Why do we actually discount Cashflows?

Your assumption in the second scenario that there is both (a) no share price appreciation, and (b) no dividends or stock repurchases, is not realistic. If a company generates $1 of FCF per year, they've got basically three things they can do with it - invest in the business [internally or via acquisition], pay out to shareholders [dividends or repurchases], or let it sit on the balance sheet, presumably waiting for a better time to do either of the first two options.

In your first case, the company pays out all free cash flow in dividends. Presumably they are investing the bare minimum to maintain the $1 of FCF [all capex is maintenance capex] and this capex figure is incorporated in getting to the $1 FCF figure. So cash flow never grows plus the company doesnt maintain it on the balance sheet as an asset, so the share price remains constant. But you collect your 10% return via the dividend.

In the second case, you'll have cash accumulating on the balance sheet as an excess asset. The market should adjust the share price to incorporate the fact that they are essentially paying less for the business itself [the operation that generate $1 per year]. Eventually, if management doesn't do anything with the cash and it's just sitting there [earning way below the cost of capital for the business] shareholders would likely push for it to be invested/returned.

Overall the lesson I think is that valuation depends on more than just free cash flow and a discount rate. It matters tremendously what management does with the free cash flow the business generates. If it sits on the balance sheet doing nothing for years, then that is worth far less than if it is invested in high return projects or good acquisitions, or if it were used to repurchase undervalued stock or pay dividends.

How did you get into hedge fund and do you know the difference between , and .?

1) Before we get to your example: the "philosophical" reason we discount cash flows is because a) future cash flows are not certain and b) we need to earn a premium over some other more-certain cash flows (for example a "risk-free" treasury bond) to reflect the uncertainty of those cash flows.

2) Your example is a bit of a chicken/egg problem. You assume both a) no chance of growth and b) effectively no risk to future cash flows when in fact there is at least some of each. Put another way, if you were 100% CERTAIN of those future cash flows, the right discount rate would probably be less than 10% (at least in today's rate environment).

This is a good time to point out that CAPM (or at least its inputs) are observed/inferred from market views on value (both bottoms-up and top-down), not the other way around.

3) On your last point, your observation is tautologically true but doesn't actually tell you anything. The 10% CAPM WACC you derived is being used as a discount rate, which could be thought of as your "required IRR" for holding the security; therefore the IRR at your expected fair value=your required IRR. "Fair value" doesn't mean "zero expected IRR," it means the IRR is equal to your required IRR to hold the investment, and (depending on your investing goals) you either buy it or look for something that's expected IRR is ABOVE your required IRR.

@Extelleron: Thanks for the andwer. Your point is obivously valid when approaching the valuation using EV by discounting FCFF. If no additional investment is made, the Enterprise Value remains the same, and as you are decreasing your Net debt by increasing cash, your equity value has to be greater. However, my problem is not reconciling this vision with the FCFE discounted at Cost of equity (I always use the former, that's why this problem hadn't popped up.

@vik2000: you must know there are countries outside the US, and that some of these minor countries use different radix points. You do know, don't you?

@Kenny: Thank you too. As per your initial comment: I agree with the uncertainity around the CFs (this would just be probability weighting the CFs). Regarding risk... I would say Cost of equity should not be that of the company, but that of the fund. In this way, you would get different upsides which you would then compare to the risks you see in the investment. I worked in PE before, so I guess I see the investments from another perspective...