The discounted valuation technique (DCF) is the backbone of modern finance and even modern business. DCF permits to measure investments, analysing in and out cash flows, and when applied to company valuations defines the intrinsic value of a company (as an alternative to market valuations like comparable companies and precedent transactions).

To understand DCF, is important to have a perspective of the company based on the following variables:

- 4 variables from the Balance Sheet: any investment can be seen as an increase the assets, net working capital or net fixed assets, and will be financed with liabilities, debt or equity
- 6 variables from the P&L: the net profit derives from the following variable, Sales, Cost of Good Sold, Selling/General/Administration, Depreciation/Amortization, Interest/Non Operating Expenses, and Taxes

Now that we have defined the 10 variables that define the finance story of a company, we can combine them to define different types of cash flows:

- Equity Cash Flow: we know that, Cash + NWC + NFA = D + E. The differential format of the previous formula is: ∆Cash + ∆NWC + ∆NFA = ∆D + ∆E. If we assume that: 1) cash is going only to the stock holders, and not to the operations, ECF=∆Cash, 2) the ∆E is generated only by the NP. We have: ECF= NP – ∆NWC – ∆NFA + ∆D
- Debt Cash flow: cash flows related to the debt can be expressed as DCF= I – ∆D. This expression shows that the cash flows to debt are composed of the payment of the interest, and the repayment of the debt (- ∆D)
- Free Cash Flow: we assume that the company is all equity financed in this case we modify the formula used for the ECF calculation: 1) NP->NP unlevered, we need to eliminate the effects of the debt adding I*(1-T), 2) ∆D=0. We can now state that: FCF= NPU – ∆NWC – ∆NFA or FCF=EBIT(1-T) – ∆NWC – ∆NFA. The relation between FCF and ECF can be expresses in the following formula: FCF=ECF – ∆D + I(1-T)
- Tax shields: using debt generates the following effects, 1) Increase of financial interests, and decrease of NP, 2) tax shields with the following value: Kd*D*T, 3) increase of liabilities, 4) the financial structure of the company changes by consequence the cost of debt can increase

There are several methods based on discounted cash flows. They differ only in the cash flows taken as the starting point for the valuation and in the discount rate used. An interesting paper from Pablo Fernandez shows 10 methods, which implies 9 different theories on the calculation of the value of tax shields and 9 definitions of levered beta, unlevered beta, required return to equity and return to assets. Let’s focus only in 3 techniques: ECF, WACC, and APV. If we observe them from the perspective of the effect of the debt on the valuation we have:

- WACC: the effect of the debt is in the discount rate, defined as a WACCt = [Et-1 Ket + Dt-1 Kdt (1-T)] / [Et-1 + Dt-1]. The cash flow used is the FCF. The value obtained is D+E
- ECF: the effect of the debt is in the cash flows, discounted at the required investors rate Ke. The cash flow used is ECF. The value obtained is E
- APC: the effect of the debt is in the tax shields (and eventual other costs like bankruptcy), discounted at the unlevered return on equity, Ku. The cash flow used is the FCF. The value obtained is D+E

We can use the 2 graphs shown in the previous picture to visualize some of the previous concepts. We observe that there is an optimal level of debt, after which, the cost of financial distress makes the company less valuable. This point is the debt level at which the WACC have a minimum, and consequently, maximizes the value of the firm, D+E (assuming that debt’s market value is the same as its book value). This may happen for two reasons: because the expected FCF decreases with debt level, or because the assets’ risk (the FCF’s risk and the likelihood of bankruptcy) increases with leverage (or because of a combination of both).