## Info

9,385

1 Except per sliarc.

1 Except per sliarc.

The Adjusted Present Value (APV) Model

The adjusted present value (APV) model is similar to the enterprise DCF model. As with enterprise DCF, the APV model discounts free cash flows to estimate the value of operations, and ultimately the enterprise value, once non-operating assets are added. From this enterprise value, the value of debt is deducted to arrive at an equity value. The difference is that the APV model separates the value of operations into two components: the value of operations as if the company were entirely equity-financed and the value of the tax benefit arising from debt financing.2

This valuation model reflects the conclusions from the Modigliani-Miller propositions on capital structure developed in the late 1950s and early 1960s. The MM propositions showed that in a world with no taxes, the enterprise value of a company (the sum of its debt plus equity) is independent of capital structure (or the amount of debt relative to equity). The intuitive logic here is that the value of a company should not be affected by how

2 For more information on the Miller-Modigliani propositions and the APV approach, see Thomas E. Copeland and J. Fred Weston, Financial Theory and Corporate Policy, 3rd ed. (Reading, MA: Addison-Wesley, 1988), pp. 439-451, and Richard A. Brealey and Stewart C. Myers, Principles of Corporate Finance, 5th ed. (New York: McGraw-Hill, 1996), pp. 525-541.

you slice it up (between debt and equity or any other claims). Professor Clifford Smith of the University of Rochester illustrates this with the story of the former American baseball player Yogi Berra at a pizza parlor. Berra is asked whether he would like his pizza cut into six or eight pieces. Berra replies: ''Six please, I am not hungry enough to eat eight." Of course, the pizza is the same size no matter how many pieces you cut it into.

The implication of MM for valuation in a world without taxes is that the weighted average cost of capital must be constant regardless of the company's capital structure. This must be so if the total value is constant and the free cash flows are by definition independent of the capital structure. The result is that capital structure can only affect value through taxes and other market imperfections and distortions.

The APV model uses these concepts to highlight the impact of taxes on valuation. The APV model first values a company at the cost of capital if the company had no debt in its capital structure (referred to as the unlevered cost of equity). It then adds the impact of taxes from leverage to this value. In most countries, interest payments made by a company are deductible for tax purposes. Therefore, the overall taxes paid by a company and its investors are lower if the company employs debt in its capital structure.

In the enterprise DCF model, this tax benefit is taken into consideration in the calculation of the weighted average cost of capital by adjusting the cost of debt by its tax benefit. In the APV model, the tax benefit from the company's interest payments is estimated by discounting the projected tax savings. If done correctly and with identical assumptions about capital structure, both models will result in the same value.

Key to reconciling the two approaches is the calculation of the weighted average cost of capital. The following equation is one approach to relating WACC to the unlevered cost of equity assuming that the tax benefit of debt is discounted at the unlevered cost of equity. (See Appendix A for alternative approaches.)

Where ku = |
Unlevered cost of equity |

kb = |
Cost of debt |

T = |
Marginal tax rate on interest expense |

B = |
Market value of debt |

S = |
Market value of equity |

Let's illustrate the APV model with the Hershey case. Estimate Hershey's ku from its WACC. Turning around the above equation, ku can be expressed in terms of WACC:

Discounting Hershey's projected free cash flow at ku results in an unlevered value of operations of $9,390 million, as shown in Exhibit 8.13. The value of Hershey's debt tax shields is $642 million, as shown in Exhibit 8.14. The result gives an equity value for Hershey of $9,200 million, as follows:

(in millions)

Value of operating free cash flow $ 9,390

Value of debt tax shield 642

Non-operating assets 450

Total enterprise value $10,482

Less: Value of debt 1,282

Equity value $ 9,200

You may have noted that the enterprise DCF value of operations does not exactly match that given by the APV approach. The difference is about 2 percent. The enterprise DCF model assumes that the capital structure (the ratio of debt to debt plus equity in market values) and WACC would be constant every period. Actually, the capital structure changes every year. If we go back to the enterprise DCF model and estimate a separate capital structure

Exhibit 8.13 Hershey Foodsâ€”APV Free Cash Flow Valuation Summary r

Year |
Free cash flow |
Unlevered cost |
Discount factor |
Present value of |

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