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 -525.000 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 FCFF6. The growth rate is:

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

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.