FB3410 Lecture Notes(3)

FB3410 Financial Management Semester A 2011 - 2012

Dr. Anson C. K. Au Yeung

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Staff Information

Instructor: Dr. Anson C. K. Au Yeung

Office: P7414

Phone: 3442-2163

Email: [email protected]

Office Hours: By Appointment

Class Schedule

C05: Friday 10:30 – 12:20, LT-12

Course Objectives

This course aims to provide students with a background in some fundamental concepts of

modern financial management. It also exposes students to some of the major financial

decision techniques used in the business world.

References

1. Course Package

2. Ross, Westerfield and Jordan, Fundamentals of Corporate Finance (9th Edition), McGraw

Hill 2010 [RWJ].

Assessment

1. Midterm (20%)

Week 7: 14 October 2011 (Friday), In-class

2. Individual Case Study (10%)

Week 10: 4 November 2011 (Friday), In-class

3. Examination (70%)

mailto:[email protected]

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Course Outline

Topic Reference

1 Introduction to Financial Management Chapter 1

2 Financial Statements Analysis Chapter 2, 3, 4

3 The Time Value of Money Chapter 5

4 Discounted Cash Flow Valuation Chapter 6

5 Investment Decisions Chapter 9

6 Bond and Stock Valuation Chapter 7, 8

7 Capital Budgeting Chapter 10, 11

8 Market Efficiency Chapter 12

9 Risk and Return Chapter 13

10 Cost of Capital Chapter 14

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Table of Contents

1 Topic 1 – Introduction to Financial Management .............................................................. 9

1.1 Introduction ................................................................................................................. 9

1.1.1 Why Study Financial Management ...................................................................... 9

1.1.2 The Objective of Financial Management ............................................................. 9

1.1.3 The Financial Decisions ....................................................................................... 9

1.2 The Corporate Firm ................................................................................................... 10

1.2.1 Sole Proprietorship............................................................................................. 10

1.2.2 Partnership ......................................................................................................... 11

1.2.3 Corporation ........................................................................................................ 11

1.2.4 A Comparison .................................................................................................... 12

1.3 The Agency Problem and Control of the Corporation .............................................. 12

1.3.1 Principal-Agency Relationship .......................................................................... 13

1.3.2 Evidence from the Oil Industry.......................................................................... 15

2 Topic 2 – Financial Statements Analysis ......................................................................... 16

2.1 The Balance Sheet ..................................................................................................... 16

2.1.1 Assets ................................................................................................................. 17

2.1.2 Liabilities ........................................................................................................... 17

2.1.3 Equity ................................................................................................................. 18

2.1.4 The Accounting Identity .................................................................................... 18

2.1.5 Managerial Issues............................................................................................... 18

2.2 The Income Statement ............................................................................................... 19

2.2.1 Revenues ............................................................................................................ 19

2.2.2 Expenses ............................................................................................................ 20

2.2.3 Depreciation ....................................................................................................... 20

2.2.4 Taxes .................................................................................................................. 20

2.3 Cash Flow .................................................................................................................. 22

2.3.1 The Importance of Cash Flow............................................................................ 22

2.3.2 The Cash Flow Identity ...................................................................................... 22

2.4 Financial Ratio Analysis ........................................................................................... 25

2.4.1 Liquidity Ratios ................................................................................................. 27

2.4.2 Solvency Ratios ................................................................................................. 27

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2.4.3 Asset Management Ratios.................................................................................. 28

2.4.4 Profitability Ratios ............................................................................................. 30

2.4.5 Market Value Ratios .......................................................................................... 30

2.4.6 Linking Ratios .................................................................................................... 32

2.4.7 Managerial Implications .................................................................................... 32

2.5 Growth Analysis ........................................................................................................ 33

2.5.1 Sustainable Growth ............................................................................................ 33

2.5.2 Du Pont Decomposition ..................................................................................... 34

2.5.3 Capital Structure and Sustainable Growth ......................................................... 35

2.5.4 A Note on Sustainable Growth Rate .................................................................. 35

3 Topic 3 – The Time Value of Money .............................................................................. 37

3.1 A Motivating Example .............................................................................................. 37

3.1.1 Basis for Comparison ......................................................................................... 40

3.2 Future Value and Compounding ............................................................................... 40

3.2.1 Effects of Compounding .................................................................................... 40

3.2.2 Calculate Future Values with BAII Plus ............................................................ 43

3.3 Present Value and Discounting ................................................................................. 43

3.3.1 Effects of Discounting ....................................................................................... 44

3.3.2 Calculate Present Values with BAII Plus .......................................................... 45

3.4 The Discount Rate ..................................................................................................... 46

3.5 The Number of Periods ............................................................................................. 48

3.6 Spreadsheet Application ............................................................................................ 49

4 Topic 4 – Discounted Cash Flow Valuation .................................................................... 50

4.1 Multiple Cash Flows ................................................................................................. 50

4.1.1 Future Value of a Series of Cash Flows............................................................. 50

4.1.2 Present Value of a Series of Cash Flows ........................................................... 51

4.2 Annuity ...................................................................................................................... 52

4.2.1 Present Value of an Annuity .............................................................................. 52

4.2.2 Future Value of an Annuity ............................................................................... 56

4.3 Annuity Due .............................................................................................................. 57

4.4 Perpetuity .................................................................................................................. 58

4.5 Comparing Rates ....................................................................................................... 58

4.5.1 Effective Annual Rate (EAR) ............................................................................ 59

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4.5.2 Annual Percentage Rate (APR) ......................................................................... 60

5 Topic 5 – Investment Decisions ....................................................................................... 62

5.1 Capital Investment Projects ....................................................................................... 62

5.2 Net Present Value ...................................................................................................... 63

5.2.1 Why Positive NPV? ........................................................................................... 64

5.2.2 More than Two Alternatives .............................................................................. 65

5.2.3 Investment Projects with Different Lives .......................................................... 66

5.3 The Internal Rate of Return (IRR) ............................................................................ 67

5.3.1 Nonconventional Cash Flows ............................................................................ 69

5.3.2 Mutually Exclusive Investments ........................................................................ 70

5.4 The Payback Rule...................................................................................................... 72

5.5 The Average Accounting Return............................................................................... 74

5.6 Profitability Index ..................................................................................................... 75

5.7 Comprehensive Problems .......................................................................................... 76

6 Topic 6 – Bond and Stock Valuation ............................................................................... 79

6.1 What is a Bond? ........................................................................................................ 79

6.2 How to Value Bonds? ............................................................................................... 79

6.2.1 Pure Discount Bonds.......................................................................................... 79

6.2.2 Coupon Bonds .................................................................................................... 80

6.2.3 Consol ................................................................................................................ 83

6.3 Yield to Maturity ....................................................................................................... 83

6.4 What is a Common Stock? ........................................................................................ 84

6.5 How to Value Stocks? ............................................................................................... 84

6.6 Modeling Dividends .................................................................................................. 85

6.6.1 Zero Growth ....................................................................................................... 86

6.6.2 Constant Growth ................................................................................................ 86

6.6.3 Nonconstant Growth .......................................................................................... 89

6.7 Total Return............................................................................................................... 89

6.8 Stock Price and Growth Opportunities...................................................................... 90

6.8.1 Concluding Remarks .......................................................................................... 94

7 Topic 7 – Capital Budgeting ............................................................................................ 95

7.1 Identify the Project Cash Flows ................................................................................ 95

7.1.1 Relevant Cash Flows.......................................................................................... 96

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7.2 Compute the Project Cash Flows .............................................................................. 97

7.2.1 Operating Cash Flow ......................................................................................... 97

7.2.2 Depreciation ....................................................................................................... 99

7.2.3 After Tax Salvage ............................................................................................ 100

7.2.4 Changes in Net Working Capital ..................................................................... 102

7.3 A Comprehensive Example ..................................................................................... 103

7.4 Evaluating NPV Estimates ...................................................................................... 105

7.4.1 Scenario Analysis............................................................................................. 105

7.4.2 Sensitivity Analysis ......................................................................................... 107

7.5 Case Study – Danforth & Donnalley Laundry Products Company ........................ 109

8 Topic 8 – Market Efficiency .......................................................................................... 114

8.1 Differences between Investment and Financing Decisions..................................... 114

8.2 Efficient Capital Markets ........................................................................................ 115

8.2.1 Implications of the Efficient Market Hypothesis ............................................. 116

8.2.2 Three Forms of Market Efficiency .................................................................. 117

8.2.3 Weak Form Efficiency ..................................................................................... 117

8.2.4 Semi-strong Form Efficiency ........................................................................... 118

8.2.5 Strong Form Efficiency.................................................................................... 118

8.2.6 Concluding Remarks ........................................................................................ 118

9 Topic 9 – Risks and Returns .......................................................................................... 119

9.1 Risk, Return and Investment Decision .................................................................... 119

9.2 Returns .................................................................................................................... 119

9.2.1 Dollar Returns .................................................................................................. 119

9.2.2 Percentage Returns........................................................................................... 120

9.2.3 The Historical Record ...................................................................................... 121

9.2.4 Arithmetic and Geometric Returns .................................................................. 122

9.3 Risks ........................................................................................................................ 123

9.3.1 Risk Premiums ................................................................................................. 123

9.3.2 Variance and Standard Deviation .................................................................... 123

9.4 Expectation .............................................................................................................. 124

9.4.1 Expected Returns ............................................................................................. 125

9.4.2 Expected Variance and Standard Deviation .................................................... 125

9.5 Portfolio Risks and Returns .................................................................................... 126

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9.5.1 Portfolio Expected Returns .............................................................................. 126

9.5.2 Systematic and Unsystematic Risks ................................................................. 127

9.5.3 Diversification.................................................................................................. 127

9.5.4 Decomposition of Total Risk ........................................................................... 128

9.5.5 Measuring Systematic Risk.............................................................................. 129

9.5.6 Beta and the Risk Premium.............................................................................. 129

9.6 The Capital Asset Pricing Model (CAPM) ............................................................. 131

10 Topic 10 – Cost of Capital ............................................................................................. 133

10.1 The Cost of Capital: Some Preliminaries ............................................................ 133

10.2 Cost of Equity ...................................................................................................... 134

10.2.1 The Dividend Growth Model Approach .......................................................... 134

10.2.2 The CAPM Approach ...................................................................................... 135

10.3 Cost of Debt ......................................................................................................... 136

10.4 Cost of Preferred Stock........................................................................................ 137

10.5 Weighted Average Cost of Capital ...................................................................... 138

10.6 A Comprehensive Example ................................................................................. 139

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1 Topic 1 – Introduction to Financial Management

1.1 Introduction

1.1.1 Why Study Financial Management

The course begins with the assumption that you are the Chief Financial Officer (CFO) of City

Corporation. As a senior executive, every day, the major role of your job is going to make

corporate financial decisions. Every decision that you made has financial implications. If

your choice is right, then the implementation of business activities will subsequently create

value.

To prepare you to become a competent CFO, an understanding of why and how financial

decisions are made is essential. The focus of this course is to teach you how to make optimal

corporate financial decisions.

1.1.2 The Objective of Financial Management

Before learning how to make optimal decisions, we better first think about “What is the

objective of financial management?”

In theory, the objective of financial management is to maximize firm value. Since you are

working for City Corporation, you act in shareholders’ best interest by making decisions that

increase the value of the stock. Any decision that increases the stock price is considered to be

“good”, whereas one that decreases the stock price is considered to be “bad”.

1.1.3 The Financial Decisions

In general, your role as a CFO will center on helping City Corporation find money to run and

develop its business, manage its assets, acquire other firms, and plan for their financial future.

More precisely, you will involve in deciding four major financial decisions:

1. Investment Decisions

How much should City Corporation invest?

Which project should City Corporation invest?

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2. Working Capital Decisions

What should be the level of investment in current assets?

How should City Corporation mange its short-term assets and liabilities?

3. Financing Decisions

How to finance the investment?

What is the optimal debt/equity ratio?

4. Distribution Decisions

How much dividend should be paid to shareholders?

1.2 The Corporate Firm

At the startup, one problem of City Corporation is how to raise capital. Organizing the firm

as a corporation is the standard method for solving the problems encountered in raising large

amounts of cash. However, the firm can organize itself in other forms.

Let’s learn the three basic legal forms of organizing firms and compare their advantages and

disadvantages under each form.

1.2.1 Sole Proprietorship

A sole proprietorship is a business owned by a single individual.

The advantage:

It is the simplest type of business to start.

It is the least regulated form of organization.

The owner of a sole proprietorship keeps all the profits.

The disadvantage:

The owner has unlimited liability for business debts.

The amount of capital that can be raised is limited to the proprietor’s personal wealth.

Ownership of a sole proprietorship may be difficult to transfer.

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1.2.2 Partnership

Partnership is a business formed by two or more individuals or entities.

In a general partnership,

All the partners share in gains or losses, and all have unlimited liability for all

partnership debts.

The partners share gains and losses as described in the partnership agreement.

In a limited partnership,

One or more general partners will run the business and have unlimited liability.

There will be one or more limited partners who do not actively participate in the

business.

A limited partner’s liability is limited to the amount that partner contributes to the

partnership.

The advantage:

It is based on relatively informal agreement and is easy and inexpensive to form.

The disadvantage:

The partnership terminates when a general partner wishes to sell out or dies.

Ownership by a general partner is not easily transferred since a new partnership must

be formed.

Although a limited partner can sell his interest without dissolving the partnership,

finding a partner may be difficult.

1.2.3 Corporation

Corporation is a business created as a distinct legal entity owned by one or more individuals

or entities. A corporation is a legal “person” separate and distinct from its owners, and it has

many of the rights, duties, and privileges of an actual person.

Corporations can borrow money and own property, can sue and be sued, and can enter into

contracts.

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The advantage:

Stockholders in a corporation have limited liability.

The separation of ownership and management makes transferring of ownership a lot

easier.

Easier to raise capital.

The disadvantage:

There is agency problem as a result of the separation of ownership and management.

Double taxation.

1.2.4 A Comparison

Let’s summarize some basic characteristics between partnership and corporation.

Partnership Corporation

Liquidity Subject to substantial

restrictions

Shares can be easily

exchanged

Voting Rights General partner is in charge

Limited partners may have

some voting rights

Usually each share gets one

vote

Taxation Partners pay taxes on

distributions

Double taxation

Reinvestment and

Dividend Payout All net cash flow is

distributed to partners

Broad latitude

Liability General partners have

unlimited liability

Limited partners enjoy

limited liability

Limited liability

Continuity Limited life Perpetual life

1.3 The Agency Problem and Control of the Corporation

The separation of ownership and management can facilitate shares exchange. Usually in a

large corporation, the ownership is dispersed. This means that a corporation has large

number of shareholders who only own small number of shares.

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1.3.1 Principal-Agency Relationship

Those small shareholders do not have effective control over the corporation. The

shareholders (the principal) will hire managers (the agent) to represent their interest.

However, we are not sure whether the managers will act in the best interests for them.

The possibility of conflict of interest between owners and management of a corporation is

called an agency problem.

Here are some possibilities of conflict of interest between owners and managers in daily life:

1. Career Concern

Managers may reluctant to take risky investments because there is a possibility

that things will turn out badly and the management jobs will be lost.

2. Empire Building

Managers would tend to maximize the amount of resources over which they have

control.

They have intention to over expand. For example, acquire and overpay irrelevant

businesses just to demonstrate corporate power.

3. Private Benefits of Control

Managers may take advantage of inside information for personal trading.

They may overuse corporate resources, such as frequent business travel with first

class ticket.

4. Shirking

The managers do not put their best effort to act in shareholders’ interest.

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Example 1.1

Suppose City Corporation is going to hire a salesman, and you decide to offer him an annual

wage of w. Your objective is to hire a hardworking salesman with a minimum wage. If the

salesman works hard, he can bring $270,000 revenue to the firm; otherwise, he can only bring

$70,000 revenue if he does not work hard.

The salesman utility can be described as ,U w e w e . His reservation level of utility is

81,000. Once this salesman accepts the offer, he can put “high” (e = 25,000) or “low” (e = 0)

effort.

What is the minimum wage that you have to offer to this salesman for accepting the job?

Will the salesman act in the best interests (by working hard) of City Corporation?

How should you decide the wage if you want to hire a hardworking salesman?

From this example, the salesman (agent) takes an action that affects his utility as well as the

corporation (principal). The insight of this example is to show you the agent does not

necessarily choose the action in the interest of the principal.

It is therefore important that managers’ incentives are aligned with those of shareholders.

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1.3.2 Evidence from the Oil Industry

The radical changes in the oil market since 1973 generated large increases in free cash flow in

the industry. From 1973 to the late 1970’s, crude oil prices increased sharply.

Price increases generated large cash flows in the industry. For example, the 1984 cash flows

of the ten largest oil companies were US$48.5 billion, 28% of the total cash flows of the top

200 firms in Dun’s Business Month survey.

The management did not pay out the excess resources to shareholders. Instead, the industry

continued to spend heavily on exploration and development (E&D) activity even though

average returns were below the cost of capital. Two studies indicate that oil industry E&D

expenditures have been too high since the late 1970’s:

John McConnell and Chris Muscarella (1986) find that announcements of increases

in E&D expenditures by oil companies in the period 1975 – 1981 were associated

with systematic decreases in the announcing firm’s stock price.

B. Picchi’s study of returns on E&D expenditures for 30 large oil firms did not earn

even a 10% return on its pretax outlays in the period 1982 – 1984.

Oil industry managers also launched diversification programs to invest funds outside the

industry. For example:

Retailing: Marcor by Mobil.

Manufacturing: Reliance Electric by Exxon.

Office equipment: Vydec by Exxon.

Mining: Kennecott by Sohio; Anaconda Minerals by Arco; Cyprus Mines by Amoco.

These acquisitions turned out to be among the least successful, partly because of bad luck and

partly because of a lack of managerial expertise outside the oil industry.

http://graphics8.nytimes.com/images/2008/03/03/business/20080304_OIL600x275_GRAPHIC.gif

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2 Topic 2 – Financial Statements Analysis

The focus of this topic is not on preparing financial statements. As a CFO, what you need is

to understand the information inside the financial statements, and recognize the importance of

cash flow.

To start with, financial statements are the key source of information for financial decisions.

The two important financial statements that we often use are:

1. The Balance Sheet

Shows a firm’s value on a particular date.

2. The Income Statement

Summarizes a firm’s performance over a period of time.

2.1 The Balance Sheet

The balance sheet is a snapshot of the firm. It summarizes what a firm owns (the assets) and

what a firm owes (the liabilities), and the difference between the two (the equity).

A simplified balance sheet:

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Below is a balance sheet for U.S. Corporation.

2.1.1 Assets

An asset is a resource controlled by the corporation as a result of past events and from which

future economic benefits are expected to flow to the corporation.

Assets can be classified into current and fixed.

Current asset has a life of less than a year, for example, inventory.

Fixed asset has a relatively long life, for example, land and building.

2.1.2 Liabilities

A liability is an obligation owed by the corporation to repay the claims in the future.

Liabilities can also be classified into current and long-term.

Current liability reflects the amount of money the firm owes and must pay within the

coming year, for example, accounts payable.

Long-term liability is debt due after one year from the date of the balance sheet.

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2.1.3 Equity

Shareholders’ equity is the total equity interest that all shareholders have in a corporation. It

is the residual value remained to the shareholders after repaying all debts by selling its assets.

Equity can be separated into capital stock and retained earnings.

Capital stock is the owners’ initial investment in the firm.

Retained earnings represent the accumulated total of after-tax earnings and losses

from operations over the life of the firm that has been retained in the corporation.

2.1.4 The Accounting Identity

The most basic accounting identity is that the balance sheet must balance. That is,

Assets = Liabilities + Equity

Although this balance sheet identity is trivial, understanding the implication behind this

identity is important. You need to know how the changes in asset value in City Corporation

would have impact on your debtholders and equityholders. For example, during the financial

crisis, the asset value of the firm dropped much. The fall in the asset value must be

compensated by the drop in either the value of debt or equity, or both.

2.1.5 Managerial Issues

1. Net Working Capital

Net working capital is the difference between a firm’s current assets and its

current liabilities.

The level of working capital naturally expands and contracts with sales activities.

Too little working capital can put a firm in a bad position since the firm may be

unable to pay its bills or to take advantage of profitable opportunities.

Too much working capital reduces profitability since that capital has a carrying

cost.

2. Inventory

Having too many inventories can fill customer orders without delay and provides

a buffer against potential production stoppages.

The flip side of plentiful inventory is the risk of deterioration in the market value

of inventory itself.

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3. Financial Leverage

Financial leverage refers to the use of debt in acquiring an asset. The more debt a

firm has, the greater is its degree of financial leverage.

Financial leverage creates an opportunity for a firm to gain a higher return on the

capital invested.

2.2 The Income Statement

The income statement indicates the results of operations over a specified period. Unlike the

balance sheet, which is a snapshot of the firm’s position at a point in time, the income

statement indicates cumulative business results within a defined time frame.

The simple income statement equation is:

Revenues – Expenses = Income

An income statement for U.S. Corporation is shown below:

2.2.1 Revenues

An income statement starts with the firm’s revenues. According to the recognition principle,

revenue is recognized when the earnings process is virtually complete and the value of an

exchange of goods or services is known or can be reliably determined.

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2.2.2 Expenses

Expenses shown on the income statement are based on the matching principle. The basic

idea is to first determine revenues and then match those revenues with the costs associated

with producing them.

As a result of the way revenues and expenses are reported, the figures reported in the

statements may not be at all representative of the actual cash inflows and outflows that

occurred during a particular period.

2.2.3 Depreciation

Depreciation is counted on the income statement as an expense, even though it involves no

cash outflows. Depreciation is a way of estimating the consumption of an asset over time.

For example, if a computer loses about a third of its value each year, the firm would not

expense the full value of the computer in the first year of its purchase, but deduct one-third

each year as an expense.

The depreciation deduction is simply an application of the matching principle in accounting.

2.2.4 Taxes

In making financial decisions, it is important to distinguish between average and marginal

tax rates.

Average tax rate is the total taxes paid divided by total taxable income.

Marginal tax rate is the amount of tax payable on the next dollar earned.

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Example 2.1

The corporate tax rates in effect for 2007 are shown below.

Taxable Income Tax Rate

0 - 50,000 15%

50,001 - 75,000 25%

75,001 - 100,000 34%

100,001 - 335,000 39%

335,001 - 10,000,000 34%

10,000,001 - 15,000,000 35%

15,000,001 - 18,333,333 38%

18,333,334 + 35%

Suppose City Corporation earns $4 million in taxable income.

What is the firm’s tax liability?

What is the average tax rate?

What is the marginal tax rate?

If City Corporation is considering a project that will increase the firm’s taxable income by $1

million, what tax rate should you use in your analysis?

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2.3 Cash Flow

Cash flow is simply the difference between the number of dollars that came in and the

number that went out.

2.3.1 The Importance of Cash Flow

Remember that the objective of financial management is to maximize firm value. As a CFO,

your job is to create value from the firm’s investing, financing, and net working capital

activities, but how?

The answer is that you must create more cash flow than it uses. For example:

Try to buy assets that generate more cash than they cost.

Sell bonds and stocks that raise more cash than they cost.

2.3.2 The Cash Flow Identity

In order to understand how to create more cash flow, let us step back and study the cash flow

identity.

Cash Flow from Assets = Cash Flow to Creditors + Cash Flow to Shareholders

This identity says that a firm generates cash through its various activities, and that cash is

either used to pay creditors or to distribute back to shareholders.

Here, we can break down the identity in details.

1. Cash Flow from Assets

= Operating Cash Flow – Net Capital Spending – Change in Net Working Capital

2. Cash Flow to Creditors

= Interest Paid – Net New Borrowing

3. Cash Flow to Shareholders

= Dividend Paid – Net New Equity Raised

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Example 2.2

Using the financial statements of U.S. Corporation, calculate the cash flow from assets, cash

flow to creditors, and cash flow to shareholders in 2008.

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1. Calculate Cash Flow from Assets

2. Calculate Cash Flow to Creditors

3. Calculate Cash Flow to Shareholders

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2.4 Financial Ratio Analysis

Next, we are going to analyze the financial statements in a meaningful manner.

Quantitatively, we can compute financial ratios to interpret the financial results.

Financial ratios can help us to examine the financial health of a corporation. The ratios fall

into five classes:

Liquidity

Solvency

Asset Management

Profitability

Market Value

Let us look at the financial statements of City Corporation and calculate some common

financial ratios.

City Corporation

2008 Income Statement

($ in thousands)

Sales 1,506

Less: Cost of goods sold 1,004

Gross profit 502

Depreciation 10

Lease rental costs 30

Other operating expenses 360

EBIT 102

Interest 5

Taxable income 97

Tax 47

Net income 50

Less: Dividends

- Preferred 1

- Common 29

Change in retained earnings 20

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City Corporation

Balance Sheet as of 31 December, 2007 2008

($ in thousands)

2008 2007

Current assets:

Cash 20 30

Accounts receivable 95 95

Inventory 130 110

Total current assets 245 235

Fixed assets:

Land 10 10

Building and equipment 120 100

Total fixed assets 130 110

Other assets:

Goodwill 10 10

TOTAL ASSETS 385 355

Current liabilities:

Accounts payable 50 40

Estimated income taxes payable 10 10

Total current liabilities 60 50

Fixed liabilities:

Mortgage bonds, 10% 50 50

TOTAL LIABILITIES 110 100

Shareholders’ equity:

Convertible preferred stock, 5% 20 20

Common stock (10,000 shares) 50 50

Retained earnings 205 185

Total shareholders’ equity 275 255

TOTAL LIABILITIES AND

SHAREHOLDERS’ EQUITY 385 355

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2.4.1 Liquidity Ratios

A corporation’s liquidity is measured by its ability to raise cash to meet its current obligations.

1. Current Ratio

Current Assets

Current Liabilities

The current ratio in 2008 245

4.1 times60

The higher the ratio, the more protection the firm has against liquidity problems.

However, the ratio may be distorted by seasonal influences, slow-moving

inventories built up out of proportion to market opportunities, or abnormal

payment of accounts payable just prior to the balance sheet date.

2. Quick Ratio (Acid-Test Ratio)

Current Assets - Inventory

Current Liabilities

The quick ratio in 2008 245 130

1.9 times60

The quick ratio measures the ability of a firm to use its “near-cash” assets to

immediately extinguish its current liabilities.

3. Cash Ratio

Cash

Current Liabilities

The cash ratio in 2008 20

0.3 times60

Very short-term creditor might be interested in this ratio.

2.4.2 Solvency Ratios

Solvency ratios generate insight into a firm’s ability to meet long-term debt payment.

1. Total Debt Ratio

Total Liabilities

Total Assets

The total debt ratio in 2008 110

0.29385

Total debt ratio indicates the proportion of a firm’s total assets financed by short-

and long-term credit sources.

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Another variation of this ratio is to measure the relative mix of funds provided by the owners

and the creditors.

2. Debt-equity Ratio

Total Liabilities

Shareholders' Equity

The debt-equity ratio in 2008 110

0.4275

3. Times Interest Earned Ratio

EBIT

Interest

Times interest earned in 2008 102

20.4 times5

This ratio indicates the extent to which operating profits can decline without

impairing the firm’s ability to pay the interest on its long-term debt.

4. Cash Coverage Ratio

EBIT Depreciation

Interest

Cash coverage in 2008 102 10

22.4 times5

This ratio uses EBIT plus non-cash charges as the numerator. The modification

indicates the ability of the firm to cover its cash outflow for interest from its funds

from operations.

2.4.3 Asset Management Ratios

Asset management ratios measure how a firm manages its investment and fixed assets. The

focus of these ratios is on the efficiency of the uses of the assets. That is, how good a firm

utilizes its assets.

1. Inventory Turnover

Cost of Goods Sold

Inventory

The inventory turnover in 2008 1,004

7.7 times130

The inventory turnover ratio indicates how fast inventory items move through a

business.

29

2. Days’ Sales in Inventory

365 days

Inventory Turnover

The average days’ sales in inventory in 2008 365

47 days7.7

This ratio estimates the average length of time items spent in inventory.

3. Receivables Turnover

Sales

Accounts Receivable

The receivable turnover in 2008 1,506

15.9 times95

Only credit sales should be used.

This ratio shows a firm’s credit policy. It looks at how fast the firm collects on

the credit sales.

4. Average Collection Period

365 days

Receivables Turnover

The average collection period in 2008 365

23 days15.9

5. Asset Turnover

Sales

Total Assets

The asset turnover in 2008 1,506

3.9 times385

This ratio is an indicator of how efficiently management is using its investment in

total assets to generate sales.

High turnover rates suggest efficient asset management.

30

2.4.4 Profitability Ratios

We look at profits in two ways. First, as a percentage of net sales; second, as a return on the

funds invested in the business.

1. Profit Margin

Net Income

Sales

The profit margin in 2008 50

3.3%1,506

It measures the total operating and financial ability of management.

2. Return on Assets (ROA)

Net Income

Total Assets

The ROA in 2008 50

13%385

This ratio measures the return on total assets after recognition of taxes and

financing costs.

3. Return on Equity (ROE)

Net Income

Total Equity

The ROE in 2008 50

18%275

The fact that ROE exceeds ROA reflects the firm’s use of financial leverage.

2.4.5 Market Value Ratios

The market value ratios are based on information on the market price of the stocks. These

measures can be calculated directly for publicly traded companies.

1. Earnings Per Share (EPS)

Net Income

Shares Outstanding

The EPS in 2008 50

$5 per share10

This EPS figure is known as “basic earnings per share”.

31

2. Price-Earnings Ratio (PE)

Price Per Share

Earnings Per Share

Assume the price for the stock of City Corporation is $40, the PE ratio

408 times

5

PE ratio measures how much investors are willing to pay per dollar of current

earnings.

Higher PEs are often taken to mean that the firm has significant prospects for

future growth.

3. Price-Sales Ratio

Price Per Share

Sales Per Share

Assume the price for the stock of City Corporation is $40, the price-sales ratio

400.27 times

150.6

Price-Sales ratio can be used when the firm reported negative earnings for the

period.

4. Market-to-Book Ratio (MB)

Market Value Per Share

Book Value Per Share

The MB ratio in 2008 40

1.45 times27.5

Note that book value per share is total equity divided by the number of shares

outstanding.

A value less than 1 could mean that the firm has not been successful overall in

creating value for its shareholders.

32

2.4.6 Linking Ratios

We can gain greater insights into a firm’s ROA and ROE by linking together selected

financial ratios.

1. ROA

Profit MarginAsset Turnover = ROA

Net Income Sales Net Income

Sales Total Assets Total Assets

3.3% 3.9 13%

This formula indicates that the return on assets is closely related to the

profitability and turnover.

2. ROE (Du Pont Identity)

Profit MarginAsset TurnoverEquity Multiplier = ROE

Net Income Sales Total Assets Net Income

Sales Total Assets Total Equity Total Equity

3.3% 3.9 1.4 18%

Du Pont identity is a popular expression breaking ROE into three parts: operating

efficiency, asset use efficiency, and financial leverage.

2.4.7 Managerial Implications

So far, we have looked at the five major types of financial ratios. As a CFO, you would

probably ask “How can we interpret all the ratios together?”

A simple way to analyze the overall picture is to group the ratios into a matrix. For example:

Liquidity / Solvency Profitability Implications

Liquid / Solvent High

Illiquid / Insolvent High

Liquid / Solvent Low

Illiquid / Insolvent Low

33

Some caveats when you are using financial ratios:

Ratio analysis deals only with quantitative data. It does not look at qualitative factors

such as the quality of management.

Management can take short-run actions to influence the ratios.

Comparison of ratios between companies must be on a comparable accounting basis.

Differences in accounting practices in such areas as depreciation, income recognition

and intangible assets can make the comparisons misleading.

Accounting records are maintained in historical dollars. In periods of inflation the

ratios may be biased upwards.

Ratios must be evaluated in a correct business context.

Past data does not necessarily reflect current situation or future expectations.

2.5 Growth Analysis

The past and the expected growth rates of a corporation’s sales, profits and dividends is a

major focus of the analysis. We are interested because there is a close relationship between

the growth rate and the equity value.

2.5.1 Sustainable Growth

Sustainable growth rate is the most realistic estimate of the growth in a firm’s earnings,

assuming that the corporation does not alter its capital structure. A common method of

estimation is:

Sustainable Growth = Return on Equity Retention Rate

g = ROE b

The retention rate (b) is the percentage of earnings retained by the firm – not paid out in the

form of dividends.

34

Example 2.3

City Corporation had earnings of $10 million during the year just ended; a net worth of $100

million at the beginning of that year; and a permanent dividend payout policy of 50%.

Thus, City Corporation earned 10% on its beginning net worth, retained $5 million of

earnings. And the ending net worth will be $105 million.

If the 10% return on beginning equity is repeated during the next year, then the firm’s earning

will grow to $10.5 million.

This 5% earnings growth rate will be repeated annually as long as City Corporation continued

to earn 10% on each year’s beginning net worth and pay out 50% of its earnings in dividends.

2.5.2 Du Pont Decomposition

This growth rate is assumed to be sustainable because the firm is growing from internally

generated funds. We can associate the sustainable growth with fundamental factors using Du

Pont decomposition.

Recall that:

Net IncomeROE

Total Equity

Net Income Sales Total Assets

Sales Total Assets Total Equity

EPS DPSRetention Rate

EPS

DPS=1

EPS

=1 Dividend Payout Ratio

Putting the two equations together and remembering that capital structure is held constant,

we can see the sustainable growth is affected by profitability, asset utilization, and earnings

retention.

ROE

Net Income Sales Total Assets DPS1

Sales Total Assets Total Equity EPS

g b

We can link the sustainable growth to fundamental factors.

35

Fundamental Factors Relationship with Sustainable Growth

Profitability Positive

Asset Utilization Positive

Financial Leverage Held Constant

Dividend Payout Negative

2.5.3 Capital Structure and Sustainable Growth

When we define sustainable growth, we assume the corporation does not alter its capital

structure. A firm’s capital structure is its mix of debt and equity that is used to finance its

long-term investment.

The intuition is that even a corporation could grow by simply increasing its borrowing, but

this practice is eventually not sustainable because there is a point at which the corporation

may not be able to handle the debt burden.

Therefore, sustainable growth is determined assuming that the firm’s capital structure

remains the same. In other words, if the firm generates and retains earnings – hence

increasing its equity, it is assumed that the firm would also borrow so that the firm’s capital

structure is constant. This is consistent to the idea that a corporation usually maintains a

relatively constant target capital structure.

2.5.4 A Note on Sustainable Growth Rate

Recall that ROE is calculated as net income divided by total equity. If the total equity is

taken from the “beginning” of the period, then:

g = ROE b

However, if total equity is taken from an “ending” balance sheet, then the formula changes

slightly:

ROE

1 ROE

bg

b

36

37

3 Topic 3 – The Time Value of Money

As a CFO of City Corporation, you have to oversee many investment decisions from time to

time. You invest the money now in hopes of yielding future returns.

However, making such decisions is difficult for a number of reasons. Perhaps the most

significant one is to predict future returns. Even if the future returns could be forecasted with

certainty, choosing among alternative investments is not without its difficulties. The problem

is that the timing of the returns associated with each alternative investment may be different.

In this topic, we are going to deal with this problem by introducing the concept of the time

value of money, understanding the relationship between future value and present value.

3.1 A Motivating Example

City Corporation has two simple investment projects. The projects have three things in

common. Each requires an initial outlay of $50,000, has returns lasting just three years into

the future, and these returns are certain to occur.

Investment 1 returns $20,000 per year at the end of the next three years. And Investment 2

pays $40,000 a year from now, and $9,000 per year at the end of the second and third years.

We can show these future patterns of returns and initial investment graphically.

So which one of these investments do you prefer? When you sum up the cash flows,

Investment 1 pays back $60,000.

Investment 2 pays back only $58,000.

Can you simply conclude you prefer Investment 1 because it pays you $2,000 more than

Investment 2?

You notice that Investment 2 pays $20,000 more in the first year. You may suggest to City

Corporation that you could do something with that extra $20,000. At least you could get -

say 5% - from a deposit account. If you are smart, you can do even better.

38

You think the time that you get the money is important as well as how much you get.

Suppose you know where to invest your extra funds and you are smart enough to earn 10%

interest. Let’s compare the two investments when the interest rate is 10%.

39

Investment 1

Year 1 Year 2 Year 3

Beginning balance 0 20,000 42,000

Earnings on the balance at 10% 0 2,000 4,200

Inflow at the end of year 20,000 20,000 20,000

Ending balance 20,000 42,000 66,200

Investment 2





Ending balance 40,000 53,000 67,300

The results indicate that Investment 2 leaves you better off if you can earn 10% interest.

What happens if you can only earn 5% interest?

Investment 1





Ending balance 20,000 41,000 63,050

Investment 2





Ending balance 40,000 51,000 62,550

In this case, Investment 1 looks better.

This example shows that not only the amount of cash flows is important, but also the timing

of receipt. The more you can earn on the receipts, the better if you can get them earlier.

40

3.1.1 Basis for Comparison

You have to think of money as having a “time unit” denoting when it is received or paid. We

can only compare money in the same time units. For instance, it does not make sense to

compare $20,000 received today with $20,000 received next year.

In order to have a fair comparison, we have to ensure the two monetary values have the same

time units.

3.2 Future Value and Compounding

One way to obtain the same time units is to get the future value. Future value refers to the

amount of money an investment will grow to over some period of time at some given interest

rate. By compounding, we can move the time units forward.

Example 3.1

Instead of investing the $50,000 in the project, you decide to deposit the $50,000 in a bank

for three years at 10%. We assume the interest rate does not change. How much you can get

after three years?

Year Beginning

Balance Interest

Ending

Balance Formula

1 50,000 5,000 55,000 1

50,000 1.1

2 55,000 5,500 60,500 2

50,000 1.1

3 60,500 6,050 66,550 3

50,000 1.1

In general, the formula for future value when interest is compounded annually is:

0 1t

tV V r

3.2.1 Effects of Compounding

In the motivating example, we understand that if we can earn a higher interest rate, it will be

better to have earlier cash flows. The secret behind this effect comes from the power of

interest on interest. That is, there will be interest earned on the reinvestment of previous

interest payment.

41

Example 3.2

Given the interest rate is 10%, what would your $100 be worth after five years?

Without compounding, you can only earn a simple interest, that is, interest is only earned on

the principal. The simple interest is 100 10% 10 per year . Over the five year span of

investment, you accumulate $50 simple interest.

The difference $11.05 is the interest on interest from compounding.

Future values depend critically on the assumed interest rate, particularly for long-lived

investments.

42

We can study how $1 of investment grows at different rates and lengths of time.

Notice that the future value of $1 after 10 years is about $6.20 at a 20% return, but it is only

about $2.60 at 10%. Doubling the interest rate more than doubles the future value.

43

3.2.2 Calculate Future Values with BAII Plus

We use Example 3.2 as an illustration. Given the interest rate is 10%, what would your $100

be worth after five years?

1. Clear the Registers

2nd {CLR TVM}

2nd {CLR Work}

2. Enter the Inputs

-100 PV

10 I/Y

5 N

3. Compute and Return the Outputs

CPT FV

The screen should show you FV = 161.0510

3.3 Present Value and Discounting

Another way to obtain the same time units is to get the present value. Present value is the

current value of future cash flows discounted at the appropriate discount rate. By discounting,

we can move the time units backward.

Example 3.3

Suppose you need $66,550 in three years, and you can earn 10% on your money. How much

do you have to invest today in order to reach your goal?

In general, the formula for present value is:

0

1

t

t

VV

r

The two simple examples serve to illustrate discounting and compounding are the inverse of

one another.

44

Future Value of $50,000 in three years at 10%:

Present Year 1 Year 2 Year 3

Cash Flow 50,000

66,550

Present Value of $66,550 in three years at 10%:

Present Year 1 Year 2 Year 3

Cash Flow 66,550

50,000

3.3.1 Effects of Discounting

There are two important relationships between present value, interest rate and time:

For a given interest rate, the longer the time period, the lower the present value.

For a given time period, the higher the interest rate, the smaller the present value.

We can plot out the present value of $1 for different periods and rates.

45

3.3.2 Calculate Present Values with BAII Plus

Redo Example 3.3. Figure out the present value.


2nd {CLR TVM}

2nd {CLR Work}

2. Enter the Inputs

66,550 FV

10 I/Y

3 N


CPT PV

You should get PV = -50,000.0000

Example 3.4

Instead of comparing the future value for the two investments in our motivating example,

let’s figure out the present value of each investment under a 10% discount rate.

Present Value of Investment 1 at 10%:

Present Value Year 0 Year 1 Year 2 Year 3

-50,000.00 -50,000 +20,000 +20,000 +20,000

18,181.82 20,000

1.1

16,528.93 2

20,000

1.1

15,026.30 3

20,000

1.1

-262.96

46

Present Value of Investment 2 at 10%:

Present Value Year 0 Year 1 Year 2 Year 3

-50,000.00 -50,000 +40,000 +9,000 +9,000

36,363.64 40,000

1.1

7,438.02 2

9,000

1.1

6,761.83 3

9,000

1.1

563.49

Once again, we confirm Investment 2 is better.

3.4 The Discount Rate

We always need to determine what discount rate is implicit in an investment. Recall that the

present value is found by discounting the future cash flow:

1

t

t

FVPV

r

Rearrange the equation, the discount rate is:

1

1t

tFVr

PV

Example 3.5

You are looking at an investment that will pay $1,200 in 5 years if you invest $1,000 today.

What is the implied rate of interest?

47

Using financial calculator,


2nd {CLR TVM}

2nd {CLR Work}

2. Enter the Inputs

1,200 FV

- 1,000 PV

5 N


CPT I/Y

We can verify I/Y = 3.7137%

Example 3.6

Suppose you are offered an investment that will allow you to double your money in 6 years.

You have $10,000 to invest. What is the implied rate of interest?

In this example, we can apply the “Rule of 72” to get an approximate of r. For reasonable

rates of return, the time it takes to double your money is given approximately by 72 / r.

48

3.5 The Number of Periods

Example 3.7

You want to purchase a new car and you are willing to pay $20,000. If you can invest at 10%

per year and you currently have $15,000, how long will it be before you have enough money

to pay cash for the car?

We start with the present value formula.

1

t

t

FVPV

r

Rearrange the formula and solve for t,

ln ln

ln 1

tFV PVt

r

In this example,



2nd {CLR TVM}

2nd {CLR Work}

2. Enter the Inputs

20,000 FV

- 15,000 PV

10 I/Y


CPT N

We can verify N = 3.0184

49

3.6 Spreadsheet Application

We can also use Excel to solve for the problems of time value of money. So far, we have

learnt to solve for any one of the following four potential unknowns:

Future value

Present value

Discount rate

Number of periods

In Excel, there is a separate formula to solve for each of the unknown.

To Solve for Excel Formula

Future Value = FV(rate, nper, pmt, pv)

Present Value = PV(rate, nper, pmt, fv)

Discount Rate = RATE(nper, pmt, pv, fv)

Number of Periods = NPER(rate, pmt, pv, fv)

Some tricks when you are using Excel spreadsheet:

The rate should be entered as a decimal, instead of a percentage.

Put a negative sign on the present value.

50

4 Topic 4 – Discounted Cash Flow Valuation

In Topic 3, most of the examples only focus on single cash flows. In reality, most

investments have multiple cash flows. For example, if City Corporation is planning to open a

convenient store, there will be a large cash outlay in the beginning and then cash inflows for

many years.

Building on the concept of time value of money, we offer you more tools to value cash flows.

In particular, we will look at some special cash flows – annuity and perpetuity. We will also

compare various interest rates in depth.

4.1 Multiple Cash Flows

4.1.1 Future Value of a Series of Cash Flows

Example 4.1

You estimate that an investment project will receive net cash inflows at the end of each of the

first five years. They are $10,000, $20,000, $30,000, $45,000, and $60,000. What is the

future value of these cash flows at the end of year 5, if the interest rate is 20% per annum?

51

4.1.2 Present Value of a Series of Cash Flows

Example 4.2

What is the present value of three cash flows $100, $200 and $600, to be received at the end

of year 1, 3 and 6, respectively, if the discount rate is 10% per annum?

If you use financial calculator, first, notice the cash flow pattern.

Year Cash Flow

0 0

1 100

2 0

3 200

4 0

5 0

6 600

Noted that the “F” displayed in the calculator means the number of times a given cash flow

occurs in consecutive years. For example, at year 4, there are 2 consecutive years of having

zero cash flow.


2nd {CLR TVM}

2nd {CLR Work}

52

2. Input

CF

(CF0=) 0 ENTER ↓

(C01=) 100 ENTER ↓

(F01=) 1 ENTER ↓

(C02=) 0 ENTER ↓

(F02=) 1 ENTER ↓

(C03=) 200 ENTER ↓

(F03=) 1 ENTER ↓

(C04=) 0 ENTER ↓

(F04=) 2 ENTER ↓

(C05=) 600 ENTER ↓

(F05=) 1 ENTER ↓

NPV

(I=) 10 ENTER ↓

CPT

You can verify the answer is 579.85.

4.2 Annuity

Annuity formula is useful in discounted cash flow valuation. Annuity means the value of

cash flows is the same for a number of years.

To use the ordinary annuity formula, the following conditions should be satisfied:

The value of the cash flows in each period is the same.

The period or the interval for the cash flows remains unchanged.

The receipt / payment of the cash flows should occur at the end of each regular period.

4.2.1 Present Value of an Annuity

1 1Present Value of an Annuity 1

1t

Cr r

53

Example 4.3

A project is expected to have an economic life of five years. The value of this project’s net

cash inflows is estimated to be $2,000 for each year and this is to be received at the end of

each year. The appropriate discount rate is 15% per annum. What is the present value of this

project’s cash inflows?

Using our old discounting approach,

Using the annuity formula,

To find annuity present value with financial calculators, we need to use the PMT key.


2nd {CLR TVM}

2nd {CLR Work}

2. Enter the Inputs

2,000 PMT

5 N

15 I/Y


CPT PV

You will also get PV = - 6,704.31.

54

Example 4.4

A project’s annual net cash inflows, to be received at the end of each year, are estimated as

follows. For the first nine years the project does not generate any cash inflow. For the next

eleven years, that is, from the tenth to the twentieth years inclusive, it generates $60 per year.

The discount rate is 10% per annum. What is the present value of this project?

The timeline of the project’s cash flow:

There is another way to view this example. We know the annuity cash flows only start at

year 10. Therefore, we can first figure out the present value of this annuity at year 9 and then

discount the whole sum back to year 0.

Example 4.5

You are 20 years old now and want to retire as a millionaire by the time you turn 70. How

much will you have to save at the end of each year if you can earn 5% compounded annually?

55

Example 4.6

Suppose you want to borrow $20,000 for new car. You can borrow at 8% per year,

compounded monthly (8/12 = 0.67% per month). If you take a 4-year loan, what is your

monthly payment?

Example 4.7

Suppose you borrow $10,000 from your friend. You agree to pay $207.58 per month for 60

months. What is the monthly interest rate?



2nd {CLR TVM}

2nd {CLR Work}

2. Enter the Inputs

- 207.58 PMT

60 N

10,000 PV


CPT I/Y

You will also get I/Y = 0.7499.

56

Without a financial calculator, then you have to go through the trial and error process.

Choose an interest rate and compute the PV of the payments based on this rate.

Compare the computed PV with the actual loan amount.

If the computed PV > loan amount, then the interest rate is too low.

If the computed PV < loan amount, then the interest rate is too high.

Adjust the rate and repeat the process until the computed PV and the loan amount are

equal.

4.2.2 Future Value of an Annuity

We already know the formula of present value of annuity. To get the future value of an

annuity, we can simply multiply that present value by 1t

r .

1 1Future Value of an Annuity

tr

Cr

Example 4.8

Suppose you begin saving for your retirement by depositing $2,000 per year in MPF. If the

interest rate is 7.5%, how much will you have in 40 years?

57

4.3 Annuity Due

Recall that one of the conditions for applying ordinary annuity is that the receipt / payment of

the cash flows should occur at the end of each regular period.

In many situations, however, the cash flows occur at the beginning of the period. For

example, when you lease an apartment, the first lease payment is usually due immediately.

An annuity due is an annuity for which the cash flows occur at the beginning of each period.

To calculate the annuity due value, we simply multiply the ordinary annuity by 1 r .

Annuity Due Ordinary Annuity 1 r

Example 4.9

Suppose an annuity due has five payments of $400 each, and the relevant discount rate is

10%. What is the present value of the cash flows?

Using the annuity due formula,

We can verify the answer by finding the present value of each cash flow.

58

4.4 Perpetuity

Perpetuity is a special case of an annuity in which the number of equal cash flows is infinite.

The formula for the present value of a perpetuity is:

Present Value of a PerpetuityC

r

Example 4.10

In the early 1900's the Canadian Government issued $100 par value 2% Consol bonds. The

holder of these bonds is entitled to receive a coupon (or interest) payment of $2 per year

forever. If the current appropriate discount rate is 5% p.a. and the next coupon is due one

year from now, how much is one of the Consols worth?

4.5 Comparing Rates

Suppose a bank offers you two deals: (1) pays you 10% interest per year or (2) pays you 5%

interest compounded every six months. Which deal would you prefer?

If you invest $1, then after a year,

Option (1) will give you:

Option (2) will give you:

Obviously, option 2 is better as you can enjoy the interest on interest. As the example

illustrates, 10% compounded semiannually is actually equivalent to 10.25% per year.

59

4.5.1 Effective Annual Rate (EAR)

In the example, the 10% is called the quoted interest rate. The 10.25%, which is actually the

rate that you can earn, is called the effective annual rate (EAR). If you want to compare two

alternative investments with different compounding periods, you need to compute the EAR

and use that for comparison.

To get the effective annual rate,

Quoted Rate1 1

m

EARm

Where m is the number of times the interest is compounded during the year.

Example 4.11

Suppose a bank offers a nominal interest rate of 5% on your time deposit. Compare the

different EARs with various times the interest is compounded each year.

Compounding Formula Effective Annual Rate

Annually

10.05

1 11

r

5.0000%

Semiannually

20.05

1 12

r

5.0625%

Quarterly

40.05

1 14

r

5.0945%

Monthly

120.05

1 112

r

5.1162%

Weekly

520.05

1 152

r

5.1246%

Daily

3650.05

1 1365

r

5.1267%

Hourly

87600.05

1 18760

r

5.1271%

Continuously 0.05 1r e 5.1271%

You will always prefer more compounding periods to less.

60

Example 4.12

You are looking at two savings accounts. HSBC pays you 5.25%, with daily compounding.

BOC pays 5.3% with semiannual compounding. Which account should you use?

HSBC:

BOC:

4.5.2 Annual Percentage Rate (APR)

Another rate we often calculate is the annual percentage rate (APR). APR is the interest rate

charged per period multiplied by the number of periods per year. Since the law requires that

lenders disclose an APR on all loans, this rate must be displayed on a loan document in an

unambiguous way.

Example 4.13

What is the APR if (1) the monthly rate is 0.5%; (2) the semiannual rate is 0.5%?

For (1):

For (2):

Remember, APR is only an annual rate that is quoted by law. In order to figure out the

actual rate, you need to compute the EAR.

61

The relationship between EAR and APR:

1 1

mAPR

EARm

If you have an effective rate, you can compute the APR.

1

1 1mAPR m EAR

Example 4.14

Suppose you want to earn an effective rate of 12% and you are looking at an account that

compounds on a monthly basis. What APR must this account pay?

62

5 Topic 5 – Investment Decisions

After learning the techniques of discounted cash flow valuation, you are now ready to deal

with one important question: “What long-term investment should City Corporation take?”

5.1 Capital Investment Projects

City Corporation has $40,000 that it can expand the current production of its smart phone by

investing in any or all of the four capital projects.

Cash Flow

Project Year 0 Year 1 Year 2 Year 3

A Investment -10,000

Revenue 21,000

Expenses 11,000

B Investment -10,000

Revenue 15,000 17,000

Expenses 5,833 7,833

C Investment -10,000

Revenue 10,000 11,000 30,000

Expenses 5,555 4,889 15,555

D Investment -10,000

Revenue 30,000 10,000 5,000

Expenses 15,555 5,555 2,222

All the projects’ capital investment will be depreciated to zero on a straight-line basis. The

marginal corporate tax rate is 40%. None of the projects will have any salvage value at the

end of their lives.

What is your advice to the management?

In this case, City Corporation processes four possible investments. Some are valuable and

some are not. Of course, our important goal is to identify which are which. We will try to

present several investment criteria commonly used in practice and introduce the techniques

used to analyze investment decisions.

63

5.2 Net Present Value

The net present value (NPV) of an investment is defined as the present value of all future

cash flows produced by an investment, less the initial cost of the investment.

0

1 1

nt

tt

CNPV I

r

Whether an investment is worth undertaking, we have to see if it creates value for its owner.

A positive NPV says the investment is worth more than it costs, and therefore creates value.

A negative NPV suggests once the investment is implemented, it will destroy value.

Based on the simple logic, in determining whether to accept or reject a particular investment,

the NPV decision rule is:

Accept an investment if its NPV > 0.

Reject an investment if its NPV < 0.

Example 5.1

Consider the following investment proposal:

Year 0 Year 1 Year 2 Year 3 … Year 25

Cash Flow -100 11 11 11 11 11

Assuming the discount rate is 10%, is it a worthwhile investment?

64

5.2.1 Why Positive NPV?

Example 5.2

You have the following investment project:

Year 2010 Year 2011 Year 2012 Year 2013

Cash Flow -100 50 30 80

The discount rate is 10%. What is the NPV of the project?

We understand this is a good investment project since the NPV is greater than zero. But what

does this 30.35 really mean?

The 30.35 is exactly the additional amount of money you can spend today if you take the

project. Suppose you can borrow and lend at 10%, then you can do the following strategy:

Spend 30.35 today and borrow the money from the bank.

Repay the loan by using the project cash flows.

Let us illustrate the strategy with the following table.

Year 2010 Year 2011 Year 2012 Year 2013

Project Cash Flow -100.00 +50.00 +30.00 +80.00

Loan Cash Flow +130.35 -50.00 -30.00 -80.00

Interest 0.00 13.04 9.34 7.27

Balance -130.35 -93.39 -72.73 0.00

Your Cash Flow 30.35 0.00 0.00 0.00

A positive NPV means you can earn extra cash flow for your consumption. In the example

here, 30.35 is your riskless profit since your project cash flow can completely repay your loan

in future. Hence, if you undertake this project, you will be better off.

65

5.2.2 More than Two Alternatives

In many cases, a firm will be faced with a choice between more than two alternatives. For

example, a firm may be considering whether to rebuild a new office building or to refurbish

an old building.

When there are more than one investment projects, the decision rule becomes:

For many independent projects, take all with positive NPV.

For mutually exclusive projects, take the one with the highest and positive NPV.

Example 5.3

City Corporation is deciding purchasing new machines, A and B. The two machines will

bring the firm the following cash flows.

Machine A

Year 0 1 2 3 4

Cash Flow -3,000 1,000 1,000 1,000 1,000

Machine B

Year 0 1 2 3 4

Cash Flow -2,000 700 700 700 700

The discount rate is 10%. What are the NPVs of the two machines?

Purchasing both machines will bring positive NPV to the firm. When there is no constraint,

City Corporation should purchase both machines. However, if the purchasing decisions are

mutually exclusive (either purchasing Machine A or B), then the decision is to choose the

highest NPV. Machine B is thus the preferred alternative.

66

5.2.3 Investment Projects with Different Lives

Example 5.4

In the coming year, City Corporation decides to replace the old machine. It is deciding

between Machine C and D. Machine C has a life of 4 years and Machine D has a life of 2

years. Both machines cost $1,000.

Machine C

Year 0 1 2 3 4

Cash Flow -1,000 350 350 350 350

Machine D

Year 0 1 2

Cash Flow -1,000 750 500

The discount rate is 10%. What are the NPVs of the two machines?

Should the firm choose Machine C or Machine D?

Even though Machine C has a higher NPV, we cannot simply draw a conclusion that

Machine C is more preferred since it has a longer useful life than Machine D. In order to

have a fair comparison, one way is to compute the relevant NPV and compare the annual

equivalent cash flows of the two alternative machines.

The equivalent annuity is a useful tool for simplifying the analysis of problems of investment

projects with different lives. The idea is to calculate the annualized net present value. The

equivalent annuity is the level annuity over the investment’s life that has a present value

equal to the investment’s NPV.

67

The decision rule is to choose the one with highest equivalent annuity. In our example,

Surprisingly, although Machine D has a lower NPV than Machine C, the firm should select

Machine D as it has a higher equivalent annuity.

5.3 The Internal Rate of Return (IRR)

The internal rate of return (IRR) is the discount rate that makes the NPV of an investment

zero. The IRR solves the following equation:

0

1

01

nt

tt

CI

IRR

In determining whether to accept or reject an investment, the IRR decision rule is:

Accept an investment if IRR > required return.

Reject an investment if IRR < required return.

The logic of IRR reverses the one of the NPV. When computing NPV, we calculate the NPV

for a given discount rate on an investment, and accept an investment whenever the NPV is

positive. If we use IRR rule, we calculate the discount rate that makes the NPV equal to zero.

The two methods are related.

68

Example 5.5

Consider the following investment project:

What is the IRR?



2nd {CLR TVM}

2nd {CLR Work}

2. Input

CF

(CF0=) -200 ENTER ↓

(C01=) 50 ENTER ↓

(F01=) 1 ENTER ↓

(C02=) 100 ENTER ↓

(F02=) 1 ENTER ↓

(C03=) 150 ENTER ↓

(F03=) 1 ENTER ↓

IRR CPT

69

If we graph NPV versus the discount rate, we can see the IRR is actually the x-intercept.

We can see that the NPV of the project decreases as we increase the discount rate. The line

cuts the x-axis at the IRR of 19.44%. For all discount rate above 19.44%, the NPV of the

project is negative; for all discount rate below the IRR, the NPV of the project is positive.

Let’s say if the required rate of return is 10%, then based on both decision rules (NPV &

IRR), they all come to the same conclusion – the project should be accepted.

5.3.1 Nonconventional Cash Flows

One problem with the IRR comes about when the cash flows are not conventional.

Example 5.6

Consider the following investment project:

What is the IRR?

-$80.00

-$60.00

-$40.00

-$20.00

$0.00

$20.00

$40.00

$60.00

$80.00

$100.00

$120.00

0% 10% 20% 30% 40% 50%

NPV

IRR

70

From the graph, there are two IRRs for this project. The curve crosses the x-axis at 0% and

100%.

The idea is that when cash flows change signs more than once, there will be more than one

IRR. In this situation, you will have to use your judgment to decide which IRR should be

used.

5.3.2 Mutually Exclusive Investments

Another problem with IRR comes about when we are trying to compare two or more

mutually exclusive investments.

Example 5.7

City Corporation has two mutually exclusive projects, A and B. The cash flows of the two

projects are as follow:


Project A -500 325 325

Project B -400 325 200

If the required return for both projects is 10%, which project should the firm accept?

-20

-10

0

10

20

30

40

50

60

70

0% 20% 40% 60% 80% 100% 120%

NPV

IRR

71

We try to compute the NPV and IRR for both projects.

In this example, NPV(A) > NPV(B) but IRR(B) > IRR(A). Based on NPV rule, we should

choose Project A. However, if we rely on IRR rule, the rule suggests us to choose Project B.

The two rules give conflicting conclusions.

The conflict between the NPV and IRR for mutually exclusive investments can be illustrated

by plotting their profiles.

(60.00)

(10.00)

40.00

90.00

140.00

190.00

0% 5% 10% 15% 20% 25% 30% 35%

NPV Project A

Project B

72

The crossover point of the two curves can be found by setting NPV(A) = NPV(B).

Crossover point:

Below the crossover point, both NPV and IRR share the same decision – investing in Project

B is more preferred. Notice that when the discount rate is less than 11.8%, the NPV for

Project A is higher even though Project B’s IRR is higher.

Remarks:

Whenever there is a conflict between NPV and IRR, you should always use NPV.

IRR is unreliable in the situations of nonconventional cash flows and mutually

exclusive projects.

5.4 The Payback Rule

The payback period is the length of time it takes to recover the initial investment of the

investment.

The payback decision rule is:

Accept an investment if payback period < pre-specified payback period.

Reject an investment if payback period > pre-specified payback period.

For mutually exclusive projects, accept the one with the lowest payback period (if payback

period < pre-specified period).

73

Example 5.8

City Corporation is considering purchasing either one machine (mutually exclusive

investment). The firm’s required rate of return is 10%.

Machine E

Year 0 1 2 3

Cash Flow -1,000 200 800 25

Machine F

Year 0 1 2 3

Cash Flow -1,000 600 300 1,000

If City Corporation requires a payback period of three years or less, which machine would

you purchase?

The payback period:

Machine E: 2 years.

Machine F: 3 years.

The payback rule dictates that Machine E should be accepted. However, if we calculate the

NPV of the two machines, we get:

Based on NPV rule, purchasing Machine E is actually not a good investment choice. This

example shows that there are problems with the payback method:

1. It ignores the time value of money.

A remedy for this problem is to use the discounted payback period.

2. It ignores the cash flows after the payback period.

3. The standard for payback period is arbitrary.

74

5.5 The Average Accounting Return

The average accounting return (AAR) is an investment’s average net income divided by its

average book value. By definition,

Average Net Income

Average Book ValueAAR

The decision rule is:

Accept an investment if AAR > target AAR.

Reject an investment if AAR < target AAR.

Example 5.9

You are looking at a three-year project with a projected net income of $1,000 in year 1,

$2,000 in year 2, and $4,000 in year 3. The cost is $9,000, which will be depreciated

straight-line to zero over the three-year of the project. What is the average accounting return?

Although the AAR seems very impressive, there are some drawbacks about this measure.

1. It is not a true rate of return and it also ignores the time value of money.

2. It uses an arbitrary cutoff rate.

3. It is based on accounting net income and book values, not cash flows and market values.

75

5.6 Profitability Index

Profitability index (PI) is the present value of an investment’s future cash flows divided by its

initial cost. PI measures the benefit per unit cost, based on the time value of money.

0

PVPI

I

The decision rule for PI is:

Accept an investment if PI > 1.

Reject an investment if PI < 1.

Example 5.10

City Corporation has a list of investment projects in the coming year. You have prepared a

table summarizing the key measures.

Project Cost PV NPV PI

A 1,000 1,600 600 1.60

B 4,000 6,000 2,000 1.50

C 6,000 8,400 2,400 1.40

D 2,000 2,700 700 1.35

E 5,000 5,500 500 1.10

In the meeting, you know from the budget that $12,000 will be available to invest in the

coming year. Which projects will you select?

By investing all projects, it will cost the firm $18,000. Since the firm only has $12,000

capital, it is not feasible to invest all projects even though all projects have positive NPV. In

this situation, you can rank the project’s PI from highest to lowest and then select from the

top of the list until the capital budget is exhausted.

Based on the PI rule, you will select Project A, B and C as the three projects will give you

highest PI.

76

However, the PI will lead you to the wrong conclusion. If you calculate the aggregate NPV

of various combinations, you have:

In this example, the best alternative is Project B, C and D with an aggregate NPV of $5,100.

5.7 Comprehensive Problems

We revisit our opening case. City Corporation has $40,000 that it can expand the current

production of its smart phone by investing in any or all of the four projects.

Cash Flow

Project Year 0 Year 1 Year 2 Year 3

A Investment -10,000

Revenue 21,000

Expenses 11,000

B Investment -10,000

Revenue 15,000 17,000

Expenses 5,833 7,833

C Investment -10,000

Revenue 10,000 11,000 30,000

Expenses 5,555 4,889 15,555

D Investment -10,000

Revenue 30,000 10,000 5,000

Expenses 15,555 5,555 2,222

All the projects’ capital investment will be depreciated to zero on a straight-line basis. The

marginal corporate tax rate is 40%. None of the projects will have any salvage value at the

end of their lives.

77

For purpose of analysis,

1. Rank the four investments according to the four commonly used criteria:

a. The payback period.

b. The average accounting return. The formula of AAR in this problem can be

modified as [Average Net Income / (Required Investment / 2)].

c. Internal rate of return.

d. Net present value, assuming alternately a 10% discount rate and a 35% discount

rate.

2. Why do the rankings differ? What does each technique measure and what assumptions

does it make?

3. If the investment projects are independent of each other, which should be accepted? If

they are mutually exclusive, which one is the best?

78

79

6 Topic 6 – Bond and Stock Valuation

When a firm needs funds for investment, it can borrow money by issuing bonds or stocks, or

both. The focus of this topic is to give you an overview on how to value bonds and stocks.

6.1 What is a Bond?

A bond is a certificate showing that a borrower owes a specified sum. To repay the money,

the borrower has agreed to make interest and principal payments on designated dates.

Example 6.1

City Corporation issued 2,000 bonds for $1,000 each, where the bonds have a coupon rate of

5% and a maturity of two years. Interest on the bonds is to be paid annually.

This means that:

$2,000,000 has been borrowed by the firm.

The firm must pay interest of $100,000 at the end of one year.

The firm must pay both $100,000 of interest and $2,000,000 of principal at the end

of two years.

6.2 How to Value Bonds?

6.2.1 Pure Discount Bonds

The pure discount bond promises a single payment at a fixed future date. If the payment is

one year from now, it is called a one-year discount bond. If it is two years from now, it is

called a two-year discount bond, and so on.

The date when the issuer of the bond makes the last payment is called the maturity date of the

bond. The payment at maturity is termed the bond’s face value or par value.

Pure discount bonds are often called zero coupon bonds to emphasize the fact that the

bondholder receives no cash payments until maturity.

80

Consider a zero coupon bond that pays a face value of F in T years. The value of this zero

coupon bond is the present value of the face amount.

1T

FP

r

Example 6.2

A zero coupon bond that matures in 20 years has a par value of $1,000. If the required return

is 4.3%, what is the value of the zero?

6.2.2 Coupon Bonds

Corporate bonds usually offer cash payments not just at maturity, but also at regular times in

between.

The payments on corporate bonds are made every six months until the bonds mature. These

payments are called the coupons of the bond.

The cash flow for a coupon bond consists of an annuity of fixed coupon interest and the par

value at maturity.

1 2 3 T

$C $C $C $C+$F

81

In general, the price of a bond is given by:

2 1

2

1 1 1 1

1 1 1 1

1 1 1 1

1 1 11

1 1

T T

T T

T T

C C C C FP

r r r r

C Fr r r r

C Fr r r

Example 6.3

A 30-year bond with an 8% (4% per 6 months) coupon rate and a par value of $1,000 has the

following cash flows:

Semiannual coupon = $1,000×4% = $40

Par value at maturity = $1,000

Therefore, there are 60 semiannual cash flows of $40 and a $1,000 cash flow 60 six-month

periods from now.

1 2 3 60

$40 $40 $40 $40+$1,000

The price of this 30-year bond:

82

Suppose the discount rate is 8% annually or 4% per 6-month, the price of the bond is:

What if the discount rate rises to 10% annually, then the bond price will fall by $189.29 to

$810.71.

The central feature of fixed income securities is that there is an inverse relation between bond

price and discount rate.

83

In this example, the price/interest relationship for a 30-year, 8% coupon bond:

Interest 4% 6% 8% 10% 12%

Price 1,695.22 1,276.76 1,000.00 810.71 676.77

Note:

When the coupon rate equals the discount rate, the price equals the par value.

When the coupon rate is less than the discount rate, the price is less than the par

value.

When the coupon rate is greater than the discount rate, the price is greater than the

par value.

6.2.3 Consol

Not all bonds have a final maturity. Consol is a bond that never stop paying a coupon, has no

final maturity date. Thus, a consol is a perpetuity.

Example 6.4

What is the price of a consol with a yearly interest of $50 if the interest rate is 10%?

6.3 Yield to Maturity

Yield to maturity (YTM) is the average rate of return that will be earned on a bond if it is

bought now and held until maturity.

Given its maturity, the principal and the coupon rate, there is a one to one mapping between

the price of a bond and its YTM.

1 1 1

Tt

t Tt

C FP

YTM YTM

84

Example 6.5

Consider a 30-year bond with $1,000 face value has an 8% coupon. Suppose the bond sells

for $1,276.76, the YTM:

60

601

40 10001276.76

1 12 2

tt YTM YTM

Solve for the discount rate, YTM = 6%.

The yield-to-maturity considers the return from interest-on-interest. It assumes that the

coupon interest can be reinvested at YTM.

6.4 What is a Common Stock?

A common stock represents an ownership interest in a firm and confers three rights on the

owner of a share:

Vote at the company meetings.

Collect periodic dividend payments.

Sell the share at the owner’s discretion.

Contrary to payments to bondholders, payments to common stockholders are uncertain in

both magnitude and timing.

There are some important characteristics of common stock:

Residual claim.

Limited liability.

Voting rights.

6.5 How to Value Stocks?

Like bonds and other assets, the value of a stock can be determined by the present value of its

future cash flows. A stock provides two kinds of cash flows. First, stocks often pay

dividends. Second, an investor will receive the sale price when selling the stock.

85

Let’s assume you buy a stock and hold it for one year. The price you are willing to pay for

the stock today is equal to the present value of the cash flows you will receive for holding a

year:

1 10

1 1

Div PP

r r

1P can be determined by the dividend you will receive and the sale price at year 2:

2 21

1 1

Div PP

r r

You can substitute the expression of 1P back into

0P :

2 2

10

1 2 2

2 2

1 1

1 1

1 1 1

Div P

Div r rP

r r

Div Div P

r r r

If you repeat this logic, the stock price for today eventually becomes:

31 20 2 3

1

1 1 1

1

t

tt

DivDiv DivP

r r r

Div

r

Thus, the value of a firm’s common stock to the investor is equal to the present value of all of

the expected future dividends. The method that we have applied to value common stocks is

called dividend discount model.

6.6 Modeling Dividends

To apply dividend discount model, what we have to do is to estimate the pattern of future

dividends. We can make some simplifying assumptions about the pattern.

86

6.6.1 Zero Growth

The case of zero growth assumes that dividend is constant through time. So the value of the

stock is:

0 2 3

1 1 1

Div Div DivP

r r r

Div

r

6.6.2 Constant Growth

Suppose that the dividend always grows at a constant rate g in perpetuity. That is,

1 0 1Div Div g

The dividend in two periods will be:

2 1

0

2

0

1

1 1

1

Div Div g

Div g g

Div g

If we repeat this process, then:

0 1t

tDiv Div g

Thus, the value of a stock under this constant growth dividend is:

31 20 2 3

2 3

0 0 0

2 3

1 1 1

1 1 1

1 1 1

DivDiv DivP

r r r

Div g Div g Div g

r r r

87

Simplifying the expression,

2 3

0 0 0

0 2 3

2 3

0

2 3

0 0

0

0

0

1 1 1

1 1 1

1 1 1

1 1 1

1 1 1 11

1 1 1 1

1

11

1

1

Div g Div g Div gP

r r r

g g gDiv

r r r

r g g gP Div

g r r r

Divg

r

Div gP

r g

Div

1

r g

The price of the stock 0P is higher when:

The expected dividend per share is larger.

The risk-adjusted discount rate or the required rate of return is lower.

The expected growth rate of dividend is higher.

Example 6.6

Suppose City Corporation just paid a dividend of $0.50. It is expected to increase its

dividend by 2% per year. If the market requires a return of 15%, how much should the stock

be selling for?

88

Example 6.7

The next dividend for City Corporation will be $4 per share and it is expected to grow at 6%

per year. The required return is 16%.

What is the current price?

What is the price expected to be in year 4?

What is the implied return given the change in price during the four year period?

This example illustrates that the constant growth model makes the implicit assumption that

the stock price will grow at the same constant rate as the dividend. In this model, both stock

price and dividends grow at g.

89

6.6.3 Nonconstant Growth

To value stock price using zero and constant growth model, the models require the growth

rate must be less than the required return. In reality, however, there are cases where growth

rates can be “supernormal” over some finite length of time.

Example 6.8

Suppose City Corporation is expected to increase dividends by 20% in one year and by 15%

in two years. After that, dividends will increase at a rate of 5% per year indefinitely. If the

last dividend was $1 and the required return is 20%, what is the price of the stock?

6.7 Total Return

Rearranging the dividend growth model 10

DivP

r g

, the model implies:

1

0

Divr g

P

This expression tells us that the total return has two components. The first part 1

0

Div

P is

called the dividend yield, and the second part of the return is the capital gain.

90

Example 6.9

Suppose a share of City Corporation is selling for $10.50. It just paid a $1 dividend and

dividends are expected to grow at 5% per year. What is the required return?

6.8 Stock Price and Growth Opportunities

As a CFO, you will be interested to know how your investment decisions are going to affect

the stock price. Let us look at the relationship between stock price and growth opportunities

in the following examples.

Example 6.10

Suppose “Growth Inc.” has an existing asset that generates an expected $5 EPS each year.

The firm pays out part of the earnings and the rest is reinvested. The payout ratio is 0.4, ROE

is 15% and the required rate of return is 12.5%, what is its stock price?

91

Example 6.10

Suppose “No-Growth Inc.” has exactly the same asset that generates an expected $5 EPS

each year. This company pays out all its earnings as dividend, what is its stock price?

Since this company pays out all its earnings as dividend,

The difference between the stock price with growth and the stock price without growth is

called the present value of growth opportunities (PVGO).

The stock is like perpetuity if PVGO is 0. $40 is the present value of perpetuity with $5 each

year. It is also called capitalized earnings, or value of assets in place.

The two examples illustrate that stock price has two components:

Present value of earnings under a no-growth policy.

Present value of growth opportunities.

92

Example 6.11

City Corporation currently has assets in place that generates x of EBIT in perpetuity. At

time t, there is an investment opportunity tI that gives a return of *r in perpetuity.

Let:

*

EBIT of current activities (perpetuity)

Investment at time

Return on investment

Discount rate

t

x

I t

r

r

The cash flows of City Corporation will be:

What is the present value of current assets in place?

What is the present value of income streams from investment at time t?

93

What is the NPV of the investment at time t?

What is the NPV of the investment at time 0?

What is the price of the firm at time 0?

If at each year t there is an investment = tI , what will be the price then?

Once again, this example shows that the stock price equals the present value of assets in place

plus the net present value of growth opportunities.

94

6.8.1 Concluding Remarks

Example 6.11 demonstrates how the investment decisions will affect the stock price. If City

Corporation is satisfied with its current activities by only relying on its current assets in place

to generate cash flows, then its stock price will stay at x

r.

When City Corporation takes the investment, its stock price will be changed accordingly. In

the case where the investment has a positive NPV ( *r r ), the stock price will be increased

by such amount. In the previous topic, we always emphasis firms should only accept an

investment when the NPV is greater than zero. Because by undertaking the investment, we

can increase the value of the firm as

*

0

1

1tt

x r r xP I

r r rr

.

However, the stock price will be decreased when firms undertake a negative NPV investment

( *r r ). It is always bad to have negative NPV investment since it will destroy the value of

the firm. It is better not to undertake the investment as

*

0

1

1tt

x r r xP I

r r rr

.

95

7 Topic 7 – Capital Budgeting

So far we have learnt various techniques to evaluate an investment project. We have also

learnt that capital budgeting decisions have a major effect on the value of the firm and its

stock price. The focus of this topic is to setup a complete assessment of the capital budgeting

process. By applying the discounted cash flow analysis, we can determine whether the long-

term capital investments are worth pursuing.

In Topic 6, we have argued why valuing projects by NPV rule can help us to make

investment decisions which are consistent with the principle of maximizing firm value.

Recall that:

0

1 1

nt

tt

CNPV I

r

In order to compute the NPV of an investment project, the general capital budgeting

procedures involve:

1. Analyze the project cash flows.

2. Estimate the appropriate discount rate.

3. Consider other strategic options if any.

We are going to start bringing all these steps together.

7.1 Identify the Project Cash Flows

The first part of the capital budgeting process is to estimate the cash flows associated with the

project. To analyze the project cash flows, we have to:

1. Identify a project’s relevant cash flows.

2. Calculate initial investment outlay, operating cash flows and terminal cash flows for asset

expansion and asset replacement project.

3. Determine the effects of depreciation on after-tax cash flows.

4. Separate the investment decision from the financing decision and distinguish between

project flows and financing flows.

96

7.1.1 Relevant Cash Flows

What are the relevant cash flows for a project? To answer this question, we need to employ a

number of principles and concepts.

1. The Stand-alone Principle

A project’s relevant cash flows can be calculated by comparing the total future

cash flows of the firm “with” and “without” the project.

In practice, comparing the “with” and “without” the project’s cash flows would be

very cumbersome.

The stand-alone principle suggests that only the project’s incremental cash flows

need to be considered.

2. Opportunity Cost

When a firm undertakes a project, various resources will be used and not be

available for other projects.

The cost to the firm of not being able to use these resources for other projects is

referred to as an opportunity cost.

The opportunity cost is the value of the most valuable alternative that is given up

if the proposed investment project is undertaken.

Example 7.1

City Corporation proposes to establish a new call center. The call center will be located

within the office building that the firm already owns. The estimated rental of the office space

is $300,000 per year. The space has not been rented in the past, but it is expected to be rented

in the future.

Since City Corporation will lose $300,000 “with” the project, the opportunity cost is

$300,000 per year in rent forgone and it should be included as a cash outflow.

Suppose City Corporation has no intention to rent and sell the office space in the future, in

this situation, the $300,000 will not be included as a cash outflow.

3. Sunk Cost

A sunk cost is an amount spent in the past but which cannot now be recovered by

the current decision.

Sunk costs are past and irreversible. They should not be included in the cash

flows.

97

Example 7.2

Two years ago, City Corporation hired a consultancy firm to do a marketing study in online

shopping at a cost of $20,000. And now it is planning to develop an online ordering site for

its latest product. Should the cost be included in the project’s cash flows?

7.2 Compute the Project Cash Flows

Capital budgeting relies heavily on pro forma accounting statements. Recall from Topic 2:

Cash Flow from Assets Operating Cash Flow

Net Capital Spending

Change in Net Working Capital

We consider these items one by one.

7.2.1 Operating Cash Flow

Suppose City Corporation can sell 50,000 units of goods per year at a price of $4 each. Each

good is cost about $2.5 to produce. The fixed cost for the project is $12,000 per year. It also

requires an investment of $90,000 in new equipment. The equipment can perform for three

years and will be worthless afterwards. This project has three-year life. Tax rate is 34%.

Consider the pro forma income statement for illustration.

Sales (50,000 units at $4.00/unit) 200,000

Variable Costs ($2.50/unit) 125,000

Gross profit 75,000

Fixed costs 12,000

Depreciation ($90,000/3) 30,000

EBIT 33,000

Taxes (34%) 11,220

Net Income 21,780

98

We have three approaches to calculate operating cash flow (OCF).

1. The Top-down Approach

2. The Bottom-up Approach

3. The Tax Shield Approach

All the three approaches give you the same OCF. The best one to use is whichever happens

to be the most convenient for the problem at hand.

99

7.2.2 Depreciation

We have two approaches to calculate depreciation.

1. Straight-line

Depreciation Initial Cost Salvage No of Years

Example 7.3

You purchase equipment for $100,000 and it costs $10,000 to have it delivered and installed.

Based on past information, you believe that you can sell the equipment for $17,000 when you

are done with it in 6 years. What is the depreciation suppose the appropriate schedule is

straight-line?

2. Modified Accelerated Cost Recovery System (MACRS)

Need to know which asset class is appropriate for tax purposes.

Multiply MACRS percentage by the initial cost.

Depreciate to zero.

The MACRS Property Classes

3-year Equipment used in research

5-year Autos and computers

7-year Most industrial equipment

MACRS Table

Year 3-year 5-year 7-year 10-year

1 0.333 0.200 0.143 0.100

2 0.445 0.320 0.245 0.180

3 0.148 0.192 0.175 0.144

4 0.074 0.115 0.125 0.115

5 0.115 0.089 0.092

6 0.058 0.089 0.074

7 0.089 0.066

8 0.045 0.066

9 0.065

10 0.065

11 0.033

100

Example 7.4

You purchase a car costing $12,000. What is the depreciation schedule if you apply MACRS?

Autos are classified as 5-year property. The depreciation each year is:

Year MACRS Percentage Depreciation

1 0.200

2 0.320

3 0.192

4 0.115

5 0.115

6 0.058

Notice that the MACRS percentages sum up to 100%. As a result, you write off $12,000 of

the cost of the asset.

7.2.3 After Tax Salvage

If the salvage value is different from the book value of the asset, then there is a tax effect.

The definition:

Book Value = Initial Cost – Accumulated Depreciation

After Tax Salvage = Salvage – T × (Salvage – Book Value)

Example 7.5

Suppose you want to sell your car after five years. The sale price is $3,000 at year 5 and the

tax rate is 34%. What is the after tax salvage?

Year Beginning Book Value Depreciation Ending Book Value

1 12,000 2,400 9,600

2 9,600 3,840 5,760

3 5,760 2,304 3,456

4 3,456 1,380 2,076

5 2,076 1,380 696

6 696 696 0

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Example 7.6

Consider a replacement problem. City Corporation has an old machine purchased 5 years

ago. The initial cost of this old machine is $100,000. The annual depreciation is $9,000.

The salvage today is $65,000. If the machine is used for another 5 years, the salvage in 5

years will be $10,000.

If City Corporation decides to replace the old machine, the new machine will cost $150,000

and is last for 5 years. Depreciation follows 3-year MACRS. Salvage in 5 years will be zero.

This new machine helps saving $50,000 cost per year. The required return is 10% and the tax

rate is 40%.

Should City Corporation replace the machine?

Remember that we are interested in incremental cash flows. If we buy the new machine, then

we will sell the old machine.

First, we have to look at the cash flow consequences of selling the old machine today instead

of in 5 years. Then, figure out the OCF.

Year 1 Year 2 Year 3 Year 4 Year 5

Cost Saving 50,000 50,000 50,000 50,000 50,000

Depreciation

- New 49,950 66,750 22,200 11,100 0

- Old 9,000 9,000 9,000 9,000 9,000

Incremental 40,950 57,750 13,200 2,100 -9,000

EBIT 9,050 -7,750 36,800 47,900 59,000

Tax 3,620 -3,100 14,720 19,160 23,600

NI 5,430 -4,650 22,080 28,740 35,400

OCF

= NI + Dep

46,380 53,100 35,280 30,840 26,400

Second, we have to deal with the incremental net capital spending.

Year 0 Year 5

Cost of New Machine -150,000

After Tax Salvage (Old Machine) = Salvage – T × (Salvage – Book Value)

61,000 -10,000

Incremental Net Capital Spending -89,000 -10,000

Third, we can compute the cash flow from assets.

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Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

OCF 46,380 53,100 35,280 30,840 26,400

NCS -89,000 -10,000

NWC 0 0

-89,000 46,380 53,100 35,280 30,840 16,400

Finally, we can compute the NPV and IRR based on the cash flows we have.

NPV = 54,801

IRR = 36.27%

7.2.4 Changes in Net Working Capital

Recall that net working capital (NWC) is the difference between current assets and current

liabilities.

1Changes in NCW NCW NCWt t

An investment in net working capital arises when:

1. Inventory is purchased.

2. Cash is kept in the project as a buffer against unexpected expenditure.

3. Credit sales are made and therefore generated accounts receivable rather than cash.

4. Credit purchases are made and therefore generated accounts payable rather than cash.

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7.3 A Comprehensive Example

City Corporation is planning to expand its business in manufacturing fine zithers. The

market for zithers is growing quickly. The firm bought some land three years ago for $1.4

million in anticipation of using it as a toxic waste dump site but has recently hired another

firm to handle all toxic materials. Based on a recent appraisal, the firm believes it could sell

the land for $1.5 million on an after tax basis. In four years, the land could be sold for $1.6

million after taxes. The firm also hired a marketing firm to analyze the zither market, at a

cost of $125,000. An excerpt of the marketing report is as follows:

“The zither industry will have a rapid expansion in the next four years. With the brand name

recognition that City Corporation brings to bear, we feel that the company will be able to sell

3,200, 4,300, 3,900 and 2,800 units each year for the next four years respectively. Again,

capitalizing on the name recognition of City Corporation, we feel that a premium price of

$780 can be charged for each zither. Because zithers appear to be a fad, we feel at the end of

the four-year period, sales should be discontinued.”

City Corporation believes that fixed costs for the project will be $425,000 per year, and

variable costs are 15% of sales. The equipment necessary for production will cost $4.2

million and will be depreciated according to a three-year MACRS schedule below. At the

end of the project, the equipment can be scrapped for $400,000. Net working capital of

$125,000 will be required immediately. City Corporation has a 38% tax rate, and the

required return on the project is 13%. What is the NPV of the project? Assume the firm has

other profitable projects.

Exhibit 7.1

MACRS Schedule

Year 3-year

1 33.33%

2 44.45%

3 14.81%

4 7.41%

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105

7.4 Evaluating NPV Estimates

NPVs are just estimates. There are two primary reasons for a positive NPV:

We have constructed a good project.

We have done a bad job of estimating NPV.

A positive NPV is a good start. Now we need to take a closer look on forecasting risk. How

sensitive is our NPV to changes in the cash flow estimates. The more sensitive is the

estimate, the greater will be the forecasting risk.

7.4.1 Scenario Analysis

One basic approach to evaluating cash flow and NPV estimates involves asking what-if

questions. What happens to the NPV under different cash flow scenarios?

At the very least, we can look at:

Best case – high revenues, low costs.

Worst case – low revenues, high costs.

We can measure the range of possible outcomes. Although best case and worst case are not

necessarily probable, they can still be possible.

Example 7.7

The project under consideration costs $200,000, has a five-year life, and has no salvage value.

Depreciation is straight line to zero. The required return is 12% and the tax rate is 34%. In

addition, we have the following information:

Base Case Lower Bound Upper Bound

Unit sales 6,000 5,500 6,500

Price per unit 80 75 85

Variable costs per unit 60 58 62

Fixed costs per unit 50,000 45,000 55,000

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Based on the information, we can establish three possible scenarios.

Base Case Worst Case Best Case

Unit sales 6,000

Price per unit 80

Variable costs per unit 60

Fixed costs per unit 50,000

We can apply the tax shield approach to compute the operating cash flows for each scenario.

Once we have the OCF, we can calculate the NPV. Noted that the five-year annuity factor is

5

1 11 3.6048

0.12 1.12

.

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In summary,

Scenario Cash Flow NPV IRR

Base Case 59,800 15,567 15.1%

Worst Case 24,490 -111,718 -14.4%

Best Case 99,730 159,506 40.9%

7.4.2 Sensitivity Analysis

A subset of scenario analysis is to look at the specific variables on NPV. That is, what

happens to NPV when only one variable is changed at a time?

The greater the volatility in NPV in relation to a specific variable, the larger the forecasting

risk associated with that variable, and the more attention we want to pay to its estimation.

The basic idea with a sensitivity analysis is to freeze all of the variables except one and then

see how sensitive our estimate of NPV is to changes in that variable.

Example 7.8

We follow the same setting as in Example 7.7. We perform a sensitivity analysis by freezing

all variables except unit sales.

Base Case Worst Case Best Case

Unit sales 6,000 5,500 6,500

Price per unit 80 80 80

Variable costs per unit 60 60 60

Fixed costs per unit 50,000 50,000 50,000

Scenario Cash Flow NPV IRR

Base Case 59,800 15,567 15.1%

Worst Case 53,200 -8,225 10.3%

Best Case 66,400 39,359 19.7%

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Graphical illustration:

The drawback of scenario and sensitivity analysis is that both methods are useful for pointing

out where forecasting errors will do the most damage, but they do not tell us what to do about

possible errors.

A final thought:

At some point, you have to make a decision.

If the majority of your scenarios have positive NPVs, then you can feel reasonably

comfortable about accepting the project.

If you have a crucial variable that leads to a negative NPV with a small change in the

estimates, then you may want to forgo the project.

-20000

-10000

0

10000

20000

30000

40000

50000

5,400 5,600 5,800 6,000 6,200 6,400 6,600

NPV

Unit Sales

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7.5 Case Study – Danforth & Donnalley Laundry Products Company

On April 14, 1993, at 3:00 p.m., James Danforth, President of Danforth & Donnalley (D&D)

Laundry Products Company, called to order a meeting of the financial directors. The purpose

of the meeting was to make a capital budgeting decision with respect to the introduction and

production of a new product, a liquid detergent called Blast.

D&D was formed in 1968 with the merger of Danforth Chemical Company, headquartered in

Seattle, Washington, producers of Lift-Off detergent, the leading laundry detergent on the

West Coast, and Donnalley Home Products Company, headquartered in Detroit, Michigan,

makers of Wave detergent, a major midwestern laundry product. As a result of the merger,

D&D was producing and marketing two major product lines. Although these products were

in direct competition, they were not without product differentiation: Lift-Off was a low-suds,

concentrated powder, and Wave was a more traditional powdered detergent. Each line

brought with it considerable brand loyalty, and by 1993, sales from the two detergent lines

had increased tenfold from 1968 levels, with both products now being sold nationally.

In the face of increased competition and technological innovation, D&D spent large amounts

of time and money over the past four years researching and developing a new, highly

concentrated liquid laundry detergent. D&D’s new detergent, which they called Blast, had

many obvious advantages over the conventional powdered products. It was felt that with

Blast the consumer would benefit in three major areas. Blast was so highly concentrated that

only 2 ounces were needed to do an average load of laundry as compared with 8 to 12 ounces

of powdered detergent. Moreover, being a liquid, it was possible to pour Blast directly on

stains and hard-to-wash spots, eliminating the need for a pre-soak and giving it cleaning

abilities that powders could not possibly match. And, finally, it would be packaged in a

lightweight, unbreakable plastic bottle with a sure-grip handle, making it much easier to use

and more convenient to store than the bulky boxes of powdered detergents with which it

would compete.

The meeting was attended by James Danforth; Jim Donnalley, director of the board; Guy

Rainey, vice-president in charge of new products; Urban McDonald, controller; and Steve

Gasper, a newcomer to D&D’s financial staff, who was invited by McDonald to sit in on the

meeting. Danforth called the meeting to order, gave a brief statement of its purpose, and

immediately gave the floor to Guy Rainey.

Rainey opened with a presentation of the cost and cash flow analysis for the new product. To

keep things clear, he passed out copies of the projected cash flows to those present (see

Exhibits 7.2 and 7.3). In support of this information, he provided some insight as to how

these calculations were determined. Rainey proposed that the initial cost for Blast included

$500,000 for the test marketing, which was conducted in the Detroit area and completed in

the previous June, and $2 million for new specialized equipment and packaging facilities.

The estimated life for the facilities was 15 years, after which they would have no salvage

value. This 15-year estimated life assumption coincides with company policy set by

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Donnalley not to consider cash flows occurring more than 15 years into the future, as

estimates that far ahead "tend to become little more than blind guesses."

Rainey cautioned against taking the annual cash flows (as shown in Exhibit 7.2) at face value

because portions of these cash flows actually are a result of sales that had been diverted from

Lift-Off and Wave. For this reason, Rainey also produced the annual cash flows that had

been adjusted to include only those cash flows incremental to the company as a whole (as

shown in Exhibit 7.3).

At this point, discussion opened between Donnalley and McDonald, and it was concluded

that the opportunity cost on funds is 10%. Gasper then questioned the fact that no costs were

included in the proposed cash budget for plant facilities, which would be needed to produce

the new product.

Exhibit 7.2

D&D Laundry Products Company Annual Cash Flows from the Acceptance of Blast

(Including flows resulting from sales diverted from the existing product lines)

Year Cash Flows Year Cash Flows

1 280,000 9 350,000

2 280,000 10 350,000

3 280,000 11 250,000

4 280,000 12 250,000

5 280,000 13 250,000

6 350,000 14 250,000

7 350,000 15 250,000

8 350,000

Exhibit 7.3

D&D Laundry Products Company Annual Cash Flows from the Acceptance of Blast

(Not including those flows resulting from sales diverted from the existing product lines)

Year Cash Flows Year Cash Flows

1 250,000 9 315,000

2 250,000 10 315,000

3 250,000 11 225,000

4 250,000 12 225,000

5 250,000 13 225,000

6 315,000 14 225,000

7 315,000 15 225,000

8 315,000

Rainey replied that, at the present time, Lift-Off’s production facilities were being used at

only 55% of capacity, and because these facilities were suitable for use in the production of

Blast, no new plant facilities other than the specialized equipment and packaging facilities

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previously mentioned need be acquired for the production of the new product line. It was

estimated that full production of Blast would require only 10% of the plant capacity.

McDonald then asked if there had been any consideration of increased working capital needs

to operate the investment project. Rainey answered that there had and that this project would

require $200,000 of additional working capital; however, as this money would never leave

the firm and always would be in liquid form, it was not considered an outflow and hence was

not included in the calculations.

Donnalley argued that this project should be charged something for its use of the current

excess plant facilities. His reasoning was that, if an outside firm tried to rent this space from

D&D, it would be charged somewhere in the neighborhood of $2 million, and since this

project would compete with the current projects, it should be treated as an outside project and

charged as such; however, he went on to acknowledge that D&D has a strict policy that

forbids the renting or leasing out of any of its production facilities. If they didn’t charge for

facilities, he concluded, the firm might end up accepting projects that under normal

circumstances would be rejected.

From here, the discussion continued, centering on the questions of what to do about the "lost

contribution from other projects," the test marketing costs, and the working capital.

1. If you were put in the place of Steve Gasper, would you argue for the cost from market

testing to be included as a cash outflow?

2. What would your opinion be as to how to deal with the question of working capital?

3. Would you suggest that the product be charged for the use of excess production facilities

and building?

4. Would you suggest that the cash flows resulting from erosion of sales from current

laundry detergent products be included as a cash inflow? If there were a chance of

competition introducing a similar product if you do not introduce Blast, would this affect

your answer?

5. What are the NPV, IRR, and PI of this project, including cash flows resulting from lost

sales from existing product lines? What are the NPV, IRR, and PI of this project

excluding these flows? Under the assumption that there is a good chance that competition

will introduce a similar product if you do not, would you accept or reject this project?

112

113

114

8 Topic 8 – Market Efficiency

We have spent much of our effort to learn how to spend the money by making good capital

budgeting decisions. In the previous topics, we often assume firms have sufficient money for

their projects. In practice, firms always need external funding. It is the time to start putting

our effort to learn how to raise money to finance the capital investments.

8.1 Differences between Investment and Financing Decisions

As a competent CFO, you have already known by undertaking positive NPV projects, you

can create value for the firm. But have you ever think of where might the value come from?

The following are some project characteristics that might be associated with positive NPVs:

Economies of scale.

Product differentiation.

Cost advantages.

Access to distribution channels.

Favorable government policy.

Example 8.1

You realize investment and financing decisions are closely related. Suppose your firm has a

project which yields perpetuity of $1 every year. This discount rate for the project is 10%.

The required initial capital outlay is $5.

The NPV of the project:

15

0.1

5

NPV

Suppose your firm has $5 to take this project, then the entire $5 NPV will belong to your firm.

What if your firm only has $3 and needs to sell 40% of the ownership to a new investor in

order to raise the additional $2, is the equity fairly priced?

Once the new investors provide you the additional $2, you will take the project as the NPV is

positive. The new investor will entitle 40% of the project’s NPV, which is $2 ( 40% $5 ).

In this example, the financing activity has a zero NPV.

115

But why the financing activity has a zero NPV? Before we look at the answer of this

question, let us think about the implications behind the zero NPV.

A zero NPV in financing means the equity issued by the firm is fairly priced. In the example

above, the 40% ownership is worth $2. As a new investor, you are willing to pay for $2 or

less in exchange for the 40% ownership. However, the firm is only willing to sell you its

shares at $2 or more.

If there is trade between the firm and the new investor, we know the shares will be eventually

settled at $2 and both party can only make a zero NPV deal at the end.

Now, the key question becomes “Are securities fairly priced?”

8.2 Efficient Capital Markets

An efficient capital market is one in which stock prices fully reflect available information.

Efficiency here means informational efficiency.

An efficient market refers to a market in which information is widely available to investors

and all relevant information is already reflected in security prices – prices are “right” at any

time.

Any new information disseminates quickly and is instantly reflected in share prices.

Efficient market is an important component of a capitalist system.

The ideal is a market where prices are accurate signals for capital allocation.

Prices of securities must be good indicators of value.

116

Example 8.2

Reaction of stock price to new information in efficient and inefficient markets:

8.2.1 Implications of the Efficient Market Hypothesis

From the investor point of view:

Investors may hope for superior returns but all they can rationally expect in an

efficient market is that they shall obtain a return that is just sufficient to compensate

them for the time value of money and for the risks they bear.

In the words of The Economist (December 5, 1992):

Because prices are “efficient” – they reflect all available facts. Future prices differ

from current prices only if buyers or sellers get new information. This by definition,

is random. But why should prices be efficient? Put simply, if they are not, it means

the market is ignoring price-sensitive information. But this gives whoever has that

information a chance to make big profits by trading on it. As soon as he does so, the

overlooked information is incorporated in the price. This will make it “efficient”.

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8.2.2 Three Forms of Market Efficiency

Weak form of market efficiency:

Stock prices fully reflect all information contained in past prices and volume.

Stock price movements are independent of what happened in the past.

Semi-strong form of market efficiency:

Stock prices fully reflect all publicly available information.

Publicly available information includes historic prices and published accounting

statements.

Strong form of market efficiency:

Stock prices fully reflect all information, public or private.

8.2.3 Weak Form Efficiency

Debate on market efficiency began with the discovery that stock prices seem to follow a

random walk. Random walk means the past movement or trend of a stock price cannot be

used to predict its future movement.

Technical analysts argue that patterns of past stock prices repeat themselves. Proper charting

of prices and perhaps related series like volume will detect when a shift has occurred.

If a market is weak form efficient, it is impossible to make consistent superior returns by

technical analysis.

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8.2.4 Semi-strong Form Efficiency

Prices incorporate all publicly available information contained in accounting statements and

in past stock prices, stock returns and trading volume.

Fundamental analysts study firm and industry fundamentals and try to judge whether a stock

is under- or over-valued.

If a market is semi-strong form efficient, then:

It is impossible to make consistent superior returns by fundamental analysis.

Markets and stock prices react exceptionally fast to the release of information. That

is, profit opportunities disappear fairly quickly before they become publicly known.

8.2.5 Strong Form Efficiency

Prices incorporate all information, public or private. Anything pertinent to the stock and

known to at least one investor is already incorporated into the stock price.

If a market is strong form efficient, it is impossible to make consistent superior returns from

insider information.

8.2.6 Concluding Remarks

The efficient market hypothesis answers the key question “Are securities fairly priced?” If

market is efficient then price impound all information about the value of each stock.

Therefore, on one can earn a positive NPV in any financing schemes.

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9 Topic 9 – Risks and Returns

The efficient market hypothesis discussed in Topic 8 provided us a foundation in examining

stock price. In this topic, we wish to investigate the stock price behavior and explore the

managerial implications behind risks and returns.

9.1 Risk, Return and Investment Decision

Since financial resources are finite, there is a hurdle that projects have to cross before being

deemed acceptable. Recall that the IRR investment rule is to accept a project where the IRR

is greater than the required return. We can label this required return as the hurdle rate.

An intuitive notion is that this hurdle rate will be higher for riskier projects than for safer

projects. Before we look at the hurdle rate in details, we can first draw a simple

representation:

Hurdle Rate = Risk-free Return + Risk Premium

Then the two basic questions arise:

1. How do we measure risk and return?

2. How do we translate the risk measure into a risk premium?

9.2 Returns

9.2.1 Dollar Returns

Total Dollar Return = Income from Investment + Capital Gain (Loss)

Example 9.1

You bought a bond for $950 one year ago. You have received two coupons of $30 each.

You can sell the bond for $975 today. What is your total dollar return?

120

9.2.2 Percentage Returns

It is generally more intuitive to think in terms of percentages than dollar returns.

Total Percentage Return = Dividend Yield + Capital Gains Yield

1

1

1

1 1

t t t

t

t

t t t

t t

Div P Pr

P

Div P P

P P

Example 9.2

You bought a stock for $35 and you received dividends of $1.25. The stock is now selling

for $40. What is your dollar return?

Dollar return = 1.25 + (40 – 35) = $6.25

What is your percentage return?

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9.2.3 The Historical Record

Lessons from capital market history:

Small stocks had the highest long-term returns while treasury bills had the lowest

long-term returns.

Small stocks had the largest fluctuations in price while treasury bills had the lowest

fluctuations.

Average returns of different classes of financial assets:

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Investment Average Return

Large Stocks 12.3%

Small Stocks 17.4%

Long-term Corporate Bonds 6.2%

Long-term Government Bonds 5.8%

U.S. Treasury Bills 3.8%

Inflation 3.1%

9.2.4 Arithmetic and Geometric Returns

To calculate the return over multiple periods, we can either compute arithmetic or geometric

return.

Arithmetic return is the return earned in an average period over multiple periods.

Geometric return is the average compound return per period over multiple periods.

Example 9.3

What are the arithmetic and geometric averages for the following returns: Year 1 = 5%, Year

2 = -3% and Year 3 = 12%?

Note that the geometric return will be less than the arithmetic return unless all the returns are

equal.

The arithmetic return is optimistic for long horizons.

The geometric return is pessimistic for short horizons.

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9.3 Risks

9.3.1 Risk Premiums

Risk premium is the “extra” return earned for taking on risk. We usually consider treasury

bills to be risk-free.

The risk premium is the return over and above the risk-free rate.

Investment Average Return Risk Premium

Large Stocks 12.3% 12.3 – 3.8 = 8.5%

Small Stocks 17.4% 17.4 – 3.8 = 13.6%

Long-term Corporate Bonds 6.2% 6.2 – 3.8 = 2.4%

Long-term Government Bonds 5.8% 5.8 – 3.8 = 2.0%

U.S. Treasury Bills 3.8% 3.8 – 3.8 = 0%

9.3.2 Variance and Standard Deviation

We use variance and standard deviation to measure the volatility of asset returns. The greater

the volatility, the greater the uncertainty will be.

Variance is the sum of squared deviations from the mean divided by the number of

observations minus one.

2

1

1

1

T

i

i

Var r rT

Standard deviation is the square root of the variance.

124

Example 9.4

A stock has a return of 15% in Year 1, 9% in Year 2, 6% in Year 3 and 12% in Year 4. What

are the variance and standard deviation of this stock?

The mean return:

Year Actual Return Mean Return Deviation from Mean Squared Deviation

1 0.15 0.105 0.045 .002025

2 0.09 0.105 -0.015 .000225

3 0.06 0.105 -0.045 .002025

4 0.12 0.105 0.015 .000225

Total 0.42 .0045

The variance:

The standard deviation:

9.4 Expectation

In reality, the stock price in future is an unknown. We now begin to discuss how to analyze

returns and variances when the information we have concerns future possible returns and

their probabilities.

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9.4.1 Expected Returns

Expected returns are based on the probabilities of possible outcomes. The expected return

does not even have to be a possible return.

1

N

i i

i

E r p r

Example 9.5

Suppose you have predicted the following returns for Stocks C & T in three possible states of

nature. What are the expected returns?

State Probability Stock C Stock T

Boom 0.3 0.15 0.25

Normal 0.5 0.10 0.20

Recession 0.2 0.02 0.01

9.4.2 Expected Variance and Standard Deviation

Using unequal probabilities for the entire range of possibilities, expected variance and

standard deviation still measure the volatility of returns.

22

1

N

i i

i

p r r

126

Example 9.6

Consider the previous example. What are the variance and standard deviation for each stock?

9.5 Portfolio Risks and Returns

If we hold more than one stock, we are holding a portfolio.

9.5.1 Portfolio Expected Returns

The expected return of a portfolio is the weighted average of the expected returns of the

respective stocks in the portfolio.

1

N

p i i

i

E r w E r

Example 9.7

Suppose you have $15,000 to invest and you have purchased stocks in the following amounts.

Stock Amount Return

A 2,000 19.65%

B 3,000 8.96%

C 4,000 9.67%

D 6,000 8.13%

What is the expected return for the portfolio?

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9.5.2 Systematic and Unsystematic Risks

When an investor buys a stock, he is exposed to many risks. Some risks may only affect one

or a few firms, and this risk is categorized as unsystematic or firm specific risk. Any price

fluctuation due to a piece of good or bad news about an individual firm is an example of

unsystematic risk.

There is another risk that is much more pervasive and affects many investments. We term

this risk systematic or market risk. News that affects all stocks, such as news about the

economy is an example of systematic risk.

9.5.3 Diversification

When many stocks are combined in a large portfolio, the firm specific risks for each stock

will average out and be diversified. The systematic risk, however, will affect all firms and

will not be diversified. To illustrate the diversification effect, we can create portfolios with

different number of stocks and compute their corresponding standard deviation1.

1 The standard deviation of a portfolio can be calculated by

12

1 1

n n

p i j ij

i j

w w

, where

ij is the covariance

between stock i and j.

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Diversification can substantially reduce the variability of returns without an equivalent

reduction in expected returns. This reduction in risk arises because worse-than-expected

returns from one stock are offset by better-than-expected returns from another stock.

However, there is a minimum level of risk that cannot be diversified away – that is the

systematic portion.

9.5.4 Decomposition of Total Risk

The total risk of a stock:

Total Risk = Systematic Risk + Unsystematic Risk

The standard deviation of returns is a measure of total risk. If we hold only one single stock,

we are going to bear both the systematic and unsystematic risk. But if we hold a well-

diversified portfolio, unsystematic risk is very small. Consequently, the total risk for a

diversified portfolio is essentially equivalent to the systematic risk.

Noted that according to the systematic risk principle,

There is a reward for bearing risk.

There is not a reward for bearing risk unnecessarily.

The expected return on a stock depends only on that stock’s systematic risk since

unsystematic risk can be diversified away.

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9.5.5 Measuring Systematic Risk

Because systematic risk is the crucial determinant of a stock’s expected return, we need some

way of measuring the level of systematic risk.

How do we measure systematic risk?

We use the beta coefficient to measure systematic risk.

A beta of 1 implies the stock has the same systematic risk as the overall market.

A beta < 1 implies the stock has less systematic risk than the overall market.

A beta > 1 implies the stock has more systematic risk than the overall market.

The idea of beta coefficient is to measure the sensitivity of co-movement between individual

stock return and market return.

Example 9.8

Consider the following information:

Stock Standard Deviation Beta

C 20% 1.25

K 30% 0.95

Which stock has more total risk?

Which stock has more systematic risk?

Which stock should have the higher expected return?

9.5.6 Beta and the Risk Premium

The systematic risk principle says there is a reward for bearing systematic risk. If you

purchase a low beta stock (beta < 1), then you are expected to get a return that is lower than

the market return. But if you purchase a high beta stock (beta > 1), then you are expected to

get a return that is higher than the market return.

Remember that:

Expected Return = Risk-free Return + Risk Premium

The higher the beta, the greater the risk premium should be, and also the greater will be the

expected return.

We can illustrate the link between beta and expected return.

130

Consider 3 stocks: T-bills, S&P500 and Apple Inc. The followings are the information:

Expected Return Beta

T-bills 5% 0

S&P500 (Market Portfolio) 10% 1

Apple Inc. (Stock A) 15% 2

We can plot out there is a linear relationship between beta and expected return. The slope of

the line is the reward-to-risk ratio.

10 5

1

5

m f

m

E r rSlope

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Suppose Stock S has a beta of 1 and an expected return of 12%. Knowing that Stock S has

the same beta risk as the S&P500, we should expect both stocks should give us the same

expected return. In this case, as the expected return of Stock S is greater than S&P500 (12%

> 10%), every investors in the market will want to buy Stock S instead of S&P500.

This will drive up the price of Stock S and push down its expected return until the reward-to-

risk ratio reaches 5.

Therefore in equilibrium, all stocks and portfolios must have the same reward-to-risk ratio,

and they all must equal the reward-to-risk ratio for the market.

A f m f

A m

E r r E r r

Since the market beta is equal to 1, we can rearrange the above equation and get the

important formula:

1

A f m f

A m

A f m f

A

A f A m f

E r r E r r

E r r E r r

E r r E r r

This important formula is known as the Capital Asset Pricing Model (CAPM).

9.6 The Capital Asset Pricing Model (CAPM)

The capital asset pricing model defines the relationship between risk and return. If we know

a stock’s systematic risk, we can use the CAPM to determine its expected return.

What are the factors affecting expected return?

Pure time value of money: measured by the risk-free rate.

Reward for bearing systematic risk: measured by the market risk premium.

Amount of systematic risk: measured by beta.

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Example 9.9

Consider the betas for each of the assets given below. If the risk-free rate is 3.15% and the

market risk premium is 9.5%, what is the expected return for each stock?

Stock Weight Beta

A 0.133 4.03

B 0.200 0.84

C 0.267 1.05

D 0.400 0.59

If we form a portfolio according to the weight, what will be the portfolio beta?

The portfolio beta is the weighted sum of each individual stock’s beta.

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10 Topic 10 – Cost of Capital

In Topic 7, we have learnt that the general capital budgeting procedures involve:

1. Analyze the project cash flows.

2. Estimate the appropriate discount rate.

3. Consider other strategic options if any.

We have already had extensive discussions on how to analyze the project cash flows. In the

previous topics, for simplicity, we assumed that the discount rate is given.

However, without knowledge of the appropriate discount rate, it is difficult for us to make

good capital budgeting decisions. In this topic, we are going to study how to estimate the

discount rate.

10.1 The Cost of Capital: Some Preliminaries

The cost of capital reflects the opportunity cost of funds for investment in a firm. It is the

rate of return that the firm must earn on its investments in order to satisfy the required rates of

return of all the firm’s sources of financing. In plain language, we need to earn at least the

required return to compensate our investors for the financing they have provided.

When a firm needs funds for investment, it can issue debt or equity, or both. Intuitively, the

cost of capital will be the “average” cost of debt and equity.

Weighted average cost of capital (WACC) can be calculated as follows:

1e d c

E DWACC R R T

V V

:

Cost of Equity

Cost of Debt

Market Value of Equity

Market Value of Debt

e

d

where

R

R

E

D

V D E

We will go over each item one by one.

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10.2 Cost of Equity

There are two approaches in finding the cost of equity:

The dividend growth model approach

The CAPM approach

10.2.1 The Dividend Growth Model Approach

Recall that the constant dividend growth model:

10

e

DivP

R g

Rearranging and solve for:

1

0

e

DivR g

P

Example 10.1

Suppose that City Corporation is expected to pay a dividend of $1.50 per share next year.

There has been a steady growth in dividends of 5.1% per year and the market expects that to

continue. The current price is $25. What is the cost of equity?

When we apply the dividend growth model approach, the two inputs: dividends and price are

observable. What we have to estimate is the growth rate. One method for estimating the

growth rate is to use the historical average.

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Example 10.2

Suppose the dividend history of City Corporation is as follows:

2005 2006 2007 2008 2009

Dividend 1.23 1.30 1.36 1.43 1.50

Estimate the growth rate using historical average.

2005 2006 2007 2008 2009

Dividend 1.23 1.30 1.36 1.43 1.50

% Change 5.7% 4.6% 5.1% 4.9%

Average growth rate = (5.7 + 4.6 + 5.1 + 4.9) / 4 = 5.1%

The advantages:

Easy to understand and use.

The disadvantages:

Only applicable to companies currently paying dividends.

Not applicable if dividends are not growing at a reasonable constant rate.

Extremely sensitive to the estimated growth rate – an increase in g of 1% will

increase the cost of equity by 1%.

Does not explicitly consider risk.

10.2.2 The CAPM Approach

We can apply the CAPM model to compute the cost of equity:

e f e m fR r E r r

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Example 10.3

Suppose City Corporation has an equity beta of 0.58, and the current risk-free rate is 6.1%. If

the expected market risk premium is 8.6%, what is the cost of equity capital?

The advantages:

Explicitly adjusts for systematic risk.

Applicable to all companies, as long as we can estimate beta.

The disadvantages:

Have to estimate the expected market risk premium, which does vary over time.

Have to estimate beta, which also varies over time.

We are using the past to predict the future, which is not always reliable.

10.3 Cost of Debt

The cost of debt is the required return on the firm’s debt. It is best estimated by computing

the yield to maturity (YTM) on the existing debt.

Example 10.4

Suppose City Corporation has a bond issue currently outstanding that has 25 years left to

maturity. The coupon rate is 9%, and coupons are paid semiannually. The bond is currently

selling for $908.72 per $1,000 bond. What is the cost of debt?



2nd {CLR TVM}

2nd {CLR Work}

137

2. Enter the Inputs

45 PMT

50 N

-908.72 PV

1,000 FV


CPT I/Y

I/Y = 5%. Double it to get the YTM = 10%.

10.4 Cost of Preferred Stock

Some firms may issue preferred stocks. In general:

Preferred stock pays a constant dividend each period.

Dividends are expected to be paid every period forever.

Preferred stock is a perpetuity. We can take the perpetuity formula and rearrange:

0

0

p

p

DP

R

DR

P

Example 10.5

City Corporation has preferred stock that has an annual dividend of $3. If the current price is

$25, what is the cost of preferred stock?

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10.5 Weighted Average Cost of Capital

Collecting together, without preferred stock,

1e d c

E DWACC R R T

V V

With preferred stock,

1e p d c

E P DWACC R R R T

V V V

:

Cost of Equity

Cost of Preferred Stock

Cost of Debt

Market Value of Equity

Market Value of Preferred Stock

Market Value of Debt

e

p

d

where

R

R

R

E

P

D

V D E P

The tax effect:

We are concerned with after-tax cash flows, so we also need to consider the effect of

taxes on the various costs of capital.

Interest expense reduces our tax liability. This reduction in taxes reduces our cost of

debt. Therefore the after-tax cost of debt 1d cR T .

Dividends are not tax deductible, so there is no tax impact on the cost of equity.

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10.6 A Comprehensive Example

You are the CFO of City Corporation. City Corporation is looking at setting a manufacturing

plant overseas to produce a new line of radar detection systems (RDS). This will be a five-

year project. The company bought some land three years ago for $6 million in anticipation of

using it as a toxic dump site for waste chemicals, but it built a piping system to safely discard

the chemicals instead. If the land were sold today, the net proceeds would be $6.4 million

after taxes. In five years, the land will be worth $7 million after taxes. The company wants

to build its new manufacturing plant on this land; the plant will cost $9.8 million to build.

The following market data on City Corporation’s securities are current:

Debt: 25,000 6.5% coupon bonds outstanding, 20 years to maturity, selling

for 96% of par. The bonds have a $1,000 par value each and make

semiannual payments.

Common Stock: 400,000 shares outstanding, selling for $89 per share. The beta is 1.2.

Preferred Stock: 35,000 shares of 6.5% preferred stock outstanding, selling for $99 per

share.

Market: 8% expected market risk premium. 5.2% risk-free rate.

The tax rate is 34%. The project requires $825,000 in initial net working capital investment

to get operational.

1. Calculate the project’s time 0 cash flow taking into account all side effects.

2. The new RDS project is somewhat riskier than a typical project for City Corporation,

primarily because the plant is being located overseas. Management has told you to use an

adjustment factor of +2 percent to account for this increased riskiness. Calculate the

appropriate discount rate to use when evaluating the project.

3. The manufacturing plant has an eight-year tax life, and uses straight-line depreciation. At

the end of the project (the end of year 5), the plant can be scrapped for $1.25 million.

What is the after tax salvage value of this manufacturing plant?

4. The company will incur $2,100,000 in annual fixed costs. The plan is to manufacture

11,000 RDS per year and sell them at $10,000 per machine; the variable costs are $9,300

per RDS. What is the annual operating cash flow from this project?

5. Finally, CEO wants you to throw all your calculations and all you assumptions. He wants

to know what are the IRR and NPV of the project.

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FB3410 Lecture Notes(3)