Dividend Discount Model (DDM)

This model assumes that dividends grow at a constant rate $g$ thus:

$$\text{Price}=\frac{Di{v}_1}{1+r_e}+\frac{Di{v}_1(1+g)}{(1+r_e{)}^2}+\frac{Di{v}_1(1+g{)}^2}{(1+r_e{)}^3}+...=\frac{Di{v}_1}{r_e-g}$$

Where:

• $Di{v}_1$ = next year’s dividend
• $g$ = constant growth rate of dividends

Example of Single-Stage DDM

The firm’s current dividend is $1 and is expected to grow at 2% forever. The required return is 10%. Use the DDM to estimate the price of the firm’s common stock.

$$\text{Price}=\frac{1\times (1+0.02)}{0.10-0.02}=\frac{1.02}{0.08}=12.75$$

Estimating Growth Rate (g)

We can use the company’s Sustainable Growth Rate as a proxy for $g$.

Accounting for Non-Constant Growth

What if projected growth is not constant?

We use a Two stage model: initial high growth period and later low growth period.

Effectively, we manually calculate the Present Value of the non-constant growth period, and then prevent value the single stage portion after growth stabilizes.

IMPORTANT: When not given the ROE, we assume that the return is equal to what investors expect. That is $ROE=r_e$, ROE = discount rate.

Example of Two-Stage DDM

The firm’s current dividend is $1 and is expected to grow at 5% for the next two years and then at 2% forever. The required return is 10%

$$\text{Price}=\frac{1\times (1+0.05)}{(1+0.10{)}^1}+\frac{1\times (1+0.05{)}^2}{(1+0.10{)}^2}+\frac{\frac{1\times (1+0.05{)}^2\times (1+0.02)}{0.10-0.02}}{(1+0.10{)}^2}=0.95+0.91+11.62=13.48$$

Another Example

Now consider the common stock of Pinky Corp.

• The company expects net income per share over the next 4 years to be: $4.00, $4.40, $4.80, and $5.00
• Dividends per share over the next 5 years are expected to be $1.20, $1.40, $1.70, and $2.00

If the required return on Pinky stock is 8% per year, what should be Pinky’s current share price?

As well, let’s graph this data

Year	1	2	3	4
EPS	4.00	4.40	4.80	5.00
Dividend per share	1.20	1.40	1.70	2.00
Payout	30.0%	31.8%	35.4%	40.0%

Using the DDM:

$$P=PV(\text{1st Stage})+PV(\text{2nd Stage})$$ $$P=\frac{1.2}{(1.08{)}^1}+\frac{1.4}{(1.08{)}^2}+\frac{1.7}{(1.08{)}^3}+\frac{2.0}{(1.08{)}^4}+\frac{PV(\text{2nd Stage})}{(1.08{)}^4}$$

We estimate $g$ as follows, assuming $ROE=r_e=8\%$

$$g=8\%\times (1+40\%)=4.8\%$$

Note: we use the latest payout ratio as the best guess. You should use the most recent information

Doing out final calculation

$$PV(\text{2nd Stage})=\frac{D_5}{r_e-g}=\frac{2.0\times (1+4.8\%)}{8\%-4.8\%}=65.5$$

Now we return and find

$$P=\$53.27$$

Sensitivity

Like all valuation methods, this method is highly sensitive to our chosen $g$ and $r_e$. Thus we should run sensitivity on both. That is we can run a two-way excel data table between $g$ and $r_e$.