the basic dividend growth model by allowing more than one stage of growth, with the growth factors being different in the different stages. As an example consider company Z. which currently distributes dividends of $\$ 10 \mathrm{M}$ annually. The dividends are expected to grow at the rate of $10 %$ for the next 5 years and at a rate of $5 %$ thereafter.

(a) Using a dividend discount approach with an interest rate of $15 %$, what is the value of the company?

(b) Find a general formula for the value of a company satisfying a two-stage growth model. Assume a growth rate of $G$ for $k$ years, followed by a growth rate of $g$ thereafter, and an initial dividend of $D_{1}$.