# 4.2. FCFF for multiple periods and a residual value

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

1. 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.
2. 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 FCFFn+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 FCFFn+1 cannot be obtained through the yearly forecasts, it is common practice to apply a growth rate g to the FCFFn.

• $${FCFF}_{n+1}={FCFF}_n\ast(1+g)$$
###### 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 35 175 225 265

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 FCFF6. The growth rate is:

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

• $$Business\ value=-14.140,87+1.574.925,87=1.560.785,00$$

#### Example case: Dutch Fabric Innovations

Dutch Fabric Innovations was able to estimate the FCFF for the first five years of its project and intends to know the prospective business value of the project. The FCFF obtained were:

 Values in EUR 2020 2021 2022 2023 2024 FCFF -153 278,41 172 771,15 670 478,29 1 893 373,16 3 530 494,02

The company previously estimated a WACC of 6.25% and, from this, it was able to calculate the following components:

 2020 2021 2022 2023 2024 WACC 0,0625 0,0625 0,0625 0,0625 0,0625 Discount factor 1,0625 1,1289 1,1995 1,2744 1,3541 Discounted FCFF -143 704,64€ 151 862,60€ 552 527,81€ 1 462 835,33€ 2 557 316,67€ Accumulated Discounted FCFF -143 704,64€ 8 157,96€ 560 685,77€ 2 023 521,10€ 4 580 837,77€

These components are essential to achieve the business value because it is through them that we get the NPV of the FCFF. According to the values in the table, we can see that the referred NPV is

• $$NPV=\ \frac{-153\ 278,41}{(1+0,0625)}+\frac{172\ 771,15}{(1+0,0625)^2 }+\frac{670\ 478,29}{ (1+0,0625)^3 }+\frac{1\ 893\ 373,16}{(1+0,0625)^4 }+\frac{3\ 530\ 494,02}{(1+0,0625)^5 }=4\ 580\ 837,77€$$

After the NPV, the only thing left to do is obtain the residual value.

We know that the inflation rate in the Netherlands is expected to be around 2% and the real growth rate is estimated to be around 1.5%, leading to a perpetuity growth of

• $$g\ =(1\ +\ 0.02)\times (1\ +\ 0.015)\ -\ 1=3,53$$%

With the perpetuity growth, we can the FCFF of 2025, as we expect the company to reach stability in the market in that year.

• $$FCFF2025\ =3\ 530\ 494,02\times (1\ +\ 0.0353)=3\ 655\ 120,46€$$

We finally have all the data needed to compute the residual value, which has a value of

• $$Residual\ Value=\frac{3\ 655\ 120,46}{(0.0625-0.0353)}\times \frac{1}{(1+0.0625)^5\ }=99\ 240\ 306,46€$$

Summing the NPV of FCFF with the residual value, we obtain the business value of

• $$Business\ Value\ =4\ 580\ 837,77\ +\ 99\ 240\ 306,46=103\ 821\ 144,23€$$

#### Example case: Golden Days

To obtain the business value of the franchise project, the franchisee of Golden Day estimated the FCFF for the first 5 years of the project, obtaining the following results:

 Values in USD 2019 2020 2021 2022 2023 FCFF -26 997,60 -31 928,58 223 939,88 220 068,69 265 351,16

Moreover, the company previously calculated the WACC and obtained the value of 7%, for all the years. Given this, it was possible to estimate the Accumulated Discounted FCFF:

 2019 2020 2021 2022 2023 WACC 0.07 0.07 0.07 0.07 0.07 Discount factor 1.07 1.14 1.23 1.31 1.40 Discounted FCFF -25 231,40$-27 887,66$ 182 801,65$167 889,35$ 189 191,71$Accumulated Discounted FCFF -25 231,40$ -53 119,06$129 682,59$ 297 571,94$486 763,65$

The Net Present Value of the FCFF estimated is then

• $$NPV=\ \frac{-26\ 997,60}{(1+0.07)}+\frac{-31\ 928,58}{(1+0.07)^2 }+\frac{223\ 939,88}{ (1+0.07)^3 }+\frac{220\ 068,69}{(1+0.07)^4 }+\frac{265\ 351,16}{(1+0.07)^5 }=486\ 763,65$$

However, the NPV is not enough to calculate the business value. We also need to calculate the residual value. The residual value is a perpetuity and, to compute it, we need the perpetuity growth rate and an estimation of the FCFF for the sixth year of the project, that is, the FCFF of 2024.

From 2024 on, Golden Days is expected to have a stable growth. Considering an inflation rate of 1.6% and a real growth rate of 2.3%, we have a perpetuity growth of

• $$g\ =(1\ +\ 0.016)\ (1\ +\ 0.023)\ -\ 1=3,9$$%

Now that we have the perpetuity growth, we can estimate the FCFF of 2024 from the FCFF of 2023:

• $$FCFF2024\ =\ 265\ 351,16\ \times (1\ +\ 0.039)\ =\ 275\ 699,86\$$

We finally have all the data needed to compute the residual value, which has a value of

• $$Residual\ Value=\frac{275\ 699,86}{(0.07-0.039)}\times \frac{1}{(1+0.07)^5\ }=6\ 340\ 973,76$$

Summing the NPV of the FCFF with the Residual Value, we can finally evaluate the Business Value:

• $$Business\ Value\ =486\ 763,65+6\ 340\ 973,76=6\ 827\ 737,41$$

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.