# Valuation Measuring and managing the value ofpanies - Koller T.

ISBN 0-471-36190-9

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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.

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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:

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ku = WACC + Jt,

(&>

= 7.5%+(5.5%x 13.8%x 39.0%) = 7.8%

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:

Value of operating free cash flow Value of debt tax shield Non-operating assets Total enterprise value Less: Value of debt Equity value

(in millions) $ 9,390 642 450 $10,482 1,282 $ 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 Foods—APV Free Cash Flow Valuation Summary

Year Free cash flow Unlevered cost Discount factor Present value of

($ million) of equity cash flow at ku

($ million) ($ million)

1399 331 7.80% 0.928 307

2000 349 7.80% 0.860 301

2001 364 7.80% 0.798 290

2002 379 7.80% 0.740 281

2003 395 7.80% 0.687 271

2004 412 7.80% 0.637 262

2005 429 7.80% 0.591 253

2006 447 7.80% 0.548 245

2007 466 7.80% 0.508 237

2008 485 7.80% 0.472 229

Continuing value 13,526 7,80% 0.472 6,380

9,056

Mid year adjustment 1.037

APV value ot FCF 9,390

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Exhibit 8.14 Hershey Foods—Interest Tax Shield Valuation Summary

Year Interest tax shields ($ million) Discount factor at 7.80% ku Present value of tax shields at ku ($ million)

1999 27.5 0.928 26

2000 26.S 0.860 23

2001 22.9 0.798 18

2002 29 .a 0.740 22

2003 25.8 0.687 18

2004 33.4 0.637 21

2005 29.2 0.591 17

2006 36 5 0.548 20

2007 31.9 0.508 16

200R 38.9 0.472 18

Continuing value 890.0 0.472 420

619

Mid-year adjustment 1.037

APV value of tax shields 642

Exhibit 8.15 Hershey Foods—Enterprise DCF Adjusted for Changing Capital Structure

Year Free cash Debt/total WACC Discount Present value

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