Chapter 6 Frameworks for Valuation: Adjusted Present Value (APV) Instructors: Please do not post raw PowerPoint files on public website. Thank you! 1

Adjusted Present Value There are five well-known frameworks for valuing a company using discounted flows. In theory, each framework will generate the same value. In practice, the ease of implementation and the interpretation of results varies across frameworks. In this presentation, we examine how to value a company using adjusted present value (APV) Frameworks for Valuation 2

Why Use APV? When building an enterprise DCF or economic-profit valuation, most financial analysts discount all future flows at a constant weighted average cost of capital (WACC). Using a constant WACC, however, assumes the company manages its capital structure to a target debt-to-value ratio. In cases where the capital structure is expected to change significantly, assuming a constant cost of capital can lead to misvaluation. In these situations, do not embed capital structure in the cost of capital, but instead model capital structure explicitly. The adjusted present value (APV) model separates the value of operations into two components: the value of operations as if the company were all-equity financed and the value of tax shields that arise from debt financing: Enterprise value as if the company were all-equity financed APV = Present value of debt-related tax shields + 3

APV Valuation: Free Cash Flow To value a company using APV, start with a forecast of free cash flow (FCF). APV-based free cash flow is identical to that of enterprise DCF. Rather than discount free cash flow at the WACC, discount free cash flow at the unlevered cost of capital, the cost of capital of an all-equity company. We discuss the unlevered cost of capital later in this presentation. Discount free cash flow at the unlevered cost of equity. For Home Depot, the unlevered cost of equity is estimated at 9.3 percent. Home Depot: Unlevered Valuation 4

APV Valuation: Interest Tax Shields Next, compute the present value of financing-related benefits, such as interest tax shields (ITS). Interest tax shields can be discounted at either the unlevered cost of equity or the cost of debt, depending on your perspective of their risk. Home Depot: Interest Tax Shield To forecast the interest tax shield, first forecast the level of debt. A forecast of the marginal tax rate is also required. Be careful; a company must be profitable to capture tax shields! ××== 5

APV Valuation: Putting It All Together Midyear adjustment factor Value of operations ,384 Present value of FCF using unlevered cost of equity + Present value of interest tax shields (ITS) = Present value of FCF and ITS 73,557 2,372 75,928 To conclude the APV-based valuation, sum the present value of free cash flow and the present value of interest tax shields (ITS). This leads to the value of operations. The value of operations for Home Depot is the same for both enterprise DCF and APV ($79,384 million). This occurs because we assumed the cost of capital for the tax shields (k tax ) is equal to the unlevered cost of equity (k u ). We used this assumption when deriving the unlevered cost of equity and while discounting the tax shields. Home Depot Valuation ($ million) 6

A Critical Component: Unlevered Cost of Equity The adjusted present value (APV) model separates the value of operations into two components: the value of operations as if the company were all-equity financed and the value of tax shields that arise from debt financing: Discounted free cash flow at the unlevered cost of capital Discounted tax shields at the unlevered cost of equity or the cost of debt 7 But how do we define the unlevered cost of equity—that is, the cost of equity when the firm has no leverage, when it is unobservable? We rely on the tools of economists Franco Modigliani and Merton Miller.

8 Modigliani and Miller In the 1950s, economists Modigliani and Miller (M&M) postulated that the value of a firm’s claims must equal the value of its assets. They also argued that the weighted average risk of a company’s financial claims must equal the weighted average.

The Levered and Unlevered Cost of Equity 9 Let’s start with M&M’s risk formula: Multiply both sides by enterprise value. This eliminates each fraction’s denominator. Next, use the first equation from the previous slide to eliminate V u (an unobservable value: Redistribute the terms on the left to collect like terms.

The Levered and Unlevered Cost of Equity (Continued) 10 Dividing the final equation on the previous slide by E leads to the generalized cost of equity equation: The cost of equity The unlevered cost of equity A premium for increasing leverage A discount for the tax deductibility of interest payments The cost of levered equity (which can be measured via regression) is a function of the underlying economic risk, the amount of leverage, and tax deductibility of interest.

The Levered and Unlevered Cost of Equity The levered cost of equity (k e ) is related to the unlevered cost of equity via the following equation: 11 Each of the variables can be estimated except the risk of tax shields. Most practitioners assume k tax = k u. This is consistent with a constant D/V ratio. When k tax = k u, the final term disappears and the equation simplifies to: Many academics assume k tax = k d. This leads to an alternative representation:

Levered Cost of Equity The grid below summarizes the formulas that can be used to estimate the levered cost of equity. The top row in the exhibit contains formulas that assume k tax equals k u. The bottom row contains formulas that assume k tax equals k d. The formulas on the left side are flexible enough to handle any future capital structure but require valuing the tax shields separately. The formulas on the right side assume the dollar level of debt is fixed over time. 12 Dollar level of debt fluctuates Dollar level of debt is constant Tax shields have same risk as operating assets k tax = k u Tax shields have same risk as debt k tax = k d

Unlevered Cost of Equity Since the unlevered cost of equity is unobservable, equations on the previous slide must be arranged to solve for the unlevered cost of equity. Depending on risk of tax shields and how the company’s debt fluctuates, the formula will vary. 13 Dollar level of debt fluctuates Dollar level of debt is constant Tax shields have same risk as operating assets k tax = k u Tax shields have same risk as debt k tax = k d

Unlevering Example Question: SampleCo maintains a debt-to-value ratio of 1/3. If the company’s cost of debt is 6 percent, its cost of equity is 12 percent, and the marginal tax rate is 30 percent, what is the company’s unlevered cost of equity? Solution: Since the company maintains a constant capital structure, we can assume k tax = k u. Therefore, k u equals: 14