# 3.2.1. Dividend-Discount Model (DDM)

As the name states it, this model is based on the prices of shares and dividends of public companies. Taking dividends as the return that investors receive for their investment, this model assumed that the value of the company corresponds to the discounted sum of dividends. Investors value less the dividends that they will receive in the future. If the foreseen dividend cash flow is constant (the dividend will not grow), the less valuable will those dividends be to an investor. Using the Present Value (PV) financial concept, each investor will value each individual dividend:

- \(PV_{div,t}=\frac {Div} {(1+r_e)^t}\)

Where:

- Div: dividend value;
- r
_{e}: return on equity; - t: period.

The dividend is one of the essential element that is usually available, either through the company’s website and financial disclosure information or through platforms of financial information, such as yahoo finance. Nevertheless, if the dividend is not known, you can calculate it through a payout ratio over the net income:

- \(Div=\frac{NI} {\text{payout ratio}} \times {NS}\)

Where:

- NI: net income;
- NS: number of shares.

This model assumes that investors believe each share will generate dividends into perpetuity. As such, the equilibrium price would be one the one that equal the price of the share to the sum of all discounted future dividends.

- \(P=\frac{Div}{{(1+r_e)}^1}+\frac{Div}{{(1+r_e)}^2}+\frac{Div}{{(1+r_e)}^3}+\dots +\frac{Div}{{\left(1+r_e\right)}^{\infty }}=\sum^{\infty }_{t=1}{\frac{Div}{{(1+r_e)}^t}}\)

That would be the maximum price that an acquiring investor would be willing to pay for the share. If the investor pays less for the share he will be having a gain through his investment and if he/she pays more he will be losing value. Likewise, a seller would not want to sell for less than the sum of the discounted cash flows, for he/she would be worse off; but if selling at a higher price then he/she would be having a gain.

If all investors have the same investment profile and risk aversion, then each and every asset will be valued at the same price by every investor. In the real world, each investor values the assets differently (if only marginally) from every other investor.

Using some financial calculus knowledge, the sum of the discounted dividends into perpetuity can be simplified through a perpetuity.

- \(P=\sum^{\infty }_{t=1}{\frac{Div}{{(1+r_e)}^t}=\frac{Div}{r_e}}\)

Taking the price as the market equilibrium at a given moment in time, under DDM, to know the cost of equity at which each share is being discounted by the market, you can invert the equation.

- \(r _e=\frac{Div _1}{P}\)

The r_{e} calculated through the DDM corresponds to the cost of equity attributed by the market and not by an individual investor.

###### Example – Calculating the cost of equity through the DDM

The following table presents the share prices and the dividends for each of the Fortix10 listed share companies. The rightmost column the presents the cost of equity for each company, as calculated through the DDM.

Fortix 10 | Share price (EUR) | Dividend (EUR) | R_{e} |

AA | 1,5 | 0,25 | 16,67% |

BB | 10,82 | 0,65 | 6,01% |

CC | 3,5 | 0,32 | 9,14% |

DD | 4,12 | 0,5 | 12,14% |

EE | 4,64 | 0,7 | 15,09% |

FF | 20,72 | 2,15 | 10,38% |

GG | 80,71 | 5 | 6,20% |

HH | 15,03 | 1,25 | 8,32% |

II | 18,59 | 1,5 | 8,07% |

JJ | 9,87 | 0,75 | 7,60% |

For non-listed companies it is not possible to calculate the market’s cost of equity:

- There is no publicly available price of the share.
- In most small to medium sized companies (and even in large ones) dividend distribution often does not take place and when it does, it hardly is constant or even known to the public.

The alternative is to use estimates and proxys based on public companies with similar characteristics or industry proxys.

Next Section: 3.2.2. Gordon Growth Model