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101 Concepts for the Level I Exam

Concept 77: Gordon (Constant) Growth Model and Multistage Dividend Discount Models


Gordon growth model (Constant growth dividend discount model): assumes that dividends will grow indefinitely at a constant growth rate. The value of the stock is calculated as:

     $$V_0={{D_1}\over {r\ -\ g}}$$

Calculate the value of a stock that paid a $10 dividend last year, if dividends are expected to grow forever at 6% and the required rate of return on equity is 8%.

Solution:

D1 = D0 x (1 + dividend growth rate) = $10 x 1.06 = $10.6

     $$V_0={{\$10.6}\over {0.08-\ 0.06}}=\$530$$

g is the sustainable growth rate i.e. rate at which earnings and dividends can continue to grow indefinitely. It is calculated as:

g = retention rate * ROE

Multi-stage dividend discount model: used for companies with high growth rate over an initial few number of periods followed by a constant growth rate of dividends forever.

     $$V_0={\sum{.}}^n_{t=1}{{{D_0(1+g_s)}^t}\over {{\left(1+r\right)}^t}}+{{V_n}\over {{\left(1+r\right)}^n}}$$

 

     $$V_n={{D_{n+1}}\over {r\ -\ g}}$$

Dividends of a company are expected to grow at 15% per year for three years, after which they are expected to grow at a constant rate of 5% per year. The last dividend paid was $2. Calculate the value of the stock of this company if the required rate of return is 10%.

Solution:

D1 = $2 x 1.15 = $2.3

D2 = $2.3 x 1.15 = $2.645

D3 = $2.645 x 1.15 = $3.042

D3 will grow at a constant growth rate of 5%. Hence,

     $$V_2={{\$3.042}\over {0.1-\ 0.05}}=\$60.84$$

Finally,

     $$V_0={{\$2.3}\over {1.1}}+{{\$2.645}\over {{1.1}^2}}+{{\$60.84}\over {{1.1}^2}}=\$54.55$$