Company Value = Cash Flow / (Discount rate - Growth rate)
Question: Why is the discount rate subtracting growth rate?
For example, a growing company has the following cf: Year 1: 100 Year 2: 103 Year 3: etc. Growth rate: 3% Discount rate: 10%
So the company value = 100 / (10% - 3%) = 1,429, meaning you would be willing to pay $1,429 for the company.
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Try that calculation again but this time don't subtract the growth rate. You should end up with a smaller valuation now than you would if you only considered your 10% discount rate. So by subtracting the growth rate, you are decreasing your denominator which will increase your company value. This difference in value is how the expected growth rate of your company will impact your valuation, hence why you want to subtract the growth rate for your calculation.
I don't really think you're answering his question, but you are merely stating mathematical fact when using smaller and larger denominators. What you have found is the terminal value of the company, which you would then present value and add to the present value of the sum of forecasted cash flows. Terminal value should almost always represent the majority of that sum.
To answer your question, I don't have a real logical explanation. That is simply the equation used, and it attempts to quantify a convergent geometric series, which is what cash flows from time x to infinity essentially is. It is simply a question and answer of mathematics, so I wouldn't get too hung up on it.
The discount rate is how much return your investor expect for investing in the firm (WACC) the growth rate, on the other hand, is how much the company is going to grow indefinitely. If you subtract the WACC to the g you are getting how much return I am expected to provide net of growth. By dividing it by my terminal cash flow I get the PV of FCF at infinity.
This is simply the formula of a growing perpetuity.
Basically, your terminal value is derived from your normative cash flow C, growing at a constant rate g, discounted back to present at a rate r.
The formula is therefore : C / (r - g)
The main assumption of the formula is that r > g (otherwise the terminal value would be negative).
If you want to understand why you have to subtract the growth rate, have a look at this page: http://financeformulas.net/Present_Value_of_Growing_Perpetuity.html
Thank you for everyone's helpful comments, really appreciate it!
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