Arzac Valuation Mergers, Buyouts and Restructuring, 2nd Edition , Solution Manual

Type:

Solution Manual

Resource:

Arzac Valuation Mergers, Buyouts and Restructuring

Edition:

2nd Edition

Author(s):

Enrique R. Arzac

Instructor’s Manual to Accompany

VALUATION FOR MERGERS, BUYOUTS, AND RESTRUCTURING Second Edition

Enrique R. Arzac Graduate School of Business Columbia University

Copyright © 2008 John Wiley & Sons, Inc. All rights reserved.

ii

Preface This manual contains solutions to all end-of-chapter problems in Valuation for Mergers, Buyouts and Restructuring, 2nd edition. The number of problems and their nature varies from chapter to chapter depending on the author’s estimate of the students’ need for reinforcement. All the problems can be solved using a readily available spreadsheet program such as MS Excel. The Valuation Aids CD-ROM included with the text contains a number of Excel spreadsheets with models for solving the most computation intensive problems; it also includes a folder with Excel spreadsheets for many of the exhibits included in the textbook and in this manual. A separate folder “Excel Files” is included with this manual contains spreadsheet models for the problems numbered in italics. The folder “Power Point Slides” contains presentation slides that complement the material covered in the text.

In Chapter 1 of this manual I have provided a guide to alternative study paths through the textbook, depending on the purpose of the course and the background of its students. Chapters 2 to 15 and Appendix A contain the answers to the problems. I have also interspersed comments about the use of the Valuation Aids software. A companion folder contains spreadsheets with solutions to most of the problems.

I have done my best to eliminate mistakes and ambiguities from the textbook and this manual, but some undoubtedly remain. I would very much appreciate any suggestions for improvements, criticisms and corrections. My addresses are: Professor Enrique R. Arzac 623 Uris Hall Graduate School of Business Columbia University New York, NY 10027 USA email: era1@columbia.edu

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Table of Contents

Part I. The Tools of Valuation Chapter 1. A User’s Guide

1

Chapter 2. Forecasting and Valuation of Free Cash Flows

4

Chapter 3. The Equity Premium and the Cost of Capital

14

Chapter 4. Metrics and Multiples

17

Chapter 5. Economic Value Added

19

Chapter 6. Valuation with Changing Capital Structure

23

Chapter 7. Debt Capacity for Acquisition Financing

27

Chapter 8. Valuing Entry and Exit Options

29

Part II: Mergers, Acquisitions and Buyouts Chapter 9. Merger and Acquisitions

34

Chapter 10. Deal making with Difference of Opinion

45

Chapter 11. Special Offer Structures: Price Guarantees and Collars

55

Chapter 12. Acquisitions in Developed and Emerging Markets

59

Chapter 13. Leveraged Buyouts

65

Part III: Recapitalizations and Restructuring Chapter 14. Recapitalization of Troubled Companies

74

Chapter 15. Asset Restructuring

80

Appendix A. Financial Options

84

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v

Chapter 1. A User’s Guide Chapter 1 provides a guide to the use of the book and recommends selected chapters depending on the pedagogical goal of the course.

1. Valuation techniques and their applications The book can be used as the core reading in a course on valuation procedures. The course can be based on the book’s table of contents, assigning selected reading and problems from the several chapters depending on the level of the class. For example, the following readings are suggested for students who have taken introductory courses in accounting and finance: 1. Forecasting free cash flows. Chapter 2: 2.1 - 2.2. Problem 2.2.

2. Free cash flow valuation. Chapter 2: 2.3 - 2.5 and 2.6.4 - 2.6.8. Problems 2.1, 2.4, 2.5, 2.7.

3. The cost of capital. Chapter 3: 3.1 - 3.4, 3.5.4, 3.6 - 3.10. Problems 3.1, 3.6 - 3.8.

4. The use of multiples in valuation. 1 Chapter 4: 4.1 - 4.3. Problems 4.1, 4.6 - 4.8.

5. Adjusted present value techniques. Chapter 6: 6.1 - 6.4. Problems 6.1 - 6.3.

6. Merger analysis. Chapter 9: 9.1 – 9.12. Problems 9.1 – 9.6.

7. Asset restructuring. Chapter 15: 15.1 – 15.8. Problems 15.1 – 15.4.

Additional topics. Depending on the length of the course the following topics can be included in an introductory course: EVA valuation can be added as a complement to standard FCF valuation. In that case the following readings and problems can be assigned: Chapter 5: 5.1 - 5.3. Problem 5.1.

Debt capacity and leveraged buyouts. Chapter 7: 7.1 - 7.8. Chapter 13: 13.1 - 13.4, 13.6 - 13.11. Problems 7.1, 7.3, 7.5, 13.1.

Although an introductory course would require the instructor to lecture on concepts and procedures, there may be room for including a number of cases. Three abridged cases included as end-of-chapter problems are: the 1

Some instructors are reluctant to discuss valuation multiples and prefer to emphasize the conceptual superiority of DCF techniques. I believe there are two important reasons that justify covering the use and limitations of valuation multiples.

First, empirical evidence suggests that valuation multiples in conjunction with DCF techniques provide more precise estimates of value. Second, most graduates end up using EBITDA and P/E multiples in practice and they would benefit from a balanced discussion of the role of multiples in valuation.

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merger of Volvo-Procordia (problem 9.10), the restructuring of BAT Industries (problem 15.5) and, Project Blue Snapper: (problem 13.4) for those courses covering Chapter 13 on leveraged buyouts.

2. Advanced valuation techniques A class already familiar with the financial forecasting and the basic free cash flow valuation model can be assigned the reading listed in 1 to 4 above for the introductory course as a review. The instructor can limit teaching to a review the main concepts, possibly in the context of a couple of cases, and reserve time for a detailed coverage of alternative estimations of continuation value, the effect of personal taxes, and analysis of valuation results. (Chapter 2: 2.4, 2.6.2-2.6.3, 2.7).

The reading on multiples can include Sections 4.4 – 4.7 on the interrelationships among the different multiples, their decomposition into franchise and growth factors and the nature of PEG ratios. This can be complemented with the material on franchise and growth as sources of value creation covered in Chapter 5 on economic value added (Sections 5.4- 5.5).

The adjusted present value coverage can include the more advanced material on recursive WACC and compressed APV (Sections 6.5 – 6.6).

Students in an advanced course would already be familiar with the basic notions of options pricing, including arbitrage pricing, risk neutral valuation and calculations using the Black-Scholes formula. A review in class or in a special review session is needed when some students have not had prior exposure to option pricing. A lecture can be based on Section 8.1 on real options, followed by the material of Section 8.2 on continuoustime models, and concluding with the standard Black-Scholes formula and some of its extensions summarized in Appendix A. After solving the examples and a sample of the problems of Appendix A with the Financial Options Calculator included in the Valuation Aids CD-ROM, students would be ready to tackle the most demanding real options models of entry and exit covered in Chapter 8.

Being able to use option models open many possibilities to a valuation course: -

APV valuation can include the option-pricing model for valuing equity when the debt ratio is uncertain (Section 6.8).

-

Equity valuation can allow for the claims of warrant, options, convertible and earnout holders (Sections 10.6-10.8, 13.5 and 14.7).

-

The valuation of entry and exit options can be incorporated into the course (Chapter 8).

-

A treatment of merger valuation can include contingent value rights and collars (Chapter 11).

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3. Mergers, acquisitions and buyouts The materials on Chapters 2-4 and 9-12, plus Chapters 7 and 13 on debt capacity and leveraged buyouts cover transactions analysis and valuation. All or part of Chapter 8 on real option analysis of entry and exit decisions can be included as well. References on Chapter 9 and 13 cover empirical evidence as well as details on legal, tax and accounting aspects.

4. Recapitalizations and restructuring Recapitalizations and restructuring can be part of comprehensive course on mergers and acquisitions or taught as a separate course. An introduction or review of valuation can be based upon Chapter 2-4. Chapter 5 on economic value added provides the paradigm for the valuation of restructuring actions treated in Chapter 15.

Chapters 7 on debt capacity and 13 on leveraged buyouts provide the basis for Chapter 14 on recapitalization of troubled companies.

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Chapter 2. Free Cash Flow Valuation Taxes

2.1.

Cash Flow

Sale price 150,000 150,000 Tax basis (20% of $500,000) 100,000 Tax profit 50,000 Tax (30%) 15,000 (15,000) After-tax cash flow ...…………………...……$135,000 2.2. See Exhibits 2.2-2.5. and the Spreadsheet Models file included in Valuation Aids.

2.3. The financial statements corresponding to the no-real growth assumptions are as follows (See also the Spreadsheet Model file in Valuation Aids):

Exhibit P2.2.1. AdvPak Technologies. Pro-Forma Income Statements Historical ($000) 2006 Total Sales 203,580 Cost of Sales 166,592 Gross Profit 36,988 Sales, General & Administrative Expenses 15,164 Research & Development 1,922 EBITDA 19,901 Depreciation 10,695 EBIT 9,206 Interest Expense Interest Income Pretax Income..............................................…

Current Income Tax ..................................…

Deferred Tax ...............................…….........…

Net Income

4

Forecast for Fiscal Years Ending 12/31

2007 208,262 164,527 43,735 14,578 2,083 27,074 10,165 16,909 6,444 157 10,622 3,869 380 6,373

2008 213,052 165,116 47,937 14,914 2,131 30,893 10,797 20,095 6,424 154 13,825 5,235 295 8,295

2009 217,953 168,913 49,039 16,346 2,180 30,513 12,000 18,514 6,524 157 12,147 4,622 237 7,288

2010 222,965 172,798 50,167 16,722 2,230 31,215 12,200 19,016 6,574 161 12,602 4,800 241 7,561

2011 228,094 176,773 51,321 17,107 2,281 31,933 12,374 19,559 6,814 164 12,909 4,919 244 7,745

Exhibit P2.2.2. AdvPak Technologies. Pro-Forma Balance Sheets Historical ($000) 2006 Assets Current: Cash and Marketable Securities 3,417 Accounts Receivable 18,119 Inventories 25,158 Other Current Assets 717 Total Current Assets 47,411

2007

2008

2009

2010

2011

3,332 18,535 24,847 733 47,448

3,409 18,962 24,935 750 48,056

3,487 19,398 25,509 768 49,162

3,567 19,844 26,096 785 50,292

3,649 20,300 26,696 803 51,449

Property, Plant & Equipment Less: Depreciation Net Property, Plant & Equipment

117,667 37,253 80,414

123,851 47,418 76,432

135,341 58,216 77,125

147,632 70,216 77,417

161,122 82,415 78,707

174,622 94,789 79,833

Other Noncurrent Assets: Total Assets

9,352 137,177

9,352 133,232

9,352 134,533

9,352 135,930

9,352 138,351

9,352 140,634

Liabilities Current: Short-term Debt & Current Portion of LTD Accounts Payable Accrued Expenses Taxes Payable Other Current Liabilities Total Current Liabilities Long-term Debt Deferred Income Taxes Total Liabilities Common Stock and Retained Earnings Total Liabilities and Net Worth

12,861 17,659 2,341 12 835 33,707 64,304 1,209 99,221 37,957 137,177

12,821 17,769 2,395 14 854 33,853 64,104 1,589 99,546 33,686 133,232

13,021 13,120 17,832 18,243 2,450 2,506 19 17 874 894 34,196 34,780 65,103 65,600 1,884 2,121 101,183 102,500.48 33,351 33,430 134,533 135,930

13,600 18,662 2,564 18 914 35,758 68,001 2,362 106,121 32,230 138,351

12,940 19,091 2,623 18 935 35,608 62,955 2,606 101,170 39,464 140,634

Forecast for Fiscal Years Ending 12/31

Exhibit P2.2.3. AdvPak Technologies. Pro-Forma Cash Flow Statements Historical ($000) 2006 Funds from Operating Activities Net Income Depreciation Deferred Tax Decrease (Increase) in Current Assets Increase (Decrease) in Current Liabilities except debt Decrease (Increase) in Net Working Capital Funds From Operations

2007

2008

2009

2010

2011

6,373 10,165 380 (121) 186 64 16,983

8,295 10,797 295 (532) 143 (389) 18,999

7,288 12,000 237 (1,027) 484 (543) 18,982

7,561 12,200 241 (1,051) 498 (552) 19,450

7,745 12,374 244 (1,075) 510 (565) 19,799

Funds for Investment Capital Expenditures

6,184

11,490

12,291

13,490

13,500

Funds to (from) Financing Decrease (Increase) in Debt Dividends Total Funds to (from) Financing Increase (Decrease) in Cash End-of-Year Cash & Marketable Securities

240 10,644 10,884 (85) 3,332

(1,198) 8,630 7,432 77 3,409

(597) 7,209 6,612 78 3,487

(2,881) 8,761 5,880 80 3,567

5,705 511 6,217 82 3,649

3,417

5

Forecast for Fiscal Years Ending 12/31

2.4. 2 (a) A first approximation to the value of Fleet is obtained by applying the comparable EBITDA multiple to Fleet's 2007 EBITDA which yields: 56.7 × 5.6 = $318 million. (b) The discounted cash flow approach can be used to better account for factors specific to Fleet during the next few years. To estimate the continuation value of the enterprise one must make an explicit post-horizon growth assumption, or use a multiple. The latter would be appropriate if the long-term growth of Fleet is expected to be similar to that of comparable companies. ($ millions) Sales EBITDA margin EBITDA Depreciation EBIT Minus taxes @ Unlevered net income Deferred taxes NOPAT Plus depreciation Minus CAPEX & NWC incr.

Free cash flow PV of FCF @ Continuation value @ growth PV of 2012 continuation value Enterprise value on 1/1/2008

2007 2,223.2 2.55% 56.69 29.00 27.69 38%

9.27% 3%

2008 2,245.6 2.57% 57.71 32.60 25.11 9.54 15.57 1.60 17.17 32.60 41.80 7.97

2009 2,284.2 2.65% 60.53 34.20 26.33 10.01 16.33 2.20 18.53 34.20 42.20 10.53

2010 2,308.0 2.71% 62.55 32.90 29.65 11.27 18.38 2.90 21.28 32.90 33.40 20.78

2011 2,550.0 2.71% 69.11 32.00 37.11 14.10 23.01 2.50 25.51 32.00 32.50 25.01

$66.22 425.79 273.28 $339.50

Debt Equity WACC

WACC (%) Weight Before-tax After-tax Weighted cost cost cost 50% 7.00% 4.34% 2.17% 50% 14.21% 14.21% 7.10% 9.27%

Cost of equity = 4.5% + (1.32)(4.4%) + 3.9% =

14.21%

GCL may be able to get about $339 million before selling expenses for Fleet.

The valuation spreadsheet is included the Excel Files that are part of this manual.

2

2012 2,616.7 2.71% 70.91 31.50 39.41 14.98 24.44 2.50 26.94 31.50 32.50 25.94

Excel models are included in the folder “Excel Files” for those problems numbered in italics.

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2.5. ($ millions) Sales EBITDA margin EBITDA Depreciation EBIT Minus taxes @ Unlevered net income Deferred taxes NOPAT Plus depreciation Minus CAPEX & NWC incr.

Free cash flow PV of FCF @ Continuation value @ growth PV of 2012 continuation value Enterprise value on 1/1/2008

2007 2,223.2 2.55% 56.69 29.00 27.69 38%

11.30% 3%

2008 2,245.6 2.57% 57.71 32.60 25.11 9.54 15.57 1.60 17.17 32.60 41.80 7.97

2009 2,284.2 2.65% 60.53 34.20 26.33 10.01 16.33 2.20 18.53 34.20 42.20 10.53

2010 2,308.0 2.71% 62.55 32.90 29.65 11.27 18.38 2.90 21.28 32.90 33.40 20.78

2011 2,550.0 2.71% 69.11 32.00 37.11 14.10 23.01 2.50 25.51 32.00 32.50 25.01

2012 2,616.7 2.71% 70.91 31.50 39.41 14.98 24.44 2.50 26.94 31.50 32.50 25.94

$62.20 321.70 188.32 $250.52

where the cost of equity is kU = 4.5% + (0.66)(4.4%) + 3.9% = 11.3% and the continuation value is computed as follows Continuation value = FCF × (1+g)/(k-g) = (25.94)(1.03)/(0.113 – 0.03).

To estimate the continuation value of equity with the DCF growth model it is assumed that free cash flows will growth at 3%, the rate of sales growth.

The all-equity financed company has lower value because it forgoes the value of the interest tax shield. On the other hand, its greater equity capitalization increases the liquidity of the stock and may reduce its size premium.

2.6. Interest expense and the amount of debt corresponding to the planned coverage ratio are projected with the following formulas: Interest coverage = EBITDA ÷ Interest expense Interest expense = EBITDA ÷ Target interest coverage Debt financing = Interest expense ÷ Interest rate 2013 EBITDA is assumed to grow 3% from its 2012 level and debt financing is assumed to take place at the beginning of the year.

7

($ millions) Sales EBITDA margin EBITDA Target interest coverage Interest expense Debt financing @ EBITDA Depreciation EBIT Interest expense Income before taxes Minus taxes @ Net income Plus depreciation Cash flow from operations Plus deferred taxes Minus CAPEX & NWC incr.

Plus increase in debt Free cash flow to equity PV of FCF @ Continuation value @ growth PV of 2009 continuation value Equity value on 1/1/2005 Debt Enterprise value Debt ratio

2007 2,223.2 2.55% 56.69

7.00%

169.29

38%

14.21% 3%

2008 2,245.6 2.57% 57.71 4.87 11.85 177.56

2009 2,284.2 2.65% 60.53 4.87 12.43 183.48

2010 2,308.0 2.71% 62.55 4.87 12.84 202.71

2011 2,550.0 2.71% 69.11 4.87 14.19 208.02

2012 2,616.7 2.71% 70.91 4.87 14.56 214.26

57.71 32.60 25.11 11.85 13.26 5.04 8.22 32.60 40.82 1.60 41.80 8.27 8.89

60.53 34.20 26.33 12.43 13.90 5.28 8.62 34.20 42.82 2.20 42.20 5.91 8.73

62.55 32.90 29.65 12.84 16.80 6.39 10.42 32.90 43.32 2.90 33.40 19.24 32.06

69.11 32.00 37.11 14.19 22.92 8.71 14.21 32.00 46.21 2.50 32.50 5.30 21.51

70.91 31.50 39.41 14.56 24.85 9.44 15.41 31.50 46.91 2.50 32.50 6.24 23.15

2013 2,695.2 2.71% 73.04 4.87 15.00

$60.56 212.73 109.48 $170.04 169.29 $339.33 49.9%

214.26 426.99 50.2%

To estimate the continuation value of equity with the DCF growth model it is assumed that free cash flows will growth at 3%, the rate of sales growth. That is, Continuation value of equity = FCF12(1 + g)/(k – g) = (22.15)(1.03)/(0.1421-0.03).

Hence, once proper account is taken of the cash flow effect of debt financing, the equity valuation approach gives the same or approximately the same result as the enterprise valuation approach. Note that the financial policies in problems 2.4 and 2.6 are approximately the same: they keep the average debt ratio at about 50%.

2.7. Let us first value TPI discounting free cash flows at WACC.

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($ millions except per share numbers) EBIT Minus taxes @ 38% Unlevered net income Deferred taxes NOPAT Plus depreciation Minus CAPEX Minus change in NWC Free cash flow Cost of debt 7.86% Cost of equity 17.20% Debt ratio 26.00% WACC 14.00% Continuation value @ growth g = 7.00%

2007

2008 24.80 9.42 15.38 0.80 16.18 5.80 18.20 (0.80) 4.58

2009 28.00 10.64 17.36 0.60 17.96 7.60 12.20 (0.80) 14.16

2010 32.00 12.16 19.84 0.70 20.54 9.20 14.30 1.00 14.44

2011 34.00 12.92 21.08 0.70 21.78 10.20 14.30 1.80 15.88

2012 37.00 14.06 22.94 1.00 23.94 11.00 12.00 22.94

350.90 * *Continuation value =(FCF2012)(1+g)/(WACC-g)

Beginning of 2005 values PV of FCF @ WACC PV of 2009 continuation value Enterprise value Net debt Value of equity Shares (million) Value per share P/E Gross IPO proceeds: 5 m shs x Fees (5%) Expenses Net IPO proceeds

25.8%

$11.28 2.82 0.60

45.98 182.29 228.27 59.00 169.27 15.00 11.28 13.54

2008 Income Statement EBIT Interest @

24.80 4.64

Riskless rate

4.50%

20.16

Equity premium

4.40%

Taxes

7.66

Beta coefficient

Net income

12.50

Shares

15.00

Micro-cap premium

3.90%

EPS

0.83

Cost of equity (k)

17.20%

2.00 13.30%

$56.42 (3.42) $53.00

Debt retirement

$53.00

Alternatively, we can value TPI by first discounting the cash flow to equity at the cost of equity. This is done in the following schedule. Debt is projected on the basis of the target coverage ratio.

9

We now value TPI using the cash flow to equity approach and base the debt projection on the target coverage ratio. ($ millions, except per share numbers) EBIT Coverage Interest expense Debt financing @ 7.86%

2007

2008 24.80 5.99 4.14 52.67

59.00

2009 28.00 5.99 4.67 59.47

2010 32.00 5.99 5.34 67.97

2011 34.00 5.99 5.68 72.22

2012 37.00 5.99 6.18 78.59

2010 32.00 5.34 26.66 10.13 16.53 9.20 0.70 14.30 1.00 11.13 4.25 15.38

2011 34.00 5.68 28.32 10.76 17.56 10.20 0.70 14.30 1.80 12.36 6.37 18.73

2012 37.00 6.18 30.82 11.71 19.11 11.00 1.00 12.00 0.00 19.11 5.50 24.61

Continuation value @ growth g =

7.00%

258.18 *

* Debt assumed to be incurred at the beginning of each year and to grow at 7% in 2013.

($ millions) EBIT Interest expense Income before taxes Taxes Net income Depreciation Plus deferred taxes Minus Capex Minus increase in NWC Cash flow from operations Change in debt Cash flow to equity

2008 24.80 4.14 20.66 7.85 12.81 5.80 0.80 18.20 (0.80) 2.01 6.80 8.81

38%

PV{Cash flow to equity} Continuation value PV{Continuation value} Value of equity Net debt Enterprise value Debt ratio

2009 28.00 4.67 23.33 8.86 14.46 7.60 0.60 12.20 (0.80) 11.26 8.50 19.76

52.51 116.76 169.26 59.00 228.26 25.85%

Value of equity Shares (million) Per share EPS(t+1) P/E (forward)

169.26 15.00 11.28 0.854 13.21

Gross IPO proceeds: 5 m shs x Fees (5%) Expenses Net IPO proceeds

$11.28 2.82 0.60

*Continuation value =(FCF2012)(1+g)/(k-g)

84.09 342.27 24.57% Riskless rate

4.50%

Equity premium

4.40%

Beta coefficient

2.00

13.30%

Micro-cap premium

3.90%

Cost of equity (k)

17.20%

$56.42 (3.42) $53.00

Debt retirement

$53.00

Note that investment requirements decrease at the end of the forecast period. The analyst should prove the assumption that projected capex and level net working capital are sufficient to support the projected 8% growth.

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2013

84.09 *

In practice, one would assume a debt ratio value, compute the enterprise value, obtain the interest coverage, and iterate for other values of the debt ratio until a satisfactory financial policy is obtained. Instead, one can use the solver tool of Excel to solve for the debt ratio that implies a desired coverage ratio.

Note from the 2008 income statement derived from the enterprise valuation spreadsheet that the EBIT coverage ratio in 2008 is 5.34 times. In practice, the approximate relation between the coverage ratio and the debt ratio is known before hand for the company being valued so one can use the enterprise method with the debt ratio that approximately corresponds to the desired coverage ratio.

2.8.

2007 EBIT Minus taxes

38%

Deferred taxes NOPAT + Depreciation - CAPEX - Increase in NWC Free Cash Flow PV{FCF 2008-2011} Continuation value Enterprise value Net debt Equity Shares Value per share

EBIT Interest Taxes Net income Shares

2008 100 38 62 2 64 30 92 (5) 7

165.4 1,033.0 1,198.4 650.0 548.4 35.0 15.67

8.50% 38%

Beginning of year EV Net debt Equity Per share P/E

11

2009 120 46 74 3 77 40 63 (5) 59

2010 150 57 93 4 97 50 64 15 68

2011 190 72 118 4 122 55 69 15 93

2012 195.7 74.4 121.3 4.1 125.5 xx xx 0.0 125.5

1,568.2 Alternative valuation: Continuation value as of 2009 PV of Continuation Value PV of FCF 2005-2009 Same EV value

1,615.2 958.6 239.8 1,198.4

2008 100.0 55.3 44.8 17.0 27.7 35.0 0.79

2012 195.7 69.7 126.0 47.9 78.1 35.0 2.23

1,198.4 650.0 548.4 15.67 19.8

1,568.2 820.0 748.2 21.38 9.6

2.9.

2007 Sales Cost of sales Operating expenses EBIT Taxes Unlevered net income Deferred taxes NOPAT Depreciation CAPEX and NWC increases Free cash flow PV {FCF 2008-2012} EBITA Continuation valued @ EBITDAx PV{CV} Enterprise value as of 1/08 Equity Shares Carve-out shares Gross proceeds

38%

9.29%

2008 4,700.5 72.5% 26.9% 28.2 10.7 17.5 2.1 19.6 30.6 45.0 5.2

2009 4,935.5 72.5% 26.8% 34.5 13.1 21.4 2.2 23.6 36.2 49.5 10.3

2010 5,182.3 72.5% 26.7% 41.5 15.8 25.7 2.3 28.0 40.9 50.0 18.9

2011 5,441.4 72.5% 26.6% 49.0 18.6 30.4 2.3 32.7 42.1 45.0 29.8

68.7 88.4 486.3

5.5

50%

2012 5,713.5 72.5% 26.6% 51.4 19.5 31.9 2.3 34.2 37.0 40.0 31.2

311.9 380.6 190.32 10 19.03 3.5 66.6

EBIT Interest Income b4 taxes Taxes Net income Equity P/E

51.4 19.2 32.2 12.2 20.0 243.2 12.2

Thus, the equity of Storr would be 50% of $380.6 million or $190.3 million, and the share price would be $19.03. 3DS would get $19.03 × 3.5 million shares = $66.6 million before fees and expenses. Note, however, that going public might be premature at this stage. The projections show that capital expenditures and reductions in operating expenses are expected to transform Storr into a strong cash flow producer but 3DS may need to wait until performance has been established in order to realize its value.

2.10.

EPS2010 = (0.53)(1.495)5(1.28)5 = $13.6 Dividend2011 = (0.51)(13.6)(1.08) = $7.5 Share value2010 = 7.5/(0.10 – 0.08) = $375 Share value1999 = $375/(1.10)10 = $145.

The pricing of AOL in 1999 was consistent with the expectations held at that time about its future growth.

AOL’s real EPS were expected to grow 20 times over a ten-year period. With hindsight, such expectations now appear irrationally exuberant.

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2.11.

EPS2013 = (0.99)(1.185)5(1.09)5 = $3.6 Dividend2014 = (0.51)(3.6)(1.04) = $1.9 Share value2013 = 1.9/(0.10 – 0.04) = $31.7 Share value2002 = $31.7/(1.12)10 = $10.2.

A combination of lower expectations and higher equity premium resulted in much lower valuations in the sober market environment of 2002.

13

Chapter 3. The Equity Premium and the Cost of Capital 3.1. See Section 3.2.3 on survivorship bias.

3.2. Review Section 3.2.5.

3.3. The required return on the S&P 500 index was k = 9% + (4%)(1) = 13.0%. (a) Since, P = Payout × E1/(k-g) and E1 = E0(1+g), where Payout is the dividend payout ratio, P/E0 = Payout (1+g)/(k–g) or k - g = yield (1+g), where yield = Payout/(P/E0) is the dividend yield 2.9% g = (k – y)/(1 + y) = (13% – 2.9%)/1.029 = 9.8% and

gReal = (9.8 – 4.5)/1.045 = 5.1% or gReal ≈ 9.8 – 4.5 = 5.3%.

This value seems unrealistic given that the historical compounded growth rate of earnings during the post-war period was only about 2%. This means that either the P/E was too high or the estimated equity premium was too high. (b) The long-term nominal growth of earnings and dividends would be about (1.02)(1.045) – 1 = 6.6% D0(1.16)t 1 D0(1.16)5(1.066) P = Σ1,5 ⎯⎯⎯⎯ + ⎯⎯ ⎯⎯⎯⎯⎯⎯⎯ (1+k)t (1+k)5 k - 0.066 P D0(1.16)t 1 D0 (1.16)5(1.066) ⎯ = Σ1,5 ⎯⎯⎯⎯ + ⎯⎯ ⎯ ⎯⎯⎯⎯⎯⎯ E0 E0(1+k)t (1+k)5 E0 k - 0.066 where D0/E0 = 0 .614 and P/E0 = 21.2. Dividing through by D0/E0 yields (1.16)t 1 2.239 34.53 = Σ1,5 ⎯⎯⎯ + ⎯⎯ ⎯⎯⎯⎯ (1+k)t (1+k)5 k - 0.066 Solving for k, it yields y = 11.17% (by trial and error or using the solver functions of Excel or HP19BII, for example). This implies a premium over long-term bonds of 2.17%. That is, a P/E = 21.2 would be justified for a more realistic long-term growth of earnings only if the equity premium were very low.

3.4. First, take into account that the P/E multiple input to enter in the Equity Premium Calculator is a forward multiple. That is, P/E1 = P/E0/(1+g) ≈ 21.2/(1.16) = 18.28. Entering the other inputs and allowing the growth

14

of earnings and payout to converge toward 2% and 51%, respectively, yields a required return on equity equal to 11.2% and a premium over the Treasury yield of 2.2%.

The difference between the model of section 3.2.5 and that of problem 3.3 is that the first assumes that payout converges toward its long-term average over the initial five years and that the growth rate converges to its long-term average over year 6 to 10. Problem 3.3 keeps the current payout ratio constant and suddenly drops the growth of earnings to its long-term average in the sixth year. Still, the change in the assumptions do not change the conclusion that, in order to support the P/E multiple of the market observed just before October 1987, the long-term growth rate of earnings had to be much higher than their historical average or the equity premium demanded by investors had to be about 2%.

3.5. k is the solution to: P0/E1 = Payout1(1+k)–1 + Payout2(1+g2)(1+k)–2 + Payout10(1+g2) … (1+g10)(1+k)–10 + Payout10(1+g2) … (1+gL)(1+k)–10 (k – gL)–1 where gL is the long-term growth rate assumed to prevail from year 11 onwards.

Substituting the data into this expression: 15.4 = 0.353 (1+k)–1 + 0.421 (1+k)–2 + 0.497 (1+k)–3 + 0.583 (1+k)–4 + 0.680 (1+k)–5 + 0.725 (1+k)–6 + 0.765 (1+k)–7 + 0.799 (1+k)–8 + 0.824 (1+k)–9 + 0.841 (1+k)–10 + 0.858 (1+k)–10 (k – 0.0202) and solving of k yields a prospective required real return equal to 6.32% or (1.0632)(1.025) = 8.98% nominal.

Hence, the equity premium is 8.98% – 4.62% = 4.36%.

3.6. The Equity Premium Calculator yields an equity premium equal to 4.25%.

3.7. βU = 1.32/(1 + 0.50/0.50) = 0.66. This is the value of the unlevered beta assumed in problem 2.5 of Chapter 2.

15

3.8.

Paper Industry Capital Structure and Beta Coefficients as of December 2002 (Million US$ except as noted) Levered Adjusted Market Net Unlevered Beta1

Beta Abitibi-Consolidated2 Bowater Inc. Domtar Inc.2 Georgia-Pacific Corp.

International Paper Co. Meadwestvaco Corp.

Packaging Corp. of America Pope & Talbot, Inc. Temple-Island Inc. Weyerhaeuser Co.

1.14 0.70 0.95 1.59 0.87 0.99 0.35 0.70 0.93 1.06

Average

1.09 0.80 0.97 1.39 0.91 0.99 0.57 0.80 0.95 1.04

Equity

Debt

4,374 1,928 3,356 2,822 16,931 4,186 1,874 186 2,149 10,070

5,770 2,278 2,655 12,905 11,823 4,809 688 226 1,772 14,041

Beta 0.47 0.37 0.54 0.25 0.54 0.46 0.42 0.36 0.52 0.43

0.44

1. Adjusted Beta = 0.34 + 0.66 Unadjusted Beta..

2. Canadian dollars.

3.9. Reproduce Exhibit 3.8. (The model is included in the Spreadsheet Models file of Valuation Aids).

16

Chapter 4. Metrics and Multiples 4.1. (a) (5)(1.17)–4 + (128)(1.17)–5 = 61.05 Initial P/E = 61.05 ÷ 5 = 12.2 (forward multiple) Continuation value P/E = 120 ÷ 11 = 10.9 (trailing multiple) (b)

D6 D5(1+g) 8 + 8g ⎯⎯ = ⎯⎯⎯ = ⎯⎯⎯ = 120 k–g k–g 0.17 – g

or 8 + 8g = 20.4 – 120g, g = 12.4 ÷128 = 9.7%.

Forward continuation value P/E = 120 ÷ (11 × 1.097) = 9.9.

4.2. (i) Rule: E/P = r, where r is the bond rate. Let b be the retention rate, then P = (1 - b)EPS/(k – g) or P/E = (1 – b)/(k – g) or E/P = (k – g)/payout.

That is, the earnings yield is not directly related to the bond rate. Let us consider the assertion in more detail. (ii) For the no-growth firm b = 0 (no retention needed), and g = bROE = 0, E/P = k but k = r + equity premium, were r is the riskless rate. Hence, for the no-growth firm E/P = k > r when stocks are fairly valued, which means that E/P will most often be higher than the yield on high-grade corporate bonds. (iii) For the growth firm, b > 0, g > 0. For example, for the long-term characteristics of the S&P 500, b ≈ 0.5 and g ≈ 6% (nominal), k ≈ 9%, and E/P = (0.09 – 0.06)/0.5 ≈ 6%. But, for example, the yield of high-grade corporate bonds was approximately 8% in 1999 and 5% in 2002. That is, for a growth firm, the earnings yield can be significantly lower or higher that the bond rate when stocks are fairly valued.

4.3.

Debt ratio P/E EBITDAx EBITx RevenueX

(a)

(b)

(b)

(c) .

30% 18.00 6.53 10.89 0.65

20% 17.10 6.25 10.42 0.63

40% 21.00 6.85 11.41 0.68

35% 8.93 3.92 6.53 0.39

The changes in (b) are accounted by the changes in the value of the tax shield. The changes in (c) are the result of the net effect of an increase in the tax shield, an increase in the cost of capital, and a decrease in the growth rate.

4.4. P/E = No-growth term + Franchise factor × Growth factor = 8.33 + (4.76)(1.40) = 15x 17

4.5. EBITDAx = 3.333 + (0.644)(2.1) = 4.69x.

4.6. Pricing the issue for US investors has to be done in terms of US GAAP earnings using US standards of value (US P/Es). Of course, the IPO price will be the same in London and New York but the existing pricing information from the US was an important input for gauging BT stock price.

Since the privatized BT would be very much like a pre-divestiture ATT, the issue can be priced as follows: US GAAP 1985 pro-forma EPS .............…………………………... 11.8 pence 1984 Bell units’ average P/E = 8.0x 1984 ATT’s average P/E = 13.7x Weighted average. (50%/50%) PE ……………………………........

10.85x Price per share ..…………………………………….......................... 128 pence or 1.28 sterling = 1.28 × 1.22 = $1.56 or $1.56 × 10 = $15.6.

British Telecom was issued at 130 pence per share or $15.9 per ADR. The issue price took into account that the subscription was to be paid in three annual installments.

4.7. The price-earnings multiples and price-to-book ratios increase with size and as the size premia of Exhibit 3.7 do.

4.8.

Paper Industry Revenue, EBITDA and P/E Multiples as of December 2002

P/E Other paper comparables: Abitibi-Consolidated Bowater Inc. Domtar Inc. Georgia-Pacific Corp.

International Paper Co. Meadwestvaco Corp.

Packaging Corp. of America Pope & Talbot, Inc. Temple-Island Inc. Weyerhaeuser Co. Mean Median

Trailing Multiples EBITDA Revenue

22.5 NM 23.0 9.9 30.9 NM 36.0 NM 27.9 58.2 29.8 27.9

11.1 15.2 7.2 6.8 8.7 10.4 8.4 15.8 7.6 10.6 10.2 9.6

18

1.91 1.63 1.08 0.65 1.15 1.20 1.45 0.76 0.85 1.30 1.2 1.2

Forward Multiples P/E EBITDA

19.8 NM 10.5 6.0 18.5 19.9 17.4 NM 13.6 20.7 15.8 17.9

7.0 10.8 5.9 5.8 7.2 7.2 6.7 7.9 6.1 9.4 7.4 7.1

Revenue

1.58 1.29 1.00 0.62 1.08 1.12 1.35 0.70 0.76 1.27 1.1 1.1

Chapter 5. Economic Value Added 5.1. The valuation of TPI Inc. using the EVA approach for an initial capital equal to $70 is as follows:

5.2. The valuation of TPI for an initial capital equal to $90 million is shown in the following table. Its value is the same as that obtained using DCF in problem 2.7 and EVA valuation in problem 5.1. The present value of future EVAs and their continuation value are smaller now because more capital is needed. However, the value of the enterprise is the same because of the higher value of the initial capital. This is so because the ultimate determinant of value is the expected level of future cash flows and those are not affected by the value of the initial capital used in EVA computations. The only thing that changes is the allocation of value between capital in place and value created. See note N5.2 for a proof of this property.

19

TPI Inc. Economic Value Added Valuation as of 12/31/2007 ($million) Year-end 2007 EBITDA Depreciation EBIT Taxes 38% Unlevered net income Deferred taxes NOPAT Capital charge @ WACC= 14.00% Economic value added PV{EVA} @ 14.00% 17.49 Continuation EVA value PV{Continuation EVA value} 120.78 Total PV of EVA 138.27 Beginning capital 90.00 228.27 Enterprise value Invested capital (year-end) Depreciation CAPEX and incr. in net WC

90.00

2008 30.60 5.80 24.80 9.42 15.38 0.80 16.18 12.60 3.58

2009 35.60 7.60 28.00 10.64 17.36 0.60 17.96 14.22 3.74

2010 41.20 9.20 32.00 12.16 19.84 0.70 20.54 14.75 5.79

2011 44.20 10.20 34.00 12.92 21.08 0.70 21.78 15.60 6.18

2012 48.00 11.00 37.00 14.06 22.94 1.00 23.94 16.43 7.51 232.50

101.60 5.80 17.40

105.40 7.60 11.40

111.50 9.20 15.30

117.40 10.20 16.10

Continuation NOPAT PV{Capital Charge} Continuation EVA Invested Capital Continuation WACC value (check)

118.40 11.00 12.00 366.20 133.70 232.50 118.40 OK

5.3. The enterprise value can be calculated using (5.10) to yield: (100)[1 + (0.2 – 0.1)/(0.1 – 0.05)(1 – (1.05/1.1)10)] = $174.4 million and the value of equity is then $174.4 – $40 = $134.4, well above the offer price.

5.4. Since the firm is growing at 30% per year both equity and net debt need to increase at 30% if the firm is going to stay within its target debt ratio. Since its ROE is 25%, the required additional equity is 120% of net income. The issuance of additional equity is a zero net present value transaction for the present shareholders if the newcomers pay the value of equity at issue time. Thus formula (5.12) still applies in this case and the value of equity is equal to 100[1 + (0.25 – 0.15)/(0.15 – 0.30)(1 – (1.30/1.15)10)] = $261 million and the firm has created value equal to $261 – $100 = $161 million for its shareholders.

5.5. The enterprise value equals 100[1 + (0.25 – 0.10)/(0.10 – 0.15)(1 – (1.15/1.10)10)] = $268 million. During the first 10 years NOPAT and capital will grow at 15% and ROC = 25%, so capital invested would equal 15%/25% or 60% of NOPAT. 20

5.6. Enterprise value = 100[1 + (0.10 – 0.15)/(0.15 – 0.05)(1 – (1.05/1.15)5)] = $82 million > $50 million offer.

Paper Clips

5.7.

Beta Cost of equity = 4.8 + 4.0%β Return on equity - First ten years - Thereafter Earnings at the end of first year (millions) Book equity (millions) Earning retention rate Growth rate first 10 years P/B Value of equity (millions) Net debt (millions) Enterprise value

Breakfast Tea 0.7 7.6%

Total

1.1 9.2%

10% 30% 10% 9.2% $320 $270 $3,200 $900 40% 80% 0.4 × 0.1 = 4% 0.8 × 0.3 = 24% 1.67 4.60 $5,343 $4,144 $2,290 $1,227 $7,633 $5,371

$ 9,487 $ 3,517 $13,004

Hence the sum-of-the-parts value of SCN equity is $47.44 a share versus its current stock price of $36.70.

Calculation of P/B ratios: Paper Clips:

1 + (0.10 – 0.076)/(0.076 – 0.04) = 1.67

Breakfast Tea: 1 + (0.30 – 0.092)/(0.092 – 0.24)[1 – (1.24/1.092)10] = 4.60 5.8. Great Dane Capital can pay a maximum price of $4.9 billion for the equity of North American Labels or $49 a share. The sum-of-the-parts valuation follows:

Invested capital (millions) Growth rate ROC first ten years ROC thereafter Cost of equity Net debt ratio Tax rate Cost of debt WACC Enterprise value/Invested capital Enterprise value at exit in 6 months (millions) Minus net debt Net proceeds at exit Present value of net proceeds @ 20%

21

Pinkerton

Pipedream

$2,000 5% 10% 10% 7.8% 35% 40% 7.0% 6.54% 3.25 $6,500 2,275 $4,225 $3,521

$1,000 10% 20% 7.21% 8.5% 30% 40% 7.0% 7.21% 2.34 $2,340 702 $1,638 $1,365

Pinkerton’s V/C = 1 + (0.10 – 0.0654)/(0.0654 – 0.05) = 3.25 Pipedream’s V/C = 1 + (0.20 – 0.0721)/(0.0721 – 0.10)[1 – (1.10/1.0721)10] = 2.34 Debt amounts are calculated multiplying debt ratios by enterprise values. However, actual debt amounts may be different from those implied by the target debt ratio, and some debt may became due and payable at a premium because of change of control. The above valuation suggests that GDC can pay the present value of $8.84 billion for the enterprise free of debt, or the present value of $8.84 minus the value of outstanding debt for the equity of North American Labels.

22

Chapter 6. Valuation with Changing Capital Structure 6.1. The reason for switching to a WACC estimation of continuation value is that original APV assumes the level of debt known with certainty. This can be a reasonable simplification for the short or medium term, but it is not so beyond the explicit forecast period. In fact, discounting the tax shield at the cost of debt in perpetuity can produce very high values. In the long run, debt and its tax shield depends on the cash flow of the business and are as risky. This is in fact the assumption implicit in WACC discounting.

6.2. Original APV gives an enterprise value 0.3% higher than that produced by WACC valuation because it discounts the explicit forecast of tax shields at the debt rate not at WACC. TPI, Inc. Adjusted Present Value Valuation as of 12/31/2007 ($ millions)

Year-end EBITDA Depreciation EBIT Taxes Unlevered net income Deferred taxes NOPAT Depreciation CAPEX & NWC incr.

Unlevered free cash flow EBIT interest coverage Interest expense @ Tax shield Unlevered beta Unlevered cost of equity PV FCF 2008-2012 @ Continuation value @ WACC PV '12 Cont. value @ PV Tax shield @ Enterprise value Net debt Value of equity Shares (mill) Value per share P/E

2007

2008 30.60 5.80 24.80 9.42 15.38 0.80 16.18 5.80 17.40 4.58 5.25 4.72 1.80

38%

7.86%

1.48 14.91% 14.91% 14.00% 14.91% 7.86%

2009 35.60 7.60 28.00 10.64 17.36 0.60 17.96 7.60 11.40 14.16 5.25 5.33 2.03

2010 41.20 9.20 32.00 12.16 19.84 0.70 20.54 9.20 15.30 14.44 5.25 6.10 2.32

2011 44.20 10.20 34.00 12.92 21.08 0.70 21.78 10.20 16.10 15.88 5.25 6.48 2.46

2012 48.00 11.00 37.00 14.06 22.94 1.00 23.94 11.00 12.00 22.94 5.25 7.05 2.68

Continuation value @ growth g =

7.00%

350.90

44.78 175.13 8.90 228.81 59.00 169.81 15.00 $ 11.32 13.64

2005 Income Statement

Riskless rate

4.50%

Equity premium

4.40%

Levered beta

2.00

Micro-cap premium

3.90%

Levered cost of equity

17.20%

EBIT

24.80

Debt ratio

26.0%

Interest

4.72

Cost of debt

7.86%

20.08

Tax rate

38.00%

Taxes

7.63

WACC

14.00%

Net Income

12.45

Shares

15.00

Unlevered beta

EPS

0.83

Unlevered k

23

1.48 14.91%

6.3. The following exhibit should be compared to the answer to problem 2.7 in order to understand why the enterprise value is higher, the value of equity is lower, the share price is higher and fewer shares are issued. Note also that this valuation has maintained the interest rate at the same level as before and it ignores the possible cost of financial distress that the higher leverage may imply.

TPI, Inc. Adjusted Present Value Valuation as of 12/31/2007 ($ millions)

Year-end EBITDA Depreciation EBIT Taxes Unlevered net income Deferred taxes NOPAT Depreciation CAPEX & NWC incr.

Unlevered free cash flow EBIT interest coverage Interest expense @ Tax shield Unlevered cost of equity PV FCF 2008-2012 @ Continuation value @ WACC PV '12 Cont. value @ PV Tax shield @ Enterprise value Net debt Equity before fees and expenses Shares (mill) Value per share P/E

2007

2008 30.60 5.80 24.80 9.42 15.38 0.80 16.18 5.80 17.40 4.58 3.10 8.00 3.04

38%

8.00%

14.91% 14.91% 14.00% 14.91% 8.00%

2009 35.60 7.60 28.00 10.64 17.36 0.60 17.96 7.60 11.40 14.16 3.50 8.00 3.04

2010 41.20 9.20 32.00 12.16 19.84 0.70 20.54 9.20 15.30 14.44 4.00 8.00 3.04

2011 44.20 10.20 34.00 12.92 21.08 0.70 21.78 10.20 16.10 15.88 4.25 8.00 3.04

2012 48.00 11.00 37.00 14.06 22.94 1.00 23.94 11.00 12.00 22.94 4.63 8.00 3.04

7.00%

350.90

44.78 Continuation value @ growth g =

175.13 12.14 232.05 100.00 132.05 11.117 $ 11.88 12.68

2005 Income Statement EBIT Interest

24.80 8.00 16.80

IPO proceeds Fees Expenses Available for debt retirement

5%

13.27 0.66 0.60 12.00

Taxes

6.38

Net Income

10.42

Shares

11.12

EPS

0.94

6.4. Compressed APV gives an enterprise value of TPI equal to $230 million and a share price equal to $11.69. The lower value is due to the higher discounting rate applied to the tax shield. Compressed APV would be the appropriate procedure if the company expects to maintain a fixed debt ratio during each year, rather than a fixed amount of debt.

24

TPI, Inc. Compressed Adjusted Present Value Valuation as of 12/31/2007 ($ millions)

Year-end EBITDA Depreciation EBIT Taxes Unlevered net income Deferred taxes NOPAT Depreciation CAPEX & NWC incr.

Unlevered free cash flow EBIT interest coverage Interest expense @ Tax shield

2007

38%

8.00%

Unlevered cost of equity PV FCF 2008-2012 @ Continuation value @ WACC PV '12 Cont. value @ PV Tax shield @ Enterprise value Net debt Value of equity Shares (mill) Value per share P/E

14.91% 14.91% 14.00% 14.91% 14.91%

IPO proceeds Fees Expenses Available for debt retirement

2008 30.60 5.80 24.80 9.42 15.38 0.80 16.18 5.80 17.40 4.58 3.10 8.00 3.04

2009 35.60 7.60 28.00 10.64 17.36 0.60 17.96 7.60 11.40 14.16 3.50 8.00 3.04

2010 41.20 9.20 32.00 12.16 19.84 0.70 20.54 9.20 15.30 14.44 4.00 8.00 3.04

2011 44.20 10.20 34.00 12.92 21.08 0.70 21.78 10.20 16.10 15.88 4.25 8.00 3.04

2012 48.00 11.00 37.00 14.06 22.94 1.00 23.94 11.00 12.00 22.94 4.63 8.00 3.04

Continuation value @ growth g =

7.00%

350.90

44.78 175.13 10.21 230.12 100.00 130.12 11.135 $ 11.69 12.49

5%

2005 Income Statement

EBIT Interest

13.26 0.66 0.60 12.00

Taxes Net Income Shares EPS

1 150 191 -

2 156 363 -

24.80 8.00 16.80 6.38 10.42 11.14 0.94

Riskless rate

4.50%

Equity premium

4.40%

Levered beta

2.00

Micro-cap premium

3.90%

Levered cost of equity

17.20%

Debt ratio

26.0%

Cost of debt

7.86%

Tax rate

38.00%

WACC

14.00%

Unlevered beta

1.48

Unlevered k

14.91%

6.5. V0 = $1906.2.

Recursive APV Computation t E[Zt] P0,t VT with assumed growth P0,T P0(VT)

0

$

0 4.0% 782.3 1,124.0

3 162 518 -

4 169 657 -

5 175 782 2,155

1,906.2 406.2

V0=V0,t+P0(VT) S0 = EV - D0

6.6. Entering the data from Exhibit 6.5 into the HLF Value Calculator yields the following values: Volatility Revenue Option

10% 15% 20% 25% 30%

22% 30% 39% 48% 57%

V0

$1,948 1,997 2,052 25 2,109 2,167

S0 $448 497 552 609 667

6.7.

Year Recursive APV Computation Free cash flow P0,t Continuation value for growth Value of levered cash flows PV{continuatin value} Enterprise value Equity value

0

0 6.5% 523 728 1,251 251

1

2

3

4

5

6

7

8

9

10

60 80 -

64 151 -

68 216 -

72 274 -

77 327 -

82 374 -

88 417 -

93 456 -

99 491 -

106 523 4,505

988 80 32

972 79 32

950 78 31

923 76 30

890 74 30

851 71 28

804 68 27

750 64 26

686 60 24

613 55 22

Simple APV Initial debt Interest @ Tax shield PV{free cash flow @ 20%} PV{continuation value} @ 20%} PV{tax shield @ 8%) Enterprise value Equity value

1,000 8.00% 310 728 194 1,231 231

Compressed APV PV{free cash flow @ 20%} PV{continuation value} PV{tax shield @ 20%) Enterprise value Equity value

310 728 124 1,162 162

26

Chapter 7. Debt Capacity for Acquisition Financing 7.1. The capital required to finance 7.02% growth is $73.7 million. A target debt ratio of 40% requires an increase in debt of 40% of $73.7 or $29.50. Furthermore, a net income margin of 5% would produce a net income equal to 5% of $1,102.5 + $77.40 or $59.0, which after a 25% dividend payout leaves $59.0 – $14.75 = $44.2 million of retained earnings, just sufficient to finance the required capital.

7.2. EBITDA = (17%)(1,102.5)(1.10) = $206.2 Interest expense = EBITDA/Coverage Ratio = 206.2/4.5 = $45.8 Net Income = (1 – tax rate)(EBITDA – Depreciation – Interest expense) = (0.6)(206.2 – 36.4 – 45.8) = $74.4 Retained earnings = (1 – 25%)(74.4) = $55.8 Increase in debt = (Increase in EBITDA)(EBITDA margin)/(Coverage ratio × 8.5%) = (110.25) (0.17)/(4.5 × 8.5%) = $49.0 _______________________________________________________________ IMT Corp. Required Financing Balance Sheet Changes Resulting from Planned Growth (Year-end 2003 in million $) Additional assets needed to support 10% growth Minus spontaneous liabilities Financing need

131.25

Retained earnings

$55.80

Debt increase

49.00

26.25 $105.00 Financing sources

$104.80

_____________________________________________________________________ 7.3. For Wotsaf’s estimates: g = 30%, σ = (65% + 5%)/6 = 11.67% and the EBIT coverage ratio is [1 – 3.09σ/(1 + g)]–1 = 1.4x, for a 0.1% probability of shortfall. (Note that for normally distributed growth, a range ± 3σ about the mean has 99% probability, which means that 1/6 the range provides an estimation of σ. For more on this see Section 8.2). For Wirst’s estimates: g = 5%, σ = (65% + 55%)/6 = 21.67%, and the coverage ratio is [1 – 3.72σ/(1 + g)]–1 = 4.3x for a 0.01% probability of shortfall. Note that in this case the coefficient of σ has been changed to 3.72 because a deviation below –3.72σ has a probability of 0.01% for a normally distributed growth rate.

27

7.4. Generate Exhibit 7.5 by entering the inputs listed in Section 7.5 into the Debt Capacity Calculator.

7.5. Substituting the data into the Debt Capacity Calculator yields a debt capacity of 4.37 times EBITDA or 4.37 × $3.085 million = $13.5 million. This means that Watt needs to raise $2.5 million of equity.

7.6. The data is given as percent of EBITDA. In order to use the Debt Capacity Calculator simply let sales growth at the same rate as EBITDA and make the EBITDA margin on sales equal to 100%. The model yields a debt capacity multiple equal to 4.12x. Hence, for a growth rate of EBITDA of 13%, the debt capacity of HLT Corp. is 4.12 × $9.7 million = $40.0 million. However, if the growth rate of EBITDA is assumed to be only 6%, debt capacity falls to 3.48 × $9.7 million = $33.8 million.

28

Chapter 8. Valuing Entry and Exit Options 8.1. Since the expected yearly cash flow is $150, the value of the venture if investment takes place at time zero is $150/0.10 = $1,500 and its NPV = $1,500 – $1,200 = $300.

8.2. If the expected free cash flows happen to be just $100 per year, the value of the venture would be $1,000 and investment would not pay. However, if the expected free cash flows becomes $200 per year, the venture would be valued $2,000 and the NPV of the investment would be $800 one year from today, with a value of $800/1.1 = $727.27 today. That would happen with probability 0.5. Hence, from the perspective of time zero, the NPV of the venture with the option to wait is 0.5 × $727.27 = $363.64.

8.3. The expansion would be undertaken next year only if the present value of future cash flows exceeds $1,150. That is, if the expected yearly free cash flow is $200. Otherwise the venture would be scraped. Then, the value of the foothold investment with expansion option is: NPV = (0.5)(–50 – 10/1.1) + (0.5)(–50 + (200/0.10 – 1,150)/1.1 = 331.8.

8.4. If such venture were initiated at time 0, it would be priced at $165/0.03 = $5,500. Let the time-zero value of the option to invest be c and consider the portfolio: {long option to invest, short n units of the comparable asset} This portfolio has a present value c – n($5,500) and it would assume one of the following two values one year hence $6,000 – $10,300n

or

$0 – $1,030n

Hence, the portfolio can be made riskless by choosing n such that $6,000 – $10,300n = –$1,030n or n = 0.64725, because if the shorted investment is undertaken at time zero, at time one it will be worth the $300 or $30 produced during year plus the value of its future cash flows at that time.

That is, by shorting 0.64725 units of the comparable asset, the value of the portfolio would be –$666.7 no matter what happen to the venture’s cash flows. Hence, the portfolio yields a cash return equal to –$666.7 – initial investment. Taking into account that initial investment equals c – ($5,500)(0.64725) gives Cash return = $2,893.3 – c.

But since the portfolio is riskless it must yield the riskless rate. That is, 2,893.3 – c = 0.03 (c – 3,560.0) or

c = 3,000/1.03 = $2,913.

8.5. The decision to invest is a call option with strike price equal to $1,200, which expires in one year. In year 1 the asset will be worth $200/0.1 – $1,200 = $800 if expected free cash flows are $200 per year and zero if they are $100 per year. Consider a portfolio made up of an option to invest in the new venture and a short 29

position of n units of the traded asset. Denote the time-zero value of the option to invest by c. Thus, the value of the portfolio at time zero as c – n($1.5/1.1) and its value one year hence will be either $800 – $2n or –$1n.

The portfolio can be made riskless by choosing n such that 800 – 2n = –1n. That is, by shorting n = 800 units of the traded asset. In that case, the value of the portfolio at time 1 will be –$800 no matter what happens to the expected cash flow from the venture, which means that the expected return on the portfolio is –$800 minus the initial investment. Since this portfolio requires an investment of c – ($1.5/1.1)(800) = c – $1,090.91, the return on the portfolio will be –$800 – (c – $1,090.91) = $290.91 – c. Because the portfolio is riskless, its initial investment must yield the riskless rate, hence we have the following equality: 290.91 – c = 0.10 (c – 1,090.91), or c = 400/1.1 = $363.64. Which is the same value as the solution to problem 8.2?

8.6. Consider a portfolio made of the option to expand the venture at a strike price of $1,150 and a short position of n units of the traded asset. The value of such a portfolio in one year would be (200/0.10 – 1,150) – 2n = 850 – 2n if the cash flow from the venture turns out to be $200 and –(10 + n) if the cash flow is $100. To make it riskless, let n = 860. Since this portfolio requires an investment of c + $50 – ($1.5/1.1)(860) = c – $1,122.73, the value of the option must satisfy –870 – (c – 1,122.73) = 0.10 (c – 1,122.73) or c = 365.0/1.1 = $331.8. This is the same value as the solution to problem 8.3. Note that buyer of the option must pay the foothold cost of $50 in addition to the value of the option, and must commit to paying a cancellation (abandonment) fee of $10.

8.7. Consider the following transaction {buy 800 units of the traded asset, sell the option to invest, borrow (or short bills) at 10%} This results in the following payoffs: Year 1 Buy 800 units Sell the call Borrow @ 10% Arbitrage profit

Now ($1,090.91) 400.00 (690.91) 727.27 $ 36.36

30

FCF = $100 800.00 0

FCF = $200 1,600.00 (800.00)

(800.00) 0

(800.00) .

0

The arbitrage profit is the difference between the value of the option calculated in 8.5 and its price: $400 – $363.64 = $36.36. This means that no rational investor would price the option above its arbitrage-free value of $363.64.

8.8. Consider the following transaction {sell 800 units of the traded asset, buy the option to invest, invest money in bills at 10%} This results in the following payoffs: Year 1 Now $1,090.91 (320.00) 770.91 727.27 $ 43.64

Short 800 units Buy the call Invest @ 10% Arbitrage profit

FCF = $100 (800.00) 0

FCF = $200 (1,600.00) 800.00

800.00 0

800.00 , 0

The arbitrage profit is the difference between the value of the option calculated in 8.5 and its price: $363.64 – $320 = $43.64. This means that no rational investor would price the option below its arbitrage-free value of $363.64.

8.9. The Real Options Calculator I values the entry option at $351 million. Entry would not take place as long as revenue stays below $227 million. In Example 5 the entry cost or exercise price was only $500 and the entry option was therefore higher at $418 million. In addition, because the entry cost was lower it paid to enter the business at a lower level of revenue.

Please, note that problem 8.9 referred to Example 5 of Section 8.6 not to Example 4 of Section 8.5.

8.10. (a) The expected free cash flows in years 1 through 5 are: Year

1

2

3

4

5 .

Expected revenue

5.00

5.36

5.75

6.17

6.62

Expected free cash flow

(0.75) (0.66) (0.56) (0.46) (0.35)

(b) Since first year revenue is R1 = $5 million, R0 = $5e–0.07 = $4.66 and using formula (8.5) to compute the present value of free cash flows in continuous time: Enterprise Value = –2/(0.05) + (0.25)(4.662)/(0.09 – 0.07) = $18.27 million (c) NPV = $18.27 – $30 = –$11.73 million.

That is, immediate entry does not pay.

31

8.11. If it is possible to wait but the entry cost would increase to $40 million, the Real Option Calculator I gives $16.23 million as the value of the entry option with entry threshold at $16.67 million of revenues. (Note that the calculator transforms annual rates into continuously compounded rates and thus requires the first as input.)

Note that problem 8.10 gives continuous compound rates. Some versions of the Real Options Calculator I require that the rate inputs be expressed as annual compound rates, which the calculator then converts into continuously compound rates, in those cases the inputs have to be expressed as follows: Revenue growth = exp(7%) −-1 = 7.2708% Riskless rate = exp(3%) − 1 = 3.0455% Pre-tax Cost of debt = (exp(5%) − 1)/(1 − 40%) = 8.5452% for an after-tax continuously compound rate of 5% and a 40% tax rate WACC = exp(9%) − 1 = 9.4174%.

8.12. The value of the entry option increases slightly to $16.71 million. Entry would take place when revenues exceed $15.2 million and exit would take place when revenue falls below $4.2 million.

8.13. First, use the Real Options Calculator I to compute the parameters A1 and λ1 for the entry-exit options F(R0) = A1R0λ1. A1 = 1.6933 and λ1 = 1.6231 with entry to take place when revenues reach $10 million. Then enter the following required input data into the Real Options Calculator II:

R α σ K Imax

$

$ $

rf wacc A1

4.662 7.000% 16.50% 18.000 7.500 3.000% 9.000% 1.6933 1.6231

λ1

Interpolating on the output of the Real Options Calculator II gives a value of $18.8 million for the foothold option. Full-scale expansion would take place after completion of the foothold investment and when revenues 32

reach $13 million. The optimal foothold investment policy requires that the investment at the rate of $7.5 million per year start when the level of potential revenues exceeds $19 million. Note that the threshold for the foothold is higher than that for the expansion. This is because by the time the foothold has been completed, the additional investment is less and most of it can be recovered via exit.

8.14. The Real Options Calculator I gives $275.1 million as the value of the acquisition, with exit when revenue falls below $74 million. Note that when FCF is proportional to revenue, a = 0 in formula (8.15) of the text, and the separate cost of debt input is not used in the valuation.

33

Chapter 9. Merger Analysis and Valuation 9.1. In a stock purchase the proceeds to the seller would be $63 [= $70 − 0.2($70 − $35)]. In an asset purchase the proceeds to the seller would be $47 [= $70 − 0.4($70 − $20) − 0.2($50 − $35)] and the buyer would be able to step up the basis of the assets by $50 to $70. Goodwill amortization would be $3.333 per year over 15 years. The tax shield would be $1.333 and have a present value of $10.74. The seller would not agree to an asset purchase or a 338 election because the buyer cannot compensate it for the additional tax it will incur.

9.2. In a stock purchases, the acquirer can use the unexpired NOLs against future taxable income subject to the annual limitation of $1.65 (3% of $55) for seven years, as per footnote 8 of Chapter 9, which discounted at 9% gives a present value of $8.3.

In an asset purchase the target would have a loss of $20 + $80 – $70 = $30, pay no corporate tax and distribute $70 to shareholders who would pay $7 of taxes [0.2($70 − $35)], and receive net proceeds of $63, the same as under a stock purchase. The present value of the asset step-up would be worth $10.74 to the seller, which exceeds the value of the NOLs attained in a stock purchase transaction.

9.3. The proceeds to the seller are $70 – 0.4($70 – $35) = $56 in a stock purchase and $70 – 0.4($70 – $20) = $50 in an asset purchase. In an asset purchase, the buyers gets $10.74 present value from the asset step-up and should be willing to compensate the seller for the additional tax. The seller would demand $6/(1 – 40%) = $10 or a total consideration of $80. The buyer’s goodwill would increase by $10 and result in an additional yearly tax shield of 40% of $10/15 or $0.2667 for fifteen years with a present value of $2.12. Thus, the buyer can make whole the seller at a net cost of $7.88 for a net gain of $10.74 – $7.88 = $2.86.

9.4. See the exhibit below.

34

ABC Corp. and XYZ, Inc. Consolidated Balance Sheet as of December 31, 2007 ($000) Eliminations and Adjustments ABC XYZ Debt Credit Consolidated Current Assets Cash and marketable securities 34,021 14,000 48,021 Accounts Receivable 196,032 81,523 277,555 Inventories 298,723 149,922 448,645 Other Current Assets 30,044 11,500 41,544 Total Current Assets 558,820 256,945 815,765 0 Investments 1,154,230 38,634 1,103,587 89,277 Net Property, Plant and Equipment 3,568,229 1,470,381 136,534 4,902,076 Intangible Assets Other 789,541 143,782 13,351 919,972 Total Assets 6,070,820 1,909,742 6,727,090 Current Liabilities Short-Term Debt and Current Portion of LTD Accounts Payable Accrued Expenses Taxes Payable Long-term Debt Deferred Income Taxes Total Liabilities

67,834 108,340 4,567 12,690 1,890,450 32,189 2,116,070

42,512 54,318 2,840 8,128 310,456 8,561 426,815

Preferred Stock Common Stock and Retained Earnings Total Net Worth Total Liabilities and Equity

3,954,750 3,954,750 6,070,820

229,455 1,253,472 1,482,927 1,909,742

110,346 162,658 7,407 20,818 2,200,906 40,750 2,542,885

1,253,472 1,253,472

1,253,472

229,455 3,954,750 4,184,205 6,727,090

9.5. (a) VG+S = [(1.2)(6) + (0.6)(2)](1 + g)/(k – g) = $88.2 million for g = 5% and k = 15%. (b)

Exchange ratio = 0.6/1 or 2 × 0.6 = 1.2 million shares issued P = Price paid for SS = [1.2/(6 + 1.2)] VG+S = $14.7 million GLS stockholders' gain = VG+S – VG – P = 88.2 – 60 - 14.7 = $13.5 million SS stockholders' gain = P – VS = 14.7 – 10 = 4.7 million Value created = $18.2 million

9.6. (a) Earnings Shares (million) EPS

Irving $118 28.966

BONY $153.5 33.092

BONY+Irving $271.5 62.058 $4.37

Exchange ratio = 1.575/1 or 18.391 × 1.575 = 28.966 million BONY shares issued.

35

(b) Pre-announcement price Shares (million) Market value (million)

Irving 39.337 18.391 723.45

BONY 31.526 33.092 1,043.26

Synergy = $300 million Cash payment = 18.391 million × $15 = $275.87 million BONY + Irving = C is the combined firm after the cash payment VC = 723.45 + 1,043.26 + 300 – 275.87 = $1,790.84 million pC = 1,790.84 ÷ 62.058 = $28.86/sh.

PI = Price paid for Irving = (28.966)(28.86) + 275.87 = $1,111.76 million or $60.45 per Irving share.

BONY’s shareholders gain = VC – VNY - (PI – 275.87) = –$88.31 or –$2.67/sh.

Plus IBC’s shareholders gain = PI – VI

= 388.31 or $21.11/sh.

Synergy = $300.00 million

(c)

Break-even synergies require that VC – (28.966/62.058)VC = VNY or

VC = 1,043.26 ÷ (1 – 0.4668) = $1,956.60 million

Hence, the value of break-even synergies is: 1,956.60 – 1,043.26 – 723.45 + 275.87 = $465.76 million (d)

At the time of the bid, the foothold was worth $39.337 a share or 2.8% × 18.391 × $39.337 = $20.26 million. Let us assume that BONY could sell it at that price if it where to abandon its bid. In addition, only 0.972 × 28.966 = 28.155 million shares of BONY would be issued resulting in a total of 28.155 + 33.092 = 61.247 million shares for the merged firm. Hence, break-even synergies require that VNY = VC – (28.155/61.247) VC or

VC = 1,043.26 ÷ (1 – 0 .4597) = $1,930.89 million

The consolidated value of the companies pre-merger minus the cash outlay is 1,043.26 – 20.26 + 723.45 – (1 – 0.028)(275.87) = $1,478.30 million.

Hence, break-even synergies are 1,930.88 – 1,478.30 = $452.59 million.

An alternative way of computing break-even synergies with a foothold is as follows: (1.575)(18,391)(1 – 2.8%)($31.526) + (18,391)(1 – 2.8%)($15) + (18,391)(2.8%)($39.337) – $723.45 = $452.55.

36

9.7. (a) Am. Micro shares = common + preferred = 4,315,000. Exchange ratio = 1.78/1 or 4.315 × 1.78 = 7.6807 million. Gould shares = 22.3/0.63 = 35.397 million.

Gould $25.0 35.397 $884.925

Pre-announcement price Shares (million) Market value (million)

Am.Micro $26.625 4.315 $114.889

VC = 884.925 + 114.889 = $999.814 million P = Price for AM = [7.6807/(35.397 + 7.6807)] VC = 0.1783 × 999.8 = $178.27 million

(b)

Gould's gain = 999.8 – 884.9 - 178.3

=

$–63.4 million

AM's gain = 178.3 – 114.9

=

$ 63.4 million

VC – VG – (7.68/43.1) VC = 0, or VC

=

$1,076.8 million

Hence, required synergy = 1,076.8 – 999.8

=

$77.0 million

Gould's gain = 1,076.8 – 884.9 – 192.0

=

0.0

AM's gain = 192 – 114.9

=

Pre-announcement market value

E-III $32 million

and P = 0.1783 × 1,076.8 = $192 million

9.8.

$77.0 million Reluctant $24 million

(a) Synergy = 0, Cash = 3 million × $5 = $15 million VC = VA + VB + Synergy - Cash = 32 + 24 + 0 – 15 = $41 million n + m = 8 + 3 × 1.5 = 12.5 million shares pC = 41 ÷ 12.5 = $3.28 PB = pC × m + cash = 3.28 × 4.5 + 15 = $29.76 million Reluctant's gain = 29.76 – 24 = $5.76 m or $1.92/sh E-III's gain (b)

= Synergy – Premium = –$5.76 m or –$.72/sh

Break-even synergy = mpA + cash – VB = 4.5 × 4 + 15 – 24 = $9.0 million Check: VC = 32 + 24 + 9 – 5 = 50 million, pC = 50/12.5 = 4.0, pB = 4 × 4.5 + 15 = $33 Reluctant's gain = 33 – 24 = 9 million. E-III's gain = 9 – 9 = 0.

9.9. (a) Net income (million) Common shares (million) EPS

Lotus $68.0 42.3 $1.61

Exchange ratio = 1.19131 37

Novell $ 48.5 33.4 $1.45

Lotus+Novell $116.5 82.0 $1.42

Lotus shares issued = 1.19131 × 33.4 = 39.79 million Total shares of merged firm = 42.3 + 39.79 = 82.09 million (b) Pre-announcement stock price Common shares (million) Value of equity (million)

Lotus $ 36.25 42.3 . $1,533.375

Novell . $ 42.875 33.4 . $1,432.025

Break-even synergy: mpL – VN + 40 = 39.79 × 36.25 – 1,432.025 + 40 = $50 million. (c) Novell shareholders' gain assuming $50 million synergy ($40 million go to fees and expenses): 39.79 × 36.25 – 1,432.025 = $10 million Synergy has to exceed $50 million by a substantial amount in order for Novell's shareholders to be willing to give up control of their company. $10 million represent 30 cents per share.

One interesting question is the synergy required for Novell's shareholders to break even: (1,533.375 + 1,432.025 – 40 + Synergy) × 39.79/82.09 = $1,432.035 million or Synergy = $29 million.

Postscript: Novell turned Lotus's offer down.

9.10. (a) Terms of the merger Volvo 393 77.6 30,497

Pre-merger price (Kr) Shares (excluding 4.1 million convertibles) million Pre-merger value (Kr million) Shares issued: 2.25 × 77.6 Value of merged companies common equity Minus exchange premium to convertibles

Procordia 212 253.6 53,763

Eliminations 212 100.1 21,221

174.6

.

Post-merger common shares Post-merger value per share

63,039 230 62,809 328.1 191.4

Price paid to Volvo's shareholders per share = 191.4 × 2.25 Premium with respect to pre-merger price of Kr 393

430.7 9.6%

(b) Distribution of Procordia voting power:

Volvo shareholders Government Others

Pre-Merger

Post-Merger

42.7% 42.7 14.6 100.0%

Million Votes Percent 68.9 40.9% 74.1 44.0 25.3 15.0 168.3 100.0% 38

Post-Merger with conversion of gvmt A to B class shares Votes Percent 68.9 67.0% 8.7 8.5 25.3 24.6 102.9 100.0%

Procordia pre-merger votes = (164.71 × 1) + (88.85 × 0.10) = 173.6 million, of which the government had 42.7% or 74.1 million votes.

Volvo shareholders votes = A + B/10 = (25.4 + 5.2) × 9/4 = 68.9, were A = 25.4 = 32.7% of 77.6 million and B = 52.2 = 67.3% of 77.6 (excluding the as yet non-voting convertibles). (c) Volvo’s share price already reflects the value of the outstanding convertibles. Thus, only the increased value of the convertible plus the cash given to the convertibles holders needs to be accounted for in valuing the terms of the merger. Cash was given to offset the increase in the conversion price of the convertibles (made to avoid additional shares coming to the market in the near term). For example, the 87/95 convertibles had a conversion price of Kr 385 that should have been reduced to Kr 385 × 4/9 = Kr 171 according to the terms of the common share exchange but was instead fixed at Kr 190 or Kr 19 higher. Thus, the holders were compensated with Kr 19 × 2.25 = Kr 43 in cash.

Let us estimate the value of the warrants embedded in the new convertibles. To do so we need to estimate the volatility of the merged company stock. Consider Volvo pre-merger as a portfolio of auto and Procordia assets with weights given by the relative value of the assets. That is, (30.5 – 21.2)/30.5 = 30.5% for auto and 21.2/30.5 = 69.5% for Procordia assets. Then solve for the covariance between auto returns (A) and Procordia returns (P), and for the variance of auto returns. First, note that the covariance of Volvo returns (V) and Procordia (P) returns in terms of auto and Procordia returns is cov(V,P) = cov(0.305A + 0.695P,P) = 0.305 cov(A,P) + 0.695 var(P), or

cov(A,P) = [cov(V,P) – 0.695 var(P)]/0.305

but, from the data in the problem, cov(V,P) = (0.85)(0.282)(0.217) = 0.0520. Hence, cov(A,P) = 0.0632.

Solving for var(A) in var(P) = 0.3052 var(A) + 0.6952 (0.217)2 + (2)(0.305)(0.695)(0.0632) = 0.2822 yields

var (A) = 0.3223 or vol(A) = 56.7%.

Finally, re-weighting the variances with the weights of auto and Procordia in the merged company: 9.3/63 and 53.8/63 yields the volatility of the merged company: var(A + P) = (0.1476)2(0.3223) + (0.8524)2(0.0471) + (2)(0.1476)(0.8524)(0.0632) = 0.0571, or

vol( A+ P) = 23.9%.

39

Embedded warrant valuation Convertible Series 87/95 Pre-merger: Stock price 393 Dividend 7.75 Number of warrants (sum of both series) 4.1 Shares outstanding 77.6 Shares per warrant 1 Volatility 28.2% Strike price 385 Warrant value 140.0 Post-merger value: Stock price 191.4 Dividend 2.85 Shares per warrant 2.25 Shares outstanding 328.1 Volatility 23.9% Strike price 190 Warrant value 154.6 Increase in value to convertibles holders 14.6 Plus cash 43 Per convertible (Kr) 57.6 Convertibles (million) 2.4 Total (million Kr) 138.2 Merged company shares Per common share (Kr)

90/95 393 7.75 4.1 77.6 1 28.2% 450 112.6 191.4 2.85 2.25 328.1 23.9% 220 122.3 9.7 45 .

54.7 1.68 891.9

230.1 328.1 0.70

The warrant values are computed in the above table with the warrant program in the Financial Options Calculator. Note that the corporate rate, not the government rate, is used as the interest rate input in order to allow for the fact that a corporate bond not cash is used to pay for the exercise price. (d) The calculation of the value of the offer to Volvo shareholders predicts that Volvo share price would increase toward Kr 431 and Procordia shares will fall toward SEK 191.4, following the announcement. How close the market price would come to these values would depend on the probability attached to the consummation of the merger on the proposed terms, assuming that the market would not factor any synergy in the valuation. (e) The terms of the merger were not very prejudicial to Procordia shareholders. However they should not need to pay a premium because in reality they were being taken over by Volvo. The recommendation should be for no merger on the stated terms. The economic logic of the merger was not compelling. Furthermore, the risk that the cash flow of Procordia might go to feed unwise expansion projects at Volvo was a factor to consider.

40

(f) If the merger was going to be effected without harming either party, assuming there were no synergies and ignoring the expenses associated with the transaction, and exchange ratio of 1.8538 (=393/212) shares of Procordia per share of Volvo would be fair because it would preserve the integrity of each shareholder group's equity value.

Postscript: The transaction was not approved. A new deal was announced in June of 1993: Procordia was split in two. Volvo took over the food and consumer groups, dubbed BCP (for Brand Consumer Products) with a 74% stake, and the government became majority shareholder of the pharmaceutical and biotechnology business (Volvo retained a 25% stake), which was to be privatized. On October of 1993 Volvo undertook a share exchange for the 26.3% stake of Procordia's food group it did not already owned. Under Swedish law a company must control 90% of the unit in order to gain access to its cash flow.

9.11.

1984-1991 1992- ...

Increase in free cash flow 2,000 million (350)

Restructuring costs One-year implementation delay

Present Value 11,679 (350)(1.0758)–8(0.0758)–1 = (2,574) 9,105 1,000 8,105 7,534 Pre-bid share price Maximum bid

Per Share

$55 6 49 $45.6 39.0 $84.6

k = 12.0% + (4.0%)(1.15) = 16.6% WACC = (0.26)(1 – 0.5)(13.5%) + (0.74)(16.6%) = 14.04% Real WACC = 1.1404/1.06 = 7.58%.

9.12. PV{Free cash flow under "exploration"} = 350(1 + g)/(WACCR – g) = 350(1.04)/(0.0758 – 0.04) = $10,168 million as of Jan. 1992 PV{$10,168 as of Jan. 1984} = 10,168 × 1.0758-8 = $5,667 Hence, PV{Incremental cash flow under "no exploration"} = 11,679 – 5,667 – 1,000 = $5,012 m or $30.3/share, which, with one-year implementation delay, becomes $31.3/1.0758 = $28/share.

Hence, the maximum bid becomes Old price + PV{incremental cash flow} = 39 + 28 = $67/sh.

9.13. Since the company has no net debt the value of equity equals the enterprise value. Selling the old shareholders equity would give the proceeds to the present owners. But a strategic partner would not want that 41

all its cash investment go to the original owners, particularly with the need to fund capital expenditures. On the other hand, selling half of the company via the issuance of new shares may give too much liquidity to the company. Consider the case in which the company issues new shares and sells a 50 percent stake. Assume there are 100,000 shares outstanding worth $1,000 a share. This means that the company would issue 100,000 shares and receive $100 million, which may exceed its reasonable cash needs for the next few years. Hence, if the cash infusion is to be limited to, say, $50 million, and the new partner has to get a 50 percent interest, the sale of equity should be structured as a mixture of old and new shares. The old shares could be paid with shares of the strategic partner, particularly if the buyer is publicly traded. That would further align the interests of the two sets of shareholders and provide liquidity in case some of the shareholders of Heavy Industries decide to cash out. In order to figure out the number of new shares to issue, note that the new enterprise value would be $150 million of which the buyer would pay $75 million with $25 million of these going to the selling shareholders. Thus, 50,000 new shares would be issued to the buyer who, in addition, would receive 25,000 old shares from the selling shareholders. Since the sale of a 50% interest is being considered, the possibility of effecting a tax-free merger with a strategic buyer should be explored.

9.14. This statement was generated with DealModeler® (see Chapter 1 for a reference to this software).

CDH GROUP INCOME STATEMENTS 2003-2007 ($000) Historical 2002

Total Sales..........................................…...….......

Cost of Sales....................................….……......

Gross Profit.........................................…...…......

Sales, General & Administrative Expenses ………

EBITDA bef. Restructuring Expenses ….………....…

EBITDA.............................................……...…...

Depreciation........................................…….........

EBIT..................................................….......…...

Interest Expense …………………………….……

Interest Income ...................................……......…

Pretax Income..............................….....……......

Current Income Tax ...........................…….....…

Deferred Tax ...............................……….........…

Net Income..........................................……….…

Dividends to other than common: Preferred stock………………………….…….…

Net Income Available to Common……..……...

Number of Shares (000) ………………….…....…

EPS..............................................…............……

$1,160,863 617,582 543,281 409,035 134,246 $134,246 46,321 $87,925

2003 $1,225,581 649,558 576,023 441,209 134,814 $134,814 43,973 $90,841 4,429 1,924 88,337 31,923 1,866 $54,548 861 53,687 27,439 $1.96

Fiscal Years Ending 1/31 2004 2005 2006 2007 $1,306,469 $1,392,696 $1,484,614 $1,574,990 692,429 738,129 786,846 834,745 614,041 654,567 697,769 740,245 463,797 494,407 519,615 551,247 150,244 160,160 178,154 188,999 $150,244 $160,160 $178,154 $188,999 51,000 59,199 60,730 68,959 $99,244 $100,961 $117,423 $120,040 5,329 5,329 5,329 5,329 2,854 3,165 3,089 3,322 96,770 98,798 115,184 118,034 33,297 33,411 39,715 41,156 3,718 4,379 4,343 3,992 $59,755 $61,008 $71,126 $72,886 861 58,895 27,439 $2.15

861 60,147 27,439 $2.19

9.15. The free cash flows associated with the synergies of the merger are as follows: 42

861 70,265 27,439 $2.56

861 72,025 27,439 $2.62

($ millions) Change in EBITDA Change in depreciation Change in EBIT Taxes @ Change in unlevered net income Change in deferred taxes Change in NOPAT Change in depreciation Change in capex Change in FCF

2005

38.25%

2006 (100) 35 (135) (52) (83) 13 (70) 35 700 (735)

2007 200 110 90 34 56 37 92 110 800 (598)

2008 900 175 725 277 448 46 494 175 500 169

2009 1,000 200 800 306 494 33 527 200 727

Valuing these free cash flows and their continuation value requires deciding on the appropriate discount rate and accounting for the fact that the depreciation tax shield associated with the change in capital expenditures has finite duration.

Furthermore, one needs to consider if the risk of the free cash flows is that of MCI, Verizon or some combination of both. A further complication has to do with the fact that these cash flows are associated with cost reductions, planned capital expenditures and depreciation tax shields and none of these have the systematic risk associated with revenue. For that reason it seems inappropriate to discount the cash flows at MCI’s WACC. Even using the WACC of the merged firm seems conservative. The following table shows (1) the cost of capital of the merged firm, where the unlevered beta coefficients of MCI and Verizon have been weighted by their pre-merger market capitalizations and relevered using the debt ratio of Verizon and (2) the cost of capital that results from assuming cost reductions have lower systematic risk (beta reduced by onethird).

Cost of Capital Riskless rate Equity premium Beta Cost of equity Cost of debt Tax rate Debt ratio WACC

4.41% 4.60% 0.94 8.75% 5.85% 38.25% 34.00% 7.00%

4.41% 4.60% 0.63 7.30% 5.85% 38.25% 34.00% 6.05%

Using these discount rates yield a value of synergies between $6.1 and $7.4 as follows: Discount rate PV of Change in FCF 2006-2009 Continuation value: Post 2009 change in EBITDA after taxes PV of post 2009 change in EBITDA after taxes PV of post 2009 depreciation tax shield PV of post 2009 changes in deferred taxes Continuation value of synergies NPV as of 2/14/2005

43

7.00%

6.05%

618 8,816 424 (83) 9,157

618 10,208 439 (87) 10,560

7.00% (487)

6.05% (483)

6,583 6,096

7,931 7,448

Note that the EBITDA run rate after taxes has been valued separately from the depreciation tax shield to take into account that the latter will be exhausted after a few years. The computation of the depreciation tax shield and deferred taxes is shown in the spreadsheet included in the Excel Files that accompany this manual.

44

Chapter 10. Deal making with Differences of Opinion 10.1. (a) If the venture capitalist (VC) is going to finance the required $1,000, she will demand the following equity participation depending on her required rate of return: Required return 10% 20% 40% 60%

Start up Valuation* 2,514 1,965 1,277 1,056

VC required stake** 39.8% 50.9% 78.3% 94.7%

* Present value of the expected future cash flows of the project. ** 1,000 ÷ PV of the project.

(b) The preferred equity should convert to a share α of the common equity that results from the solution to: 1,000 = 150(1.4)–1 + 150(1.4)–2 + 0.5(1,000)(1.4)–3 + 0.5[150 + α(5,000 – 150)](1.4)–3 That is, α = 68.7 %. (c) The expected third year cash flow of the entrepreneur would be $868 under a common equity arrangement and $1,205 under the convertible preferred arrangement.

10.2. (a) NPV = (0.5)(5) – 2 = $0.5 million and the VC would demand $2/$2.5 = 80% of the equity. (b) NPV = (0.5)(5 – 1) – 1 = $1 million and the VC would demand ($1 + 0.5 × $1)/$2.5 = 60%.

10.3. 84.25% and 75.38%, respectively.

10.4.

VC's investment Required IRR Required year-5 exit proceeds Diluted stake after 5 years Required pre-money IPO value

$ 300,000 50% $ 2,278,125 5% $45,562,500

10.5.

Required pre-money IPO value IPO revenue multiple Required revenues CPM (cost per 1,000 impressions) Impressions required Impressions per year per subscriber Subscribers required

$45,562,500 5x $ 9,112,500 $5 1,822.5 million 1,000 1,822,500

10.6.

Initial investment = $2 million Required value in 4 years = $2 × (1.4)4 = $7.683 million Value of equity in 4 years = $1.5 × 13 = $19.5 mil.

45

(a) VC required ownership = 7.683/19.5 = 39.4% (b) New Shares/(Old Shares + New Shares) = 39.4% or New Shares = 39.4/(1 – 0.394) × Old Shares = 325,100 shares (c) Price per share = $2 million/325,100 = $6.152 (d) Post-money valuation = $6.152 × 825,100 = $5.08 million or

= $2 million/0.394 = $5.08 million FLEA Post-Money Valuation (millions) ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ Cash from new equity $2.00 Debt $1.00 Other assets 4.08 New equity 2.00 Old equity 3.08 Assets $6.08 $6.08

10.7.

Exit proceeds = $1million × (1.4)4 = $3.842 million Total required equity at exit time = $3.842 ÷ 0.25 = $15.366 million Equity + Net Debt = $15.366 + $6 = $21.366 million Asset-sale gross proceeds prior to fees and expenses = $21.366 ÷(1 – 0.04) = $22.256 million Exit EBITDA = $22.256 ÷ 8 = $2.782 million Exit Sales = 2.782 million ÷ 0.1 = $27.82 million Required Sales growth rate = ($27.82 ÷ $8.1)1/4 – 1 = 36.1% Let sales grow at 18%, then Exit Sales = $15.7 million and Exit EBITDA = $1.57 million. Hence, Exit Sale Price = $1.57 × 6 = $9.4 million that, after fees and expenses, equals $9 million or $3 million for the equityholders of which $0.75 million are yours. This yields an annual loss of 7%.

10.8. Since the fixed costs are small the probability of negative EBITDA is negligible. This permits valuating the earnout using straight DCF. Another way of saying this is that for small fixed costs the call on revenue is deep in the money and DCF applies.

46

($ 000) EBITDA Multiple

$ 4,000 9 36,000 15,000 $21,000

Assumed debt TUV-TUV's maximum bid for Balkan's equity Minus Cash 8,000 Minus Annuity PV @ 9% 2,567 10,567 Maximum earnout present value 10,433 Compound interest factor = 1.133 1.443 Undiscounted earnout on 3rd year 15,055 Third year EBITDA = (4,000)(1.2)3 6,912 Earnout EBITDA multiple 2.18

10.9. Since fixed costs are relatively small we will first ignore the option value of the earnout and apply straight DCF. ($ 000) Cash $ 5,000 Subordinated note Year 2006 2007 2008 2009 2010 Interest 525 525 525 525 525 Tax shield 210 210 210 210 210 Principal 7,000 After-tax cash flow 315 315 315 315 7,315 PV (@ (1 - 40%)9% Earnout: EBITDA (2005) = $6,000 EBITDA (2010) = 0.15(50,000)(1.10)3 – 1,500 = Multiple

$6,730 $ 8,483 × 0.5 $ 4,241

PV (@ 14%) Value of Prentice's offer for VASM equity Assumed debt Value of offer for enterprise EBITDA EBITDA (trailing) multiple at sale time

2,863 $ 14,593 14,800 $ 29,393 6,000 4.90x

A more precise valuation of the earnout would take into account that fixed costs have no systematic risk. Let us assume that WACC = 14% applies to the variable component of revenues. Also, let the riskless rate equal 5%. Then, the value of the earnout is: (0.5)[(0.15)(50)(1.10)3 (1.14)-3 – 1.5(1.05)-3] = $2.721 million.

Substituting above gives the value of offer for the enterprise equal to $29.251 million with an EBITDA multiple equal to 4.88.

47

Let us verify that the option value of the earnout is negligible in the present case. Let the 95% confidence range of revenue growth be [-20%, 40%] and the riskless rate be 5%. Then, the call on revenue can be valued using the following inputs: PV(Revenue3) Exercise price Riskless rate Volatility Expiration

= 50(1.10)3/(1.14)3 = $44.92 million = 1.5/0.15 = $10 million = 5% = (20% + 40%)/4 = 15% = 3 years

The Financial Options Calculator yields $36.283 million as the value of the call. Which means that the earnout is worth (0.5)(0.15)(36.283) = $2.721. This value is the same as the one computed above.

10.10. First, value the call on revenue for an exercise price = (1.5 + 6)/0.15 = $50 million and the other inputs used in Problem 10.9.

The Financial Options Calculator yields $5.478 million as the value of the call. Therefore, the earnout is worth (3.484)(0.15)(5.478) = $2.863 million.

Note that the simple DCF valuation of this earnout would yield a much lower and incorrect valuation: (3.484)[(0.15)(50)(1.10)3 (1.14)-3 – (1.5 + 6.0)(1.05)-3] = $0.90 million.

Prentice Work would be paying approximately the same present value under this earnout than under the earnout of problem 10.9. But this earnout pays only when EBITDA exceeds the threshold of $6 million.

10.11. (a) Capping the earnout at $10 million means that the seller is long (3.484)(0.15) = 0.5226 calls on revenue with exercise price equal to the threshold of $50 million (see answer to 10.11) and short 0.5226 calls (caps) on revenue with exercise price equal to $50 + $10/0.5226 = $69.1351 million. The Financial Options Calculator gives a value for this last call equal to $0.930 million, which means that the earnout is equal to the value calculated in 10.10 minus 0.5226 × $0.930 = $0.486 million, or $2.863 – $0.486 = $2.377 million. (b) In order to maintain the value of the capped earnout at $2.721 million, we can increase the earnout multiple and account for its effect on the exercise value of the cap. A few iterations show that increasing the multiple to 4.9 gives an exercise price equal to $50 + $10/[(4.475)(0.15)] = $64.90 and a value of the earnout equal to (4.475)(0.15)(5.478 – 1.425) = $2.721 million.

10.12. Using the Financial Options Calculator to compute the Asian options yields the value of the seller's call equal to (3.484)(0.15)(3.058) = $1.598 million versus $2.863 million attained in 10.10. Similarly, the value of the Asian cap is (3.484)(0.15)(0.160) = $0.084 million versus $0.486 attained in 10.11. Hence, the net value of the earnout is (1.598 – 0.084) = $1.514 million versus $2.377 attained in 10.11. The earnout multiple needs to 48

be increased if the goal is to keep the earnout value at $2.721. Trial an error yields 9.785x. In fact, for this multiple the exercise price of the cap is 50 + $10/[(9.785)(0.15)] = $56.81 million and the earnout is worth (9.785)(0.15)(3.058 – 1.204) = $2.721 million.

10.13. The exercise price of the repurchase option is 0.90 × $6.05 = $5.445 million. The value of the seller's equity is $14.451 million. The Financial Options Calculator gives a value for the seller's repurchase option equal to $9.771 million. Since this option would be exercisable only in the event of the buyer's default and the latter has 5% probability, the value of the option is only $0.489 million. The value of the buyer's offer is then (0.95)($14.451) + (0.05)($9.771 + $5.582) = $14.496 million, where $5.582 million is the present value of the cash payments to be made by the buyer prior to its default, computed as in problem 10.9.

10.14. The earnout equals (2.5)(0.15) = 0.375 times the difference between (i) three yearly calls on revenue, each based upon the present value of the respective expected revenue and an exercise threshold equal to $50 million and (ii) three yearly calls (the caps) each with exercise price equal to 50 + 2/0.375 = $55.333 million.

The value of the earnout is $2.2 million. The Financial Options Calculator can be used to compute the value of these options. Details are shown in the following table.

VASM: Valuation of multi-year earnout ($000) Year Revenue Revenue value at Revenue volatility Riskless rate Call with strike price @ Call with strike price (cap) @ Earnout base Earnout multiple x EBITDA margin Value of yearly payment Earnout value

0 $ 50,000 14%

1 2 3 $ 55,000 $ 60,500 $ 66,550 48,246 46,553 44,919 15.00% 15.00% 15.00%

5% $50,000 55,333

3,213 1,318 1,895

4,523 2,532 1,991

5,477 3,496 1,981

0.375 $

711

$

747

$

743

$ 2,200

10.15. Open the Financial Options Calculator. Click the Call tab and Toggle down past the call option panel.

Enter a column of 100 years starting with year 2007, this is the input column. Go one column to the right and on the row above the row corresponding to the first year enter the address of the cell that corresponds to the European call value. Then follow Excel’s steps to create a data table, click on Data, Table, etc. Sum the resulting call values. Verify that call values corresponding to far out years are zero so that the sum has converged. This is the value of a perpetual call on revenues. Multiply it by the earnout multiple times the 49

EBITDA margin. This is the value of the earnout. Verify that your result agrees with that given in Section 10.7.

10.16. Substituting the data in the formulas of Section 10.7 yields: (1 – τ)(1 – δ – rd q) = (1 – 0.40)(1 – 0.10 – (0.09)(3)) = 0.378 pθ(1 – τ)(1 – δ – rd q)b = (0.75)(0.30)(0.378)(0.15) = 0.0128 X = −ab–1 + H((1−τ)(1 – δ – rd q)b)–1 = 1.5/0.15 + 2.5/[(0.378)(0.15)] = $54.092 million.

Also, since Net Income = 0.378(0.15Revenue – 1.5), the last year revenue corresponding to $2 million net income was R0 = (2/0.378 + 1.5)/0.15 = $45.273 million.

Use the call option module with the data table to compute the value of Class A shares detailed in problem 10.15. The inputs for year t are: PV(Rt) = R0(1 + g)t/(1 + w)t = $45.273(1.10)t/(1.14)t X = $54.092,

σ = 15%,

rf = 5%,

expiration date = t.

The sum of the calls over 150 years is $402.807 million and the total value of Class A shares is attained multiplying $402.807 by 0.0128 given by expression (10.7) of the main text and calculated above. That is, (0.0128)(402.807) = $5.156 million in total or $5.156 a share. And Mr. Webster’s earnout would be worth 97% of $5.156 million or $5 million, after fees and expenses.

10.17. The value of the holdback is equal the holdback amount times the probability that first-year EBITDA be greater or equal to $6.66 million. Note that the contingent payment does not have to be discounted because it earns the riskless rate in escrow. From Chapter 10, section 10.2 we can approximate the probability distribution of Revenue1 by the lognormal distribution. Hence, ln(Revenue1) follows the normal distribution with mean ln(PV(Revenue1) + (w – ½σ2) and standard deviation σ where w = ln(1.14) = 13.1% is the continuous time WACC of VASM and σ = 15% is the volatility of Revenue1. Now, since the value of Revenue1 at time zero is $55/1.14 = $48.246 million (see answer to 10.15 above), the mean of ln(Revenue1) is 3.996. Thus, Prob(EBITDA1 ≥ 6.66) = Pr(Revenue1 ≥ (6.66 + 1.5)/0.14 = 1 – N[ln(54.4); 3.996, 15%] = 0.3221.

Where N[.] is the normal distribution and its value can be obtained from tables or using Excel's NORMDIST function. Therefore, the value of the holdback is 0.3221 × $2 million = $0.644 million.

50

10.18. (a) (millions)

Equity stakes pre-IPO

Acquisition price: Sources: Seller financing Allen Venture Management Public shareholders

$15.00

Notes

Calculations of returns and proceeds have to be based on percent ownerships.

7.0 5.0 3.0

10% 51% 39%

$15.00

100%

IPO valuation Pro-forma revenues 2004-2005 Revenue multiple Enterprise value Debt (principal + interest) Colossus Allen Venture Partners Equity IPO % equity sold in IPO

(b) Gustav Gustav's associates Allen Colossus Public shareholders

(c)

Equity stakes post-IPO

4.45% 22.70% 17.36% 55.48% 100%

$40.00 4.00

Here, the stakes pre-IPO and post-IPO are summarized. The post-IPO stakes require valuing the enterprise and pricing the issue. This is done immediately below.

Here, the value of the enterprise as of the IPO date (June 30, 2004) is estimated.

$160.00 The outstanding debt is the principal

7.34 8.47

of the two notes plus the accrued interest.

15.81 $144.19 80.00 55.48%

The valuation assumes that $100 million are raised in the IPO, and the value of equity already includes the IPO proceeds.

Equity stakes 8.68% $12.52 8.68% 12.52 22.70% 32.74 4.45% 6.42 55.48% 80.00 $144.19

The post-IPO stake of mgt. Is

17.36%

of which Gustav would have half or 8.68%

Allen Venture Partners Proceeds: Note Equity

$8.47 32.74

Investment: Return multiple (d)

= $8 (1.12)^.5

$41.20 8.00 5.2

The value of Allen's stake is made up of the equity participation plus the note principal plus the accrued interest. $41.20

Colossus' proceeds through June 30, 2002

divided by

$8.00

Colossus would receive: the initial cash payment plus the note principal and accrued

Cash Note Equity

$8.00 7.34 6.42

interest plus the value of its equity =$7 (1.10)^.5

$21.76

participation. $3 m of its proceeds go to settle NetTune management' stock

Note: Time value of money ignored for Colossus's proceeds.

appreciation rights and severance. Strictly, in present value, Colossus receives just $15 m but by taking a risky equity partipation it stands to make much more. Note that the timing of the cash flows is different. This can be accounted for by accruing a return to the $8 m received on 12/31/01.

(e)

Allocation of IPO proceeds

The allocation of the IPO proceeds is detailed on this panel.

Gross proceeds Fees & expenses Net proceeds

$80.00 4.80

Debt & interest pymts.

Expansion & operation Cash for use in 2003

$15.81 39.00

$75.20 Payments on Allen and Colossus notes.

54.81 $20.39

Cash to cover year 2002 shortfall.

Cash to cover year 2003 shortfall.

51

(f) NetTune.com - Income and cash flow projection, 2004-2006 (in millions) Revenues Expenses Operating income Interest expense Allen loan @ Colossus loan Interest earned @ Income before taxes Net operating loss carryforward Taxes Net income Non-cash interest expense Depreciation Other noncash Capex and NWC incr.

Net IPO proceeds Debt retirement Cash surplus (deficit) Cash balance Debt: Allen Colossus

12/31/2003

3/31/2004

$

2.87% 2.41% 1.25%

40%

6/30/2004

2.50 $ 3.20 (0.70)

7.00 4.80 2.20

0.23 0.17 0.04 (1.06) (1.06) (1.06) 0.40

0.24 0.17 0.02 1.81 0.30 1.51 0.41 0.10

(1.10)

$

3.00 3.00

(1.76) 1.24

8.0 7.0

8.2 7.2

(3.50) 75.20 (15.81) 57.91 59.15

9/30/2004

$

12/31/2004

3/31/2005

6/30/2005

9/30/2005

14.50 $ 18.80 (4.30)

8.50 $ 24.00 (15.50)

10.00 $ 19.80 (9.80)

18.30 $ 20.50 (2.20)

25.60 22.00 3.60

0.74 (3.56) (3.56) (3.56)

0.58 (14.92) (18.48) (14.92)

0.27 (9.53) (28.01) (9.53)

0.08 (2.12) (30.13) (2.12)

0.01 3.61 (26.52) 3.61

0.25 0.04 (9.30)

0.85 0.05 (11.30)

1.25 0.05 (6.60)

1.40 0.10 (5.10)

(12.57) 46.58

(25.32) 21.26

(14.83) 6.42

(5.72) 0.70

12/31/2005

3/31/2006

$

$

34.40 24.00 10.40

26.20 23.10 3.10

0.04 10.44 (16.09) 10.44

0.17 (2.73) (18.82) (2.73)

0.10 3.20 (15.62) 3.20

1.90 0.20 (3.50)

2.10 0.20 (2.40)

2.30 0.20 (4.70)

2.40 0.20 (6.00)

2.21 2.91

10.34 13.25

(4.93) 8.32

(0.20) 8.12

8.5 7.3 15.8

IPO proceeds and disposition: Gross proceeds Fees and expenses Net Proceeds Debt retirement Cash yielded

$

80.0 4.8 75.2 15.8 59.4

Question (g): Enterprise value at IPO Pro-forma 7/31/05 - 6/30/06 EBITDA Implied EBITDA multiple

$ 160.00 $ 22.90 6.99

10.19. (a) Bondholders cannot be sure of the nature of TVL's new project. Management may plan to undertake a high-risk, negative-NPV project in order to gamble a solution to TVL's problems. In that case they would be gambling their lenders' capital. So lenders will discount the issue in order to account for the additional risk.

The call provision gives management the option to recapture some of the value given to the lenders in case the project is successful (see (b)). (b) As with any option, the call provision has a value determined by the value of the underlying asset (the bond in this case). If the firm chooses a negative NPV project, the value of the bond will decline and so will the value of the call. On the other hand, if the firm were to undertake a positive NPV project, the value of the bonds will increase beyond the lenders' expectations but so will the value of the call. The firm will then be able to capture part of the value it has created by exercising its call option. (c) The call provision normally depresses the initial price of the offer in order to compensate lenders for giving away the call right to the firm. However, in the present case the call provision would not be costly to the firm 52

6/30/2006

18.20 $ 21.10 (2.90)

when lenders assume the firm would not be able to undertake high NPV projects and attach a low probability to the value of the bonds increasing substantially to justify their call in the future.

10.20. The answers are contained in the following exhibits.

NetServices Inc. Capitalization Table Prior to DesignPlus Acquisition Post-money Shareholder $ Invested Valuation Morningside STL Letts Total

$75,000,000 $70,000,000 $22,500,000 $167,500,000

Pre-money Valuation

Ownership

167,500,000

$0

44.78% 41.79% 13.43% 100.00%

NetServices Inc. Capitalization Table After DesignPlus Acquisition Post-money Shareholder $ Invested Valuation

Pre-money Valuation

New Ownership

Morningside STL Letts Georgetown Design Plus Management Total

Shares

11,194,030 10,447,761 3,358,209 25,000,000

Shares

$75,000,000 $70,000,000 $22,500,000 $10,793,103 $6,206,897 $184,500,000

40.65% 11,194,030 37.94% 10,447,761 12.20% 3,358,209 5.85% 1,610,911 3.36% 926,402 184,500,000 167,500,000 100.00% 27,537,313 2,462,687 shares to be granted in the future but prior to the IPO (see below).

* There is an employee pool of

Price Per Share $6.7000 $6.7000 $6.7000 $6.7000

Price Per Share $6.7000 $6.7000 $6.7000 $6.7000 $6.7000 $6.7000

Valuation of DesignPlus 2000 pro-forma revenues Revenue multiple Series A shares Cash In shares @ Management @ Total

12,000,000 3 36,000,000 82.76%

29,793,103

$6.7000 $6.7000

1,610,911 926,402

2/15/1998 (4,000,000)

11/20/1998 (4,000,000)

19,000,000 10,793,103 6,206,897 36,000,000

Return to Georgetown Group

Investment Sale of DesignPlus IPO: Enterprise value Net debt Equity Fully diluted number of shares Per share Proceeds Cash flow IRR

7/30/1997 (3,000,000)

10/27/1999 (4,000,000)

10/15/2000

6/30/2003

19,000,000

(3,000,000) 44.88%

(4,000,000)

53

(4,000,000)

(4,000,000)

19,000,000

810,000,000 25,000,000 785,000,000 30,000,000 26.17 42,152,170 42,152,170

10.21. The answer is contained in the following exhibits.

Valuation of DesignPlus 2000 pro-forma revenues Revenue multiple Enterprise value Net debt Equity before option exercise Exercise money @ $1.50 Equity after option exercise Series A shares 82.76% Series B shares 17.24% Cash In shares @ Management @* Total

2,500,000 12,000,000 2,500,000

$6.70 $5.4586

2,074,112 2,500,000

$12,000,000 3 36,000,000 36,000,000 3,750,000 39,750,000 32,896,552 6,853,448 19,000,000 13,896,552 3,103,448 36,000,000

* $5.4586 is the exercise price of the new options.

Return to Georgetown Group

Investment Sale of DesignPlus IPO: Enterprise value Net debt Equity Fully diluted number of shares Per share Proceeds to Georgetown Group Cash flow IRR

7/30/1997 (3,000,000)

2/15/1998 (4,000,000)

11/20/1998 (4,000,000)

10/27/1999 (4,000,000)

10/15/2000

6/30/2003

19,000,000

(3,000,000) 49.67%

(4,000,000)

54

(4,000,000)

(4,000,000)

19,000,000

810,000,000 25,000,000 785,000,000 30,000,000 26.17 54,272,603 54,272,603

Chapter 11. Special Offer Structures: Price Guarantees and Collars 11.1. Let μ be the annual continuously compounded rate of return of the stock and δ the continuous dividend yield, then the price Pt over any given week obeys Pt = Pt – 1 e(μ – δ)/52 Hence, the weekly return is μ/52 = ln(Pteδ/52/Pt – 1).

That is, the rate of return on any given week is attained by adding to the closing price any dividend received during that week, dividing it by the closing price of the previous week and taking the natural logarithm of the resulting price relative. The weekly volatility is the standard deviation of μ/52. The volatility is computed in following exhibit. The standard deviation is computed with Excel’s STDEV function that already adjusts for sample bias. The annual volatility is computed multiplying the standard deviation of weekly returns by the squared root of 52.

11.2. The volatility of General Mills is estimated following the same steps as in 11.1. It equals 24.63%.

11.3. The value of the gold price guarantee is 5 million times the difference between two Asian puts minus 2.5 million times an Asian call. The common inputs for the option are: Initial price = $277.45 Valuation date = August 17, 2001 Expiration = August 17, 2002 Number of averaging point (trading days) = 252 Volatility = 10.45% Annual risk-free rate = 3.38% Storage costs = $2/year (negative dividend paid daily over 365 days) The exercise prices the long put and the short call are $265 and $300, respectively. The exercise price of the short put is 265 – 75/5 = $250. These options are valued with the Financial Options Calculator over 365 calendar days with 365/252 = 1.448413 days between averaging points. This approximation permits generating the 252 days average points throughout the year. The results are: Put(265) = $1.104, Put(250) = $0.107 and Call (300) = $1.593. Hence, the value of the guarantee is: 5(1.104 – 0.107) – 2.5(1.593) = $1.0 million.

55

M arion Laboratories Volatility Closing Price W eek Price plus Relative Dividend P' t/P t-1 t P't = P t+Div t

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

19.625 18.500 0.9427 19.375 1.0473 20.000 1.0323 19.000 0.9500 18.750 0.9868 18.750 1.0000 18.750 1.0000 18.875 1.0067 17.820 0.9441 17.000 0.9577 17.000 1.0000 17.375 1.0221 17.250 0.9928 18.750 1.0870 20.375 1.0867 20.500 1.0061 19.750 0.9634 19.375 0.9810 19.500 1.0065 19.625 1.0064 20.250 1.0318 19.840 0.9798 20.125 1.0190 20.125 1.0000 21.500 1.0683 22.125 1.0291 22.750 1.0282 23.625 1.0385 24.750 1.0476 22.750 0.9192 23.590 1.0369 22.750 0.9681 23.375 1.0275 23.375 1.0000 24.125 1.0321 24.375 1.0104 25.125 1.0308 25.875 1.0299 25.875 1.0000 26.625 1.0290 25.375 0.9531 25.375 1.0000 26.500 1.0443 27.500 1.0377 27.375 0.9955 27.250 0.9954 26.500 0.9725 25.090 0.9468 25.750 1.0300 23.500 0.9126 23.875 1.0160 25.250 1.0576 W eekly Volatility Annual Volatility

W eekly Return ln(P' t /P t-1 )

-0.0590 0.0462 0.0317 -0.0513 -0.0132 0.0000 0.0000 0.0066 -0.0575 -0.0432 0.0000 0.0218 -0.0072 0.0834 0.0831 0.0061 -0.0373 -0.0192 0.0064 0.0064 0.0314 -0.0205 0.0188 0.0000 0.0661 0.0287 0.0279 0.0377 0.0465 -0.0843 0.0363 -0.0324 0.0271 0.0000 0.0316 0.0103 0.0303 0.0294 0.0000 0.0286 -0.0481 0.0000 0.0434 0.0370 -0.0046 -0.0046 -0.0279 -0.0547 0.0296 -0.0914 0.0158 0.0560 3.879% 27.97%

11.4. Two alternative interpretations of Borland’s offer are (1) 0.398 P – 0.398 Call(X = $43.97) + 0.346 Call(X = $50.58) (2) 0.346 P + 0.346 Put(X = $50.58) - 0.398 Put(X = $43.97), 56

where P is the price of Borland, which is the present value of the stock to be received at consummation of the merger because Borland paid no dividend. Recall the put-call parity (see Appendix A): P + Put(X) = PV(X) + Call(X), where X is the exercise price. Apply it to expand 0.398 Call($43.97) = 0.398[P + Put($43.97) – PV($43.97)] = 0.398 P + 0.398 Put($43.97) – PV($17.50) which yields (3) PV($17.5) + 0.346 Call(X = $50.58) – 0.398 Put(X = $43.97).

This is the expression used in section 9.3.

In order to get (3) from (2) substitute Put(X = $50.58) = PV(X) + Call(X) – P into (2).

11.5. The value of the collar offer per share of U S West is PV($69) + 1.729932 Call(X = $39.90) – 2.44161 Put (X = $28.26).

As in Section 9.3, the value of the collar options as of July 16 are approximated by the average of their European and Asian values over the period July 16 1999 – July 30, 2000 with a 15-day price average, $35 Qwest’s initial stock price, zero dividend, 4.71% interest rate and 47.35% volatility, estimated as the weighted average of Qwest and U S West volatilities. Using Qwest’s pre-announcement stock price assumes that investors would consider the merger to be a break-even transaction. Note, however, that the value of an option spread is not very sensitive to the price input. (Qwest stock closed on Monday, July 19 at 3315/16.)

The Financial Options Calculator yields the following values: European

Asian

Average

Call($39.90)

$5.53

$5.43

$5.48

Put($28.26)

$2.70

$2.64

$2.67

In order to take dilution into account one computes: Exchange ratio 1.72932 2.44161 U S West shares

508

878.5 1,204.3

Qwest shares

747

747

747 .

1.176

1.660 .

Ratio of new to old shares Therefore, the value of the exchange offer is:

69 (1.0471)–379/365 + 1.72932 × 5.48/2.176 – 2.44161 × 2.67/2.660 = 65.78 + 4.36 – 2.45 = $67.69.

57

11.6. One first notes that the terms for Canada Dry and McCall's are the same but Canada Dry is $1 cheaper.

Thus, one can simply buy 1 CD and short 1 MC. Wyser-Pratte (1982)3 suggests the following more interesting arbitrage:

1 Canada Dry 1 Hunt Foods Common exchange ratio Long: 1 Canada Dry Short: 0.55 Hunt Foods Net

Norton Simon .

Common Preferred 0.6875 0 .3125 1.25 0.3125 0.55 .

0.6875 0.3125 –0.6875 –0.1719.

0 0.1406

$36 $58 –$36 31.9 –$4.1

or 4.10/0.1406 = $29.12 cost per each preferred vs. ≈ $40 estimated value.

Gross spread = 0.1406 × 40 – 4.1 = $1.52 or $152 per 100 Canada Dry Shares.

11.7. From the put-call parity: P + Put = Call + PV(X) Put (42.55) = Call (42.55) + PV (42.55) – P Put (38.00) = Call (38.00) + PV (38.00) – P Put (42.55) – Put (38) = Call (42.55) – Call (38) + PV (4.55) = 1.65 – 3.07 + 4.30 = $2.88 That is, Diageo’s put spread is equivalent to a call spread plus the present value of $4.55.

3

See references in the textbook.

58

Chapter 12. Acquisitions in Developed and Emerging Markets 12.1. Consider for example the forecast of the 2008 future $/€ spot rate. From r€’08 = 3.89%, r$’08 = 4.82%, S0 = 1.3197, it results S’08 = (1.3197)(1.0482/1.0389)2 = 1.3434 and FCF$’09 = (€93.12)(1.3434) = $125.10.

12.2. The inputs are as follows: Debt ratio

40%

Equity premium

3.2%

Small-cap premium

2.7%

U.S. Treasury rate

5.79%

Beta coefficient

1.014

Cost of debt

9.2%

Corporate tax rate

40%

South African sovereign spread over U.S. Treasury

2.12%

Thus, the cost of capital is 0.60(5.79% + 3.2% × 1.014 + 2.7%) + 0.40(1 – 40%)(9.2%) + 2.12 = 9.25%.

12.3. The valuation of Bolivian Power can be greatly simplified by taking into account that the company paid no profit tax because taxes were recovered from the rate it charged to consumers. This means that the classical Modigliani-Miller proposition that the value of the firm and its cost of capital are both independent of debt financing holds in this case. 4 Thus, the net income of Bolivian Power was actually income before taxes because the tax rate applied simply offset the tax credit already in the revenue. Another thing to notice is that the company recovered the excess interest on debt over 6%. That is, Bolivian Power paid only 6% interest on debt. This is why only 6% interest on the debt balance has to be added back for calculating unlevered net income and this interest has to be before tax in the present case. Finally, the value of the tax shield in the APV valuation is zero because debt does not generate a tax shield. Similarly, EBITDA here is net income, plus depreciation, minus credited and earned interest plus 6% of the interest on debt. The following exhibits present the APV valuation and the cash flow statements.

It should be pointed out that export profits would not be subject to tax credit or excess interest credit.

However, that would be a relatively small fraction of Bolivian Power cash flow.

4

See Chapter 6 to verify that, when the tax rate is zero, enterprise value equals the value of the unlevered firm.

59

On November 1993, Bolivian Power issued 2,700,000 shares, of which 1,250,000 were primary shares, at $24 a share ($22.65 a share net proceeds to the company).

BOLIVIAN POWER COMPANY Ltd. ADJUSTED PRESENT VALUE VALUATION In thousands of U.S. dollars, except for per share data 1993 Net income for common Minus capitalized interest Minus interest income Plus 6% interest on debt NOPAT Depreciation Capex Working cap. increases Net proceeds from equity issue Unlevered free cash flow Expected dollar inflation 3.00% Present value of FCF @ 17.9% Continuation value @ PV of cont. value @ 17.9% Enterprise value (incl. net proceeds) Cash Debt Equity Shares after issue Estimated share price Gross proceeds Fees and expenses 5.625% Net proceeds EBITDA EBITDAx Comparable EBITDAx (median) Chile US

1994

1995

1996

1997

1998

7,140 (1,977) (1,570) 290 3,883 3,324 (40,726) (244)

9,656 (5,522) (1,385) 2,859 5,608 3,579 (47,722) (2,380)

12,889 (5,032) (1,200) 3,699 10,356 5,402 (22,943) (4,669)

12,327 0 (1,140) 3,274 14,461 8,444 (8,448) (1,715)

12,731 0 (1,520) 3,233 14,444 8,782 (9,024) (516)

(33,764)

(40,915)

(11,854)

12,742

13,686

8.50% => nominal

11.76%

249,919

28,555

(52,714) real growth

109,822 85,663 16,000 0 101,663 4,200 $24.21 30,257 1,702 28,555

U.S. Treasury rate Equity premium Bolivian Power beta Micro-cap premium Country risk premium Cost of equity 7,207 11.9

9,187

15,758

6.8% 3.5% 0.45 4.5% 5.0% 17.9% 22,905

23,226 10.8

11.7 7.3 Value Matrix Share Price for Different Continuation Value Growth Rates 8.0% 8.5% 9.0% $21.23 $24.21 $27.73

Postscript: By mid-1996 the Bolivia Power stock traded at about $40/share. In September it reached a peak of $46/share and fell to $42 by the end of October. On November 20, NRG Energy launched a tender offer for 100% of the shares at $43/share, following an expression by the then largest shareholder (Liberty Power) of selling its 17.1% stake. The acquisition was completed on December 18, with NRG sharing ownership with 60

BOLIVIAN POWER COMPANY Ltd. CASH FLOW STATEMENTS 1994-1998 In thousands of U.S. dollars Net income for common Depreciation Capitalized interest Cash flow from operations Capex Working cap. increases Cash flow before debt financing Cumulated debt Proceed from equity issue Change in Cash End of year cash

1993

1994

1995

1996

1997

1998

7,559 3,400 (329) 10,630 7,000 0 3,630

7,140 3,324 (1,977) 8,487 40,726 244 (32,483) 4,825 28,346 688 4,318

9,656 3,579 (5,522) 7,713 47,722 2,380 (42,389) 42,825

12,889 5,402 (5,032) 13,259 22,943 4,669 (14,353) 13,992

12,327 8,444 0 20,771 8,448 1,715 10,608 (7,081)

12,731 8,782 0 21,513 9,024 516 11,973 (674)

436 4,754

(361) 4,393

3,527 7,920

11,299 19,219

3,630

Nordic Power Invest AB, a subsidiary of Swedish utility Vattenfall AB, by virtue of an agreement of coownership prior to the tender offer.

12.4. Petöfi’s free cash flows are computed in the following exhibit.

PETÖFI PRINTING COMPANY LTD. PROJECTED FREE CASH FLOWS 1992-2000 HUF (Hungarian Forint) millions

Fiscal year ending December 31

1991

EBITDA Net income Net interest after tax NOPAT Depreciation and amortization Sale of assets CAPEX & Net WC increase Unlevered free cash flow HUF inflation rate HUF accumulated inflation rate Real unlevered free cash flow

354

1992

1993

1994

1995

1996

1997

1998

1999

2000

475 949 1,308 1,553 287 682 1,092 1,342 52 57 (1) (75) 339 739 1,091 1,267 118 234 244 262 0 52 0 0 (1,516) (509) (450) (548) (1,059) 517 885 982 24.0% 14.0% 11.0% 9.0% 24.0% 41.4% 56.9% 71.0% (854) 365 564 574

1,744 1,424 (173) 1,251 286 0 (516) 1,021 7.5% 83.9% 555

1,714 1,697 1,759 1,865 1,454 1,485 1,592 1,632 (249) (316) (392) (454) 1,205 1,169 1,200 1,177 313 341 367 394 0 0 0 0 (479) (463) (468) (504) 1,039 1,046 1,099 1,068 6.5% 5.5% 5.0% 5.0% 95.8% 106.6% 116.9% 127.8% 530 506 507 469

Petöfi’s financial policy does not produce a tax shield in every year except 1995. Note that it enjoys a tax holiday until 1995 while it has debt, and its debt goes to zero after 1995. In 1995 it pays an average tax rate of 4% (16% on the last quarter) and interest expense is only HUF56 million such that the tax shield has negligible present value. Hence, the value of the enterprise can be computed with the APV procedure, discounting the free cash flows at the unlevered cost of capital and taking into account that the value of the tax shield is negligible.

61

12.5. (a) Company Engraph Sonoco David Smith

Beta Debt/Equity 0.99 0.29 1.07 0.14 0.99 0.06

Low & Bonar

1.03

Average

Unlevered Beta 0.77 0.94 0.93

0.13

0.91

0.16

0.89

PETÖFI PRINTING COMPANY Ltd. Cost of equity of unlevered large-cap printer 30 yr US Treasury bond yield Large cap equity premium Unlevered beta Equity premium Large cap cost of equity + Micro-cap premium Small-cap cost of equity + Country risk premium 3yr US$ Hungarian gvt. bond yield 3yr US Treasury benchmark = Cost of capital of unlevered Petöfi (prior to private equity discount) US$ expected inflation Real cost of capital

7.55% 3.2% 0.89 2.84% 10.38% 4.50% 14.88% 9.5% 5.9% 3.6% 3.60% 18.48%

3.30% 14.70%

(b) and (c). The valuation of Petöfi and its sensitivity to changes in the cost of capital and the EBITDA multiple are shown in the following exhibits. Continuation value was estimated using the median EBITDA multiple of precedent transactions. Petöfi’s multiple can be lower because of its private nature but higher because of its higher potential growth. Petöfi’s private placement took place in July of 1992 at HUF101.

62

PETÖFI PRINTING COMPANY Ltd. Present value of FCF @ 14.7% HUF Yr 2000 value @ EBITDAx 7.3 5,978 PV of continuation value @ 14.7% Total enterprise value Net proceeds from equity issue Enterprise value after equity issue Private equity discount 20% EV after private equity discount Implied LTM EBITDAx 8.3 Outstanding net debt Value of equity HUF Common share equivalents Value per share HUF Per share @ HUF/$ 78.3 $

75 2,856 million 30.949 million 92 1.18

Issue price Shares issued Gross proceeds Fees and expenses Net proceeds to company

92 7.755 million 716 million 42 674 million

HUF

5.88%

1,250 million 1,740 2,990 674 3,664 733 2,931

PETÖFI PRICING MATRIX Share price in HUF Yr. 2000 EBITDA Multiple

Real cost of equity

6.0 101 94 82 80 73

12.0% 13.0% 14.7% 15.0% 16.0%

63

7.3 115 106 92 90 83

8.0 122 112 98 96 88

12.6.

PETÖFI PRINTING COMPANY LTD. HUF (Hungarian Forint) millions

Fiscal year ending December 31 1991 Discounting (nominal) dollar cash flows Unlevered free cash flows in HUFs Continuation value in HUFs Exchange rate HUF/$ US expected inflation Estimation of future exchange rate

1992

1993

1994

1995

1996

1997

1998

1999

2000

(1,059)

517

885

982

1,021

1,039

1,046

1,099

1,068 13,616

94.0

103.7

111.5

117.6

122.4

126.2

128.9

131.0

133.1

78.3 3.3% Future exchange rate = Previous year exchange rate x (1+HUF inflation)/(1+US$ inflation)

Unlevered free cas flows in US$ Continuation value in dollars PV of FCF @ PV of continuation value @ Enterprise value in US$ Enterprise value in HUFs @

(11.3)

5.0

7.9

8.3

8.3

8.2

8.1

8.4

8.0 102.3

18.5% $ 16.0 18.5% 22.2 $ 38.2 78.3 2,990

12.7.

PETÖFI PRINTING COMPANY LTD. HUF (Hungarian Forint) millions

Fiscal year ending December 31 1991 1992 1993 Discounting nominal cash flows at the nominal cost of capital

1994

1995

1996

1997

1998

1999

2000

Unlevered free cash flow Continuation value (nominal) Real cost of capital HUF inflation rate Nominal cost of capital PV of FCF Sum of PV of FCF PV of continuation value Enterprise value in HUF

(1,059)

517

885

982

1,021

1,039

1,046

1,099

1,068 13,616

24% 42% (745) 1,250 1,740 2,990

14% 31% 278

11% 27% 374

9% 25% 332

8% 23% 280

7% 22% 233

6% 21% 194

5% 20% 169

5% 20% 136

14.7%

64

Chapter 13. Leveraged Buyouts 13.1. Assuming that the credit line takes care of cash needs, the existing cash balance can be used to fund part of debt retirement. The statements of income and cash flow, exit valuation, and calculation of returns follow.

(1) Cash Flow Statement $ millions (except per share data) Revenue EBITDA Depreciation EBIT Senior debt interest Subordinated debt interest Income before tax Taxes Net income Depreciation Capital expenditures Net working capital increase Free cash flow before debt amort.

Senior LBO debt amortization

8% 14% 1%

40%

1.0% 0.5%

Current 18.00

Capital structure Senior debt @

7.75%

2007 49.55 6.94 0.50 6.44 1.62 4.82 1.93 2.89 0.50 0.50 0.25 2.65

LBO 22.48

@

2010 62.42 8.74 0.62 8.11 1.72 2.24 4.16 1.66 2.49 0.62 0.62 0.31 2.18 2.18

2011 67.41 9.44 0.67 8.76 1.53 2.24 5.00 2.00 3.00 0.67 0.67 0.34 2.66 2.66

2012 72.81 10.19 0.73 9.46 1.29 2.24 5.94 2.37 3.56 0.73 0.73 0.36 3.20 3.20

21.11

19.36

17.18

14.52

11.32

18.73

18.73

18.73

18.73

18.73

11.95% Total debt capacity: 5.5x 2003EBITDA => Sub debt 2.5x 2003 EBITDA

41.21

Total debt

(2) Sources and Uses of Funds

39.84 Offer Premium

Shares outstanding (millions) EPS Share price P/E

5.00 $0.58 $7.25 12.53

Senior debt Subordinated debt Management equity rollover Sponsor's equity

22.48 18.73 2.59 16.54

Total Sources

60.34

(3) Sponsor's equity participation Exit Valuation Exit enterprise value Minus debt Minus expenses Net equity proceeds at exit Sponsor's required return and proceeds Sponsor's required participation

2009 57.80 8.09 0.58 7.51 1.88 2.24 3.40 1.36 2.04 0.58 0.58 0.29 1.75 1.75

8.89% Senior Debt Capacity: 3x 2003 EBITDA

18.73

Subordinated debt

2008 53.51 7.49 0.54 6.96 2.00 2.24 2.72 1.09 1.63 0.54 0.54 0.27 1.36 1.36

15%

10 x EBITDA

@

2%

(4) Management's return (a) With sponsor's stake equal to Management's stake Management's rollover IRR

$8.34

33.25

$41.69

10%

88.0% 3.7 12.0% 26.5% 30.1% 3.7

8.41

Net proceeds at exit

$ 61.43 8.41

29.6% 86.5% 3.6 13.5% 29.6% 33.2% 4.2

9.46

$* 60.37 9.46

* This alternative corresponds to valuing the sponsor's and management's stakes at $2.59 and $16.54 respectively.

65

19.80 2.65 17.15 41.69 1.50 60.34

101.93 30.05 2.04 69.84 61.43 87.95%

87.95% 12.05% 2.59 Net proceeds at exit 26.54%

(5) Returns for different equity splits subject to negotiation Sponsor's return 30.0%

30.05

Purchase Price for Equity

30%

(b) With participation proportional to initial equity investment Sponsor's stake 86.45% Management's stake 13.55% Management's rollover 2.59 IRR 29.55%

Sponsor's equity Sponsor's return multiple Management's share Management's return on rollover Management's return on pre-LBO equity Management's return multiple on pre-LBO equ

Offer Price

35.91

Old debt retirement @ premium Minus cash Net Debt Purchase price of equity Expenses Total Uses

@

@

38.09

25.0% 72.3% 3.1 27.7% 49.5% 53.7% 8.6

$ 50.49 19.35

13.2. Substituting into the Debt Capacity Calculator the values from Exhibit 13.3 yields:

Grow th of sa les .........…..................

EBITDA m a rg in …………..................

Dep rec ia tion/ sa les .........................

Other non-c a sh/ sa les ....................

(CAPEX+Inc r. in NWC)/ sa les*.........

Ca sh b a la nc e/ sa les Interest on c a sh b a la nc e ..............

Ta x ra te ........................ ..................

Deb t fina nc ing : 60% Senior @ ....................

40% Sub ord ina ted @ .......

Am ortiza tion of senior b y yea r ......

Net c a sh to senior a m o rtiza tion ...

First yea r sa les ............ …………

First yea r EBITDA .......... ..................

Deb t c a p a c ity ............. ..................

As m ultip le of EBITDA .. ..................

7.9% 17.6% 3.0% 2.0% 5.3% 2.0% 5.0% 40.0% 6.7% 8.0% 7.0 100%

$630 $107 $558 5.21

13.3. First, let us confirm the value of the management stock options given in the problem: The volatility of Peregrine’s equity would be much higher than that of comparables because of its higher leverage. Let the rate of return of comparables be R = (1 – t)(EBIT – rD)/E, where E denotes initial equity, etc. Then, the variance of the rate of return is var(R) = [(1 – t)2/E2] var(EBIT) and a company with the same EBIT and equity E’ has volatility vol(R') = [var(R')]½ = (E/E')vol(R). For Peregrine, using the average market equity ratio and volatility of comparables of 65% and 18%, respectively, and reducing the equity ratio to 25% for private equity, yields an estimate of volatility equal to (0.65)/(0.25)(0.18) = 47%.

The Black-Scholes option pricing formula adjusted for dilution for a stock price equal to $59.41/1.255 = $19.49, an exercise price equal to $20.66, a riskless rate of 5% and volatility of 47%, gives a value of $7.56 per option. This value can be verified using the warrant module of the Financial Options Calculator.

Taking into account that the present value of the management options is $7.56 per option, compounding it at 25% one gets an exit value of $23.07 per option or a total value of $23.07 × 500,000 options = $11.5 million.

Subtracting its value from the exit value of equity yields the amount available to common equity and results in lower values for the stakes of the mezzanine investor and the sponsor. The sponsor should expect to get about $552 million or an IRR = (552 /190)1/5 – 1 = 23.8%, which is approximately the same value obtained in Section 13.8 using the exit value calculated in Exhibit 13.8. Details are shown in the following exhibit.

66

Peregrine Coatings Ownership with Management Stock Options ($ millions, except option value) 2011 Enterprise value Minus fees and expenses Net debt 2011 Equity value Mgt options Value per option FV @ Available to common

2%

1,102.1 22.0 466.5 613.5

500,000 7.56 25%

Mezzanine investors Sponsor

23.07

11.5 602.0

8.30% 91.70%

50.0 552.0 602.0

13.4. Project Blue Snapper was modeled using DealModeler®. See the demo file in the DealModeler CDROM. (a) The following statement of sources and uses of funds shows a capital structure that satisfies the lenders requirements such that senior debt is amortized by 2005. Note that the sponsor receives 46.485/(37.500 + 46.485) = 55.35% of the equity. Management rolls over 2.093 million shares and the sponsor receives 2,595 million shares.

SOURCES AND USES OF FUNDS AT CLOSING ON CAP & SEAL ($000) Uses: Sources:

Closing:

Offer Price per Share………..………......

Shares Outstanding ...……..….…….…..

Equity Purchase Price ……...………..…

Transaction Expenses .…...……….……

Total Purchase Price ….…...……….…..

Retire Short-Term Debt ………..………

Retire Senior Debt ………….……..……

Retire Preferred Stock …....…....….……

Assumed Debt ……………………………

Total Uses ……………………………..

$16,025 37,500 46,485 186,830 126,802 10,170 15,889

3.6% 8.5% 10.6% 42.5% 28.8% 2.3% 3.6%

$439,700

100.0%

$17.91 Cash in the Company.......…..…

9,259 Equity Rollover ………...…...… $165,877 New Common Stock Issued ….

19,700 Senior Debt …….……………… $185,577 OID Debt …………...………….

27,523 Assumed Debt ………….………

202,370 Warrants Issued …………………

14,060 10,170 $439,700 Total Sources …………...…….

67

6/30/2000

% of Capital

(b)

CAP & SEAL INCOME STATEMENTS ($000) Fiscal Years Ending 8/31

2 Months Ending 1999-10 Months

Total Sales..........................................…...….....…

Cost of Sales....................................….……....…

Gross Profit.........................................…...….....…

Sales, General & Administrative Expenses …..

EBITDA bef. Restructuring Expenses ….……..…..

Restructuring Expenses …………………….…

EBITDA.............................................………....…

Depreciation........................................….........…

Intangible Amoritzation Financing Cost Amortization …………..…...…

EBIT..................................................…....…....…

Interest Expense ………………………………..

Interest Income ...................................……......…

Pretax Income...................................……......…

Current Income Tax ...........................…….....…

Deferred Tax ...............................……….........…

Net Income..........................................……….…

Number of Shares (000) …………………....…..

EPS..............................................…............…….

$237,330 134,892 $102,438 40,100 $62,338 0 $62,338 13,597 8,511 0 $40,230

2000 $64,000 35,648 $28,352 10,381 $17,971 0 $17,971 3,376 1,818 295 $12,482 5,752 72 6,802 2,946 (225) 4,081 4,688 $0.87

2001 $334,800 186,484 $148,316 52,664 $95,652 0 $95,652 21,713 10,906 1,771 $61,262 35,336 923 26,849 12,118 (1,378) 16,110 4,688 $3.44

2002 $359,910 200,470 $159,440 54,490 $104,950 0 $104,950 23,435 10,906 1,771 $68,837 32,818 520 36,539 15,475 (859) 21,924 4,688 $4.68

68

2003 $386,903 215,505 $171,398 56,372 $115,026 0 $115,026 24,626 10,906 1,771 $77,723 30,221 619 48,122 20,236 (987) 28,873 4,688 $6.16

2004 $415,921 231,668 $184,253 58,229 $126,024 0 $126,024 25,105 10,906 1,771 $88,242 26,740 611 62,112 23,996 849 37,267 4,688 $7.95

2005 $447,115 249,043 $198,072 60,361 $137,711 0 $137,711 26,450 9,950 1,771 $99,540 22,579 631 77,592 29,619 1,418 46,555 4,688 $9.93

2006 $480,649 267,721 $212,927 62,388 $150,539 0 $150,539 27,240 9,950 1,771 $111,578 18,164 679 94,093 35,855 1,782 56,456 4,688 $12.04

2007 $516,697 287,800 $228,897 64,535 $164,361 0 $164,361 29,285 9,950 1,476 $123,650 18,232 3,953 109,371 41,256 2,492 65,622 4,688 $14.00

2008 $555,450 309,385 $246,064 66,932 $179,133 0 $179,133 29,610 9,950 0 $139,573 3,118 784 137,238 52,241 2,654 82,343 4,688 $17.56

2009 $597,108 332,589 $264,519 69,384 $195,135 0 $195,135 30,000 9,950 0 $155,185 75 2,855 157,965 60,402 2,784 94,779 4,688 $20.22

CAP & SEAL BALANCE SHEETS ($000) ASSETS Current: Cash and Marketable Securities ........................

Accounts Receivable..............…..…………..…

Inventories...................................………….......

Other Current Assets....................………..........

Total Current Assets...................…………......

Pro-Forma

Fiscal Years Ending 8/31

6/30/2000

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

$7,120 42,350 29,143 3,460 82,073

$15,209 36,622 30,370 3,013 85,214

$8,572 40,690 30,655 3,348 83,264

$10,205 43,741 32,954 3,599 90,499

$10,069 47,022 35,425 3,869 96,385

$10,398 50,549 38,082 4,159 103,188

$11,178 54,340 40,939 4,471 110,928

$65,119 58,415 44,009 4,806 172,350

$12,917 62,796 47,310 5,167 128,190

$47,038 67,506 50,858 5,554 170,956

$125,592 72,569 54,672 5,971 258,804

PP&E and Capitalized Leases..............................

Less: Depreciation.........................………….......

Net PP&E and Capitalized Leases………........

104,168 0 104,168

107,501 3,376 104,125

135,941 25,089 110,852

160,941 48,524 112,417

186,341 73,150 113,191

214,341 98,255 116,086

249,341 124,705 124,636

289,341 151,945 137,396

339,341 181,230 158,111

394,341 210,840 183,501

449,341 240,840 208,501

Other Noncurrent Assets: Investments ……………………………....…....

Intangible Assets..........................………..........

Other Assets...............................…………........

4,160 109,009 8,660

4,160 107,191 8,660

4,160 96,285 8,660

4,160 85,379 8,660

4,160 74,473 8,660

4,160 63,567 8,660

4,160 53,617 8,660

4,160 43,667 8,660

4,160 33,717 8,660

4,160 23,767 8,660

4,160 13,817 8,660

Capitalized Transaction Expenses ..………….....

Total Assets.................................………….......

12,400 320,470

12,105 321,455

10,333 313,555

8,562 309,677

6,790 303,660

5,019 300,680

3,248 305,249

1,476 367,709

0 332,838

0 391,044

0 493,942

18,760 12,220 0 30,980

14,951 12,656 560 28,167

16,349 14,062 2,302 32,713

17,575 15,116 2,940 35,632

18,894 16,250 3,845 38,988

20,311 17,469 4,559 42,338

21,834 18,779 5,628 46,240

25,232 21,701 7,839 54,772

27,124 23,329 9,926 60,379

29,159 25,079 11,476 65,713

186,830 0 10,170 142,691 (15,889) 323,801 6,050 360,831 15,889 (56,250) (40,361) 320,470

186,830 0 10,000 142,691 (15,777) 323,743 5,825 357,735 15,889 (52,169) (36,280) 321,455

158,805 0 9,330 142,691 (14,260) 296,565 4,447 333,725 15,889 (36,059) (20,171) 313,555

130,781 0 7,780 142,691 (12,547) 268,704 3,588 307,924 15,889 (14,136) 1,753 309,677

93,415 0 5,950 142,691 (10,611) 231,445 2,601 273,034 15,889 14,737 30,626 303,660

46,707 2,143 3,880 142,691 (8,423) 186,998 3,450 232,787 15,889 52,005 67,894 300,680

0 1,391 1,560 142,691 (5,951) 139,691 4,868 190,799 15,889 98,560 114,449 305,249

23,471 20,187 6,813 50,471 0 0 0 150 142,691 (3,157) 139,684 6,650 196,804 15,889 155,016 170,905 367,709

31,916 482 0 0 0 32,398 9,142 96,311 15,889 220,638 236,527 332,838

0 0 0 0 0 0 11,796 72,175 15,889 302,981 318,870 391,044

0 0 0 0 0 0 14,580 80,293 15,889 397,760 413,649 493,942

LIABILITIES Current: Accounts Payable....................................……...

Accrued Expenses...................................……...

Taxes Payable ........................................……....

Total Current Liabilities............................……

Long-term Debt: Senior debt ……………...………...……………

Revolver...................................………………..

Subordinated Debt …………………………….

OID Debt …………………….……...…………

OID contra account ……….……...…………..

Total Long-term Debt.......................................

Deferred Income Taxes...............…………………

Total Liabilities...........................………………

Warrants ………………………………………...

Common Stock and Retained Earnings................

Total Net Worth ................................................

Total Liabilities and Equity................................

67

(c) and (d)

EXIT VALUATION

CAP & SEAL

($000)

Fiscal Year Ending 8/31 6/30/2000

Exit Year EBITDA Enterprise Value @ EBITDA exit multiple Plus Cash Less: Debt and Lease Obligations Less Call Premiums Less Minority Interest Value of equity Expenses Proceeds to common shareholders

8/31/2000

8/31/2001

8/31/2002

8/31/2003

8/31/2004

8/31/2005

$80,309

$95,652

$104,950

$115,026

$126,024

$137,711

-

-

-

-

-

688,557 11,178

-

-

-

-

-

(145,642) (14,269) 539,825 (21,593) 518,232

2005

5.0 x

68

RETURN TO INVESTORS

CAP & SEAL

($000)

Fiscal Year Ending 8/31 6/30/2000

CAP & SEAL Subordinated Lenders Initial Investment Subordinated loan interest Subordinated loan principal Equity kicker (shares in (000), %) Equity Cash flow Pre-Tax IRR Management Initial investment Initial ownership Diluted percentage owned Equity Cash flow Pre-Tax IRR Return multiple Sponsor Initial investment Initial ownership Diluted percentage owned Equity Cash flow Pre-Tax IRR Return multiple

8/31/2001

8/31/2002

8/31/2003

8/31/2004

8/31/2005

2,497 -

14,983 -

14,983 -

14,983 -

14,983 -

14,983 142,691

2,497

14,983

14,983

14,983

14,983

68,109 225,782

-

-

-

-

-

200,984 200,984

-

-

-

-

-

249,139 249,139

2,497

14,983

14,983

14,983

14,983

675,905

($142,691)

709 shs

13.14%

(142,691) 17.00%

2,093 shs

44.65%

2,093 shs

38.78%

2,595 shs

Total cash flow to sponsor, management and mezzanine Blended IRR Initial shares outstanding Total shares outstanding at exit

8/31/2000

-

(37,500)

-

(37,500) 38.34% 5.36

-

(46,485)

-

(46,485) 38.34% 5.36

-

(226,675) 27.57%

55.35% 48.07%

4,688 shs 5,397 shs

69

13.5. First find the required kicker. Value the bond without the warrant.

Year Bond cash flow

1 2 3 4 5 6 7 8 9 10 4 4 4 4 4 4 4 4 4 54

PV =$34.5. Hence PV{kicker} = $50 – $34.3 = $15.7 million.

Let m = number of warrants and n = number of shares outstanding. Here the number of warrants to issue is unknown but equal to $15.7/warr. Thus, m and warr have to be solved simultaneously. This is achieved by entering 15.7/warr for the number of warrants in the Financial Options Calculator, where w is the program solution for the warrant value. The other inputs are stock value = $14, exercise price = $20, time = 7 years, volatility = 65%, interest rate = 4% and n = 5 million. The solution is warrant value = $7.73 and m = 2.031 million. That is, the value of the kicker is m × warrant value = 2.031 × 7.73 = $15.7 million as required and 40.62 warrants need to be attached to each bond.

13.6. (a) Debenture valuation Coupon = 6.50% × $1000/2 = Number of periods = Required yield = 12.00%/2 = Present value of {32.5, ... ,32.5 + 1000} =

$32.50 per semester 20 semesters 6.000% per semester $684.58 million.

(b) Warrant valuation Gross proceeds from unit package Debentures value Gross proceeds from warrant issue Fees (0.75%) Net proceeds Net proceeds per warrant

$1,000.00 million 684.58 315.42 7.50 307.92 million $23.69

Inputs for warrant valuation: Stock value Exercise price* Net proceeds per warrant Issue date Expiration Return volatility Interest rate (bond yield) = (1 + 6.0%)2 – 1 = CWI shares Number of warrants Warrant value from the Financial Options Calculator**

$47.00 $61.35 $23.69 10/31/2001 5 yrs.

54.0% 12.36% 117.20 million 13.00 million $24.79

* Bond value in five years/11.5. The bond value is equal to the present value of 10 semiannual payments of $32.5 million plus the principal payment of $1,000 in 5 years, discounted at 6% per semester, and brought back to present value from year five to time zero at 6% per semester. **Note that the bond yield rather than the Treasury yield is used in this case. This is so because the exercise price is to be paid by surrendering the bonds rather than in cash.

70

(c) Cost comparison All-in cost of straight subordinated issue: Net proceeds ........……....……………….

Coupon .........………...…………………..

Maturity ..........……….…………………..

AIC ..............……………………………..

$496.3 million 6.00% per semester 10 years 12.13%

All-in cost of unit package: Net proceeds ........……….……………….

Coupon ...........…………………………...

Maturity .........…………..………………..

Warrants value ..……....………………….

AIC ................…………………………….

$992.5 million 6.50% per semester 10 years $322.3 12.33%

The AIC of the unit is 2 times the IRR that equates 992.5 – 322.3 = PV(19 semiannual coupons of $32.5 and a final payment of $1,032.5) Thus, CDW would pay 20 additional basis points by issuing the unit package. In exchange, it would raise twice the money and get low coupon payments.

13.7. The value of the 11% coupon loan is PV = 2.2 × 1.13–1 + .... + 2.2 × 1.13–7 + 22.2 × 1.13–8 = $18.08 million Hence, Proceeds from debt + warrant issue Value of debt Proceeds attributable to warrants Proceeds per warrant

$19.90 million 18.08 $ 1.82 million $ 1.82

The warrant program of the Financial Options Calculator gives $2.63/warrant. (a) Cost of warrant kicker = 2.63 × 1 million = $2.63 million. (b) The all-in cost (AIC) of the debt plus warrant package is 13.9% vs. the AIC of the straight debt issue that is 13.1% (verify). The package AIC is computed as the IRR of the following cash flows: 0 Proceeds Value of kicker Net cash flow

1

2

3

4

5

6

19.90 2.63 17.27 –2.2

–2.2

–2.2

–2.2

–2.2

–2.2

71

7

8 .

–2.2 –22.2

13.8. The modified warrants are knock-up warrants with rebate. They can be valued with the knock-out program of the Financial Options Calculator after accounting for dilution. As shown in Appendix A, the value of a warrant is given by the formula warr = (1 + λ)–1c(p + λwarr, X; σ, r, t), where c is the value of the call (here, the knock-out call) and λ = number of warrants/number of shares = 0.1.

Iterating in the knock-out program yields $2.14 for the knock-out warrant and $0.49 for the rebate, giving a total value of the warrant plus rebate equal to $2.63 as in the solution to problem 13.7.

13.9. In order to value the warrants, the value of the equity after the warrants are issued is needed. This is so because the issuance of the warrants will in this case increase the value of equity. A reasonable assumption is that the warrants will be priced according to option pricing theory. This permits solving simultaneously for the value of equity and the value of the warrants. Once this is done, it is easy to compute the coupon rate required

by Provident. In fact, the warrant program of the Financial Options Calculator already takes into account the value of the warrants in the value of equity and price them at $0.606 per warrant.

Provident will be indifferent between receiving 14% or a rate r < 14% if B(r) + mwarr = $10 million. That is, if B(r), the present value of principal plus interest under the reduced coupon rate, plus the value of the warrants, equals the $10 million to be loaned to Fly-By-Dusk. In this case, the proceeds to the company per warrant issued would be warr, and its equity will increase to np + mwarr.

Hence, warr = $0.606 and mwarr = $0.606 million. Therefore, Provident can afford to charge an interest rate r such that B(r) = $10 – $0.606 = 9.394 million. r is obtained as follows: Year 0 1 Principal -10 2 Warrants 0.606 Interest 10r Net cash flow -9.394 2+10r

2 2

3 2

4 2

5.

2

8r 2+8r

6r 2+6r

4r 2+4r

2r 2+2r

and should be such that 9.394 = PV($2 for 5 yrs @14%) + PV(10, 8, 6, 4, 2 @14%) × r or

9.394 = 6.87 + 22.38 r,

r = 11.28%.

Verify that a 11.28% coupon plus the warrants yields 14% to Provident. Note however that in practice Provident is likely to demand either more warrants or a higher coupon in order to attain a blended rate above the 14% it would charge on a straight loan.

72

13.10. The present value approach to value equity kickers and the option pricing model for warrants give approximately the same solution for cases in which the value per share is much greater than the exercise price, that is, for deep-in-the-money warrants. However, when that is not the case, the present value approach underestimates the value of the equity kicker because it does not capture the value of not exercising the option it when it is out of the money.

13.11. (a) Note: ($000) Year 2007 2008 2009 Principal –10,000 Interest 800 800 Cash flow –10,000 800 800 Present value (@17%) – 2,879 Required kicker (Note that (2,879)(1.17)5 = 6,313)

2010

2011

800 800

800 800

2012 10,000 800 10,800 6,313

Current revenue = 30,000 Year-5 revenue = (30,000)(1.12)5 = Year-5 EBITDA = (0.2)(52,870) – 1,000 = EBITDA multiple Enterprise exit value Minus net debt

52,870 9,574 6x 57,444 15,000 42,444

Therefore, Equity participation = 6,313 ÷ 42,444 = 14.87% The return will exceed (be less than) 17% if revenue grows more (less) than 12% per year. (b) The payoff of the put is α max(35 – [6(0.20R5 – 1) – 15], 0) = 1.2α max(46.667 – R5, 0) million, where α is the equity participation, R5 is year-5 revenue and max (46.667 – R5, 0) is the payoff of a European put on revenue. The solution approach consist of first computing the value of the put and then solving for α such that the value of the common equity plus its put yields the value of the required kicker ($6,313 million). The following inputs are entered in the European put module of the Financial Options Calculator: PV(R5) = 30(1.20)–5 = $12.056 million,

X = $46.667,

r = 5%,

σ = 20%,

t = 5 years.

The Financial Options Calculator gives $24.524 million as the value of this put. Hence the guarantee is worth 1.2α(24.524). And α is the solution to: α(42.444 + (1.2)(24.534)) = 6.313

73

or α = 8.78%.

Chapter 14. Recapitalization of Troubled Companies 14.1.

Growth of sa les ....... ...............

EBITDA ma rgin ………...............

Deprecia tion/ sa les .................

4.0% 15.0% 1.5%

Other non-ca sh/ sa les ............

(CAPEX+Incr. in WC)/ sa les*....

Ca sh ba la nce/ sa les Interest on ca sh ba la nce .......

Ta x ra te .... ............... ...............

Debt fina ncing: 84.19% Senior @...............

0.2% 1.7% 0.2% 4.5% 40.0% 6.5%

15.82% Subordina ted @ ..

8.0% Amortiza tion of senior by yea 7 Net ca sh to senior a mortiza tio 100% First yea r sa les ........ ………… $ 1,000 $150 First yea r EBITDA ..... ...............

Initia l ca sh ba la nce ……………

1.9 Debt ca pa city ......... ...............

As multiple of EBITDA...............

$616 4.11

14.2. Southland’s case serves to illustrate the use and limitation of the debt capacity formula in a complex recapitalization. Since the EBITDA margin increases over time, it is better to base the calculation of debt capacity directly on EBITDA growth rather than on sales. This is done on the spreadsheet by simple letting EBITDA be 100% of sales and entering the growth of EBITDA as the growth of sales. All other percentages are also made based upon EBITDA. From Exhibits 14.2 and 14.3, one notes that the plan provides for about 4.5% cash interest to subordinated debt and that secured debt is about 71% of the total debt at the end of 1990.

Substituting these values and the relevant percentages of EBITDA into the Debt Capacity Calculator shows that it will take more than 8 years to retire the senior debt of $1.4 billion. This is in agreement with the balance outstanding at the end of 1997. The model can be used to test the time to retire the senior debt for several amounts and coupons of subordinated debt before putting together an explicit cash flow model like the one shown in Exhibit 14.3.

74

Growth of sales ........ ................

8.6% EBITDA margin ………................

100.0% Depreciation/sales .....................

43.3% Other non-cash/sales ................

2.2% (CAPEX+Incr. in WC)/sales*.......

30.7% Cash balance/sales 4.3% Interest on cash balance ...........

5.0% Tax rate .... ................ ................

40.0% Debt financing: 71% Senior @ ................

10.5% 29% Subordinated @ .....

4.5% Amortization of senior by year .

8 Net cash to senior amortization 100% First year sales ........ ………… $ 367 $367 First year EBITDA .... ................

Inicial cash balance ………………

8.0 Debt capacity ............ ................

As multiple of EBITDA .…………

$1,909 5.20

14.3. (a) Reset notes issued by highly leveraged firms present an interesting valuation problem. While the company is legally obliged to set the interest rate sufficiently high in order to bring the notes to par value, the market may not consider it possible because a higher rate would increase the already high risk of default of the company. In fact, no rate, no matter how high, may exist that will bring the notes to par and the company will default at reset time if nothing is done to avert default. (b) On the other hand, Ingersoll's getting financing from Chase to buy back the notes is signaling that the company is not in such a bad shape, and bondholders will initially balk at the buy-back offer in the hope of negotiating better terms. This is an asymmetric information situation that leads investors to ask why Ingersoll is willing to pay a premium over the current market price of the notes, and how much that premium should be.

After all, by portraying a gloomy situation and scaring bondholders to sell, equity holders (Mr. Ingersoll and Warburg, Pincus Capital Partners) stand to benefit. By threatening to push the company into bankruptcy, bondholders can hope to extract better terms for their notes. (c) By not tendering, bondholders would be engaging in a "game of chicken". Bondholders would take whatever they can when it is obvious that doing otherwise will push the company to protracted bankruptcy proceedings in which everybody loses. The company is likely to sweeten the offer either by improving the cash terms or by adding an equity kicker or some other type of bond to the package.

75

14.4. Exhibit A shows that retiring all senior debt by year six leaves almost no cash flow for the subordinated debtholders during that period. The latter will need to accept much lower coupon payments from years 2 to 5 or 6. For example, they can receive a deferred interest bond, which would pay no interest from years 2 to 5 and 14% thereafter. Alternatively, interest could be accrued during years 2 to 6 or paid with PIK (paid in kind) bonds. As noted in Section 14.5, these alternatives would result in taxable gain for cancellation of indebtedness but would produce a tax shield for the firm because accrued interest would be deductible for tax purposes. In turn, they would require taxable lenders to pay taxes on interest they do not receive. Tax shield consequences and the taxable gains from debt restructuring are not taken into account in Exhibit A. Note, however, that if REFC were to opt for a court-approved recapitalization it would avoid the tax on reduction of indebtedness by forgoing its ability to deduct interest on restructured debt.

Discounting the subordinated holders’ cash flow computed in Exhibit A below at 15% (100 bp above the coupon rate) yields a present value of $308 million. This means the new bonds would be worth 550 – 308 = $242 million less than the original bonds. On the other hand, the equity of the firm would now be worth only $79 million, that is, $225 × 4 = Senior debt Sub debt

$900 million (513) (308) $ 79 million

Assuming subordinated holders receive all the equity of the firm, their loss will be $163 million. The old shareholders will be wiped out in the process and will lose $150 million. This number comes from the data on the original LBO: Acquisition price Debt Equity

$1,250 million 1,100 $ 150 million

The total loss of value (1,250 – 900 – 37 = $313 million) is then absorbed by the subordinated bondholders ($163 million) and by the old shareholders ($150 million).

The outcome in practice is likely to be somewhat different, as the old shareholders would propose a recapitalization plan that would allow them to keep some of the equity. Subordinated holders would of course attempt to negotiate the old shareholders claim downward but, in order to prevail, they may need to force the firm into bankruptcy proceedings and that may impair the very value they are trying to get for themselves. In addition, some equity would need to be set aside for (old or new) management, in order to provide adequate incentive for superior performance during the work out.

76

Exhibit A - REFC Inc. Projected Cash Flows as of Year 1 under Recapitalization Plan Year

0

EBIT (g= 4.0%) Interest expense Senior 12.0% Sub 14.0%

250 200 208 216 225 234 243 253 263 274 285

Tax 35.0% Net after tax Debt amortization: Cash sweep 100% Senior Subordinated Cash balance Debt balance: Senior Subordinated

0

1

2

3

4

5

6

7

8

9

10

66 77 57 20 37

62 50 37 23 6 0 0 0 0 0 0 0 0 77 69 53 34 12 146 166 188 211 160 184 210 240 273 51 58 66 74 56 64 74 84 96 95 108 122 137 104 119 137 156 177

37 0 0

95 108 122 137 50 0 0 0 0 0 0 0 54 119 137 156 0 0 0 0 0 0 0 0

0 84 94

550 513 418 310 188 50 0 0 0 0 0 550 550 550 550 550 550 496 377 240 84 0 1,100 1063 968 860 738 600 496 377 240 84 0 Subordinate cash flow 0 0 0 0 0 131 188 190 190 96 Shortcut: While not a substitute for the detailed projection of cash flows under the recapitalization plan, one can get an approximate feel for the nature of the recapitalization via the use of debt capacity multiples. As of the end of the first year the situation is as follows: Next year EBITDA Growth rate Tax rate Time to retire senior Senior interest Subordinated interest

$233 million 4% 35% 5 years 12% 14%

In order to use the Debt Capacity Calculator one needs to simplify the inputs to the program. For example, let first-year sales be $2,330, assume a 10% margin, and let depreciation, capital expenditures, etc. offset each other. Also, assume that both notes pay cash interest. The debt capacity multiple for these data, assuming a 50/50 senior/junior debt ratio, is about 3.5x. This multiple implies a debt capacity of about $233 × 3.5 = $815 million, with $407.5 million going to each group of bondholders. Of course, such an arrangement would be infeasible because the senior holders would insist in recovering their full $513 claim. Hence, the distribution of claims would have to be $513 to senior holders and $302 million to subordinated holders. In other words,

77

subholders would receive new bonds worth approximately $302 million. In addition, they would receive some (hopefully most) of the equity. The equity would be worth approximately 900 – 815 = $85 million (with the assets being valued at 4x current EBITDA).

14.5. (a) Exhibit B shows that the proposed recapitalization is feasible.

Exhibit B (revised) SM Holdings Revised Projected Cash Flows Year 0 1 2 3 4 5.

EBIT (g= 5.0%) 300 160 168 176 185 194 Interest expense Senior 8.0% 78 46 41 36 30 Sub 10.0% 75 17 17 17 17 7 105 118 138 147 Tax 35.0% 2 37 41 46 51 Net after tax 5 68 77 86 96 Debt amortization: Senior 80 63 63 63 63 Subordinated 0 0 0 0 0 Cash balance 0 5 19 42 75 Debt balance: Senior 650 570 507 444 381 318 Subordinated 500 172 172 172 172 172 1,150 742 679 616 553 490 (b) Note that under the recapitalization plan cash accumulates rather fast and reaches $75 million by year five.

Senior bondholders are likely to demand faster amortization of principal if they are going to accept a belowmarket coupon. In general, senior bondholders will demand higher coupon, faster repayment or both. They would also demand part of the equity.

Subordinated bondholder will also attempt to obtain better terms and will demand more equity. Given the seriousness of the financial situation faced by SM Holdings, shareholders’ attempt to keep 55% of the equity will most likely be rejected by the bondholders. Stockholders usually start by offering terms such as those of the present plan as an initial move in the debt renegotiation game. (c) The bargaining power of the parties is determined by (i) The nature of the bond covenants: If any group of bondholders can force the company into bankruptcy without suffering significant consequences, then its bargaining position is strong with respect to the other parties. Also, well-established lenders are able to influence management and equity investors when the latter wants to minimize damage to their reputation.

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(ii) The ability of the creditors to control the terms of the recapitalization also depends on how crucial current management is to the future functioning of the company. When management is perceived to be essential, it can extract larger concessions from creditors. (d) Valuation (i) Senior notes: Discount promised cash flow at a market rate, which takes into account default risk. (ii) Subordinated notes: Same as senior, with a higher default premium. (iii) Equity: Estimate year-5 enterprise value using an EBITDA multiple, for example. Subtract outstanding debt, add cash and discount the resulting amount back to time zero at the high discount rate representing the equity risk, lack of marketability of the holding and current market conditions.

Alternatively use APV and account for lack of marketability as discussed in Chapter 13. Under the above plan, 45% of the value of equity value would correspond to subordinated holders and 55% to SM-II. 14.6. The 25.7 million convertibles contain 25.7 × 1.361 = 34.98 million warrants with exercise price equal to €21.3343 × 1.1 ÷ 1.361 = €17.243. An approximation to the value of the embedded warrants can be attained valuing them separately. The Financial Options Calculator gives a value of €0.014 for each warrant and €0.014 × 34.98 = €0.49 million in total. Since the exercise price would be made “in kind” by delivering the convertible bonds instead of cash, a better approximation to the value of the convertibles can be attained by using Disney’s debt rate (9.5%) instead of the government rate. Making this substitution yields €0.018 per warrant or €0.0181 × 34.98 = €0.63 million in total.

14.7. The value of the equity per share is (€1,370.7 + €10.7)/809 = €1.7075, the exercise price is €6.098 and the rest of the input is as in the previous problems. The warrant model gives a value of €0.328 per each three warrants or €0.328 × 96.667 million = €31.7 million.

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Chapter 15. Asset Restructuring 15.1. Expressions (5.1) and (5.2) give: Continuation EVA = Adj. NOPAT2012 (1 + g)/(w – g) – PV{Capital Charge} where, as before, g and w are the future growth rate and WACC, respectively. And PV{Capital Charge} = (Capex + Increase in Net Working Capital – Depreciation)2012 (1 + g)/(w – g) + Invested Capital2012 The following table computes Continuation EVA by making the appropriate substitutions for each unit.

2012 NOPAT

Machine Tools Electronics Metal Products

106.3 38.9 30.9

WACC

9.6% 10.5% 10.0%

2012 Growth Capex & Rate Incr. in NWC 5.8% 101.0 9.8% 88.8 4.0% 69.8

2012 Dep.

68.3 53.8 49.9

2012 Invested

Capital

PV of Capital Charge

2012 Cont.

EVA

601.7 394.0 518.6

1,495.6 5,515.5 864.4

1,409.1 176.5 (329.3)

15.2.

FCF Valuation of Restructuring Actions for Metal Product Unit (in million $) Stop Volume Growth 2007 Sales Growth of sales EBITDA margin EBITDA Depreciation Operating income Taxes @ 40% Unlevered net income Deferred taxes Depreciation Capex and Increase in NWC Continuation value PV{Free cash flow} PV{Continuation value} Business unit value

2008 487.0 2.5% 13.0% 63.3 36.0 27.3 10.9 16.4 1.2 36.0 57.0 (3.4)

2009 499.2 2.5% 13.3% 66.4 38.1 28.3 11.3 17.0 1.2 38.1 44.7 11.7

2010 511.7 2.5% 13.6% 69.6 38.8 30.8 12.3 18.5 1.3 38.8 45.5 13.1

77.1 85.1 162.2

80

2011 524.4 2.5% 13.9% 72.9 39.4 33.5 13.4 20.1 1.3 39.4 46.3 14.5

2012 537.6 2.5% 14.2% 76.3 40.1 36.2 14.5 21.7 1.3 40.1 47.1 16.1

2013 551.0 2.5% 14.2% 78.2 40.8 37.4 15.0 22.5 1.4 40.8 47.9 16.7

2014 564.8 2.5% 14.2% 80.2 41.5 38.7 15.5 23.2 1.4 41.5 48.8 17.3

2015 578.9 2.5% 14.2% 82.2 42.3 39.9 16.0 24.0 1.4 42.3 49.7 18.0

2016 593.4 2.5% 14.2% 84.3 43.0 41.3 16.5 24.8 1.5 43.0 50.6 18.7

2017 608.2 2.5% 14.2% 86.4 43.8 42.6 17.0 25.6 1.5 43.8 54.7 16.1 220.7

15.3.

WTT Inc. FCF Valuation of Restructuring Actions for Metal Products Unit

Harvest

(in million $) 2007

Sales Growth of sales EBITDA margin EBITDA Depreciation Operating income Taxes @ 40% Unlevered net income Deferred taxes Capex and Increase in NWC Depreciation Free cash flow Recovery at exit WACC PV{Free cash flows} PV{Recovery} Business unit value

10.00% 175.07 112.19 287.26

Invested capital

360.0

2008 487.0 -12.9% 13.0% 63.3 36.0 27.3 10.9 16.4 1.2 0.0 36.0 53.6

2009 424.4 -9.3% 13.5% 57.3 32.4 24.9 10.0 14.9 1.1 0.0 32.4 48.4

2010 384.9 -9.3% 14.0% 53.9 29.2 24.7 9.9 14.8 1.0 0.0 29.2 45.0

2011 349.1 -9.3% 14.5% 50.6 26.2 24.4 9.7 14.6 0.9 0.0 26.2 41.7

2012 316.5 -9.3% 15.0% 47.5 23.6 23.9 9.5 14.3 0.8 0.0 23.6 38.7 180.7

324.0

291.6

262.4

236.2

212.6

15.4. (a) Racal Electronics Plus debt Total assets Break up: Racal Telecom Racal Chubb Rump assets

Valuation of Racal Electronics Share price Shares Units Total 190 p 1.3 bn £2.5 bn 0.4 2.9 275 p

0.8 bn £2.2 bn 0.4 2.6 0.3

Note: p = pence, bn = £ billions

The market was giving a very low value to the rump. While Racal had obtained promising government contracts, significant investments had to be made for a number of years. In addition, the market had only partial information on the expected profitability of those contracts. Sir Ernest was saying that if the market priced the rump at nothing then he would have it for nothing or, perhaps, it was just a ploy directed to talking Racal's price up and divert a possible hostile takeover.

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(b) The rump was not a good MBO candidate, at least not to be financed mainly with debt. It needed cash and was in competition with larger and better financially endowed firms. Racal's contracts offered long-term payoffs, which were more appropriate for equity investors. (c) Racal could have sold its crown jewel, Racal Telecom. This would have averted the takeover of the whole BAT - Return to Bidding Consortium (Billion £)

Conservative 1989

Proceeds from break-up

Optimistic

1990

1990

14.300

20.100

Minus expenses (3%)

0.429

0.603

Proceed from sale

13.871

19.497

Taxable gains

2.000

3.500

Minus corporate taxes

0.800

1.400

Net proceeds

13.071

18.097

BAT 1990 free cash flow

1.077

1.077

Consortium's subscription

0.868

0.868

15.016

20.042

Acquisition debt Senior notes

6.500

12%

7.280

7.280

Sub. notes

3.900

16%

4.524

4.524

Acquisition costs (1.5% of £13bn)

0.195

Proceeds after acquisition debt and costs Bidders' share (25% + 9.1% x 75%)

31.8%

Bidders' initial investment

0.868

Bidders' break-up profit Bidders' profit on initial BAT holding of

0.195

0.195

11.999

11.999

3.017

8.043

0.960

2.560

0.868

0.868

0.092

1.692

1.235%

Proceeds (see below, "Shareholder Value in Hoylake's Offer) Cost (£5.90 x 18.89 mil. sh.)

0.111

0.171

0.213

0.111

0.111

Bidders' pre-tax profit

0.152

1.793

Bidders' pre-tax rate of return

15.5%

183.1%

company and provided cash, about £2.2 billion from which a substantial cash dividend could have been paid to shareholders and the rest used to finance Racal Electronics' growth.

15.5. (a) (b) BAT - Shareholder value in Hoylake's offer Conservative (Billion £)

Total

Per share

Optimistic Total

(pence)

Hoylake's proceeds Participation in Hoylake's proceeds

3.02 67.5%

Debt instruments received plus interest

Per share (pence)

8.04

2.04

5.43

11.80

11.80

13.84

905

17.23

1126

Pre-bid value

10.62

694

10.62

694

Total increase in value

3.22

211

6.61

432

Return

30.3%

30.3%

62.3%

62.3%

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(c) To avoid the corporate tax on the disposition of low tax basis assets, spin-off Argos and the paper business. (d) BAT Restructuring Sale of retail business and share repurchase (Billion £, except per share numbers) Value of net assets in retail business Argos valuation Pro-forma EPS (pence) P/E Shares Gross proceeds Expenses Net proceeds Tax basis Taxable profits Taxes on sale profits Net proceeds after taxes BAT shares (million) Repurchase price (pence) Repurchase (million) Deficit financed with funds from operations

2.000 14.3 12.0 296.8 3.0%

0.509 1.491 0.045 1.446

0.890 0.556 40.0%

0.222 1.224

1,530 10.0%

1,000 153.0

1.530 (0.306)

(e) Postscript: On April 8, 1990, California Insurance Commissioner Roxani Gillespi ruled against Hoylake's purchase of Farmers Insurance citing as her main concern dangerous levels of debt possibly affecting policyholders' welfare. On April 23, 1990, Sir James Goldsmith surrendered his bid for BAT Industries, his U.S. regulatory battle had proven too difficult.

"Hoylake announces that it will not renew its offer for BAT. The directors of Hoylake wish BAT and its unbundled offspring great success within their new structures."

Hoylake Press Release Financial Times, April 24, 1989 BAT went ahead with its restructuring plan but limited share repurchase to 4.9% of the outstanding shares.

The performance of the plan as measured one year later was as follows:

Shareholder value created as per realization of actual restructuring as of June 1990 (Billion £) Shares Price million pence Share repurchase 4.9% 75.3 792 BAT 95.1% 1,454.7 657 Argos 0.1984 for 1 spin-off 296.8 232 WigginsTeapleAppleton 0.3271 for 1 spin-off 494.4 211 Total value Pre-bid 1,530 694 Value created Value created per cent Pre-bid dividend yield Total return FT-100 7/13/89 2273.7 FT-100 6/30/90 2374.6 FT-100 appreciation 4.4%

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Value £ million 596 9,557 689 1,041 11,883 10,618 1,264

Per original BAT share 39 625 46 69 779 694 85 12.2% 4.3% 16.5%

Appendix A. Financial Options A.1. Motorola call value = $0.68. Implied volatility = 27.63 %.

A.2. (a) The computation of the Black-Scholes value of the call proceeds as follows: P

$51.125

X

$50.0

t

18 days = .04932 years

r

4.65% (for Treasury bill maturing in 18 days)

σ

20%

The continuous-time interest rate is ln(1.0465) = 4.545% d1 = [ln(51.125/50.0)+(0.04545 + ½(0.2))2(0.04932)]/[(0.2)(0.0493)½] = 0.02548/0.04441 = 0.5737 d2 = 0.5737 − 0.0444 = 0.5292 N(0.5737) = 0.7169 N(0.5292) = 0.7017 Xe-rt = (50.0)e-(0.04545)(0.04932) = 49.888 Call value = (51.125) N(0.5737) − 49.888 N(0.5292) = $1.646. (b) The put-call parity condition yields Put value = Call value − P − Xe–rt = 1.646 − 51.125 + 49.888 = $0.409.

Alternatively, one can compute these values with the call sheet in the Financial Options Calculator using calendar-day volatility or with the program for the HP-19B of Note NB.2.

A.3. The Financial Options Calculator gives a value for the warrants of $4.72. The computed price is higher than the actual price of $4.44. This may be due to the Black-Scholes formula, which tends to overprice high volatility and long maturity options. On the other hand, the formula tends to underprice deep out-of-themoney options like Xidex's. At that time, First Boston valued Xidex warrants at $4.70 and concluded that the warrants were underpriced and that those holding Xidex stock should swap it for its warrants.

A.4. (a) The payoff of a SAR is the same as the payoff of a standard option. Thus, from the point of view of ABC Inc.’s shareholders, SARs should be valued as standard options. However, since SRAs are illiquid, they may be worth less to management than they cost to shareholders. (In practice, executives may not be able to fully hedge their positions, either because the negative information that shorting by insiders would convey or because of the transactions costs associated with maintaining the hedge.)

84

(b) For valuation of long-term options such as these it makes sense to assume a constant dividend yield. The warrant-pricing model included in the Financial Options Calculator can be used for this purpose. Since SARs do not result in dilution, the number of warrants is set to zero and the number of outstanding shares is set to one. This eliminates the dilution correction to the Black-Sholes value (see Section A.7). In order to take into account that the strike prices changes every year one values SARs assuming exercise takes place each year and select the maximum value as the value of the SRA. This slightly underestimate the true value of SRAs because the decision whether or not to exercise will be evaluated every year rather than decided at the time of the grant. The SRA values are as follows: Year to exercise 0 1 2 3 4 5 6 7 8 9 10

Adjusted strike price* $30.00 28.57 27.21 25.92 24.68 23.51 22.39 21.32 20.31 19.34 18.42

*Adjusted strike price = 30(1.05)–t

Interest rate %

SRA value

1.17 1.60 2.13 2.62 2.96 3.23 3.54 3.72 3.89 3.99

$2.64 3.72 4.59 5.34 5.94 6.44 6.90 7.22 7.48 7.64

.

Hence, the optimal time to exercise these SARs is at expiration. (c) The value of each SAR at grant time is $7.64. (d) The reduction of the strike price in order to discourage premature exercise is not necessary because keeping it at $30 would still result in optimal exercise at expiration (With an exercise price of $30 the value of the SAR would increase from $2.03 for first-year exercise to $4.28 for exercise at expiration. Verify.) The 5% reduction of the strike price results in the value of the SARs growing at an average rate of 12.5% per year.

With a strike price fixed at $30, the value of the SARs would grow at 8.6% per year. (e) For the executives, SARs are more attractive than regular stock options in the sense that they receive cash at expiration and do not have to put down the exercise price money. In addition, they do not have to sell the stock in order to realize their gains. As an incentive device, SARs can be less effective than regular stock options if the recipients of the latter maintain their equity interest in the company.

A.5. (a) Option pricing theory requires both the current price of the stock and its volatility as inputs for valuation. These were not directly available for RJR Holdings. Proxies could have been obtained from

85

comparables, the behavior of high yield debt, convertible and warrant prices and pre-LBO RJR-Nabisco data.

But the results were not likely to be reliable. (b) The low exercise price of the warrants (7 cents a share) suggests that they are deep-in-the-money. This makes the present value approach to the valuation of equity kickers applicable to the valuation of RJR warrants. In fact, this was the way analysts priced the warrants at that time. Since RJR had to release information for its public debt security holders, its EBITDA was known.

Applying market multiples to RJR's EBITDA gives its enterprise value, which after subtracting outstanding net debt gives the value of equity. The dilution adjusted warrant-holders' share of this equity (5.2%) divided by the number of warrants minus the present value of the dilution adjusted exercise price (which is negligible here and can be ignored) gives the warrant value.

A.6.

Year Cash flow (millions) Face value Coupon Market rate Value of bond Required value of warrants Number of warrants (millions) Per warrant

0

1 $ 40.00

2 $ 40.00

3 $ 40.00

$ 500.00 8.0% 12.5% $419.89 $ 80.11 10.00 $ 8.01

Imputs for warrant valuation: Warrant value (value of equity kicker from above) Stock price Implied volatility (from call program) Expiration Interest rate Annual dividend on common Number of shares outstanding (millions) Increase in common shares upon exercise of warrants Implied exercise price (from warrant program)

$ 8.01 $ 34.00 34.45% 3 years 6.22% BEY $ 0.87 483 10 $ 35.85

A.7. The data needed for designing the Percs are: Stock price Stock quarterly div.

Leap call option price Strike price Calendar days to expiration Treasury notes Jan'97 Treasury notes June'97 IBM '97 bonds 86

$62.000 $0.250 $9.125 $70.000 933 6.27% 6.36% 6.61%

4 $ 40.00

5 $ 540.00

First, value the Percs and common stock dividends: Percs dividend:

6.00%

$62.00

$3.72

$0.930 quarterly

Year Div dates Dividends Quarter rate PV

1994 Sept 30 0.93

1994 Dec 31 0.93

1995 March 31 0.93

1995 June 30 0.93

1995 Sept 30 0.93

1995 Dec 31 0.93

1996 March 31 0.93

1996 June 30 0.93

1996 Sept 30 0.93

Common divividend foregone in Percs: 0.25 PV $2.708

0.25

0.25

0.25

0.25

0.25

0.25

0.25

0.25

1996 1997 1997 Dec 31 March 31 June 30 0.93 0.93 0.93

1.612% $10.074

0.25

0.25

0.25

Next, compute the implied volatility of the Leap call: Implied volatility in Leap call: Input to American call option propram: Stock price Strike Expiry (days) Riskless rate Rate for discounting div.

Annual div.

Implied vol.

$62.00 $70.00 933 6.27% 6.61% $1.00 24.29%

Now, you are ready to determine the cap for a simple Percs and to make it puttable: Value of simple Percs call (cap): Input to European call program: Stock Price $62.000 Annual div. $1.000 Strike: cap @ 28.58% $79.720 --> Riskless rate 6.36% Rate for discounting div.

6.61% Expiry (days) 1,096 Volatility 24.29% Call value* $7.366 --> * Call value equals Percs div. - Stock div.

Strike price of Percs put (floor): Input to European put program: Price Annual div.

Put value (given from above) Riskless rate Rate for discounting div.

Expiry (days) Volatility Strike:* floor @ 72.42% *Floor solved to yield put value.

Make the Percs puttable: (Lower cap to make room por put) Input to European call program: Stock Price $62.000 Annual div. $1.000 Strike: cap @ 20.97% $75.000 Riskless rate 6.36% Rate for discounting div.

6.61% Expiry (days) 1,096 --> Volatility 24.29% | Call value* $8.715 --*Call value increased by lower cap

Implied put value:

Stock price $62.000 Value of Percs Stock $62.00 -Stock div (2.708) +Percs div 10.074 -Call (8.715) 60.651 Value of put* $1.349 * Put value equals increase in call value.

SUMMARY FOR PUTTABLE PERCS $62.000 $1.000 $1.349 6.36% 6.61% 1,096 24.29% $44.900

Stock price Value of Percs Stock -Stock div +Percs div -Call +Put

87

$62.00 $62.000 (2.708) 10.074 (8.715) 1.349

Issued Price Expiry Dividend Cap $62.00 Floor

Parameters of Putable Percs

01-Jul-94 $62.00 30-Jun-97 $3.72 $75.00 $44.90

Puttable Percs without Knockout 100.00

Percs & Stock Price

80.00

60.00 40.00

20.00

0.00 30

40

50

60

70

80

90

Stock Price

Next, attach a knock-out barrier to the put: Percs put (floor) with knockout: Input to Knockout program: Price $62.000 Annual div. $1.000 Put value (given from above) 1.349 Riskless rate 6.36% Expiry (days) 1,096 Volatility 24.29% Knockout barrier: appreciation @ 15.00% $71.30 Strike:* floor @ 77.90% $48.300 *Floor increased to yield knock-out put with same value as above.

SUMMARY FOR KNOCKOUT PERCS

Stock price Value of Percs Stock -Stock div +Percs div -Call Knockout @ +Put

$62.00 $62.000 (2.708) 10.074 (8.715) 71.30 1.349

Puttable Percs with Knockout 100.00

Percs & Stock Price

80.00

60.00

40.00

20.00

0.00 30

40

50

60 Stock Price

88

70

80

90

Issued Price Expiry Dividend Cap Knockout $62.00 Floor

Parameters of Knockout Puttable Percs

01-Jul-94 $62 30-Jun-97 $3.72 $75.00 $71.30 $48.30

Consider now reducing the depth of the floor.

Reducing the depth of the floor Strike price floor @ Depth

88.7% 9.35%

$55.00 49.86 $5.14

SUMMARY FOR PUTTABLE PERCS WITH LIMITED FLOOR DEPTH

Put Value $3.563 2.274 $1.289

Stock price Value of Percs Stock -Stock div +Percs div -Call +Put (floor) - Put (depth)

Since the value of the floor is 6 cents lower, reduce the deph to 9.85% or a strike price of $49.585, which results in a put value of $2.214 and a floor value equal to $1.349 as required.

$62.00 $62.000 (2.708) 10.074 (8.715) $3.563 (2.214)

Issued Price Expiry Dividend Cap Floor $62.00 Depth

Parameters of Puttable Percs with Limtied Floor

01-Jul-94 $62 30-Jun-97 $3.72 $75.00 $55.00 $49.59

A.8. Enter the following input into the warrant sheet of the Financial Options Calculator: stock price = $35.75, annual dividend = $1.80, dividends per year = 4, strike price = $62, number of warrants = 18.391, shares outstanding = 63.897, current warrant price = 0, interest rate = 8.68%, volatility = 28%, current date = 7-101988, expiration date = 1-10-1998, trading days to expiration = US. The value of the American call is $6.28 or $6.28 × 18.391 = $115.5 million in total. (The Wall Street Journal reported on 10/10/1988 that the warrants were being valued at $5 or more and so did Value Line on 12/16/1988.)

89