Understanding the Constant Growth Theorem in Excel

The Constant Growth Theorem is another name for Uzawa’s Theorem, which is a theorem in economic growth theory that describes the conditions for balanced growth1. Balanced growth is a situation where output, capital, and consumption grow at constant rates, and the capital-output ratio, the interest rate, and the factor shares remain constant.

The theorem consists of two parts. The first part states that, if the economy is on a balanced growth path, then the growth rates of output, capital, and consumption must be equal, and the saving rate and the depreciation rate must be constant2. The second part states that, if the production function exhibits constant returns to scale and has the form Y = F(K, AL), where A is technology and L is labor, then the only type of technological change that can support balanced growth is labor-augmenting, meaning that technology affects output only through multiplying labor.

The Constant Growth Theorem shows the limitations of the Solow and Ramsey models, which assume balanced growth and labor-augmenting technology. In reality, balanced growth may not be attainable or desirable, and technological change may not be labor-augmenting. Therefore, the theorem should be applied with caution and complemented with other models that allow for more general forms of technological change and growth dynamics.

Basic Theory:

The Constant Growth Theorem formula is represented as follows:

$P_0 = \frac{D_0 \times (1 + g)}{r - g}$

Where:

$P_0$ is the current stock price,
$D_0$ is the most recent dividend payment,
$r$ is the required rate of return, and
$g$ is the constant growth rate of dividends.

Procedures:

Gather Data: Collect the most recent dividend payment ( $D_0$ ), the required rate of return ( $r$ ), and the constant growth rate ( $g$ ).
Apply the Formula in Excel: Use the Constant Growth Theorem formula in an Excel spreadsheet to calculate the current stock price ( $P_0 )$ .
Scenario: Let’s consider a scenario with the following data:
- $D_0$ (most recent dividend) = $2.50
- $r$ (required rate of return) = 8%
- $g$ (constant growth rate) = 5%

Excel Table:

Data	Values
Most Recent Dividend	$2.50
Required Rate of Return	8%
Constant Growth Rate	5%

Excel Formula:

In Excel, you can use the following formula to calculate $P_0$ :

=($B$2 * (1 + $B$3)) / ($B$4 - $B$3)

Calculation:

=($2.50 * (1 + 5%)) / (8% - 5%)

Result:

The calculated stock price ( $P_0$ ) is $83.33.

Other Approaches:

Two-Stage Dividend Growth Model: If the company is expected to have different growth rates in the future, a two-stage model can be applied.
Sensitivity Analysis: Perform sensitivity analysis by changing the growth rate and observing its impact on the stock price.
Monte Carlo Simulation: Utilize Monte Carlo simulation to account for uncertainty in growth rates and required rates of return.