# 4.1.2. FCFF for multiple periods and a residual value

This approach is used in CASFLO APP feasibility analysis. It comprises two segments:

- An estimate of the NPV of the FCFF for a given number of years (usually between 3 to 5 years), taken from a forecast of the financial statements.
- A residual value (perpetuity).

- \(Business\ vale=NPV\ of\ FCFF+Residual\ value\)

The NPV of FCFF corresponds to the accumulated discounted FCFF:

- \(NPV\ FCFF=\frac{{FCFF}_t}{\left(1+WACC\right)^t}+\frac{{FCFF}_{t+1}}{\left(1+WACC\right)^{t+1}}+\ldots+\frac{{FCFF}_n}{\left(1+WACC\right)^n}\)

- \(Residual\ value=\frac{{FCFF}_{n+1}}{(WACC-g)}\frac{1}{{(1+WACC)}^n}\)

The first fraction of the residual value is a perpetuity of the FCFF_{n+1} (the year right after the forecasts); that perpetuity is at the value of year n. The second fraction sets the discount factor to calculate the present value of the perpetuity.

Since the FCFF_{n+1} cannot be obtained through the yearly forecasts, it is common practice to apply a growth rate g to the FCFF_{n}.

- \({FCFF}_{n+1}={FCFF}_n\ast(1+g)\)

###### Example – 5-year NPV of FCFF and residual value

Kevin has a startup project and he was able to estimate the FCFF for the first five years of business. At the sixth year, he expects the company to be within a stable position and that it will only grow at a constant 0,25% real rate. The inflation rate is of 1%. These are the FCFF of the three first years that he has estimated:

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

FCFF | -525.000 | 35.000 | 175.000 | 225.000 | 265.000 |

The WACC of Kevin’s company is 1,25%.

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

FCFF | -525.000 | 35.000 | 175.000 | 225.000 | 265.000 |

WACC | 0,1125 | 0,1125 | 0,1125 | 0,1125 | 0,1125 |

Discount factor | 1,1125 | 1,23765625 | 1,376892578 | 1,531792993 | 1,704119705 |

Accumulated FCFF | -525.000,00 | -490.000,00 | -315.000,00 | -90.000,00 | 175.000,00 |

Discounted FCFF | -471.910,11 | 28.279,26 | 127.097,79 | 146.886,69 | 155.505,51 |

Accumulated discounted FCFF | -471.910,11 | -443.630,85 | -316.533,07 | -169.646,38 | -14.140,87 |

The NPV of the five-year forecast is -14.140,87 EUR.

To compute the residual value, we need an estimate on the FCFF_{6}. The growth rate is:

- \(g=\left(1+inf\right)\left(1+real.g\right)-1\)
- \(g=\left(1+0,01\right)\left(1+0,0025\right)-1=0,012525\)
- \({FCFF}_6=265.000\times(1+0,012525)=268.319,13\)
- \(Residual\ value=\frac{268.319,13}{(0,1125-0,012525)}\times\frac{1}{{(1+0,1125)}^5}=1.574.925,87\)

The business value is:

- \(Business\ value=-14.140,87+1.574.925,87=1.560.785,00\)

Note how it would be difficult to use a straight perpetuity to this example. With a significant change in the cash-flows in every year during the first 5 years, the decision of which FCFF to use would be complicated. That is why the best option is to forecast the business until stability and then employ the residual value calculation.