# 4.1. Valuing a company or project through FCFF

Valuation of companies and projects through FCFF presupposes that the cash flows of future years can be made available to holders of capital. The accumulation of future cash flows will return the business value: the value that will be created by the company’s operations and investment for capital holders.

Remember: while working with forecasts of the FCFF, the business value is itself based on assumptions and not a statement that the forecasted FCFF will become true as assumed.

As in any valuation of financial flows, it is necessary to incorporate the cost of capital, so that the future FCFF have a common correspondence to a present value. Because the FCFF corresponds to the cash flows available to the entirety of capital, the adequate discount factor is the WACC. Summarizing, the business value corresponds to the sum of the discounted FCFF:

- \(Business\ value=\ \frac{{FCFF}_1}{{(1+WACC)}^1}+\frac{{FCFF}_2}{{(1+WACC)}^2}+\frac{{FCFF}_3}{{(1+WACC)}^3}+\frac{{FCFF}_4}{{(1+WACC)}^4}+\ldots\)

Simplifying:

- \(Business\ value=\sum_{i=1}^{\infty}\frac{{FCFF}_t}{(1+{WACC)}^t}\)

**Example – Calculating the business value**

Kimi has a business project that he expects will earn him the following array of FCFF:

Year | 1 | 2 | 3 | 4 | 5 |

FCFF | -500.000 EUR | 450.000 EUR | 350.000 EUR | 250.000 EUR | 150.000 EUR |

After these five years, the project will end and no further FCFF will be generated. He has estimated that the WACC of his project is 11,35%. The business value of the project is calculated the following way:

- \(Business\ value=\ \frac{500.000}{{(1+0.1135)}^1}+\frac{450.000}{{(1+0.1135)}^2}+\frac{350.000}{{(1+0.1135)}^3}+\frac{250.000}{{(1+0.1135)}^4}+\frac{150.000}{{(1+0.1135)}^5}\)

Year | 1 | 2 | 3 | 4 | 5 |

FCFF | -500.000 | 450.000 | 350.000 | 250.000 | 150.000 |

Cost of capital | 0,1135 | 0,1135 | 0,1135 | 0,1135 | 0,1135 |

Discount factor | 1,1135 | 1,239882 | 1,380609 | 1,537308 | 1,711792 |

Discounted FCFF | -449.035 | 362.938 | 253.511 | 162.622 | 87.627 |

Accumulated discounted FCFF | -449.035 | -86.097 | 167.414 | 330.036 | 417.664 |

The value business value, as the sum of the discounted FCFF, is: 417.664 EUR. The payback (of the discounted FCFF) of the project is the third year.

The previous example illustrated the valuation of only 5 years of business (that was a case assumption). But there are situations in which the valuation is for a longer extent of time. It is a common practice to value a businesses on a continuous basis, meaning that the company does not have a foreseeable end. Although that can be debatable, such assumption is grounded on the belief that a business provides goods and services that are always necessary. Furthermore, due to the minor relevance of the present value of the cash flows of the years that are further way in time (consequence of the cost of capital), the business value is usually less affected by the later years.

###### Example – the discounted value of FCFF through the years

Take company AAA. It is forecasted to generate a constant yearly FCFF of 100 EUR per year. It was also assumed a WACC of 5%. The following graph represents the present value contribution of each year for a 100 year period.

The “incline” of the curve is influenced by the cost of capital. If the WACC was 10% instead of 5%, it would increase the “speed” at which the present value of the cash flow of each year would become smaller.

Remember that this example is just a simplification that does not consider any growth or any other assumption.

Taking into consideration the timeline of value, while valuing a business or project through FCFF you can:

Next Section: 4.1.1. Use a perpetuity on a FCFF