Lezione 11 Metodologie di valutazione: APV

Transcription

1 Lezione 11 Metodologie di valutazione: APV See T. Koller, M. Goedhart, D. Wessels, Valuation, 2010, Chapter 6

2 Adjusted Present Value There are five well-known frameworks for valuing a company using discounted flows. Frameworks for Valuation Model Measure Discount factor Assessment Enterprise discounted cash flow Free cash flow Weighted average cost of capital Works best for projects, business units, and companies that manage their capital structure to a target level. In theory, each framework will generate the same value. In practice, the ease of implementation and the interpretation of results varies across frameworks. Discounted economic profit Adjusted present value Capital cash flow Economic profit Weighted average cost of capital Free cash flow Unlevered cost of Capital cash flow Unlevered cost of Explicitly highlights when a company creates value. Highlights changing capital structure more easily than WACC-based models. Compresses free cash flow and the interest shield in one number, making it difficult to compare operating performance among companies and over time. In this presentation, we examine how to value a company using adjusted present value (APV) Equity cash flow Cash flow to Levered cost of Difficult to implement correctly because capital structure is embedded within the cash flow. Best used when valuing financial institutions. 2

3 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- financed and the value of shields that arise from debt financing: APV = Enterprise value as if the company were all- financed + Present value of debt-related shields 3

4 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- company. We discuss the unlevered cost of capital later in this presentation. Home Depot: Unlevered Valuation Free Discount Present cash flow factor value of FCF Year ($ million) (@ 9.3%) ($ million) , , , , , , , , , , , , , , , , , , , ,660 Continuing value 78, ,256 Present value 53,240 Discount free cash flow at the unlevered cost of. For Home Depot, the unlevered cost of is estimated at 9.3 percent. 4

5 APV Valuation: Interest Tax Shields Next, compute the present value of financing-related benefits, such as interest shields (ITS). Interest shields can be discounted at either the unlevered cost of or the cost of debt, depending on your perspective of their risk. Home Depot: Interest Tax Shield Prior-year Expected Interest Marginal Interest net debt interest rate payment rate shield Forecast year ($ million) (percent) ($ million) (percent) ($ million) , , , , , , , , , , , = 1, = , , , , , , , , Continuing-value forecast 29, , To forecast the interest shield, first forecast the level of debt. A forecast of the marginal rate is also required. Be careful; a company must be profitable to capture shields! 5

6 APV Valuation: Putting It All Together To conclude the APVbased valuation, sum the present value of free cash flow and the present value of interest 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 ($62,694 million). We assumed the cost of capital for the shields (k ) = (k u ). 6

7 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- financed and the value of shields that arise from debt financing: Free Cash Flow (T m)interest V = + t (1+k ) (1+k ) t t=1 u t=1 Discounted free cash flow at the unlevered cost of capital Discounted shields at the unlevered cost of or the cost of debt But how do we define the unlevered cost of that is, the cost of when the firm has no leverage, when it is unobservable? We rely on the tools of economists Franco Modigliani and Merton Miller. 7

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. V u + V = V enterprise = D + E They also argued that the weighted average risk of a company s financial claims must equal the weighted average. V V D E k k k k V V V V u u d e Enterprise Enterprise Enterprise Enterprise 8

9 The Levered and Unlevered Cost of Equity Let s start with M&M s risk formula: V V D E k k k k V V V V u u d e Enterprise Enterprise Enterprise Enterprise Multiply both sides by enterprise value. This eliminates each fraction s denominator. Vu ku Vk Dkd Eke Next, use the first equation from the previous slide to eliminate V u (an unobservable value: (D+E-V )k u V k Dk d Ek e Redistribute the terms on the left to collect like terms. Ek V k k D k k Ek u u u d e 9

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

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

12 Levered Cost of Equity The grid below summarizes the formulas that can be used to estimate the levered cost of. The top row in the exhibit contains formulas that assume k equals k u. The bottom row contains formulas that assume k equals k d. The formulas on the left side are flexible enough to handle any future capital structure but require valuing the shields separately. The formulas on the right side assume the dollar level of debt is fixed over time. Dollar level of debt fluctuates Dollar level of debt is constant Tax shields have same risk as operating assets k = k u D k = k + k -k E e u u d D k = k + k -k E e u u d Tax shields have same risk as debt k = k d D-V k = k + k -k E e u u d (1-T )D k = k + k -k E m e u u d 12

13 Unlevered Cost of Equity Since the unlevered cost of is unobservable, equations on the previous slide must be arranged to solve for the unlevered cost of. Depending on risk of shields and how the company s debt fluctuates, the formula will vary. Dollar level of debt fluctuates Dollar level of debt is constant Tax shields have same risk as operating assets k = k u D E k = k + k D + E D + E u d e D E k = k + k D + E D + E u d e Tax shields have same risk as debt k = k d D V E k = k + k u d e D V + E D V + E D(1- T ) E k = k + k m u d e D(1-T m)+ E D(1-T m) + E 13

14 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 is 12 percent, and the marginal rate is 30 percent, what is the company s unlevered cost of? Solution: Since the company maintains a constant capital structure, we can assume k = k u. Therefore, k u equals: D E k = k + k D + E D + E u d e 1 2 k u = (6%) + (12%) = 10%

15 Cash flow to There are five well-known frameworks for valuing a company using discounted flows. Frameworks for Valuation Model Measure Discount factor Assessment Enterprise discounted cash flow Free cash flow Weighted average cost of capital Works best for projects, business units, and companies that manage their capital structure to a target level. In theory, each framework will generate the same value. In practice, the ease of implementation and the interpretation of results varies across frameworks. Discounted economic profit Adjusted present value Capital cash flow Economic profit Weighted average cost of capital Free cash flow Unlevered cost of Capital cash flow Unlevered cost of Explicitly highlights when a company creates value. Highlights changing capital structure more easily than WACC-based models. Compresses free cash flow and the interest shield in one number, making it difficult to compare operating performance among companies and over time. At last, we examine CFE Equity cash flow Cash flow to Levered cost of Difficult to implement correctly because capital structure is embedded within the cash flow. Best used when valuing financial institutions. 15

16 CASH-FLOW-TO-EQUITY VALUATION MODEL Each of the preceding valuation models determined the value of indirectly by subtracting debt and other non claims from enterprise value. The cash flow model values directly by discounting cash flows to at the cost of, rather than at the weighted average cost of capital. Cash flow to = dividends plus share repurchases minus new issues. 16