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%.