# 4.1.2. 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:

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

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