1. General Considerations

We have reviewed the notions of the cost of debt, the cost of equity, and the cost of the firm's overall capital. In this section, we learn how we can apply these costs to discount the firm's future cash flows. 

From Financial Planning, we know the various cash flow definitions. In particular, we know that the free cash flow indicates how much cash a firm generates with its operations after the relevant investments have been made. This is the amount of cash that is available for distribution to all providers of capital. 

Moreover, we know that the cash flow from debt financing and the residual cash flow indicate how the free cash flow is actually distributed to the providers of capital:

  

Free cash flow = Cash flow from debt financing + Residual cash flow.

  

When capitalizing cash flows, it is imperative that the discount rate we choose reflects the riskiness of the cash flow stream under consideration:

  • If we want to value the debt of the firm, we capitalize the cash flows from debt financing using the required rate of return of the debtholders (the cost of debt, \( k_D \)) as the discount rate.
  • If we want to value the firm's equity, we capitalize the residual cash flows with the shareholders' required rate of return (the cost of equity,  \( k_E \)).
  • Finally, if we want to estimate the overall value of the firm's capital, we capitalize the free cash flow at the required return on assets (in a world without taxes, this return corresponds to the overall cost of capital,  \( k_A \).

  

The simple example in the previous section has used that very same logic. Remember that the firm we have considered there is expected to provide a single cash flow in 1 year. The relevant information of that example are summarized in the following table (values in thousands):

  

Claim

Relevant cash flow

Average cash flow

Average return

Overall firm

Free cash flow

1'500

20.00%

Debt

Cash flow from debt financing

800

10.00%

Equity

Residual cash flow

700

33.91%

  

Based on this information, we can compute the overall value of the firm as well as its debt and equity (remember that the firm only lasts one year):

  

Firm value = \( \frac{\text{Free cash flow}}{1+k_A}=\frac{1'500}{1.2}=1'250. \)

  

Value of debt = \( \frac{\text{Cash flow from debt financing}}{1+k_D}=\frac{800}{1.1}=727. \)

  

Value of equity = \( \frac{\text{Residual cash flow}}{1+k_E}=\frac{700}{1.3391}=523. \)

   

Because the value of the firm corresponds to the overall value of the financial claims on the firm, we know:

  

Firm value = Value of debt + Value of equity = 727 + 523 = 1'250.

  

Therefore, to estimate firm value, we can either value the financial claims separately or we can capitalize the free cash flows at the overall cost of capital. In most instances, we will rely on the latter approach because it involves fewer computations.

In a world without taxes and other frictions, the overall value of a company therefore corresponds to the present value of all future free cash flows capitalized at the cost of assets ( \( k_A \)):

  

Firm value (no taxes) = \( \sum\frac{FCF_t}{(1+k_A)^t} \).

  

However, as we have seen before, the free cash flow ignores interest tax savings because they are a cash flow from financing activities. At the same time, however, these tax savings constitute a source of value and therefore have to be incorporated in our firm valuation approach.

The discounted cash flows (DCF) approach has two major variations, depending on how we want to take into consideration the interest tax savings the firm can claim if it has debt outstanding:

  • The first approach is the so-called Adjusted Present Value (APV) approach.
  • The second is the Weighted Average Cost of Capital (WACC) approach.

 

When properly implemented, the two approaches lead to the same result. This is the topic of the following section.