Deze samenvatting is geschreven in collegejaar 2012-2013.

1. Introduction to Corporate Finance

The global credit crisis was a major event that shook the business world in 2007 and 2008. With the crisis in the back of our minds, it is essential for corporate managers to understand how to value investments accurately, choose the best funding mix for their operations, manage the risk of their short- and long-term capital, and satisfy the expectations of their investors.

1.      What is Corporate Finance?

When starting a firm, one needs to make investments in assets such as inventory, machinery, and labor. Eventually, when selling the products you produce, the firm generates cash. In other words, the objective of a firm is to create value for the owner. This is the basis of value creation, which is explained in a simple balance sheet model of the firm (figure 1.1, p. 2).

The Balance Sheet Model of the Firm

The model depicts the assets of the firm on the left side, which can be divided in two categories:

• Non-current assets: long-term assets that will last a long time (buildings). Some are tangible (machinery), others are intangible (patents)
• Current assets: short-term assets, which will leave the firm shortly (inventory)

The forms of financing are depicted on the right side of the balance sheet, which can be divided in two categories:

• Non-current liabilities: long-term debt that does not have to be repaid within one year
• Current liabilities: short-term debt and other obligations that must be repaid within one year

Referring to the balance sheet of the firm, we can see why finance can be thought of as the study of the following terms:

• Capital budgeting: describes the process of making and managing expenditures on long-lived assets
• Capital structure: represents the proportions of the firm’s financing from current and long-term debt and equity
• Net working capital: current assets minus the current liabilities

Capital Structure

Creditors, bondholders or debt holders are people or institutions that lend money to firms. The holders of equity shares are called shareholders. The value of the firm (V) is written as:

V = B + S

• B: Market value of debt
• S: Market value of equity
• V: Value of the firm

The Financial Manager

The financial manager is responsible for the finance activity within a firm. The most important task is to create value from the firm’s capital budgeting, financing, and net working capital activities. Simply put, the firm must create more cash flow than it uses. To put this process into perspective, the cash flow from the firm to the financial markets is followed and traced back (figure 1.3, p. 6).

• Identification of cash flows: since it is difficult to observe cash flows directly. Much of the information we obtain is in the form of accounting statements, and much of the work of financial analysis is to extract cash flow information from accounting statements.
• Timing of cash flows: the value of an investment made by a firm depends on the timing of cash flows. One of the most important principles of finance is that individuals prefer to receive cash flows earlier rather than later.
• Risk of cash flows: the amount and timing of cash flows are not usually known with certainty. Most investors have an aversion to risk.

2.      The Goal of Financial Management

A few possible financial goals to consider:

• Beat the competition
• Minimize costs
• Maximize profits

Although there are numerous other goals one could think of, these are the ones that come to mind most often. All the goals are different, but we can roughly categorize them in two classes:

• Profitability: the goals listed in this category involve sales, market shares and cot control. All are related to earning or increasing profits.
• Bankruptcy avoidance: the goals listed in this category involve stability and safety. They relate to the controlling of risks.

However, we can also look at the goal of the financial manager from a shareholder’s point of view. In this context, the financial manager should act in the shareholders’ best interest by making decisions that increase the value of the company’s shares. The corresponding goal of the financial manager would therefore be:

The goal of financial management is to maximize the share price of the company.

More precise, the goal is to maximize the current share value. From this perspective, we can define corporate finance as the study of the relationship between business decisions and the value of the shares in the business.

3.      Financial Markets

Firms require cash in order to invest in projects. They must choose whether to borrow money or sell fractions of ownership of their firm. When borrowing money, the firm agrees to pay back the borrowed amount with interest. There are several options to choose from:

• The firm can go to a bank for a loan
• The firm can issue debt securities. These are contractual obligations to repay corporate borrowing.

 If the firm chooses to give up leadership, it sells parts of the firm for a set amount of money. There are several ways to do this:

• Through private negotiation
• Through a public sale, this is undertaken through the marketing and sale of equity securities. Equity securities are shares (known as ordinary shares or common stock) that represent non-contractual claims on the residual cash flow of the firm. Issues of debt and equity that are publicly sold by the firm are then traded in the financial markets.

The financial markets consist of the money markets and the capital markets:

• Money markets are the markets for debt securities that will pay off in the short term (within a year). It also applies to a group of loosely connected markets.
• Capital markets are the markets for long-term debts (longer than a year) and for equity shares.

The money market consists of a dealer market and an agency market. A dealer market refers to firms that make continuous quotations of prices for which they stand ready to buy and sell money market instruments for their own inventory and at their own risk. The difference between the dealer’s buying and selling price is known as the bid-ask spread.

On the other hand, in an agency market, a stockbroker is acting as an agent for a customer in buying or selling shares. The stockbrokers (or agents) do not acquire the securities for themselves (figure 1.4, p. 10).

The Primary Market: New Issues

A market used when governments and public corporations want to sell securities. Corporations engage in two types of primary market sales of debt and equity: public offerings and private placements.

Secondary Markets

This transaction within this market involves one owner or creditor selling to another. Means for transferring ownership of corporate securities are provided by this market. There are two kinds of secondary markets:

• Dealer markets: when trading equities and long-term debt, these markets are called over-the-counter (OTC) markets. Most of the buying and selling is done by a dealer.
• Auction markets: differs from dealer markets in two ways. First, an auction market or exchange has a physical location (e.g. Wall Street New York). Second, the main purpose of an auction market is to match those who wish to sell with those who with to buy. Dealers play a limited role.

Listing

Company shares that are being traded on an organized exchange are said to be listed on that exchange. There are a few criteria which have to be met in order to be listed. The company must have at least 25 per cent of its shares listed on the exchange, and the value of these shares must be at least 5 million. Apart from that, the listing firm must have at least three years of financial accounts filed with the regulator. And finally, all of the company’s financial statements must follow recognized international financial reporting standards, also known as IFRS. 

Summary and Conclusions

This chapter introduced some of the basic ideas in corporate finance.

• There are three main areas of concern:
  • Capital budgeting: What long-term investments should the firm take?
  • Capital structure: Where will the firm get the long-term financing to pay for its investments? Also, what mixture of debt and equity should it use to fund operations?
  • Working capital management: How should he firm manage its everyday financial activities?
• The goal of financial management in a for-profit business is to make decisions that increase the value of the shares or, more generally, increase the market value of the equity.

2. The Corporate Firm

A firm is a way of organizing the economic activity of many individuals. Raising cash is one of the many problems a firm has to deal with.

The Sole Proprietorship

A sole proprietorship is a business owned by one person, which is the most common form of business structure in the world. As the owner of a sole proprietorship, one can hire as many people as needed and borrow whatever money is required. There are a few important factors considering a sole proprietorship:

• A sole proprietorship is the cheapest business form.
• A sole proprietorship pays no corporate income taxes. All profits are taxed as individual income.
• No distinction is made between personal and business assets. If a sole proprietorship owes has debt which it cannot pay, the owner’s own possessions must be used to repay the debts.
• The life of the sole proprietorship is limited by the life of the sole proprietor.
• Because the only money invested in the firm is the proprietor’s, the equity money that can be raised by the sole proprietor is limited to the proprietor’s personal wealth.

The Partnership

A partnership is formed with two or more people. There are two categories:

• General partnerships: all partners agree to provide some fraction of the work and cash and to share the profits and losses. Also, each partner is liable for all of the debts.
• Limited partnerships: these permit the liability of some of the partners to be limited to the amount of cash each has contributed to the partnership. Limited partnership usually requires at least one partner to be a general partner and the limited partners do not participate in managing the business.

There are a few important factors considering a partnership:

• Partnerships are inexpensive and easy to form. Complicated arrangements require written documents. Business licenses and filing fees may also be necessary.
• General partners have unlimited liability for all debts. Limited partners are limited to the contribution each has made to the partnership.
• The general partnership is terminated when a general partner dies or withdraws (not the case for a limited partner).
• Equity contributions are limited to a partner’s ability and desire to contribute to the partnership. Therefore it is difficult to raise large amounts of cash.
• Income from a partnership is taxed as personal income to the partners.
• Management control lies with the general partners.

The Corporation

The corporation is by far the most important form of business enterprise. A corporation can have a name and enjoy many of the legal powers of natural persons. When starting a corporation, one needs to prepare articles of incorporation and a memorandum of association. These must include:

• Name of the corporation
• Intended life of the corporation (may be for ever)
• Business purpose
• Number of shares that the corporation is authorized to issue
• Nature of the rights granted to shareholders
• Number of members of the initial board of directors

A corporation will normally start off as a private limited corporation, in which the shares of the firm are not permitted to be traded or advertised in the public arena. In small corporations, there may be a large overlap among the shareholders, the directors and the top management. On the other side, in larger corporations the shareholders, directors and top management are likely to be distinct groups. The corporation will then comprise four sets of distinct interests: the shareholders (the owners), the directors, the corporation officers (top management), and the firm’s stakeholders (e.g. lenders, employees, local community).

The separation of ownership from management gives the corporation several advantages over proprietorships and partnerships:

• Because ownership is represented by shares and equity, it can be readily transferred to new owners.
• The corporation has unlimited life. Death or withdrawal of an owner does not affect the corporation’s legal existence.
• The shareholders’ liability is limited to the amount invested in the ownership shares.

One great disadvantage to corporations is that there is an effect of double taxation when compared with taxation on proprietorships and partnerships. Many countries tax corporate income in addition to the personal income tax that shareholders pay.

Bank-based versus Market-based Financial Systems

In a bank-based financial system, banks play a major role in facilitating the flow of money between investors with surplus cash and organizations that require funding. Corporations in countries with a well –developed financial market, will find it easier to raise money by issuing debt and equity to the public than through bank borrowing. In market-based systems, financial markets take on the role of the main financial intermediary. Corporations in countries with bank-based systems have very strong banks, which actively monitor corporations and are often involved in long-term strategic decisions.

2.2 The Agency Problem and Control of the Corporation

Financial managers (should) act in the best interests of the shareholders.

Agency Relationships

The relationship between shareholders and management is called an agency relationship. Basically, it means that someone (the principal) hires another (the agent) to represent his or her interests. A conflict between the principal and the agent is called an agency problem.

Management Goals

The term agency cost refers to the costs of the conflict of interest between shareholders and management. These costs can be indirect or direct:

• Indirect agency cost is a lost opportunity
• Direct agency costs come in two forms. The first type is a corporate expenditure that benefits management but costs the shareholders. The second type of direct agency cost is an expense that arises from the need to monitor management actions.

Do Managers act in the Shareholders’ Interests?

Whether managers will act in the best interests of shareholders depends on two factors:

• How closely are management goals aligned with shareholder goals?
• Can managers be replaced if they do not pursue shareholder goals?

When managers do act in the best interest of the shareholders, they can achieve many advantages. For example, managers who perform better will tend to get promoted. Managers who are successful in pursuing shareholders goals will be in greater demand in the labor market and thus command higher salaries.

An important mechanism by which unhappy shareholders can replace existing management is called a proxy fight.

Stakeholders

Apart from shareholders, there are other parties that have a financial interest in the firm, such as the employees, customers, suppliers and the government. These groups together are called stakeholders. Apart from the shareholders and creditors, the stakeholders also have a potential claim on the cash flows of the firm.

2.3 The Governance Structure of Corporations

The Sole Proprietorship

All business activities are concentrated in one individual, the owner/manager. Business decisions, long-term strategy, short-term cash management, and financing decisions are all made by the owner/manager. All functions, sometimes with the exception of a few, are being conducted by the owner. They are executed informally on a day-to-day basis. In these types of organizations there is no real need for formal governance structures.

Partnerships

Partnerships are similar to a sole proprietorship in many ways. However, all the partners are personally liable for all of their firm’s debts. Every partnership will have some form of partnership agreement that governs the financial affairs of the firm.

Corporations

A corporation is a separate legal entity; therefore the informality that is common among sole proprietorships and partnerships is substituted by the formal corporate governance structure. A formal structure is necessary because the owners of the firm are less likely to be involved in management.

2.4 The 2004 OECD Principles of Corporate Governance

The 2004 OECD Principles of Corporate Governance set the basis by which individual countries can set their own corporate governance codes. The principles are centered on six major areas, and concern all aspects of corporate governance.

1. Ensuring the Basis for an Effective Corporate Governance Framework

The corporate governance framework should promote transparent and efficient markets, be consistent with the rule of law and clearly articulate the division of responsibilities among different supervisory, regulatory and enforcement authorities.

2. The Rights of Shareholders and Key Ownership Functions

The corporate governance framework should protect and facilitate the exercise of shareholders’ rights.

3. The Equitable Treatment of Shareholders

The corporate governance framework should ensure the equitable treatment of all shareholders, including minority and foreign shareholders. All shareholders should have the opportunity to obtain effective redress for violation of their rights. This principle also holds that company insiders should be forbidden from trading when they have private specific and precise information that could be used to benefit themselves personally at the expense of other shareholders. This is known as insider dealing, and is illegal in most countries.

4. The Role of Stakeholders in Corporate Governance

The corporate governance framework should recognize the rights of stakeholders established by law or through mutual agreements and encourage active co-operation between corporations and stakeholders in creating wealth, jobs, and the sustainability of financially sound enterprises.

5. Disclosure and Transparency

The corporate governance framework should ensure that timely and accurate disclosure is made on all material matters regarding the corporation, including the financial situation, performance, ownership, and governance of the company.

6. The Responsibilities of the Board

The corporate governance framework should ensure the strategic guidance of the company, the effective monitoring of management by the board, and the board’s accountability to the company and the shareholders.

Bringing it All Together

The basis of all good corporate finance decisions is a sound framework of corporate governance. A company with a weak corporate governance may make decisions that do not maximize share values. For example, a firm may choose to invest in projects that maximize managers’ own wealth and not that of the shareholders.

Summary and Conclusions

Corporate governance is concerned with the way in which a firm is managed. The financial manager must make the best financial decisions in the interests of the company’s shareholders. Unfortunately, this is not always the case.

3. Financial Statement Analysis and Long-Term Planning

Key Notations

• ACP: Average collection period
• b: Ploughback (or retention) ratio
• CF: Cash flow
• EBIT: Earnings before interest and taxes
• EBITD: Earnings before interest, taxes, and depreciation
• EFN: External financing needed
• EPS: Earnings per share
• P/E: Price-earnings ratio
• ROA: Return on assets
• ROE: Return on equity
• SIC: Standard Industrial Classification
• TIE: Times interest earned ratio

3.1 The Statement of Financial Position

The statement of financial position (or balance sheet) is an accountant snapshot of a firm’s accounting value on a particular date. The assets are on the left, while the liabilities and shareholders’ equity are on the right. The accounting definition that underlies the statement of financial position and describes the relationship is:

Assets = Liabilities + Shareholder's equity

Liquidity

Liquidity refers to the ease and rapidity with which assets can be converted into cash. Liquidity includes:

• Current assets are the most liquid, including cash and assets that will be turned into cash within a year.
• Non-current assets: the least liquid kind of assets. Tangible non-current assets include property, plant, and equipment, intangible assets have no physical existence but can be very valuable (trademark, patents).
• Trade receivables: amounts that are not yet collected from customers for goods or services sold to them.
• Inventories: are composed of raw materials to be used in production, work in process, and finished goods.

Debt versus Equity

Liabilities are obligations of the firm that require a payout of cash within a stipulated period. Shareholders’ equity is a claim against the firm’s assets that is residual and not fixed. It is the residual difference between assets and liabilities:

Assets - Liabilities = Shareholder's equity

Value versus Cost

The accounting value of the firm’s assets is frequently referred to as the book value of the assets. Since 2005, all EU countries have been required to use International Financial Reporting Standards (IFRS). However, the US uses what is known as Generally Accepted Accounting Principles (GAAP). The main difference is that under GAAP the audited financial statements of firms value assets such as property, plant, and equipment at cost. This book accounts IFRS as the main accounting system.

3.2 The Income Statement

The income statement measures performance over a specific period. The accounting definition of income is:

Revenue - Expenses = Income

Non-Cash Items

There are several non-cash items which are expenses against revenues but do not affect cash flow:

• Depreciation: reflects the accountant’s estimate of the cost of equipment used up in the production process.
• Deferred taxes: result from differences between accounting income and true taxable income.

Time and Costs

It is useful to think of time as two distinct parts:

• Short run: the period in which certain equipment, resources and commitments of the firm are fixed
• Long run: all costs are variable

3.3 Taxes

Taxes can be one of the largest cash outflows of a firm. The size of the tax bill is determined by the tax code, an often amended set of rules.

Average versus Marginal Tax Rates

The average tax rate is the tax bill divided by your taxable income. In other words, the percentage of the income that goes to pay taxes. The marginal tax rate is the tax you would pay (in per cent) if you earned one more unit of currency.

3.4 Net Working Capital

Net working capital is the current assets minus current liabilities. In addition to investing in fixed assets, a firm can invest in net working capital. This is called the change in net working capital.

3.5 Cash Flow

One of the most important items that can be extracted from financial statements, is the actual cash flow of the firm. Cash flow is not the same as net working capital. Just as we established that the value of the firm’s assets is always equal to the combined value of the liabilities and the value of the equity, the cash flows received from the firm’s assets (operating activities), CF (A), must equal the cash flows to the firm’s creditors, CF (B), and equity investors, CF (S):

CF(A) = CF(B) + CF(S)

In order to determine the cash flows of a firm, we need to:

• Determine the operating cash flow, or net cash provided by operating activities
• Determine changes in cash flow from investing activities, or investing activities

Some important observations that can be drawn from out discussion of cash flow:

• Several types of cash flow are relevant to understanding the financial situation of the firm. Operating cash flow measures the cash generated from operations, not including investments. The total cash flow of the firm includes adjustments for capital spending and new financing.
• Profit is not cash flow.

3.6 Financial Statement Analysis

Standardizing Statements

One thing we might do with a company’s financial statements is compare it to those of other, similar companies. However there are always differences between firms in size. In order to make comparisons, we have to standardize the financial statements. The resulting financial statements are called common-size statements. In this form, financial statements are relatively easy to read and compare.

Common-Size Income Statements

A useful way of standardizing the income statement is to express each item as a percentage of total revenues.

3.7 Ratio Analysis

Another way to compare companies is to calculate and compare financial ratios. These ratios are ways of comparing and investigating the relationship between different pieces of financial information.

Short-Term Solvency or Liquidity Measures

Short-term solvency ratios are intended to provide information about a firm’s liquidity (also called liquidity measures). These ratios focus on current assets and current liabilities.

1. One of best-known and most widely used ratios is the current ratio. To a creditor, the higher the current ratio, the better. To the firm, a high current ratio indicates liquidity, but it also may indicate an inefficient use of cash and other short-term assets. It is defined as:
   • Current Ratio = Current assets / Curret liabilities
2. Quick (or Acid-Test) Ratio is a ratio regarding the inventory of a firm. It is defined as:
   • Quick ratio = (Current assets - inventory) / Current liabilities
3. Cash ratio, a ration that might be very interesting for short-term creditors. It is defined as:
   • Cash ratio = Cash and cash equivalents / Current liabilities

Long-Term Solvency Measures

Long-term solvency ratios are intended to address the firm’s long-run ability to meet its obligations, or more generally, its financial leverage. These ratios are called financial leverage ratios or just leverage ratios.

1. The Total Debt Ratio takes into account all debts of all maturities to all creditors. It is defined as:
   • Total debt ratio = (Total assets - total equity) / Total assets
   • We can define two useful variations on the total debt ratio: the debt-equity and the equity multiplier:
     • Debt - equity ratio = Total debt / Total equity
     • Equity multiplier = Total assets / Total equity
2. Time Interest Earned is another common measure of long-term solvency. It measures how well a company has its interest obligations covered. It is defined as:
   • Total interest earned ratio = EBIT / Interest
3. The problem with the TIE ratio is that it is based on EBIT, which is not really a measure of cash available to pay interest. The reason if that depreciation, a non-cash expense, has been deducted out. Therefore we can define the interest (which is definitely a cash outflow) with the cash coverage ratio. It is defined as:
   • Cash coverage ratio = (EBIT + Depreciation) / Interest

Asset Management or Turnover Measures

Asset management or utilization ratios are intended to describe how efficiently, or intensively, a firm uses its assets to generate sales.

1. Inventory Turnover and Day’s Sales in Inventory
   • Inventory turnover = Cost of goods sold / Inventory
   • Days sales in inventory = 365 days / Inventory turnover
2. Receivable Turnover and Days Sales in Receivables give us an indication of how fast we can sell products.
   • Receivable turnover = Sales / Trade receivables
   • Days sales in receivables = 365 / receivables turnover
3. Total Asset turnover provides a 'big pictures'ratio. It is defined as:
   • Total asset turnover = Sales / Total assets

Profitability Measures

These measures are intended to measure how efficiently the firm uses its assets, and how efficiently the firm manages its operations. The focus is the net income.

1. Profit Margin is defined as
   • Profit Margin = (Net income / Sales)
2. Return on Assets (ROA) is a measure of profit per asset value. It can be defined as:
   • Return on assets = Net income / Total assets
3. Return on Equity (ROE) is a measure of how the shareholders fared during the year. Since benefiting the shareholders is out goal, ROE is, in an accounting sense, the true bottom-line measure of performance. It is usually defined as:
   • Return on equity = Net income / Total equity

Market Value Measures

The final group of measures is based on information about the share price (not necessarily contained in the financial statements).

• Earnings Per Share (EPS) is defined as: 
  • EPS = Net income / Shares outstanding 
• Price-Earnings Ratio (PE ratio) is defined as:
  • PE ratio = Price per share / Earnings per share
• Market-to-Book Ratio is defined as:
  • Market-to-book ratio = Markt value per share / Book value per share                                         

3.8 The Du Pont Identity

The difference between ROA and ROE reflects the use of debt financing or financial leverage.

A Closer Look at ROE

We could multiply ROE by Assets/Assets without changing anything:

Return on equity = Net income / Total equity  = (Net income/Total equity) * (assets * assets) = (Net income/ assets) / (assets / total equity)

Now tht we have expressed the ROE as the product of two other ratios, ROA and the equity multiplier:

ROE = ROA * Equity multiplier = ROA * (1 + Debt - Equity ratio)

The difference between ROE and ROA can be substantial, particularly for certain businesses. We can further decompose ROE by multiplying the top and bottom by total sales:

ROE = (Sales / Sales) * (Net Income / Assets) * (Assets * Total equity)

If we rearrange this a bit, ROE is:

Roe = (Net Income / Sales) * (Sales / Assets) * (Assets / Total Equity) = Profit margin * total asset turnover * equity multiplier

We have now partitioned ROA into its two component parts: profit margin and total asset turnover. The last expression of the preceding equation is called the Du Pont identity, which is defined as:

ROE = Profit margin * Total asset turnover * equity multiplier

The Du Pont identity tells us that TOE is affected by three things:

• Operating efficiency (as measured by profit margin)
• Asset use efficiency (as measured by total asset turnover)
• Financial leverage (as measure by the equity multiplier)

3.9 Using Financial Statement Information

Choosing a Benchmark

• Time Trend Analysis: One standard we could use is history. Did the company make changes that could allow it to use its current assets more efficiently for example.
• Peer Group Analysis: indentify firms that are similar in the sense that they compete in the same markets, have similar assets and operate in similar ways. Also called a peer group. One way of indentifying peers is based on Standard Industrial Classification (SIC) codes. These are alphabetical categories subdivided by four-digit codes that are used for statistical reporting purposes.

Problems with Financial Statement Analysis

Many firms are conglomerates, owning more less unrelated lines of business. The kind of peer group analysis we have been describing is going to work best when the firms are strictly in the same line of business, the industry is competitive, and there is only one way of operating. Another problem that is becoming increasingly common is that major competitors and natural peer group members in an industry may be scattered around the globe.

3.10 Long-Term Financial Planning

Another important use of financial statements is long-term planning.

The Percentage of Sales Approach

Our goal when using the percentages of sales approach, is to develop a quick and practical way of generating predicted financial accounts.

• The Income Statement, is calculated with the dividend payout ratio:
  • Divident payout ratio = Cash dividends / Net income
• The Statement of Financial Position, is calculated with the amount external financing needed (EFN)
  • EFN =  ((Assets/Sales) x ∆Sales) – ((Spontaneous liabilities/Sales) x ∆Sales) - [(PM x Projected sales) x (1-d)]

3.11 External Financing and Growth

Financial Policy and Growth

There is a link between growth and external financing.

• The Internal Growth Rate is the maximum growth rate that can be achieved with no external financing of any kind. It is defined as:
  • Internal growth rate = (ROA * b) / (1 + ROA * b)
• The Sustainable Growth Rate is the maximum growth rate a firm can achieve with no external equity financing while it maintains a constant debt-equity ratio. It is defined as:
  • (ROE * b) / (1- ROE * b)

Summary and Conclusions

This chapter focuses on working with information contained in financial statements. Specifically, we studied standardized financial statements, ratio analysis, and long-term financial planning.

• Differences in firm size make it difficult to compare financial statements, and we discussed how to form common-size statements to make comparisons easier and more meaningful
• Evaluating ratios of accounting numbers is another way of comparing financial statement information. We defined a number of the most commonly used ratios, and we discussed Du Pont identity.
• We showed how pro forma financial statements can be generated and used to plan for future financing needs.

4. Discounted Cash Flow Valuation

Key notations:

• APR: Annual percentage rate
• Co: Cash to be invested at date 0
• Ct: Cash flow at date T
• EAR: Effective annual rate
• EAY: Effective annual yield
• FV: Future value
• g: Rate of growth
• NPV: Net present value
• PV: Present value
• r: Rate of return, or discount rate
• r²: interest on interest
• T: Number of periods
• TCC: Total charge for credit

4.1 Valuation: The One-Period Case

The future value (FV) or compound value is the value of a sum after investing over one or more periods. An alternative method employs the concept of present value (PV). The formula for PV can be written as follows:

Present value of investment (PV) = C1 / (1+r)

Where C1 is the cash flow at date 1, and r is the rate of return. Also referred to as the discount rate.

Frequently, businesspeople want to determine the exact cost or benefit of a decision. The formula for the net present value (NPV) can be written as follows:

Net present value of investment (NPV) = -Cost + PV

4.2 Valuation: The Multi-Period Case

The previous section presented the calculation of future value and present value for one period only. We shall now perform the calculations for the multi-period case.

Future Value and Compounding

The process of leaving the money in the financial market and lending it for another year is called compounding. The lender gets back an amount r², which is the interest in the second year on the interest that was earned in the first year. The term 2 x r represents simple interest over the two years, and the term r² is referred to as the interest on interest.

When cash is invested at compound interest, each interest payment is reinvested. With simple interest, the interest is not reinvested. In addition, the longer the loan lasts, the more important interest on interest becomes. The general formula for an investment over many periods can be written as follows:

Future value of an investment : FV = Co x (1+r)^T

Where Co is the cash to be invested at date o, r is the interest rate per period, and T is the number of periods over which the cash is invested.

Present Value and Discounting

The process of calculating the present value of a future cash flow is called discounting. It is the opposite of compounding. The present value factor is the factor used to calculate the present value of a future cash flow. In the multi-period case, the formula for PV can be written as follows:

Present value of investment, PV = CT / (1-r)^T

Here, CT is the cash flow at date T and r is the appropriate discount rate.

The Algebraic Formula

To derive an algebraic formula for the net present value of a cash flow, recall that the PV of receiving a cash flow one year from now is:

PV = C1 / 1+ r

And the PV of receiving a cash flow two years from now is:

PV = C2 / (1+r) ^2

We can write the NPV of a T-period as:

NPV =             - Co + C1 / (1+r) +  C2 / (1+r)² + …..+ Cr / (1+r)^T     

The initial flow, -Co is assumed to be negative because it represents an investment.

4.3 Compounding Periods

So far, we have assumed that compounding and discounting occur yearly. Sometimes, compounding may occur more frequently than just once a year. More generally, compounding an investment m times a year provides end-of-year wealth of

Co (1+(r / m))^m

Where Co is the initial investment and r is the stated annual interest rate. The stated annual interest rate is the annual interest rate without consideration of compounding.

Compounding over Many Years

For an investment over one or more (T) years, the formula becomes:

FV = Co (1+(r / m))^mT

The Annual Percentage Rate

The EU has introduced a directive in 2004 that harmonized the way in which interest rates in any credit agreement for under €50,000 are presented. This harmonized interest rate is called the annual percentage rate (APR); it expresses the total cost of borrowing or investing as a percentage interest rate.

                          C1              C2                    CT

 PV =  Co     + -----  +  --------   + ---------

                      1+APR        (1+APR)²         (1+APR)^T    

 Continuous Compounding

The limiting case would be to compound every infinitesimal instant, which is commonly called continuous compounding. With continuous compounding, the value at the end of T years is expressed as:

Co x e^rT

Where Co is the initial investment, r is the stated annual interest rate, and T is the number of years over which the investment runs. The number e is a constant.

4.4 Simplifications

Although the concepts introduced earlier allow us to answer a lot os problems concerning the time value of money, the human effort involved can be excessive. Therefore we seek for simplifications. We provide simplifying formulae for four classes of cash flow stream:

• Perpetuity
• Growing perpetuity
• Annuity
• Growing annuity

Perpetuity

Perpetuity is a constant stream of cash flows without end. Simply applying the PV formula gives  us:

PV = C / (1+r) + C / (1+r)²  + C / (1+r)³  + ..... = C/r

The dots indicate the infinite string of terms that continues the formula. Series like this one are called geometric series.

Growing Perpetuity

If a cash flow is expected to rise 10 per cent each year, and one assumes that this rise will continue indefinitely, the cash flow stream is termed a growing perpetuity. The present value of the cash flows can be represented as:

          C           C x (1+g)      C x (1+g)²              C x (1+g)^N

PV = ----- + -------- + -------- + ..... + ---------- + ....

          1+r         (1+r)²           (1+r)³                      (1+r)^N

Where C is the cash flow to be received one period hence, g is the rate of growth per period, expressed as a percentage, and r is the appropriate discount rate. It can be reduced to the following simplification:

PV =  C / (r-g)

Annuity

An annuity is a level stream of regular payments that lasts for a fixed number of periods. Annuities are among the most common kinds of financial instruments. The present value of an annuity can be calculated with the following function:

          C               C                  C                    C

PV = ----- + -------- + -------- + --------

          1+r         (1+r)²           (1+r)³            (1+r)^N

This can be simplified to the following:

PV =    C [(1-(1 / (1+r)^T)) / r ]

We can also provide a formula for the future value of an annuity:

FV =    C [((1 / (1+r)^T)) /(1- r) ] = C [((1 / (1+r)^T) – 1) / r ]

Growing Annuity

The growing annuity is a finite number of growing cash flows. The formula is the following:

PV =    C [(1 / r-g) – (1 / r-g) x (1+g / 1+r)^T]

Summary and Conclusions

This chapter introduced two basic concepts, future value and present value. There are a few practical considerations in the application of all the formulas:

• The numerator in each of the formulae, C, is the cash flow to be received one full period hence
• Cash flows are generally irregular in practice. To avoid unwieldy problems, assumptions to create more regular cash flows are made both in this textbook and in the real world.
• A number of present value problems involve annuities beginning a pew periods hence.
• Annuities and perpetuities may habe periods of every two or every n years, rather than once a year.
• We frequently encounter problems where the present value of one annuity must be equated with the present value of another annuity.

5. How to Value Bonds and Shares

Key notations:

• A(TR): Present value of annuity of 1 unit per period for T periods at interest rate per period of R
•  C: Coupon payment
• Div: Dividend
• DPS: Dividends per share
• EPS: Earnings per share
• F: Face value of a bond
• f: Forward rate
• g: Growth rate of a dividend
• HPY: Holding period yield
• m: Number of compounding intervals
• NPVGO: Net present value (per share) of a growth opportunity
• P: Price of an equity
• R: Interest rate; discount rate for an equity
• ROE: Return on equity
• T: Numbers of years
• YTM: Yield to maturity

5.1 Definition and Example of a Bond

A bond is a certificate showing that a borrower owes a specified sum. In order to pay back the borrowed amount of money, the borrower agrees to add interest and principal payments designated dates. The government bond market is one of the largest and most liquid market in the world, whereas the corporate bond market is a lot smaller. Unlike governments, companies have the option to issue both debt and equity.

5.2 How to Value Bonds

Pure Discount Bonds

The pure discount bond is perhaps the simplest kind of bond. It 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 the payment is two years from now, it is called a two-year discount bond, etc. The date of the last payment is called the maturity date (or maturity for short). The payment at maturity is termed the bond’s face or par value.

Pure discount bonds are also called zero coupon bonds, because the holder receives no cash payment until maturity.

Value of a pure discount bond:

PV =    F/ (1+R)^T

Level Coupon Bonds

Typical bonds issued either by governments or by corporations offer cash payments not just at maturity, but also at regular times in between. These payments are called the coupons of the bond. The value of a bond is simply the present value of its cash flows. The value of a level coupon bond is therefore calculated as:

             C                      C                    C                   .......          C 

PV =   -------  + ---------  + --------- +  -------+ ------- + €1,000

            1+R                 (1+R)²             (1+R)³          (1+R)^T      (1+R)^T

Where C is the coupon and the face value, F,  is €1.000. The formula can be rewritten as:

Where C is the coupon and the face value, F, is €1.000. The formula can be rewritten as:

Value of a level coupon bond:

PV = C x A(TR) + €1,000

(1+R)^T

Consols

Consols are bonds that never stop paying a coupon, they do not have a final maturity date, and therefore never mature. Thus a consol is a perpetuity. An important example is the preferred stock (or preferred shares). These are shares that are issued by corporations and provide the holder with a fixed dividend in perpetuity.

Consols:

PV = C / R
5.3 Bond Concepts

Interest Rates and Bond Prices

Bond prices fall with a rise in interest rates, and rise with a fall in interest rates. A level coupon bond sells in the following ways:

• At the face value if the coupon rate is equal to the market-wide interest rate
• At a discount If the coupon rate is below the market-wide interest rate
• At a premium if the coupon rate is above the market-wide interest rate

5.4 The Present Value of Equity

Dividends versus Capital Gains

An equity provides two kinds of cash flow. First, equities often pay dividends on a regular basis. Second, the shareholder receives the sale price when selling the equity. To value equity, we need to answer an interesting question: Which of the following is the calue of an equity equal to?

• The discounted present value of the sum of next period’s dividend plus next period’s share price
• The discounted present value of all future dividends

Po = (Div 1 + P1­) / (1+R 1+R)

Where Div1 is the dividend paid at year’s end, and P1 is the price at year’s end. Po is the PV of the equity investment. The term R is the appropriate discount rate for the equity. A buyer determines price as follows:

Po = (Div 2 + P2­) / (1+R 1+R)

This process can be repeated ad nauseam. Which leads up to:

Po = (Div 1 + Div 2­ + Div 3 + …..) / (1+R (1+R)^2 (1+R)^3 )

So the value of a firm’s equity to the investor is equal to the present value of all of the expected future dividends.

Valuation of Different Types of Equity

The general model of a firm’s dividends are expected to follow some basic patterns:

• Zero Growth: The value of an equity with a constant dividend is given by

Po = (Div 1 + Div 2­ + ... + Div 1) / (1+R (1+R)^2 R )

• Constant Growth: Dividends grow at rate g, as follows

End-of-year dividend:

• Differential Growth: In this case an algebraic formula would be too unwieldy.

5.5 Estimates of Parameters in the Dividend Growth Model

Where Does g Come From?

We now want to estimate the rate of growth. A net investment of zero occurs when total investment equals deprecation. If total investment is equal to depreciation, the firm’s physical plant is maintained, consistent with no growth in earnings. Net investment will be positive only if some earnings are not paid out as dividends, that is, only if some earnings are retained. This leads to the following equation:

Earnings next year = Earnings this year + (Retained earnings this year * Return on retained earnings) / Increase in earnings

The increase in earnings is a function of both the retained earnings and the return on the retained earnings. We now divide both sides by earnings this year:

Earnings next year     Earnings this year       ( Retained earnings this year )

-------------- = ---------------- + ----------------------

Earnings this year       Earnings this year            ( Earnings this year )

The left side of the equation is simply 1 plus the growth rate in earnings which we write as 1+g. The ratio of retained earnings to earnings is called the retention ration:

1+g = 1+(retention ratio x return on retained earnings)

Here we can estimate the anticipated return on current retained earnings by the historical return on equity or ROE. From the previous equation, we have a simple way to estimate growth:

g = Retention ratio x Return on retained earnings

Where does R come from?

We calculated Po as:

Po = Div1 / (R-g)

If we rearrange this to solve R, we get:

R = (Div1)/Po) + g

R has two components. The first one (Div1/Po) is called the dividend yield. The second part is the growth rate, g. This one can be interpreted as the capital gains yield, the rate at which the value of the investment grows.

The dividend growth model calculates total return as:

R = Dividend yield + Capital gains yield

A Healthy Sense of Skepticism

Note that we are estimating g, our approach does not determine g. One should be particularly skeptical of two polar cases when estimating R for individual securities. First, consider a firm currently paying no dividend. However, when a firm goes from no dividends to a positive number of dividends, the implied growth rate is infinite. Second, we mentioned earlier that the value of the firm is infinite when g is equal to R. However, firms simply cannot maintain an abnormally high growth rate for ever.

5.6 Growth Opportunities

We have:

EPS = Div

Where EPS is earnings per share and Div is dividends per share. A company of this type is frequently called a cash cow.

Value of a share of equity when a firm acts as a cash cow:

EPS / R = Div / R

What would be the share price at date 0 if the firm decides to take on the project at date 1?

Share price after firm commits to new project:

EPS /R + NPVGO

Two conditions must be met in order to increase value:

• Earnings must be retained so that projects can be funded
• The projects must have positive net present value

Growth in Earnings and Dividends versus Growth Opportunities

Dividends grown whether projects with positive NPV’s or negative NPV’s are selected.

Dividends or Earnings: Which to Discount?

We can get two things out of shares: dividends and the ultimate share price, which is determined d by what future investors expect to receive in dividends.

The No-Dividend Firm

A firm with many growth opportunities faces a dilemma. The firm can pay out dividends now, or it can forgo dividends now to that it can make investments that will generate even greater dividends in the future.

5.7 The Dividend Growth Model and the NPVGO Model

We use the growing perpetuity formula to price an equity security with a steady growth in dividends. When the formula is applied to shares, it is typically called the dividend growth model.

The Dividend Growth Model

From the dividend growth model, the price of a share today is:

Div1 / (R-g)

The NPVGO Model

To value according to the NPVGO model, we need to calculate on a per-share basis:

• The value per share of a single growth opportunity
• Value per share of all opportunities
• Value per share if the firm is a cash cow

6. Net present Value and Other Investment Rules

Key Notations:

• AAR: Average accounting return
• IRR: Internet rate of return
• NPV: Net present value
• PI: Profitability index
• R: Discount rate

6.1 Why Use Net Present Value?

This chapter focuses on capital budgeting, the decision-making process for accepting or rejecting projects. The basic investment rule can be generalized as:

• Accept a project if the NPV is greater than zero
• Reject a project if NPV is less than zero

This is also called the NPV rule. The value of a firm is merely the sum of the values of the different projects, divisions, or other entities within the firm. This property, called value additivity, implies that the contribution of any project to a firm’s value is simply the NPV of the project.

Conceptually, the discount rate on a risky project is the return that one can expect to earn on a financial asset of comparable risk. This discount rate is often referred to as an opportunity cost, because corporate investment in the project takes away the shareholder’s opportunity to invest the dividend in a financial asset.

NPV is a sensible approach, but how can we tell whether alternative methods are as good as NPV? The key to NPV is its three attributes:

• NPV uses cash flows. Cash flows from a project can be used for other corporate purposes. By contrast, earnings are an artificial construct.
• NPV uses all the cash flows of the project. Other approaches ignore cash flows beyond a particular date.
• NPV discounts the cash flows properly. Other approaches may ignore the time value of money when handling cash flows.

6.2 The Payback Period Method

Defining the Rule

One of the most popular alternatives to NPV is payback. The payback period rule for making investment decisions is simple. A particular cut-off date, say two years is selected. All investment projects that have payback periods of two years or less are accepted, and all of those that pay off in more than two years are rejected.

Problems with the Payback Method

There are at least three problems with payback:

• Problem 1: Timing of Cash Flows within the Payback Period. Sometimes the payback method is inferior to NPV because, the NPV method discounts the cash flows properly.
• Problem 2: Payments after the Payback Period. The NPV does not have this flaw, because the NPV uses all the cash flows of the project.
• Problem 3: Arbitrary Standard for Payback Period.

Managerial Perspective

The payback method is often used by large, sophisticated companies when making relatively small decisions. The payback method also has some desirable features for managerial control. Under the NPV method a long time may pass before one decides whether a decision was correct. With the payback method we know in two years whether the manager’s assessment of the cash flows was correct.

It is surprising that as the decisions grow in importance, which is to say when firms look at bigger projects, NPV becomes the order of the day. When questions of controlling and evaluating the manager become less important than making the right decision, payback is used less frequently. For big-ticket decisions, the payback method is seldom used.

6.3 The Discounted Payback period Method

Some decision-makers use a variant called the discounted payback period method. First, we discount the cash flows. Then we ask how long it takes for the discounted cash flows to equal the initial investment. The discounted payback period of the original investment is simply the payback period for these discounted cash flows.

6.4 The Average Accounting Return Method

Defining the Rule

Another approach to financial decision-making is the average accounting system. This is the average project earnings after taxes and depreciation, divided by the average book value of the investment during its life. It is used frequently.

To continue the average accounting return (AAR) on a project, we divide the average net income by the average amount invested. This can be done in three steps:

• Step 1: Determining Average Net Income. The net income in any year is the net cash flow minus depreciation and taxes. Depreciation is not a cash outflow, it is a charge reflecting the fact that the investment in the store becomes less valuable every year.
• Step 2: Determining Average Investment. Because of depreciation, he investment in the store becomes less valuable every year.
• Step 3: Determining AAR.

Analyzing the Average Accounting Return Method

The most important flaw with AAR is that it does not work with the right raw materials. It uses net income and book value of the investment, both of which come from the accounting figures. These accounting numbers are somewhat arbitrary. For example, certain cash outflows (such as the cost of a building), are depreciated under specific accounting rules. Other flows, such as maintenance, are expensed, the decision to depreciate of expense an item involves judgment. Thus the basic inputs of the AAR method – income and average investment – are affected by the accountant’s judgment. While the NPV method uses cash flows. Accounting judgments do not affect cash flows.

6.5 The Internal Rate of Return

One of the most important alternatives to the NPV method is the internal rate of return, universally known as the IRR. This method provides a single number summarizing the merits of a project. That number does not depend on the interest rate prevailing in the capital market. In general, the IRR is the rate that causes the NPV of the project to be zero. The implication of this exercise is very simple. The general investment rule is thus:

Accept the project if the IRR is greater than the discount rate. Reject the project is the IRR is less than the discount rate.

We refer to this as the basic IRR rule. Sometimes, the IRR rule coincides exactly with the NPV rule. However, several problems with the IRR approach occur in more complicated situations.

6.6 Problems with the IRR Approach

Definition of Independent and Mutually Exclusive Projects

An independent project is one whose acceptance or rejection is independent of the acceptance or rejection of other projects.

The other extreme is mutually exclusive investments. What does it mean for two projects, A and B to be mutually exclusive? You can accept A or you can accept B, or you can reject both, but you cannot accept both of them,

Two General Problems affecting both Independent and Mutually Exclusive Projects

• Problem 1: Investing or Financing? The following rule applies:

Accept the project when the IRR is less than the discount rate. Reject the project when the IRR is greater than the discount rate.

• Problem 2: Multiple Rates of Return.

6.7 The Profitability Index

The profitability index is the ratio of the present value of the future expected cash flows after initial investment divided by the amount of the initial investment. This can be presented as:

Profitability index (PI) = PV of cash flows subsequent to initial investment / Initial investment

Calculation of Profitability Index

Application of the profitability index:

• Independent projects:
• Accept an independent project if PI > 1
• Reject it if PI < 1
• Mutually exclusive projects: when the cash flow is greater than 1.0, we should choose the bigger project.
• Capital rationing: consider a case where a firm does not have enough capital to fund all positive NPV projects. This is the case of capital rationing.

7. Making Capital Investment Decisions

Key Notations:

• A(tr): Present value of annuity of 1 unit per period for T periods at interest rate per period of R
• CCCTB: Common Consolidated Corporate Tax Vase
• EAC: Equivalent annual cost
• EBIT: Earnings before interest and taxes
• NPV: Net present value
• OCF: Operating cash flow
• PV: Present value
• T(c): Corporate tax rate

7.1 Incremental Cash Flows

Cash Flows – not Accounting Income

There is a big difference between corporate finance courses and financial accounting courses. Techniques in corporate finance generally use cash flows, whereas financial accounting generally stresses income or earnings numbers.

Corporate finance always discounts cash flows, not earnings, when performing a capital budgeting calculation. In addition, it is not enough to use cash flows. In calculating the NPV of a project, only cash flows that are incremental to the project should be used. These cash flows are the changes in the firm’s cash flows that occur as a direct consequence of accepting the project. In short, we are interested in the difference between the cash flows of the firm with the project and the cash flows of the firm without the project.

Sunk Costs

A sunk cost is a cost that has already occurred. They happened in the past, so therefore they cannot be changed by the decision to accept or reject the project. Sunk costs are not incremental cash outflows.

Opportunity Costs

A firm may have an asset that is considered being sold, leased, or employed elsewhere in the business. If the asset is used in a new project, potential revenues from alternative uses are lost. These lost revenues can meaningfully be viewed as costs. They are called opportunity costs. By taking the project, the firm forgoes other opportunities for using the assets.

Side Effects

A side effect is classified as either erosion or synergy. Erosion occurs when a new product reduces the sales, and hence the cash flows, of existing products. Synergy occurs when a new project increases the cash flows of existing projects.

Allocated Costs

Frequently a particular expenditure benefits a number of projects. Accountants allocate this cost across the different projects when determining income. However, for capital budgeting purposes, this allocated cost should be viewed as a cash outflow of a project only if it is an incremental cost of the project.

7.3 Inflation and Capital Budgeting

Inflation is an important fact of economic life, and it must be considered in capital budgeting.

Interest Rates and Inflation

For an example of a specific nominal interest rate and a specific inflation rate, see figure 7.2, page 186.

The formula between real and nominal interest rates can be written as follows:

1+ Nominal interest rate = (1+Real interest rate) x (1+Inflation rate)

Rearranging term, we have:

Real interest rate =( (1+Nominal interest rate) / (1+Inflation rate) ) - 1

The following formula is an indication:

Real interest rate = Nominal interest rate – Inflation rate

Cash Flow and Inflation

There are two types of interest rate, nominal rates and real rates. Like interest rates, cash flows can be expressed in either nominal or real terms. A nominal cash flow refers to the actual money in cash to be received. A real cash flow refers to the cash flow’s purchasing power.

Discounting: Nominal or Real?

Financial practitioners correctly stress the need to maintain consistency between cash flows and discount rates:

• Nominal cash flows must be discounted at the nominal rate
• Real cash flows must be discounted at the real rate

As long as one is consistent, either approach is correct.

7.4 Alternative Definitions of Operating Cash Flows

We have the following estimates:

Sales = € 2000

Costs = € 800

Depreciation = € 700

For these estimates, the earnings before interest and taxes (EBIT) is

EBIT = Sales – costs – depreciation

€ 2000 – 800 – 700 = € 500

The tax bill is:

Taxes = EBIT x t(c)

= € 500 x 0,28

= € 140

Where t(c), the corporate tax rate is 28 per cent.

Putting it together, the project operating cash flow (OCF) is:

OCF = EBIT + deprecation – taxes

= €500 + 700 – 140 = € 1060

The Bottom-Up Approach

Project net income = EBIT – Taxes

= € 500 – 140 = € 360

If we add the depreciation to both sides, we get:

OCF = Net income + Depreciation

= € 360 + 700 = € 1060

This is the bottom-up approach. We start with the accountant’s bottom line (net income) and add back any non-cash deductions such as depreciation.

The Top-Down Approach

OCF = Sales – costs – taxes

= € 2000 – 800 – 140 = € 1060

This is the top-down approach, the second variation on the basis OCF definition. Here we start at the top of the income statement with sales, and work out way down to net cash flow by subtracting costs, taxes and other expenses. We leave out any strictly non-cash items such as depreciation.

The Tax Shield Approach

OCF = (sales-costs) x (1-t(c)) + depreciation x t(c)

This approach has two components, the first part is what the project’s cash flow would be if there were no depreciation expense. The second part of OCF in this approach is the depreciation deduction multiplied by the tax rate. This is called the depreciation tax shield.

8. Risk Analysis, Real Options, and Capital Budgeting

Key Notations

• A(TR): Present value of annuity of 1 unit per period for T periods at interest rate per period of R
• NPV: Net present value
• OCF: Operating cash flow
• t(c): Corporate tax rate

8.1 Sensitivity Analysis, Scenario Analysis, and Break-even Analysis

One main point of the NPV analysis is a superior capital budgeting technique. Because the NPV approach uses cash flows rather than profits, uses all the cash flows, and discounts the cash flows properly, it is hard to find any theoretical fault with it.

Sensitivity Analysis and Scenario Analysis

The sensitivity analysis examines how sensitive a particular NPV calculation is to changes in underlying assumptions.

Managers frequently perform scenario analysis, a variant of sensitivity analysis. This approach examines a number of different likely scenarios, where each scenario involves a confluence of factors.

Break-Even Analysis

The break-even approach determines the sales needed to break even. We calculate the break-even point in terms of both accounting profit and present value.

8.3 Real Options

The NPV analysis, as well as all the other approaches ignore the adjustments that firm can make after a project is accepted. These adjustments are called real options.

• The Option to Expand
• The Option to Abandon
• Timing Option

Part Three: Risk

9. Risk and Return: Lessons from Market History

Key Notations:

• Div(t): Dividend at time t
• N: Number of assets
• N: Number of observations
• P(t): Price of an equity at time t
• R(t): return on investment at time t
• r(t): Observed return at time t
• Ṝ: Mean return
• SD: Standard deviation
• T: Number of years
• Var: Variance
• σ: Standard deviation
• σ²: Variance

9.1 Returns

Monetary Returns

The return you get on investment in shares, like that in bonds or any other investment, comes in two forms. first, over the year most companies pay dividends to shareholders. if the company is profitable, it will generally distribute some of its profits to the shareholders. therefore, as the owner of shares, you will receive some cash, called a dividend. This cash is the income component of your return. In addition to the dividends, the other part of your return is the capital gain, or is it is negative, the capital loss.

The total monetary return on your investment is the sum of the dividend income and the capital gain or loss on the investment:

Total monetary return = Dividend income + Capital gain (or loss)

Percentage Returns

How much return do we get for each unit of currency invested? The percentage income return (dividend yield) is calculated as follow:

Dividend yield = Div (t+1) / P(t)

The capital gain (or loss) is the change in the price of shares divided by the initial price.

Capital gain = (P(t+1) – P(t)) / P(t)

Combining this, the total return would be:

R(t+1) = (Div(t+1) / P(t))  + ( P(t+1) – P(t) ) / P (t)

9.2 Holding Period Returns

If R(t) is the return in year t (expressed in decimals), the value you would have at the end of year t is the product of 1 plus the return in each of the years:

(1+R1)x(1+R2)x…x(1+R(t))x…x(1+R(T))

The result is called the holding period return.

9.3 Return Statistics

To calculate the average or mean of a distribution, we add up all the values and divide by the total (T) number.

9.4 Average Stock Returns and Risk-Free Returns

Governments borrow money by issuing bonds, which the investing public holds. As we discussed in an earlier chapter, these bonds come in many forms, and the ones we shall look at here are called Treasure bills, or T-bills. Once a week the government sells some bills at an auction. A typical bill is a pure discount bond that will mature in a year or less. Because governments can raise taxes to pay for the debt they incur, this debt is free of the risk of default. Thus they are called risk-free return over a short time (one year of less).

The difference between risky returns and risk-free returns is often called the excess return on the risky asset.

9.5 Risk Statistics

A distribution whose returns are all within a few percentage points of each other is tight, and the returns are less uncertain. The measures of risk we shall discuss are variance and standard deviation.

Variance

The variance and its square root, the standard deviation, are the most common measure of variability or dispersion.

Normal Distribution and Its Implications for Standard Deviation

The normal distribution looks like a bell-shaped curve. This distribution is symmetrical and the standard deviation is the usual way to represent the spread of a normal distribution.

Other Measures of Risk

Asymmetric measures of risk use only the downside variation in returns from some target return, which could be the mean historical return or some benchmark return set by the investor. The semi-variance has the advantage that only those deviations that are below the target or benchmark return are considered in the risk measure (for the formula, see page 246).

Another measure of risk that incorporates asymmetry in investment returns is that of skewness. Skewness refers to the extent to which a distribution is skewed to the left or upside observations are equally likely.
 

9.6 More on Average Returns

Arithmetic versus Geometric Averages

The geometric average return answers the question ‘what was your average compound return per year over a particular period?’. The arithmetic average return answers the question ‘what was your return in an average year over a particular period?’

Calculating Geometric Average Returns

The geometric average return over T years is calculated as:

Geometric average return = [(1+R1)x(1+R2)x…x(1+R(T))]^(1/T) – 1

10. Risk and Return: The Capital Asset Pricing Model

Key Notations

• C: Cash flows
• CAPM: Capital asset pricing model
• CCAPM: Consumption capital asset pricing model
• CML: Capital market line
• Cov: Covariance
• Cov(average): average covariance
• Div(t): Dividend at time t
• HCAPM: Human capital CAPM
• M/B: Market-to-book ratio
• N: Number of assets; number of years
• n: Number of observations
• P/E: Price-earnings ratio
• P(t): Price of an equity at time t
• R: Return on investment
• Ṝ: Expected or mean return
• R(F): Risk-free rate
• Ṝ(F): Return on financial assets
• R(i): Return on an individual equity
• R(M): Return on the market
• Ṝ(M): Expected return on the market
• Ṝ(NF): Return on non-financial assets
• R(p): Expected return 
• R(t): Return on investment at time t
• r(t): Observed return at time t
• SD; Standard deviation
• SML: Security market line
• T: Number of years
• Var: Variation
• Var(average): Average variance
• X: Percentage of a portfolio in a particular security
• β: Beta
• β(c): Consumption beta
• β(F): Financial beta
• β(NF): Non-fictional beta
• p: Correlation
• σ: Standard deviation
• σ²: Variance

10.1 Individual Securities

The following characteristics of individual securities shall be discussed:

• Expected return: the return that an individual expects a security to earn over the next period. Although only a expectation.
• Variance and standard deviation: the variance is the measure of the squared deviations of a security’s return from its expected return. Standard deviation is the square root of the variance.
• Covariance and correlation: returns on individual securities are related to one another. Covariance is a statistic measurement of the interrelationship between two securities.

10.3 The Return and Risk for Portfolios

The investor would like a portfolio with a high expected return and a low standard deviation of return. Therefore we must consider:

• The relationship between the expected return on individual securities and the expected return on a portfolio made up of these securities.
• The relationship between the standard deviations of individual securities, the correlations between these securities, and the standard deviation of a portfolio made up of these securities.

The Expected Return on a Portfolio

The formula for expected return on a portfolio is calculated as:

The expected return on a portfolio is simply a weighted average of the expected returns on the individual securities.

Variance and Standard Deviation of a Portfolio

The variance of the portfolio (for formula, see page 263) leads to the following result:

As long as p<1, the standard deviation of a portfolio of two securities is less than the weighted average of the standard deviations of the individual securities.

10.5 The Efficient Set for many Securities

Variance and Standard Deviation in a Portfolio of Many Assets

The variance of the return on a portfolio with many securities is more dependent on the covariances between the individual securities than on the variances of the individual securities.

10.6 Diversification: An Example

Total risk, which is var (average), is the risk we bear by holding onto one security only. Portfolio risk is the risk we still bear after achieving full diversification, which is cov(average). Portfolio risk is often called systematic or market risk as well. Diversifiable, unique, or unsystematic risk is the risk that can be diversified away in a large portfolio which must be (var(average)-cov(average)) by definition.

Risk and the Sensible Investor

Our typical investor is risk-averse. Risk-averse behavior can be defined in many ways.

10.7 Riskless Borrowing and Lending

The Optimal Portfolio

The previous section concerned a portfolio formed between one riskless asset and one risky asset. In reality, an investor is likely to combine an investment in the riskless asset with a portfolio of risky assets.

10.8 Market Equilibrium

Definition of the Market Equilibrium Portfolio

Financial economists often imagine a world where all investors possess the same estimates of expected returns, variances and covariances. This assumption is called homogeneous expectations.

In a world with homogenous expectations, all investors would hold the portfolio of risky assets represented by point A.

Common sense tells us that it is a market-value-weighted portfolio of all existing securities, the market portfolio.

Definitions of Risk when Investors Hold the Market Portfolio

Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta of the security.

Beta measures the responsiveness of a security to movements in the market portfolio.

The Formula for Beta

The definition of Beta is:

β(i)= Cov ((R(i), R(M))

σ² (R(M))

Where Cov ((R(i), R(M)) is the covariance between the return on asset i and the return on the market portfolio, and σ² (R(M)) is the variance of the market.

10.9 The Capital Asset Pricing Model

Expected Return on Market

The expected return on the market can be represented as:

Ṝ(M) = R(F) + Risk premium

The expected return on the market is the sum of the risk-free rate plus some compensation for the risk inherent in the market portfolio. This is all an expected return on the market, not the actual return.

Expected Return on an Individual Security

The relationship between expected return and beta can be represented as:

Capital asset pricing model:

Ṝ(M) = R(F) + β x (Ṝ(M) – R(F))

This is called the capital asset pricing model (CAPM), it implies that the expected return on a security is linearly related to its beta. Three additional points concerning the CAPM should be mentioned:

• Linearity: the intuition behind an upwardly sloping curve is clear. The relationship between return and beta corresponds to a straight line.
• Portfolios as well as securities: CAPM considers individual securities as well as portfolios.
• A potential confusion: CAMP is often confused for SML.

12. Risk, Cost of Capital, and Capital Budgeting

Key notations

• B: Market value of a firm’s debt
• CAPM: Capital Asset Pricing Model
• COGS: Cost Of Goods Sold
• Cov: Covariance
• EBIT: Earnings Before Interest and Taxes
• EVA: Economic Value Added
• IRR: Internal Rate of Return
• NPV: Net Present Value
• R_B: Cost of debt; a firm’s borrowing rate
• R_F: Risk-free rate of return
• R_M: Expected return on market portfolio
• R_S: Cost of equity
• R_WACC: Weighted average cost of capital
• ROA: Return On Assets
• S: Market value of a firm’s equity
• SGA: Sales, General and Administration costs
• SML: Security Market Line
• t_c: Corporate tax rate
• Var: Variance
• β: Beta

12.1 The Cost of Equity Capital

Whenever a firm has extra cash, it can take one of two actions: pay out the cash immediately as a dividend or invest extra cash in a project, paying out the future cash flows of the project as a dividend.

The project should be undertaken only if its expected return is greater than that of a financial asset of comparable risk.

RULE: The discount rate of a project should be the expected return on a financial asset of comparable risk.

Under CAPM, the expected return on equity can be written as:

R_S = R_F + β * (R_M – R_F)

12.2 Estimation of Beta

In the real world, beta must be estimated. Beta of an equity is the standardised covariance of a security’s return with the return on the market portfolio.

Beta of security i = Cov (R_i, R_M)/Var (R_M) = σ_i,M/σ²_M

Using an Industry Beta

It is frequently argued that people can better estimate a firm’s beta by involving the whole industry (Table 12.3/323 shows the betas of some prominent firms in the UK oil and gas industry). If one believes that the operations of a firm are similar to the operations of the rest of the industry, the industry beta should be used, simply to reduce the estimation error.

Determinants of Beta

Beta is determined by the characteristics of the firm:

• Cyclicality of Revenues: the revenues of some firms are cyclical; these firms do well in the expansion phase of the business cycle but so poorly in the contraction phase;
• Operating Leverage: the difference between variable and fixed costs. It refers to the firm’s fixed costs of production;
• Financial Leverage: the extent to which a firm relies on debt. Because a levered firm must make interest payments regardless of the firm’s sales, financial leverage refers to a firm’s fixed costs of finance.

12.4 Extensions of the Basic Model

The Firm versus the Project

If a project’s beta differs from that of the firm, the project should be discounted at the rate proportionate with its own beta. Unless all projects in the corporation are of the same risk, choosing the same discount rate (hurdle rate or cost of capital) is incorrect.

The Cost of Capital with Debt

If a firm uses both debt and equity to finance its investments, the cost of capital is a weighted average of each:

R_s + R_B,

Where is the proportion of total value represented by the equity and

is the proportion of total value represented by debt

The after-tax cost of debt is:

Cost of debt (after corporate tax) = R_B × (1 – t_C), where t_C is the corporation’s tax rate

Assembling the two, we get the average cost of capital (after tax) for the firm:

Average cost of capital = R_s + R_B × (1 – t_C) = R_WACC (weighted average cost of capital)

12.6 Reducing the Cost of Capital

A firm can actually lower its cost of capital through liquidity enhancement.

What is Liquidity?

Liquidity is the cost of buying and selling equities. Equities that are expensive to trade are considered less liquid than those that trade cheaply. There are generally three costs involved: brokerage fees, the bid-ask spread, and the market impact costs.

Liquidity, Expected Returns, and the Cost of Capital

The cost of trading non-liquid shares reduces the total return that an investor receives. Investors demand a high expected return as compensation when investing in high-risk (e. g. high-beta) equities. Because the expected return to the investor is the cost of capital to the firm, the cost of capital is positively related to beta (fig. 12.8/334).

Liquidity and Adverse Selection

A counterparty will lose money on a trade if the trader has information that the counterparty does not have (the counterparty has been picked off, or has been subject to adverse selection).

Therefore, informed traders in an equity raise the required return on equity, increasing the cost of capital.

What can corporations do? The corporation has an incentive to lower trading costs because a lower cost of capital should result.

Amihud and Mendelson identify two general strategies for corporations.

1. Firms should try to bring in more uninformed investors;
2. Corporations can disclose more information (narrowing the gap between informed and uninformed investors, thereby lowering the cost of capital).

12.7 How Do Corporations Estimate Cost of Capital in Practice?

The most commonly used method is CAPM and beta. Historical returns on share prices are also commonly used, and in the Netherlands a significant number of companies use a cost of capital estimate that is set by investors (table 12.3/337 shows the responses of several executives in the US, UK, Netherlands, Germany and France).

The Economic Value Added approach is calculated using the following formula:

(ROA – Weighted Average Cost of Capital) × Total Capital

13 Corporate Financing Decisions and Efficient Capital Markets

Key notations

• AR: Abnormal Return
• CAR: Cumulative Abnormal Return
• EMH: Efficient Market Hypothesis
• IPO: Initial Public Offering
• NPV: Net Present Value
• P_t: Price of an equity at time t
• SEO: Seasoned Equity Offering
• SML: Security Market Line

13.1 Can Financing Decisions Create Value?

Typical financing decisions include how much debt and equity to sell, what types of debt and equity to sell, and when to sell them.

There are basically three ways to create valuable financing opportunities:

1. Investors lack an understanding of risk and valuation of complex securities
2. Reduce costs or increase subsidies. A firm packaging securities to minimize taxes can increase firm value.
3. Create a new security. New, complex securities cannot easily be duplicated by combinations of existing securities.

13.2 A Description of Efficient Capital Markets

An efficient capital market is one in which share prices fully reflect available information. It processes the information available to investors, and incorporates it into the prices of securities.

Market efficiency has two general implications:

1. In any given time period, an equity’s abnormal return depends of information or news received by the market in that period;
2. An investor who uses the same information as the market cannot expect to earn abnormal returns. In other words, systems for playing the market are doomed to fail.

Foundations of Market Efficiency

The conditions that cause market efficiency, as argued by Andrei Shleifer, are:

• Rationality. When new information is released in the marketplace, all investors will adjust their estimates of share prices in a rational way.
• Independent deviations from rationality. Market efficiency does not require rational individuals – only countervailing irrationalities.
• Arbitrage. If the arbitrage of professionals dominates the speculation of amateurs, markets would still be efficient.

13.3 The Different Types of Efficiency

In actuality, certain information may affect share prices more quickly than other information.

To handle differential response rates, researchers separate information into different types:

• The Weak Form. The market uses the history of prices, and is, therefore, efficient to these past prices. This implies that security selection based on patterns of past share price movements is no better than random selection;
• The Semi-Strong Form. The market uses all publicly available information in setting prices;
• The Strong Form. The market uses all of the information that anybody knows about equities, including inside information.

Much evidence from different financial markets supports weak form and semi-strong form efficiency, but not strong form.

13.4 The Evidence

The evidence on the efficient market hypothesis is extensive, with studies covering the broad categories of weak, semi-strong and strong form efficiency:

1. The weak form. Serial correlation involves only one security (it is the correlation between the current return on a security and the return on the same security over a later period.

A positive coefficient of serial correlation indicates a tendency towards continuation (a higher-than-average return today is likely to be followed by a higher-than-average return in the future). A negative coefficient of serial correlation indicates a tendency towards reversal. Serial correlation coefficients for share price returns near zero would be considered with weak form efficiency.

2. The semi-strong form.

   1. Event studies. The abnormal return (AR) on a given security for a particular day can be calculated by subtracting the market’s return on the same day (R_m) from the actual return (R) on the equity for that day:

AR = R - R_m

1. The Record of Mutual Funds. If the market is efficient on the semi-strong form, then no matter what publicly available information mutual fund managers rely on to pick equities, their average returns should be the same as those of the average investor in the market as a whole.

2. The strong form. If an individual has information that no one else has, it is likely that he/she can profit from it. One group of studies that investigated insider trading by examining cumulative abnormal returns from UK director trading. Given that it seems one can make abnormal profits from private information, strong form efficiency does not seem to be substantiated by evidence.

13.5 The Behavioural Challenge to Market Efficiency

Rationality

The behavioural view is that not all investors are irrational. Rather, it is that some, perhaps many, investors are.

Independent deviations from rationality

A market dominated by representativeness (to believe that the sample observed is more representative of the population than it really is) leads to bubbles.

Behavioural finance suggests that investors exhibit conservatism because they are too slow to adjust their beliefs to the new information.

Arbitrage

Arbitrage strategies may involve too much risk to eliminate market efficiencies.

13.6 Empirical Challenges to Market Efficiency

Limits to arbitrage

Risk considerations may force arbitrageurs to take positions that are too small to move the prices back to parity.

Earnings surprises

Earnings surprise is the difference between current quarterly earnings and quarterly earnings four quarters in the past, divided by the share price.

Size

In the US, the returns on equities with small market capitalizations were greater than the return on equities with large market capitalization throughout most of the 20^th century.

Value versus Growth

A number of papers have argued that equities with high book-value-to-share-price ratios and/or high earnings-to-price ratios (value stock) outperform equities with low ratios (growth stocks).

Crashes and Bubbles

Bubble theory of speculative markets: security prices sometimes move wildly above their true values.

Four implications of market efficiency for corporate finance are:

• Managers cannot fool the market through creative accounting;
• Firms cannot successfully time issues of debt and equity;
• Managers cannot profitably speculate in foreign currencies and other instruments;
• Managers can reap many benefits by paying attention to market prices.