Question

What is constant and non constant growth in free cash flow valuation model? (Please include an example question and formulas used)

Answer 1

Constant growth involves free cash flows fixed growth of free cash which is discounted at (Required rate of return - growth) to provide enterprise value of the firm.
Formula : Value of Firm = Free Cash Flow *(1+ growth)/((Required rate of return - growth)
Example
The free cash flow of a firm in current year = 100 million
Required rate = 15%
The growth of Free cash fkow from next year till perpetuity = 5%
What is the value of the firm ?
Answer: The value of firm = 100*(1+15%)/(15% - 5%) = 115/0.1 = 1150 million.

Non Constant growth involves no growth or varying growth over a period which has to be discounted by the required rate to arrive at the valuation of the firm.

Formula : Value of Firm = Free cash flow *(1+growth 1)/(1+Rate) + Free cash flow *(1+growth 1)*(1+growth 2)/(1+Rate)² + Free cash flow *(1+growth 1)³/(1+Rate)³ + ....... + Free cash flow *(1+growth 1)ⁿ/(1+Rate)ⁿ
Example
For 3 years A firm will have growth of 25%, 20%,15% respectively in its free cash flow. With required rate of 10% what will be value of firm Free Cash Flow = 10million

Solution
Value of Firm = 10*(1+25%)/(1+10%) +  10*(1+25%)*(1+20%)/(1+10%)² + 10*(1+25%)*(1+20%)(1+15%)/(1+10%)³ = 36.16