Dividend Discount Model Calculator

Dividends per Share ($):

Risk-Free Rate (%):

Beta:

Market Risk Premium (%):

Dividend Payout Ratio (%):

Return on Equity (%):

Expected Growth Rate (%):

Expected Dividend ($):

Cost of Equity (%):

Present Stock Value ($):

1. What is the Dividend Discount Model Calculator?

Definition: The Dividend Discount Model Calculator computes the present value of a stock using the Gordon Growth Model (GGM), a popular variant that assumes dividends grow at a constant rate in perpetuity. It calculates the expected dividend, cost of equity, and expected growth rate based on provided financial inputs.

Purpose: Used by investors to assess the intrinsic value of a stock based on future dividends, aiding in decisions to buy, hold, or sell shares.

2. How Does the Calculator Work?

The calculator uses the following formulas:

$ EGR = (1 - DPR) \times ROE $

$ ED = DPS \times (1 + EGR) $

$ CE = R_f + \beta \times (R_m - R_f) $

$ PSV = \frac{ED}{CE - EGR} $

Where:

$ PSV $: Present Stock Value ($);
$ ED $: Expected Dividend ($);
$ CE $: Cost of Equity (%);
$ EGR $: Expected Growth Rate (%);
$ DPS $: Dividends per Share ($);
$ R_f $: Risk-Free Rate (%);
$ \beta $: Beta (stock volatility relative to market);
$ R_m - R_f $: Market Risk Premium (%);
$ DPR $: Dividend Payout Ratio (%);
$ ROE $: Return on Equity (%).

Steps:

Enter the dividends per share (e.g., $2).
Enter the risk-free rate (e.g., 2.4).
Enter the beta (e.g., 0.47).
Enter the market risk premium (e.g., 5.6).
Enter the dividend payout ratio as a percentage (e.g., 50).
Enter the return on equity (e.g., 10).
Calculate the expected growth rate: $ EGR = (1 - DPR) \times ROE $.
Calculate the expected dividend: $ ED = DPS \times (1 + EGR) $.
Calculate the cost of equity: $ CE = R_f + \beta \times (R_m - R_f) $.
Calculate the present stock value: $ PSV = \frac{ED}{CE - EGR} $.
Display the expected growth rate (%), expected dividend ($), cost of equity (%), and present stock value ($), formatted appropriately.

3. Importance of Dividend Discount Model Calculation

Calculating the present stock value is essential for:

Investment Decisions: Helps investors determine if a stock is undervalued (when $ PSV > $ market price) or overvalued (when $ PSV < $ market price).
Valuation Benchmarking: Provides a theoretical fair value based on dividend growth, useful for comparing against market prices.
Financial Analysis: Assists in evaluating a company’s dividend policy, growth potential, and required return on equity.

4. Using the Calculator

Example 1: Calculate the present stock value with $ DPS = \$2 $, $ R_f = 2.4\% $, $ \beta = 0.47 $, $ MRP = 5.6\% $, $ DPR = 50\% $, $ ROE = 10\% $:

$ DPS $: $2;
$ R_f $: 2.4% (0.024);
$ \beta $: 0.47;
$ MRP $: 5.6% (0.056);
$ DPR $: 50% (0.5);
$ ROE $: 10% (0.10);
$ EGR $: $ (1 - 0.5) \times 0.10 = 0.05 $ (5%);
$ ED $: $ 2 \times (1 + 0.05) = 2 \times 1.05 = 2.10 $;
$ CE $: $ 0.024 + 0.47 \times 0.056 = 0.024 + 0.02632 = 0.05032 $ (5.032%);
$ PSV $: $ \frac{2.10}{0.05032 - 0.05} = \frac{2.10}{0.00032} \approx 6562.50 $.

Result: Expected Growth Rate = 5.0000%, Expected Dividend = $2.10, Cost of Equity = 5.0320%, Present Stock Value = $6,562.50.

Example 2: Calculate the present stock value with $ DPS = \$5 $, $ R_f = 3\% $, $ \beta = 1.2 $, $ MRP = 7\% $, $ DPR = 40\% $, $ ROE = 12\% $:

$ DPS $: $5;
$ R_f $: 3% (0.03);
$ \beta $: 1.2;
$ MRP $: 7% (0.07);
$ DPR $: 40% (0.4);
$ ROE $: 12% (0.12);
$ EGR $: $ (1 - 0.4) \times 0.12 = 0.6 \times 0.12 = 0.072 $ (7.2%);
$ ED $: $ 5 \times (1 + 0.072) = 5 \times 1.072 = 5.36 $;
$ CE $: $ 0.03 + 1.2 \times 0.07 = 0.03 + 0.084 = 0.114 $ (11.4%);
$ PSV $: $ \frac{5.36}{0.114 - 0.072} = \frac{5.36}{0.042} \approx 127.62 $.

Result: Expected Growth Rate = 7.2000%, Expected Dividend = $5.36, Cost of Equity = 11.4000%, Present Stock Value = $127.62.

5. Frequently Asked Questions (FAQ)

Q: What is the Gordon Growth Model?
A: The Gordon Growth Model calculates the present stock value ($ PSV $) by discounting an infinite stream of dividends, where the expected dividend ($ ED $) grows at a constant rate ($ EGR $), divided by the cost of equity ($ CE $).

Q: Why must the cost of equity exceed the growth rate?
A: The cost of equity ($ CE $) must exceed the expected growth rate ($ EGR $) to ensure a positive denominator, avoiding undefined or negative stock values.

Q: How are the inputs derived?
A: $ EGR $ is calculated as $ (1 - DPR) \times ROE $, $ ED $ as $ DPS \times (1 + EGR) $, and $ CE $ as $ R_f + \beta \times (R_m - R_f) $, using provided financial data.