Reading: Free Cash Flow Capitalization

The APV approach involves the following steps:

• Assume the firm is financed exclusively with equity capital

• Discount the projected free cash flows with the cost of equity the firm would have if it had no debt outstanding. In other words, we discount these free cash flows with the required rate of return on the firm's assets (\( k_A \)). This will yield the unlevered value of the firm.

• Add the present value of the future annual tax savings from debt financing. Let us refer to those savings as the debt tax shield (DTS).

Under that approach, firm value is:

Firm value= PV(Free Cash Flows) + DTS = \( \sum\frac{FCF_t}{(1+k_A)^t}+DTS \).

The opportunity cost of the firm's assets can be found by usin market data for the firm in question or, if no data are available, by obtaining data from firms in the same industry as the firm in question. Let's see now how we can compute the firm's overall cost of capital (\( k_A \)). In the previous section, we saw that we can impute \( k_A \) from the firm's costs of debt and equity with the following formula:

It is important to realize that this equation is not a causal relation. We should think of \( k_A \) as being given by the risk class of the firm's assets.The equation simply shows how we can impute \( k_A \) when we are unable to estimate it directly. All we have to do is infer it from the firm's costs of debt and equity.

Under what conditions can we compute \( k_A \)  with the above equation? One situation is when the firm pursues a capital structure with fixed proportions of debt and equity. In that case, the amount of debt outstanding and the associated tax savings will be proportional to firm value over time. If so, the correct discount rate to compute the firm's DTS is \( k_A \).  Since a policy of fixed proportions of debt and equity is an economically reasonable assumption, that's the policy we will assume.  Hence, interest tax savings will be discounted with \( k_A \), and \( k_A \) will be computed according to the above equation. In the appendix to this module, we will also derive the relevant expressions for an alternative financing policy, under which the tax savings are discounted with the cost of debt (k_D).

Let's illustrate the DCF-APV approach with a simple example. Suppose a firm that lasts only one year has the following cash flow statement:

Let's also assume the following:

• The amount of debt outsanding is 2'000 at a cost of debt (\( k_D \)) of 10%. 
• The firm's tax rate is 30%
• The firm's overall cost of capital (\( k_A \)) is 15%.

Based on this information, the unlevered value of the firm is 3'478:

This valuation ignores the fact that interest payments allow the firm to lower its tax bill. Given the information provided above, the firm's interest expenses are 200 (= 2'000 \( \times \) 0.1). Debt financing therefore allows the firm to lower its taxable income by 200. Given a tax rate of 30%, the tax savings that debt financing brings about correspond to 60:

Note that these tax savings only occur in 1 year. Therefore, we have to compute their present value to determine the firm's debt tax shield:

Consequently, the overall value of the firm is 3'530: 

 
Compared to a firm without debt, firm value is 52 higher. This value added goes to the shareholders. The value of the firm's equity is:

Without debt financing, equity value would only be 1'478 (= 3'478 - 1500).