# 4.1. Use a perpetuity on a FCFF

Valuing a business through a perpetuity is advisable when in the presence of the following features:

• There is a foreseeable stability of demand in time.
• The business and industry are in a mature state and it is not expected to happen any significant growth, at least in the closer years.
• It is not foreseeable a significant modification in the technology, in the industry, on the regulation or any other feature that would significantly alter the productions costs.

This approach assumes that a fixed FCFF will grow at the rate g and discounted through a WACC:

• $$Business\ value=\frac{{FCFF}_1}{WACC-g_{FCFF}}$$

Where:

gFCFF: growth rate of the FCFF.

Remember that the perpetuity should be calculated with the FCFF of the next period in time:

• $${FCFF}_1={FCFF}_0\times(1+g_{FCFF})$$

It is a relatively simple approach to calculate and one that does give much freedom to adjust the forecast of the FCFF according to foreseeable economic conditions. In circumstances with a foreseeable growth, restructuring or changes in the economic cycles of the company, it is advisable to opt for solutions that stabilize the FCFF before applying a perpetuity for the remaining periods.

#### Estimating the growth rate (gFCFF)

A correct growth rate estimation is quite relevant, as in most cases the value of the perpetuity can be quite sensitive to changes of the growth rate.

Important: remember that the growth rate is not the growth rate of the net revenue. It is the growth rate of FCFF. Although there is a relation between both variables, in most situations, FCFF and net revenue will have different growth rates.

Different practices may be undertaken to determine the growth rate:

• Combine inflation rate with a real growth rate.
• Use the ROIC.
• Carefully analyze the past growth of the FCFF, and use it as a reference for future an evolution (beware that business that have a high growth rates are likely to end once a business reaches a certain dimension).
##### Combine inflation rate and real growth rate

The estimate of both variables must be taken under judicious care.

• $$g_{FCFF}=\left(1+inf\right)\left(1+{real\ g}_{FCFF}\right)-1$$

Where:

• Inf: inflation rate.
• real.gFCFF: real growth rate of the FCFF.
###### Example – Using a perpetuity to compute the business value

Felipe’s company had a FCFF of 345.750 EUR in 2017 and when he asked a professional assessment of his WACC, he was handed 5,33% estimate. The most likely expectation is that the company will grow at a 0,25% rate every year. He wants to know the business value of his company. The inflation forecasts point to an average of 1,25%.

 Variables FCFF 345.750 WACC 5,33% Real gFCFF 0,25% Inf 1,25%

First, we need to know the growth rate. We can use the real growth rate formula and inflation.

• $$g=\left(1+inf\right)\left(1+real.g\right)-1$$
• $$g=\left(1+0,0125\right)\left(1+0,0025\right)-1=0.01503$$

Once g is known, we can calculate the FCFF1

• $${FCFF}_1={FCFF}_0\times(1+g)$$
• $${FCFF}_1=345.750\times\left(1+0,01503\right)=\ 350.947,05$$

We can now calculate the business value:

• $$Business\ value=\frac{{FCFF}_1}{WACC-g}$$
• $$Business\ value=\frac{350.947,05}{0,0533-0,01503}=9.170.591,01\ EUR$$

Be aware that the perpetuities can be quite sensitive to changes in the discount factor or on the growth rates of the FCFF. Hence, you should be quite careful while deciding the best values for your inputs.

###### Example – The sensitivity of the perpetuity to different discount factors and growth rates

Take a company with an estimated FCFF of 100.000€. This would be the business value returns for different WACC, while keeping the growth rate fixed.

 FCFF 100.000 100.000 100.000 100.000 100.000 100.000 10.000 10.000 WACC 5,00% 6,00% 7,00% 8,00% 9,00% 10,00% 11,00% 12,00% g 1,00% 1,00% 1,00% 1,00% 1,00% 1,00% 1,00% 1,00% Business value 2.500.000 2.000.000 1.666.667 1.428.571 1.250.000 1.111.111 1.000.000 909.091

Starting with a 5% WACC, the business value goes down to 36% as the used WACC is 12%. Misusing a perpetuity can lead to a large warping of your results. As one can expect, due to the mathematical properties, the same is true for a change in the growth rate. In the following example a change from 0% growth rate to a 3% growth provides a 60% increase on the business value estimate.

 FCFF 100.000 100.000 100.000 100.000 100.000 100.000 100.000 100.000 WACC 8,00% 8,00% 8,00% 8,00% 8,00% 8,00% 8,00% 8,00% g -1,00% 0,00% 1,00% 2,00% 3,00% 4,00% 5,00% 6,00% Business value 1.111.111 1.250.000 1.428.571 1.666.667 2.000.000 2.500.000 3.333.333 5.000.000