Capital investment and financing a practical guide to financial evaluation by christopher agar

CAPITAL INVESTMENT & FINANCING
A Practical Guide to Financial Evaluation


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CAPITAL INVESTMENT & FINANCING
A Practical Guide to Financial Evaluation

Christopher Agar


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In memory of Carrie


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CONTENTS
List of Equations, Examples, and Exhibits
Preface

xi
xix

Chapter 1

CAPITAL INVESTMENT
Introduction
Capital Expenditure on Tangible Assets
Acquisitions – an Overview
Introduction
The Acquisition Process
Financial Due Diligence
Financial Evaluation
Corporate Valuation
Introduction
Discounted Cash Flow Valuation
Valuing Real Options
Valuation Using Multiples
Acquisition Structuring & Evaluation
Introduction
Purchase Price
Purchase Consideration

3
3
4
5
5
6
8
11
13
13
15

28
31
33
33
33
36

Chapter 2

CAPITAL RAISING
Introduction
Debt
Introduction
Loans
Corporate Bonds
Equity
Introduction
Initial Public Offerings
Rights Issues
Warrants

43
43
44
44
46
61
68
68
68

70
72

Chapter 3

CAPITAL MANAGEMENT
Introduction
Long Term Capital Management
Debt
Equity

73
73
74
74
76
vii


viii

CONTENTS

Short Term Capital Management
Working Capital
Short Term Instruments – the Money Market

82
82
87

Chapter 4

FINANCIAL RISK MANAGEMENT
Introduction
Interest Rate Risk
Measuring Interest Rate Risk
Managing Interest Rate Risk with Derivatives
- Forward Rate Agreements
- Short Term Interest Rate Futures
- Long Term Interest Rate Futures
- Interest Rate Swaps
- Interest Rate Options
Currency Risk
Nature of Currency Risk
Managing Currency Risk with Derivatives
- Forward Currency Contracts
- Currency Futures
- Currency Swaps
- Currency Options

91
91
92
92
93
93
96
111
128

132
134
134
135
135
138
138
140

Appendix A

Financial Ratios
Equity Ratios
Debt Ratios

143
143
153

Appendix B

Pricing Techniques

B1

Corporate DCF Valuation
Discounting and Present Values
The Cost of Capital (and CAPM)
The Discount Rate for Domestic Investments
The Discount Rate for International Investments

DCF Valuation Methods
Valuation Approaches
Terminal Values

157
157
166
166
184
187
187
195

B2

Straight Bond Pricing
Introduction to Interest Rates
Bond Prices
Bond Yields
Bond Price Volatility

205
205
211
214
218


ix

B3

Forward Pricing
Forward Prices
Forward Interest Rates
Forward Interest Rates and FRAs
Forward Rates and Spot Rates
Forward Bond Prices

225
225
229
231
233
237

B4

Basic Option Pricing
Overview of Pricing Approach
Binomial Model
Probability Distributions: Towards Black-Scholes
Black-Scholes Model
Convergence of Binomial and Black-Scholes Models
Binomial Model Revisited – Setting the Parameters
Option Price Sensitivity
Advanced Option Pricing - further study

243
243

244
262
273
276
279
283
287

B5

Option Pricing Applications
Real Options
Convertible Bonds
Warrants
Interest Rate and Currency Options

289
289
297
308
309

Appendix C

Leasing
Nature and Characteristics
Lease Classification
Lease Financial Evaluation
Leveraged Leasing

315
315
316
317
326

Appendix D
D1
D2
D3
D4
D5
D6

Examples
Management Buyout
Bank Lending Review
Initial Public Offering
Valuation
Acquisition
Short Term Interest Rate Futures Hedging

345
357
367
375
387
399

Bibliography

409

Index

413


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LIST OF EQUATIONS, EXAMPLES AND EXHIBITS
Equations
Chapter 1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8

Constituents of Enterprise Value
Terminal Value – Perpetuity
Terminal Value – Multiples
Real Rate vs. Nominal Rate
Dividend Discount Model
International DCF Approaches
Minimum Exchange Ratio

Maximum Exchange Ratio

13
19
19
21
23
25
37
37

Chapter 2
2.1

Risk Adjusted Return On Capital (RAROC)

52

Chapter 3
3.1
3.2
3.3

Money Market Yield to Maturity
Money Market Realised Yield
Money Market Yield / Discount Rate Comparison

87
88
89

Chapter 4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15

Forward Rate Agreement (FRA)
Interest Rate Futures (Short Term)
"
"
"
"
"
"
"
Interest Rate Futures (Long Term)
“
“

“
“
Forward Exchange Rate

- Settlement Amount
- Pricing
- Hedge Ratio I
- Hedge Ratio II
- Hedge Ratio III
- Number of contracts
- Hedge Ratio using Regression
- Hedge Ratio using Duration
- Hedge Ratio for Spot Instrument
- Invoiced Amount
- Forward Bond Price
- Basis
- Number of contracts
- Hedge Ratio using Duration

94
96
100
101
102
106
107
107
107
112
115

118
120
121
136

Appendix A
A1.1
A1.2

Return on Equity - Leverage Effect
P/E Components

147
148
xi


xii

A1.3
A1.4
A1.5

LIST OF EQUATIONS, EXAMPLES AND EXHIBITS

Constant Growth Formulae
Price-To-Book Ratio and Constant Growth
Dividend Cover and P/E

149

150
152

Appendix B1
B1.1
B1.2
B1.3
B1.4
B1.5
B1.6
B1.7
B1.8
B1.9
B1.10
B1.11
B1.12
B1.13
B1.14
B1.15
B1.16
B1.17
B1.18
B1.19
B1.20
B1.21
B1.22
B1.23
B1.24
B1.25
B1.26

B1.27
B1.28
B1.29

Future Value After n Years
Simple Discount Factor
Cumulative Discount Factor (No Growth)
Annuity
Present Value of Perpetuity (No Growth)
Present Value of Perpetuity (Constant Growth)
Cumulative Discount Factor (Constant Growth)
Cumulative Discount Factor (Two Growth Rates)
Shareholder's Rate of Return
Cost of Equity under Capital Asset Pricing Model (CAPM)
Equity Beta Components
Stock Risk Components
Equity Beta vs. Asset Beta
Weighted Average Cost of Capital (WACC)
Traditional Theory of Capital Structure
Modigliani & Miller: No Taxes
Modigliani & Miller: Taxes
Modigliani & Miller: WACC and Cost of Equity (Taxes)
WACC in terms of the Ungeared Cost of Equity I
WACC in terms of the Ungeared Cost of Equity II
WACC in terms of the Risk Free Rate I
WACC in terms of the Risk Free Rate II
Enterprise / Equity Value DCF Methods
Economic Profits
Marginal Return on Invested Capital
Reinvestment Rate and Marginal Return

Terminal Value Perpetuity: No Growth
Terminal Value Perpetuity: Growth
Terminal Value Perpetuity: Constant Marginal Return on Capital

157
157
158
158
158
159
159
159
166
169
171
172
174
177
178
179
179
180
181
182
183
183
188
195
196
196

197
197
198

Appendix B2
B2.1
B2.2
B2.3
B2.4
B2.5
B2.6
B2.7
B2.8

Simple Rate of Interest
Simple Compound Rate (one year, same frequency)
Exponentials and Logarithms
Simple Simple Rate (one year, different frequencies)
Simple Continuous Rate
Future Value (Simple and Compound Rates) (more than one year)
Daycount Conventions
Annual Coupon Bond Price at Start of Coupon Period

205
207
208
208
209
210
210

211


xiii

B2.9
B2.10
B2.11
B2.12
B2.13
B2.14
B2.15

Semi-Annual Coupon Bond Price at Start of Coupon Period
Macaulay Duration
Modified Duration
Effective Duration
Price change due to Duration
Effective Convexity
Price change due to Convexity

212
220
221
222
222
223
223

Appendix B3

B3.1
B3.2
B3.3
B3.4
B3.5
B3.6
B3.7

Forward Price (discrete - interim income)
Forward Price (discrete - no interim income)
Forward Price (continuous - interim income)
Forward Rate
Zero Coupon Discount Factor – Bootstrapping
Zero Coupon Discount Factor Zero Coupon (Spot) Rate
Zero Coupon (Spot) Rate Forward Rate

226
227
227
231
235
236
236

Appendix B4
B4.1
B4.2
B4.3
B4.4
B4.5

B4.6
B4.7
B4.8
B4.9
B4.10
B4.11
B4.12
B4.13
B4.14
B4.15
B4.16
B4.17
B4.18
B4.19

Replicating Portfolio - Share Component (Hedge Ratio)
Replicating Portfolio - Debt Component
Risk Neutral Probability - Call Option value
Risk Neutral Probability
Continuing Value of Option at Binomial Node
Mean and Variance for Two State prices (Discrete)
Mean and Variance for Two State prices (Continuous)
Binomial Probability Distribution
Binomial Probability - Call price I
Binomial Probability - Call price II
Standard Normal Distribution Function
Approximating the Standard Normal Distribution Function
Stock price following a Geometric Brownian Motion
Mean and Variance of Logarithmic Returns I
Mean and Variance of Logarithmic Returns II

Black-Scholes (No Dividends)
Black-Scholes (Dividends)
Cox, Ross & Rubinstein Binomial Parameters
Jarrow & Rudd Binomial Parameters

246
247
247
247
249
263
263
266
266
267
269
269
270
270
271
273
275
280
282

Appendix B5
B5.1
B5.2
B5.3
B5.4

B5.5

Convertible Bond Payback
Convertible Bond pricing with Black-Scholes
Convertible Bond pricing with Binomial Tree
Convertible Bonds - Debt and Equity Discounting
Convertible Bonds - Blended Discount Rate

298
299
300
301
302


xiv

B5.6
B5.7
B5.8

LIST OF EQUATIONS, EXAMPLES AND EXHIBITS

Futures Option Pricing
Currency Option Pricing I
Currency Option Pricing II

309
310
311

Examples
Chapter 1
Example
1.1
Discounting
1.2
Weighted Average Cost of Capital
1.3
DCF Equity Value
1.4
Dividends vs. Free Cash Flow to Equity Valuation
1.5
International DCF Valuation with Parity Conditions
1.6
Exchange Ratios and NPV Sharing (Unquoted Companies)
1.7
EPS Bootstrapping (Quoted Companies)

15
16
22
24
26
38
41

Chapter 2
Example
2.1

Loan Repayment Profiles
2.2
Risk Adjusted Return On Capital (RAROC)
2.3
Rights Issue

49
52
71

Chapter 3
Example
3.1
Bond Refinancing
3.2
Share Buyback Impact
3.3
Trade Receivables Securitisation
3.4
Yield calculation - Certificate of Deposit (CD)

75
77
85
88

Chapter 4
Example
4.1
Forward Rate Agreement (FRA) Hedging

4.2
Forward Rates
4.3
Hedging with Short Term £ Interest Rate Futures - One Interest Period
4.4
Hedging with Short Term £ Interest Rate Futures - Two Interest Periods
4.5
Basis Risk for Short Term Interest Rate Futures
4.6
The Price Factor for a Long Term Interest Rate (Bond) Future
4.7
The Cheapest-To-Deliver (CTD) Eligible Bond for a Bond Future
4.8
The Theoretical Futures Price for a Bond Future
4.9
Basis Risk for Bond Futures
4.10
Hedging with Bond Futures I
4.11
Hedging with Bond Futures II

95
97
99
103
108
114
116
118
119

121
124


xv

4.12
4.13
4.14
4.15
4.16

Plain Vanilla Fixed-Floating Interest Rate Swaps
Basic Pricing of an Interest Rate Swap
Cross Exchange Rates
Forward Exchange Rates
Basic Pricing of a Currency Swap

128
130
135
137
139

Appendix A
Example
A1
Constant, Sustainable Growth Ratio

151

Appendix B1
Example
B1.1
Present Value of a single cash flow received after n years
B1.2
Present Value of a constant cash flow received annually for n years
B1.3
Present Value of a growing cash flow received annually for n years
B1.4
Net Present Value (NPV) and Internal Rate of Return (IRR)
B1.5
NPV and IRR using 'Loan Balance' Method
B1.6
Pre- and Post-tax IRR
B1.7
Multiple IRRs
B1.8
Adjusting for Multiple IRRs: Sinking Fund Method
B1.9
Adjusting for Multiple IRRs: Initial Investment Method
B1.10 IRRs and Reinvestment Rates
B1.11 NPV and the Return On Invested Capital (ROIC)
B1.12 Equity Return Components
B1.13 Certainty Equivalents
B1.14 Estimating the Equity Beta using Regression
B1.15 Estimating the Cost of Capital using the CAPM
B1.16 Modigliani & Miller: WACC
B1.17 WACC in terms of the Ungeared Cost of Equity
B1.18 Enterprise / Equity Value DCF Methods I – VII

B1.19 Terminal Value: Constant Marginal Return on Capital
B1.20 Terminal Value: Two Stages – Assumed Growth Rates
B1.21 Terminal Value: Two Stages – Reducing Marginal Return on Capital
B1.22 Terminal Value: Two Stages – Reducing Average Return on Capital

157
158
159
160
161
161
162
162
163
163
164
167
167
172
177
180
182
188
198
199
200
201

Appendix B2
Example

B2.1
Simple Interest, paid annually
B2.2
Simple Interest, paid semi-annually
B2.3
Nominal
Effective: various compounding frequencies
B2.4
Effective
Nominal: various compounding frequencies
B2.5
Nominal
Nominal: different frequencies p.a.
B2.6
Comparing Nominal, Effective and Continuous Rates
B2.7
Daycount Conversions

205
206
207
208
209
209
210


xvi

B2.8

B2.9
B2.10
B2.11
B2.12
B2.13
B2.14
B2.15

LIST OF EQUATIONS, EXAMPLES AND EXHIBITS

Semi-Annual Coupon Bond Price at start of Coupon Period
Semi-Annual Coupon Bond Price during Coupon Period
Impact of Reinvestment of Coupons on Return
Valuing a Bond with Zero Coupon Discount Rates
Bond Price Volatility: Coupon and Maturity effect
Macaulay Duration
Effective Duration
Convexity: Coupon and Maturity effect

212
213
215
217
218
221
222
224

Appendix B3
Example

B3.1
Forward Price - 'Cash and Carry'
B3.2
Forward Price - 'Reverse Cash and Carry'
B3.3
Replicating Cash Flows - Fixing a Borrowing / Lending Rate
B3.4
FRA Settlement Amount
B3.5
Zero Coupon Rates & Forward Rates: 'Bootstrapping'
B3.6
Forward Bond Price and Theoretical Futures Price

225
228
229
231
234
237

Appendix B4
Example
B4.1
Call Option - No dividends - Replicating Portfolio - One period
B4.2
Call Option - No dividends - Risk Neutral Probability - One period
B4.3
American Call Option - No dividends - Binomial Tree - 5 periods
B4.4
American Call Option - No dividends - Binomial Tree - 12 periods

B4.5
American Put Option - No dividends - Binomial Tree - 12 periods
B4.6
American Put / Call Option - Dividends - Binomial Tree - 12 periods
B4.7
Pricing a Call Option using the Binomial Distribution
B4.8
Estimating Probability based on the Normal Distribution
B4.9
Simulating a Random Walk using a Logarithmic Return
B4.10 European Call Option - No dividends - Black-Scholes Model
B4.11 European Call Option - Dividends - Black-Scholes Model
B4.12 European Call Option - Convergence of Black-Scholes to Binomial
B4.13 European Call Option - Interpreting the Black-Scholes Model
B4.14 Cox, Ross & Rubinstein Binomial Parameters
B4.15 Jarrow & Rudd Binomial Parameters

245
248
250
252
253
257
266
270
271
274
275
277
278

280
282

Appendix B5
Example
B5.1
Real Options Valuation - Binomial Tree
B5.2
Convertible Bond Pricing - Debt and Equity components
B5.3
Convertible Bond Pricing - Blended Rate (Delta)
B5.4
Convertible Bond Pricing - Blended Rate (Probability of Conversion)
B5.5
Convertible Bond Pricing – Non-callable - No dividends - Binomial Tree
B5.6
Convertible Bond Pricing - Callable - No dividends - Binomial Tree

290
301
302
303
303
306


xvii

B5.7
B5.8

B5.9
B5.10

Convertible Bond Pricing - Callable - Dividends - Binomial Tree
Warrants Pricing
Currency Option Pricing - Black-Scholes adjusted model
Currency Option Pricing - Binomial Tree

307
308
310
311

Appendix C
Example
C1
Lessor's NPV and IRR (Pre-tax)
C2
Lessor’s IRR and Residual Values
C3
Lessee Lease vs. Purchase decision
C4
Lessor Yield / Profit measures
C5
UK Accounting - 90% Finance Lease Test
C6
UK Lessee - Finance Lease Accounting
C7
UK Lessor - Finance Lease Accounting
C8

UK Lessee - Finance Lease Taxation
C9
UK Lessor - Finance Lease Taxation
C10
Leveraged Lease

317
318
319
323
330
331
332
333
334
335

Exhibits
Chapter 1
Exhibit
1.1
The Transaction Process for a Majority Acquisition – Key Stages
1.2
Financial Due Diligence – Key questions
1.3
Accounting Measures used for Valuation
1.4
Main Valuation Multiples
1.5
Purchase Consideration – Issues

6
8
14
31
36

Chapter 4
Exhibit
4.1
LIFFE June 2004 Long Gilt Contract (Bond Futures)

113

Appendix C
Exhibit
C1
UK Accounting and Tax treatment for Leases

329


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PREFACE
This book discusses practical ways of carrying out a financial evaluation when
making corporate capital investment, financing and financial risk management
decisions that involve questions such as:
•

What is the intrinsic value of a tangible asset, business, or company? What
financial risks are associated with an investment, and how can these be identified
and controlled? What should the purchase price and form of consideration be?

•

What type of funding should be raised? What alternative forms of finance are
possible? How are financial instruments priced? How will the risk for the
financier affect the terms of any financing offer and agreement?

•

How do the providers of debt, equity and other finance evaluate their
investment, and what returns do they require? How can capital, and its
associated risks, be managed by a company so as to maximise returns for its
owners (shareholders)?

The practical application of established corporate finance theories and techniques is
discussed in the context of capital investment (Chapter 1) and financing (raising and
managing capital, so as to maximise returns and minimise risk for capital
providers)(Chapters 2 to 4). These chapters are non-technical, written with the aim
of guiding the reader through the subject matter fairly quickly (the Futures examples
in Chapter 4 being an exception). More quantitative analysis is covered in technical
Appendices that deal with traditional financial ratio analysis (A), techniques to price
and value equity, bonds and derivatives or related instruments and investments
(Forwards, Options, Real Options, Convertible Bonds)(B1 to B5), and lease finance
(C). Over 100 ExcelTM based examples are provided (with workings shown), and a
detailed case study involving a fictional company is used to illustrate some of the
techniques discussed (Appendices D1 to D6).

Only traditional theories about pricing the Cost of Equity and Options are discussed
in any detail. Basic mathematics is involved, and the discussion goes no further than
is needed in order to understand the background to a theory or technique. The book
does not discuss (1) subjects involving more advanced mathematics, (2) subjects that
are more relevant for financial institutions compared to a corporate, and (3) current
market conditions or market evidence for the theories discussed.
All the methods and techniques are universal, although the examples given are UK
focused (i.e. £ cash flows, UK financing instruments, risk for a UK based investor,
and UK tax and accounting). Capital instruments and derivatives are based on UK
markets; these will have comparables in other areas and be priced in the same way,
although market conventions may differ.
I would like to thank Mike Cash and his colleagues at Butterworth-Heinemann for
their patience and support.
xix


xx

PREFACE

Structure of Capital Investment & Financing

Technical Appendices
A
B1
B2
B3
B4
B5
C

Financial Ratios
Corporate DCF Valuation
Straight Bond Pricing
Forward Pricing
Basic Option Pricing
Option Pricing Applications
Leasing

Case Study
D1
D2
D3
D4
D5
D6

Management Buyout
Bank lending review
Initial Public Offering (IPO)
Valuation
Acquisition
Short Term Interest Rate Futures hedging

The following subjects (that either involve fairly advanced mathematics or are not wholly relevant
for a corporate borrower) are not discussed:
-

Volatility and correlation measurement
‘Value At Risk’ and other risk models

Portfolio / Investment management
Derivatives not wholly relevant for a
borrower (credit derivatives, stock index
futures, asset swaps etc.)
- ‘Exotic’ options pricing
- Advanced derivative mathematics

- Credit risk measurement and modeling
- Interest rate models
- Option-embedded bonds
(other than Convertibles)
- Insurance and operating risk
- Trading strategies
- Valuation of Intangible Assets


CAPITAL INVESTMENT & FINANCING
A Practical Guide to Financial Evaluation


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1

CAPITAL INVESTMENT
INTRODUCTION

The Financial Evaluation of Capital Investment Decisions
A corporate investor should undertake a financial evaluation when deciding whether

to invest in tangible assets (capital expenditure on plant, machinery, equipment and
other fixed assets required to generate revenues and grow the business ‘organically’)
or other businesses (acquisitions). The investor needs to ensure that it pays no more
than a fair value to purchase the investment (and acquire ownership of economic
benefits to be derived from the investment) and that financial gains for its owners
(shareholders) are maximised.
The fair, or intrinsic, value of an asset, project or business can be determined by
estimating the current value of expected future cash flows (net cash flows arising
over the investment holding period and any sale proceeds), taking into account the
risk that actual cash flows, in terms of amount and timing, differ to those initially
expected at the date of valuation (risk, in this context, is traditionally defined as the
variation, or volatility, of cash flows around the expected level). The investor’s
shareholders will require a higher return (in the form of income and a capital gain) if
their capital is invested in assets and businesses with greater risk. Before committing
capital, the investor should estimate the investment’s intrinsic value, based on a
reasonable forecast of future cash flows (taking into account the most likely
scenarios) and an acceptable method of capturing relevant risk. Economic gains will
arise for shareholders if the intrinsic value of the investment exceeds the cost of
investment.
Financial evaluation is one part of the investment process, and contributes to the
overall objective of managing risk (identified from ‘Due Diligence’ and other
analysis) and maximising financial returns for the investor, based on a set of
assumptions and expectations at the date of the investment transaction.

Chapter Contents
This chapter discusses financial evaluation in the context of investment decisions,
with a focus on investment valuation (mainly Discounted Cash Flow and ‘Real
Options’ approaches), structuring and evaluation techniques. Technical issues and
practical examples can be found in the Appendices (A, B1, B4, B5, D1, D4 and D5).

3


4

CAPITAL INVESTMENT

CAPITAL EXPENDITURE ON TANGIBLE ASSETS
Investment Rationale
Capital provided to a company, and any equity generated internally (i.e. accumulated
profits), should only be invested in assets if value is created for shareholders, when
the value of economic benefits arising from the assets exceeds the cost of acquiring
those benefits. Since capital is a limited resource, it should be allocated to those
assets that maximise the value created (shareholders would invest elsewhere if a
higher return, for the same level of risk, was available).

Estimating Value
The intrinsic value of an asset should be estimated using cash flows (receipts and
payments are recognised as and when received or incurred) rather than profit (which
reflects local accounting treatment and the normal policy of matching costs to
revenues, and may involve estimation – for example, the amount of capital
expenditure charged to profit via depreciation would partly reflect the investor’s own
estimate of the asset’s expected economic life). Over the investment holding period,
cash inflows from revenues and any sale proceeds should exceed cash outflows
(including tax payments) by a sufficient amount to justify the initial expenditure (and
any subsequent repairs and maintenance, or modification or enhancement, costs).
The relevant cash flows to be assessed are the total incremental, net after-tax cash
flows that the investor expects to receive as a result of the expenditure. The
evaluation should compare the investor’s total net cash flows with and without the
new investment; any change in cash flows arising on existing investments, as a result

of the new investment, should be taken into account.
Cash flows should be stated in economically equivalent amounts at the date of
valuation (‘discounted’ to their ‘Present Value’). The decision to invest should only
be taken if the asset or project has a positive ‘Net Present Value’ (NPV): the present
value of all future net cash flows exceeds the cost of investment.
Discounting and NPV analysis are discussed in more detail in ‘Discounting and
Present Values’ in Appendix B1 (an alternative measure, the Internal Rate of Return,
is also discussed – ‘Payback’, which shows the number of years it takes to recover
the cost of the investment from its cash flows, will not be discussed further, since it
fails to capture the true economic value of an investment).