Share with the class the topics covered (see attached of covered topics) in Managerial Finance that you found most interesting and useful to you in your professional and/or personal life. What topics did you find particularly challenging? See the attached of topics covered in this class. The most difficult topics for me were NPV and WACC. Please write to how these topics are useful as a manager and write to the challenging topics of NPV and WACC.
Required sources:
Berk, Jonathan and Peter DeMarzo. Corporate Finance (Looseleaf) – with Access. 3rd ed.. Pearson/Prentice Hall, 2014. ISBN-978-0-13-442679-2
Chapter 1: The Corporation
Chapter 1 begins by discussing the “birth” of the modern corporation. The chapter examines important characteristics of the four major types of firms in the United States; however, the focus is on the corporation. Section 1.2 defines the agency relationships that sometimes occur in a corporation. Section 1.3 focuses on the stock market and its advantages in raising capital.
1.1 The Four Types of Firms
The four major types of firm in the United States are the sole proprietorship, partnership, limited liability company, and corporation. The section begins by defining each type, then highlights the differences among them. Particular emphasis is placed on the following areas that distinguish the four types:
- Ease of formation.
- Separation between the firm and the owner from the perspective of the owner’s personal liability.
- Lifespan of the firm.
- Ease of transference of ownership.
The text emphasizes the corporate form. In this chapter, the authors focus on the fact that, although corporations take a great deal of effort to form, they have some distinct advantages. The life of the firm is not limited by the life of any particular individual. Ownership in the corporation is very easy to transfer either via purchase, or sale of shares of stock. However, there are some disadvantages as well. Each shareholder is likely to own only a small percentage of the stock; agency problems can be pretty serious (see Section 1.3). There is extreme separation between the firm and its owner.
In U.S. finance, the primary goal is to maximize shareholder wealth or the current market value of the firm. This model is often termed ‘Shareholder Capitalism’. Shareholder wealth (in publicly traded companies) is measured by the value of a share of stock. This goal differs from the goal of maximizing profit or keeping customers happy or other goals we observe in other areas of business. This goal is directly related to the evolution of the firm to its current corporate form and is directly tied to agency problems that arise because of the separation of ownership and control of the firm. (Be sure you understand and can explain why this is the case).
It should be noted that this model of the corporation is not universal. In Europe and Asia, models of ‘Stakeholder Capitalism’ predominate which emphasize not just the maximization of shareholder wealth, but rather the maximization of the wealth of all stakeholders—customers, employees, shareholders, creditors, community, society.
Corporations are taxed in a very different way than other types of firms. Example 1.1 shows the double taxation of corporate earnings when dividends are paid. Example 1.2 shows how taxation of S corporations differs from that of C corporations.
1.2 Ownership Versus Control of Corporations
Section 1.2 highlights the separation of ownership and control in the corporation, with particular emphasis on principal-agent problems. The chapter emphasizes the market for corporate control as the primary means for encouraging managers and boards of directors to act in the best interest of shareholders.
One further stakeholder in a corporation is debt holders. If the corporation fails to repay the debt holders, it will be forced into bankruptcy.
1.3 The Stock Market
An important feature of equity investment is its liquidity. Stock markets improve liquidity for investors by enabling investors to trade shares of public corporations. The NYSE is the world’s largest stock market. It has a physical location, where market makers match buyers to sellers. The Nasdaq is an electronic network, where prices are posted so that they can be viewed by all participants.
Chapter 2: Introduction to Financial Statement Analysis
This chapter reviews the four main financial statements and discusses some useful financial ratios. The chapter closes with a look at some recent financial scandals.
2.1 Firms’ Disclosure of Financial Information
The four statements that are required by the U.S. Securities and Exchange Commission (SEC) are the balance sheet, the income statement, the statement of cash flows, and the statement of stockholders’ equity.
The section includes a summary of steps taken toward standardizing financial statements across countries via International Financial Reporting Standards.
2.2 The Balance Sheet
The balance sheet lists the firm’s assets and liabilities. This section describes current assets, long-term assets, current liabilities and long-term liabilities, with examples of the major components of each. The authors emphasize the difference between market value and book value of equity, and give some specific reasons why the two are seldom the same. Example 2.1 illustrates a case in which they are different.
2.3 Balance Sheet Analysis
Book value of equity is sometimes used as an estimate of the liquidation value of the firm. Important tools for analyzing the firm’s value, leverage, and short-term cash needs, from information found on the balance sheet include:
- the market-to-book ratio, which is often used to classify firms as value stocks or growth stocks.
- the debt-equity ratio, a measure of the firm’s leverage.
- enterprise value, which assesses the value of underlying business assets, not including cash (Example 2.2 shows how enterprise value is calculated).
- current and quick ratios, which are sometimes used to assess the firm’s working capital position.
2.4 The Income Statement
The income statement lists the firm’s revenues and expenses over a period of time. This section of the text discusses the calculation of earnings from the components of the income statement. Earnings per share (and diluted earnings per share) are often calculated to assess the size of net income relative to that of similar firms.
2.5 Income Statement Analysis
Profitability ratios, such as operating margin and net profit margin, are often used to measure the fraction of revenues that is available to common shareholders. Some examples of ratios that use both income statement and balance sheet items are working capital ratios, such as accounts receivable days (or average collection period), inventory days, and accounts payable days. Leverage is often assessed using ratios such as interest coverage, which is also a mixed ratio. Investment returns are measured by return on equity or return on assets, although these measures are both flawed in their use of book value measures. The DuPont Identity allows the analyst to break down the determinants of a firm’s ROE. Example 2.3 illustrates this decomposition for Wal-Mart and Target. Valuation ratios include the price-earnings ratio. Example 2.4 shows students how to calculate profitability and valuation ratios for Wal-Mart and Target.
2.6 The Statement of Cash Flows
The statement of cash flows converts accrual-based income into cash flow. Cash flows are separated into operating activities, investment activities, and financing activities. Example 2.5 shows the impact of depreciation on cash flows.
2.7 Other Financial Statement Information
The management discussion and analysis provides management’s interpretation of the planned activities of the firm. The statement of stockholders’ equity provides detailed information about additions to, or reductions in, the stockholders’ equity accounts. Notes to the financial statements are an integral part of the statements, as they show detail about stock-based compensation plans, leases, principal payments on debt, and many other items. Example 2.6 uses a note to the financial statement reporting sales by product category to find the sales unit with the highest growth.
2.8 Financial Reporting in Practice
There have been several recent abuses of financial rules, including Enron and WorldCom. Enron sold assets at inflated prices to other firms, together with a promise to buy back assets at an even higher future price. WorldCom reclassified $3.85 billion in expenses as long-term investment. The Sarbanes-Oxley Act was passed in 2002 to improve accuracy of information provided to boards and shareholders. It attempts to achieve this goal by 1) overhauling incentives and the independence in the auditing process, 2) stiffening penalties for providing false information, and 3) forcing companies to validate their internal financial control processes. It holds CFOs and CEOs accountable for the firm’s financial statements. A call-out box describes the Madoff Ponzi scheme.
Chapter 4: The Time Value of Money
Overview
The introduction to Chapter 4 draws on the discussion of NPV in Chapter 3. The text puts a great deal of emphasis on drawing a timeline when approaching every problem, so that students may better visualize the problems they are solving. Another distinguishing feature of this text is that this chapter puts virtually everything in the context of present value. Hence all future value problems are illustrated as they relate to present value. The chapter covers present and future values of a single sum, an uneven stream of cash flows, and an annuity; present value of a perpetuity; present value of a growing perpetuity; and present and future value of a growing annuity.
4.1 The Timeline
Drawing a timeline as the first step in solving a problem will often clarify any confusion about amount and/or timing of cash flows, making problems much clearer. The timeline is a very important part of calculating the time value of money.
4.2 The Three Rules of Time Travel
There are three rules of time travel. They are:
- It is only possible to compare or combine values at the same point in time.
- To move a cash flow forward in time, you must compound it.
- To move a cash flow backward in time, you must discount it.
To compound cash flows, multiply the amount by (1 + r)n, where r is the periodic interest rate and n is the number of compounding periods. To discount cash flows, divide the amount by (1 + r)n, where r and n are as defined previously. Figure 4.1 shows the composition of interest over time.
The rules of time travel allow us to compare and combine cash flows that occur at different points in time. In order to compare or combine them, they must be either discounted or compounded.
4.3 Valuing a Stream of Cash Flows
This section shows how to calculate the present value or future value of an uneven cash flow stream. Note that FV can be solved by calculating the present value (discounting each cash flow), then compounding that total, n periods into the future. This information makes FV of an uneven cash flow stream solvable in a financial calculator.
Present Value of a Cash Flow Stream
PV=∑ N n=0 PV(C n )=∑ N n=0 C n (n+r) n PV=∑n=0NPV(Cn)=∑n=0NCn(n+r)n
4.4 Calculating the Net Present Value
The logic developed in Chapter 3 is reexamined here in the context of the time value of money. NPV will be a concept that we continue to revisit in the context of capital budgeting and valuation.
4.5 Perpetuities, Annuities, and Other Special Cases
Several alternatives to the formulas developed earlier are addressed at this point in the chapter. In every case, the formula is derived using algebra:
- Present value of a perpetuity.
PV(C in perpetuity) = Cr PV(C in perpetuity) = Cr
- If we have several cash flows of the same size occurring at regular intervals, starting either now or sometime in the future, this is a present value or future value of an annuity. Annuities due are treated as ordinary annuities with one extra period of interest.
Present Value of an Annuity
PV(annuity of C for Nperiods with interest rate r ) = C×1r (1−1(1+r) N ) PV(annuity of C for Nperiods with interest rate r ) = C×1r(1−1(1+r)N)
Future Value of an Annuity
FV(annuity)=PV×(1+r) N = Cr (1−1(1+r) N )×(1+r) N = C×1r ((1+r) N −1) FV(annuity)=PV×(1+r)N = Cr(1−1(1+r)N)×(1+r)N = C×1r((1+r)N−1) {“version”:”1.0″,”size”:{“width”:”422″,”height”:”226″,”auto”:true},”math”:”<math><mrow><mi>F</mi><mi>V</mi><mo>(</mo><mtext>annuity</mtext><mstyle><mrow><mo>)</mo></mrow></mstyle><mtext>=PV</mtext><mo>×</mo><msup><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>r</mi><mo>)</mo></mrow><mrow><mi>N</mi></mrow></msup><msp - The authors introduce the concept of valuing an infinite stream of cash flows that grow at a constant rate each period, using the formula for present value of a growing perpetuity. This development is particularly useful in later chapters.
Present Value of a Growing Perpetuity
PV(growing perpetuity) = Cr−g PV(growing perpetuity) = Cr−g Several cash flows occurring at regular intervals, which grow at a constant rate each period. Present value or future value of a growing annuity.
Present Value of a Growing Annuity
PV=C×1r−g (1−(1+g1+r ) N ) PV=C×1r−g(1−(1+g1+r)N)
4.6 Solving Problems with a Spreadsheet Program
Time value of money problems lend themselves well to spreadsheet solutions. The following functions are mentioned in the chapter: NPV, FV, PV, PMT, IRR, and NPER. Example 4.11 uses the annuity spreadsheet available on the textbook’s website to solve for future value.
4.7 Solving for Variables Other Than Present Value or Future Value
This section explains how to solve for (1) cash flows, (2) internal rate of return, or (3) number of periods. Again, the derivation uses strictly algebra.
Working Capital and Forecasting Short-term Financing Needs
The topics covered this week are very important to the short-term operations of the firm and its ability to meet its needs for financing.
Chapter 26 covers Working Capital. Working Capital is technically calculated as: Working Capital = Current Assets – Current Liabilities. This basically measures the size of permanent financing the firm used to finance its day-to-day operations. A positive WC number suggests that the firm uses long-term debt and equity to meet its daily financing needs for cash, inventory, and accounts receivables. A negative WC balance suggests an aggressive financing strategy where the firm uses short-term sources of financing (e.g., Accounts payables, short-term debt, etc.) to finance its long-term assets. As one can see, working capital involved decisions about risk and return for a firm.
Chapter 27 looks at forecasting short-term financing needs. It is very important that a firm understand what its cash flow will be in the short-term in order to adequately prepare for financing needs. The key tools used in forecasting short-term financing needs are pro forma income statements and balance sheets. This week we will explore methods to construct these pro forma statements and learn how they help firms identify financing needs in the short-term.
Analyzing Financial Performance Using the Beginning and Ending Time Periods
Financial Measures Analysis
Often when we perform a financial analysis, we will construct various financial measures and analyze them using a variety of types of comparisons. The various financial measures will provide a way to assess the income statement, balance sheet, and cash-flow statements for a firm. Once the measures are calculated, we will then to analyze them in order to draw some conclusions about the firm’s financial performance. There are several ways in which this analysis can be done:
- we might do a trend analysis and see how these measures change on a year-by-year basis over time.
- we can compare our financial measures to an industry benchmark.
- we might compare our numbers to another firm or firms in the industry.
All of these are very good methods of analysis.
In this Course
In this course, we are going to use a slightly different approach to analysis in order to see if we can evaluate a firm’s financial performance and, perhaps, identify an overriding financial strategy that the firm is using. This method is very simple: we will calculate the various financial measures for a beginning year and compare them to the same financial measures for a later year. By focusing on a beginning and ending period, we can start to identify major changes in the firm’s financing strategy. This method has the advantage of not “getting bogged down” in the year-to-year changes. Rather, the focus is on the “big picture.” What major changes and financial policies has the firm been pursuing.
Of course, no method of financial analysis is perfect. A complete financial analysis would include an industry comparison and trend analysis, as well as the end-point method. Our goal here is to learn a different approach that lends itself to understanding an overall financial strategy for a firm.
Chapter 7: Fundamentals of Capital Budgeting
Overview
Chapter 6 described the use of NPV (and some other tools) to make investment decisions. Chapter 7 demonstrates how to derive the cash flows for a given project in order to determine which projects or investments a firm should undertake. This is the most difficult and important part of the capital budgeting process.
7.1 Forecasting Earnings
The chapter teaches the concept of forecasting earnings by considering a hypothetical capital budgeting decision faced by managers of the Linksys division of Cisco. The project is called HomeNet. The issues addressed are summarized here:
- The company has already conducted a feasibility study, which cost $300,000.
- Sales are expected to be 100,000 units per year.
- The project is estimated to have a four-year life.
- It will retail for $375, with an expected wholesale price of $260.
- Engineering and design costs will be $5 million.
- Actual production will cost $110 per unit.
- Software development will require 40 software engineers at $200,000 per year, each.
- Lab facilities are already available, but will require $7.5 million of new equipment.
- The software and hardware design will be completed and the lab will be operational at the end of one year.
- At that time, HomeNet will be ready to ship.
- The company will spend $2.8 million per year on marketing and support.
- The lab equipment will be depreciated straight line over a five-year period.
- The marginal corporate tax rate is 40%.
The net income from the project is in Table 7.1 Spreadsheet. Additional issues addressed in this section of the chapter are:
- Interest income is not included—the investment decision is separate from the financing decision.
- Project externalities affect cash flows. These include cannibalization and opportunity costs.
- Sunk costs, such as the study already conducted and paid for, should not be included.
- Fixed overhead expenses should be included only if they are in addition to those that would be incurred without the project.
7.2 Determining Free Cash Flow and NPV
This section shows how to convert net income to free cash flow. Free cash flow is calculated directly by using the following formula:
Free Cash Flow = (Revenues − Costs− Depreciation)× (1−τ c )+Depreciation−CapEx−ΔNWC Unlevered Net Income Free Cash
When free cash flow is calculated for a period shorter than the horizon of the project, a terminal or continuation value must be calculated. This can be calculated as a constant growth perpetuity. That value must then be discounted back to the present, along with the remaining cash flows.
7.3 Choosing Among Alternatives
Because not launching a project produces an additional NPV of zero for the firm, launching a project is the best decision for the firm, if its NPV is positive. In many situations, however, we must compare mutually exclusive alternatives, each of which has consequences for the firm’s cash flows. In such cases we can make the best decision by choosing the alternative with the highest NPV.
7.4 Further Adjustments to Free Cash Flow
We must also consider tax carryforwards and carrybacks when calculating NPV, which allow corporations to take losses during a current year and offset them against gains in nearby years. In addition, other non-cash items, the timing of the cash flows, accelerated depreciation, liquidation or salvage value, and the terminal or continuation value must be considered when calculating NPV.
7.5 Analyzing the Project
Finally, there are several tools to analyze the project’s sensitivity to assumptions used in deriving the cash flows. Break-even analysis can be done for each input. This involves solving for the break-even level of that input—the level that makes NPV equal zero. If there is a great deal of uncertainty regarding that input, this provides valuable information. IRR is the breakeven point for the cost of capital.
The chapter summarizes sensitivity analysis and scenario analysis. These are very robust methods for identifying how sensitive a NPV calculation is to changes in the various components of the cash flows and discount rate. Various software tools make sensitive analysis relatively simple to implement.
The Appendix to the chapter provides detail regarding MACRS depreciation.
Chapter 8: Valuing Bonds
Overview
Chapter 8 examines basic types of bonds and their valuation, and relies on the Law of One Price in many discussions. It describes how bond prices change dynamically over time and when interest rates change. The chapter also examines the effect of changes in coupon payment on bond prices, and the relationship between prices and returns of different bonds, including those with default risk.
8.1 Bond Cash Flows, Prices, and Yields
Terminology is an important part of understanding bonds. The authors use zero-coupon bonds as examples in much of the chapter. Yield to maturity for a zero-coupon bond is:
P=FV(1+YTM n ) n P=FV(1+YTMn)n
Example 8.1 shows how to calculate yields for different maturities of zero-coupon bonds. The authors revisit their discussion of the yield curve from Chapter 5, renaming it the zero-coupon yield curve. Much of the remaining discussion in the chapter draws on the zero-coupon yield curve. Also note that the authors often use face values of $100 instead of $1000, making prices look more like those that are quoted in the financial press.
The yield to maturity on a coupon bond can be calculated using equation 8.5, using trial and error, or by using an Excel spreadsheet. Example 8.3 shows how to use a spreadsheet to compute the yield to maturity. Example 8.4 shows how to calculate a bond price, given its yield to maturity. Later in the chapter, the authors show how to replicate a coupon bond with zero-coupon bonds, and calculate the price in that way.
8.2 Dynamic Behavior of Bond Prices
The authors begin with a discussion of discount and premium bonds. A bond sells at a discount when interest rates today are greater than the coupon rate of the bond. A bond selling at a premium has a coupon rate that exceeds current interest rates in the market. Table 8.1 summarizes the properties of coupon bond prices.
The rest of the section examines the effect of time and interest rates on bond prices. Bond prices (PV) vary inversely with changes in market interest rates. That is, as market rates increase, bond prices will fall and as rates decrease, bond prices rise—i.e., the longer (shorter) the maturity of the bond, the greater (less) the change in the bond price for every change in bond discount rates. If the bond is sold before maturity, the seller will receive the market price which, depending on the direction of market rates since the bond was issued, will be higher or lower than face value.
Figure 8.1 shows the pattern of bond prices as they approach maturity, assuming the yield remains constant. The graph is a little different from the common illustration, in that it includes lines illustrating the actual price path of the bond between coupon payments. A box on page 221 describes clean and dirty prices.
8.3 The Yield Curve and Bond Arbitrage
This section shows how the yield curve relates to the valuation of coupon bonds. The Law of One Price dictates that the price of a coupon bond must equal the sum of the prices of a series of zero-coupon bonds. The yield to maturity can be calculated once that price is derived. In Example 8.8, the authors show the effect of changing the coupon on bond price, keeping time to maturity constant.
The authors point out that most of the time, when bond traders mention the yield curve, they’re referring to the coupon-paying Treasury yield curve; by convention, they plot the most recently issued bonds (termed on-the-run bonds).
8.4 Corporate Bonds
In this section, the authors use the two extremes of no default and certain default to show that the yield to maturity is not equal to the expected return of a defaultable bond, since we used promised cash flows to calculate the yield to maturity and expected cash flows to calculate the expected return. The authors then show how the two extremes can be used to value a bond with a risk (not a guarantee) of default. Table 8.3 summarizes the results, showing that the yield to maturity is an increasing function of risk, but that expected return is not. So: “the bond’s expected return, which is equal to the firm’s debt cost of capital, is less than the yield to maturity if there is a risk of default. Moreover, a higher yield to maturity does not necessarily imply that a bond’s expected return is higher.”
The remainder of the chapter discusses bond ratings and the corporate yield curve. Table 8.4 shows Moody’s and Standard & Poor’s bond ratings, while Figure 8.3 shows the corporate yield curves for AAA, BBB, and B compared to the Treasury yield curve. Figure 8.4 shows yield spreads between long-term corporate and Treasury bonds, and the TED spread. A brief discussion of the financial crisis appears on page 238.
Chapter 6: Investment Decision Rules
Overview
This chapter introduces techniques that firms use to evaluate investments and decide which projects to pursue, including NPV, payback period, internal rate of return, profitability index, incremental IRR, and EVA, with an emphasis on NPV.
6.1 NPV and Stand-Alone Projects
The text emphasizes NPV as the only reliable way to make capital budgeting decisions. The internal rate of return can provide a measure of the sensitivity of the NPV to changes in the opportunity cost of capital. Since the IRR is the point at which NPV equals zero, it can be used to measure the maximum estimation error in the cost of capital that can exist without changing the decision.
6.2 The Internal Rate of Return Rule
This section defines IRR and gives the IRR decision rule. The authors then discuss reasons that NPV and IRR can result in conflicting decisions. They describe how delayed investment can cause a faulty decision, and how multiple IRRs and nonexistent IRRs can happen. Example 6.1 shows NPV profiles for four projects: a normal project, a delayed investment, one with multiple IRRs, and one with nonexistent IRR.
6.3 The Payback Rule
Payback period is discussed as being easy to compute, but the procedure ignores time value of money and cash flows that occur after the payback period. Example 6.2 shows how to compute payback.
6.4 Choosing Between Projects
The previous discussion addressed only stand-alone projects. Sometimes firms must decide among mutually exclusive projects. The manager must rank the projects and choose the best one. In this case, NPV again yields the correct decision.
Suppose a project with a positive NPV is being compared with another project that is identical in all respects, except that the size is double. Then the larger project will have an NPV that is double that of the first, meaning it is clearly the better project. However, the IRRs for the two projects will be the same. Hence IRR cannot be used to evaluate mutually exclusive projects of different scales. By the same token, IRR cannot be used consistently to evaluate two projects with different timing or different risk. Example 6.3 presents four companies that have positive NPV projects. Each project can be used to discuss a different problem faced by IRR and how it’s solved using NPV.
One improvement of IRR is included here. The incremental IRR investment rule applies the IRR rule to the difference between the cash flows of the two mutually exclusive alternatives. This approach will give the same answer as NPV. However, incremental IRR still has some problems. First, the incremental IRR could not exist, or there could be several. The fact that the incremental IRR exceeds the cost of capital does not imply that the NPV of either project is positive. In addition, it is sometimes difficult to keep track of which project is the incremental project. Example 6.4 shows use of incremental IRR.
6.5 Project Selection with Resource Constraints
The previous discussion has assumed that resources are unlimited. If resource constraints exist, simply picking the highest NPV project will not always lead to the best decision. Sometimes a different combination of projects will result in a higher overall NPV. In this case, a profitability index often helps. The profitability index can be computed as follows:
Profitability Index = Value CreatedResource Consumed =NPVResource Consumed Profitability Index = Value CreatedResource Consumed=NPVResource Consumed
Note that this text treats PI a little differently than the typical text. Here, the resource constraint need not be financial. Example 6.5 shows how to use the PI with a human resources constraint.
The result of the PI calculation can be used to rank projects. In some situations, however, PI does not give an accurate answer. For example, sometimes there are leftover resources if PI is strictly applied. If projects could be found that would use only those resources, the overall NPV would improve. Also, in some cases there is more than one resource constraint. In those cases, the only way to assess the best scenario is to sort through all the possibilities. With computer-based linear programming tools, this is not as difficult as it sounds. The models developed in the Decision Science course lend themselves to solving more complex capital budgeting problems.
Chapter 9: Valuing Stocks
Overview
This chapter shows how to use the Law of One Price to compute the value of a stock. The chapter begins by discussing the dividend-discount model. Next, they use tools learned in Chapter 7 to value the firm using the discounted free cash flow model. Finally, the authors use valuation multiples. The authors conclude the chapter with a discussion of the role of competition and efficient markets in determining stock price.
9.1 The Dividend-Discount Model
The authors begin by showing that a one-period investor will be willing to pay the same price as a two-period investor. From there, they develop the dividend-discount model, showing that the price of the stock is equal to the present value of the expected future dividends it will pay, no matter the time horizon of each individual investor.
9.2 Applying the Dividend-Discount Model
The section begins with the assumption that dividends will grow at a constant rate. The constant dividend growth model is given in equation 9.6.
Po = Div1 / re – g
In the next equation (9.7), they solve for the equity cost of capital, to show that the constant growth model assumes that dividends grow at the same rate as the share price.
re = Div1 / Po + g
Since g is the same for share price as it is for dividends, the firm must increase its dividend in order for the stock price to increase. There are three ways to increase dividends: (1) increase earnings, (2) increase payout ratio, and (3) decrease shares outstanding. Suppose the number of shares outstanding is fixed. The authors show that in this case, the earnings growth rate = retention rate × return on new investment. See equations 9.8 through 9.12 for the development of this relationship. Equation 9.12 shows that a firm can increase its growth rate by retaining more earnings.
g = Retention Rate x Return on New Investment
In order to do so, it must cut its dividend, which reduces the stock price. Examples 9.3 and 9.4 show that if the firm’s investments are profitable, cutting the dividend will increase stock price.
The section continues with a discussion of changing growth rates. Example 9.4 illustrates using an Excel spreadsheet and the formulas. Finally, the authors mention the limitations of the dividend-discount model.
9.3 Total Payout and Free Cash Flow Valuation Models
The total payout method uses the present value of the dividends paid, plus share repurchase amounts divided by the number of shares outstanding, to compute share value.
The discounted free cash flow model begins by estimating the firm’s enterprise value as defined in Chapter 2 and repeated in equation 9.17. To estimate the value of the firm’s equity, we begin with free cash flow, given in equation 9.18. From there, we compute enterprise value. To solve for market value of equity, add back cash and subtract debt. Divide by shares outstanding to get stock price, as in equation 9.20. Note that the discount rate should be the weighted average cost of capital, rather than equity cost of capital, since it is the total firm value being computed. Example 9.7 shows how to compute the value of equity using free cash flow.
The authors discuss the relationship between capital budgeting and the discounted free cash flow model. Included is a summary of using sensitivity analysis for stock valuation, resulting in a range of possible stock prices. Figure 9.1 summarizes the discounted cash flow models of stock valuation.
9.4 Valuation Based on Comparable Firms
The use of comparables analysis is also based on the Law of One Price, since a new firm that is identical to an existing publicly traded company should be priced the same. The multiples discussed in this chapter are the price-earnings ratio and enterprise value multiples. Examples 9.9 and 9.10 show how firms can be valued using these multiples.
The authors discuss the limitations of multiples analysis. Table 9.1 shows the dispersion among multiples in the footwear industry. In addition, the authors point out that these are relative measures, so they don’t tell us when an entire industry is over or under valued. Figure 9.2 shows the range of valuations for Kenneth Cole Productions, using alternative valuation methods.
9.5 Information, Competition, and Stock Prices
The first part of this section discusses the fact that the only way that two investors will come up with an identical value for a given stock is if they both use the same inputs and valuation method. This seldom happens, but with many transactions occurring every day on the stock market, a market price is agreed upon.
The idea that competition among investors works to eliminate all positive-NPV trading opportunities is introduced in this section. If new information becomes available, its impact depends on whether the information is public and easily interpretable, or private, or difficult-to-interpret. If the information is public and easily interpretable, investors can trade on the information and the stock price will react very quickly. People who obtain private information or who are able to interpret difficult-to-interpret information can sometimes trade profitably on that information. These scenarios are illustrated in examples 9.12 and 9.13.
The section concludes with a brief discussion of implications for investors and corporate managers. The major consequence for investors is that there are seldom positive-NPV trading opportunities. The major consequence for corporate managers is that they should focus on raising the stock price by maximizing the present value of the free cash flow from the firm’s investments, rather than relying on accounting illusions. They should also use financial transactions, like equity offerings, to support investment in positive-NPV projects, since participants in efficient financial markets will always be willing to buy securities that are fairly priced.
Finally, the chapter distinguishes between the efficient markets hypothesis and no-arbitrage requirements. The efficient markets hypothesis states that securities with equivalent risk should have the same expected return. The efficient markets hypothesis is best viewed as an idealized approximation for highly competitive markets.
Chapter 10: Capital Markets and the Pricing of Risk
Overview
This chapter begins the discussion of risk and return. The authors begin with probability distributions and realized returns. They show that the expected return of individual stocks is higher for the amount of risk taken than it is for the portfolios typically examined. They then describe idiosyncratic and systematic risk. The CAPM is also introduced. Throughout the discussion the authors emphasize no-arbitrage conditions to explain idiosyncratic and systematic risk.
10.1 A First Look at Risk and Return
This section compares returns on several types of investment. Figure 10.1 shows the returns from a $100 investment at the end of 1925 from the world portfolio, the portfolio of small stocks, the S&P 500, Corporate Bonds, Treasury Bills, and CPI during the period 1925 to 2005. The difference in returns is dramatic—I am sure we all wish we had invested in small stocks back in 1925!
10.2 Common Measures of Risk and Return
This section introduces the probability distribution of returns and describes how mean, variance, and standard deviation are computed when the probability distribution is known. Example 10.1 shows how those values are calculated. The authors explain that, in most cases, we don’t have an explicit probability distribution, so we must use historical returns to learn about the relationship between risk and return.
10.3 Historical Returns of Stocks and Bonds
This section begins with an explanation of how to compute realized returns, including an explanation of how those returns are annualized with equations 10.4 and 10.5. Example 10.2 shows how to calculate returns using those equations for GM stock for the years 1999 and 2008. Table 10.2 summarizes realized returns for the S&P, GM, and the 3-month T-bill. Again, the differences are quite dramatic.
The section next shows how average, variance, and standard deviation are computed for realized returns. Equation 10.8 shows how variance is calculated. Example 10.3 uses data from Table 10.2 to illustrate the calculation of variance for the S&P 500. The realized returns and variances for small stocks, the S&P 500, corporate bonds, and treasury bills are summarized in Tables 10.3 and 10.4. The conclusion one reaches from reviewing this data is that the price of increased return is an increase in risk or variability.
The text then describes the estimation error faced when a sample is being used to estimate a population. Equation 10.8 shows how to calculate the standard error of the estimate of the expected return. The standard error is the standard deviation of the average return. Example 10.4 then shows how to compute a 95% confidence interval using that information. Note there is a box on page 305 that addresses the difference between arithmetic and geometric means.
10.4 The Historical Trade-Off Between Risk and Return
The section begins by discussing the excess returns of large portfolios over Treasuries. Figure10.5 plots those returns and volatilities and the authors provide some discussion in the text about the relationship that appears.
Next the returns of individual stocks are discussed. Returns and volatilities are plotted in Figure 10.6, along with the portfolios that appear in Figure 10.5. This graph shows that, even though risk and return are positively related and almost linear for the portfolios, the same is not true of individual stocks. So “while volatility seems to be a reasonable measure of risk when evaluating a large portfolio, it is not adequate to explain the returns of individual securities.”
10.5 Common Versus Independent Risk
This section explains why the risk of an individual security is different from that of a portfolio. The authors explain this concept using an insurance company example. Suppose an insurance company offered two types of insurance: theft and earthquake. If the company insures 100 houses in San Francisco, the two types of insurance will have very different risk profiles for the insurance company, since the risk of theft in any one house is independent and identically distributed, while the risk of earthquake is not. The authors use this example through the remainder of the chapter to illustrate idiosyncratic risk (theft) and systematic risk (earthquake). This example also illustrates the risk and return trade-off, as well as the principle of diversification. Example 10.5 shows how casinos make a profit on roulette wheels, and why some casinos place limits on the amount of any individual bet.
10.6 Diversification in Stock Portfolios
The authors begin with two extremes: companies (firm S) with no idiosyncratic risk and companies (firm I) with no systematic risk. Figure 10.8 shows how volatility declines with the size of the portfolio for type S and I firms. The volatility of the portfolio does not change with an increase in the number of firms for type S firms. For type I firms, as more firms are added to the portfolio, volatility declines. This example explains why, in Figure 10.6, the S&P 500 had so much lower volatility than any of the individual stocks.
Now consider only type I firms. The authors describe how investors who hold a large portfolio of type I firms could diversify away (nearly) all the risk of the portfolio, since the firms have only idiosyncratic risk. This concept is illustrated in Figure 10.7. Hence, in an efficient market, the portfolio must earn the risk-free rate. Otherwise, there would be an arbitrage opportunity. From this we conclude that “the risk premium for diversifiable risk is zero, so investors are not compensated for holding firm-specific risk.” Also, “the risk premium of a security is determined by its systematic risk and does not depend on its diversifiable risk.” This insight also provides an answer for the second puzzle in Figure 10.6; volatility is not a good measure of risk for an individual security. Example 10.6 shows volatility for ten type S firms versus ten type I firms. There is a box on page 314 that describes diversification benefits during market crashes.
10.7 Measuring Systematic Risk
In order to estimate the expected return, we must first measure the investment’s systematic risk, then determine the risk premium required to compensate for that amount of systematic risk. The authors introduce the idea of efficient portfolios. An efficient portfolio is one that offers the highest return for the level of risk—that is, there is no way to reduce the risk of the portfolio without lowering its expected return. The market portfolio is an efficient portfolio. They do not develop the computation for beta in this chapter—they do that in Chapter 12. Here, they simply define beta as “the expected percent change in the excess return of a security for a 1% change in the excess return of the market portfolio.”
In Example 10.8, the authors show how to estimate beta from type S and type I firms. Table 10.6 shows betas with respect to the S&P 500 for individual stocks from a number of different industries.
10.8 Beta and the Cost of Capital
In this section, the authors show how the CAPM can be used to calculate the cost of capital for a firm or project. This is done using the following relationship:
rI = Risk-Free Interest Rate + ß x Market Risk Premium
They begin by estimating the risk premium for the market, then for the investment. Example 10.9 shows how to estimate expected returns for type S firms.
Chapter 12: Estimating the Cost of Capital
Overview
This chapter introduces the additional assumptions of the Capital Asset Pricing Model and describes the CAPM. The CAPM forms the foundation of pricing risk for equity securities.
12.1 The Equity Cost of Capital
This section reviews the use of the CAPM’s SML for cost of equity estimation. The SML is the relationship developed in Chapter 10 to estimate the cost of capital of an investment from its beta. Example 12.1 shows two companies with their volatility and beta estimates, contrasting the two. The company with a higher beta (Google) has a higher cost of equity capital (than UPS) even though it has a lower volatility.
12.2 The Market Portfolio
This section shows how a value-weighted portfolio is constructed. Further, it describes common market indexes and their weighting schemes. A call-out box shows how a value-weighted portfolio is passive, so that no rebalancing is required. The ability to invest in market indexes using index funds or ETFs is also discussed. The section also describes common choices for the market risk premium and the risk-free rate. Finally, the authors show how dividend yield and expected growth rate can be used to estimate the expected return on the market.
12.3 Beta Estimation
This section describes the use of historical returns to calculate beta. Figure 12.1 shows monthly returns for Cisco stock and the S&P, while figure 12.2 shows the scatterplot of those returns and discusses the “eyeball” estimate of the beta. The final part of the chapter describes the use of linear regression to estimate beta. Example 12.2 illustrates calculation of 95% confidence intervals for beta.
In practice, there are a number of sources that estimate beta—e.g., Yahoo Finance, Valueline, Morningstar, etc. It is logical that the estimates of beta will vary, depending upon the source due to differences in the timeframe, data (monthly, quarterly), and choice of market index proxy.
12.4 The Debt Cost of Capital
This section discusses main methods for estimating debt cost of capital—i.e., the cost of capital that a firm must pay on its debt. The most common method for doing so is to use the company’s yield to maturity on existing debt. However, as the authors show, in the presence of default risk, the YTM is overstated. Example 12.3 shows a method for adjusting the YTM when a high degree of default risk is present.
A second way to calculate debt cost of capital is to use the debt beta. However, debt betas are hard to find so we can approximate them using bond rating, whose average betas are shown in Table 12.3. Chapter 21 develops a method for estimating debt betas from stock price data.
12.5 A Project’s Cost of Capital
Calculating the project cost of capital can be done using all-equity comparable firms (Example 12.4). In this approach, the equity beta and cost of capital of comparable or similar firms is used as an estimate or proxy for the cost of capital of the project.
A second approach is to use levered firms and removing the effects of leverage to arrive at the asset beta. The unlevered cost of capital can be calculated as the weighted average of the equity and debt costs of capital.
Asset or Unlevered Cost of Capital
ru = E /E + D (rE) + D / E + D (rd)
Asset or Unlevered Beta
ßU = E / E + D (ßE ) + D / E + D (ßD)
Example 12.5 illustrates the use of these concepts. Example 12.6 shows the effect of excess cash on the unlevered beta. Holding cash is equivalent to having a amount of negative debt. A final estimate for a project’s beta is the industry average asset beta.
12.6 Project Risk Characteristics and Financing
This section of the chapter discusses the differences in market risk across projects within a firm due to differences in operating leverage. Operating leverage is the relative proportion of fixed versus variable costs in a firm. It then introduces financial risk and adds the effect of debt financing to the unlevered cost of capital equation, resulting in the weighted average cost of capital. Equations 12.13 and 12.13 give alternative ways to calculate the WACC. Example 12.9 illustrates.
rWACc = E /E + D (rE) + D / E + D (rd) (1-τC)
12.7 Final Thoughts on Using the CAPM
The CAPM uses several assumptions and approximations. This section discusses its reliability. The authors offer several thoughts on this. First, the types of approximations used to estimate cost of capital are the same as those used to estimate cash flows, but have far less impact on project value than errors in the estimates used for cash flows. Second, the CAPM is practical, straightforward, and very robust. Third, the CAPM imposes a disciplined process on managers with little room for manipulation without justification. Finally, the CAPM gets managers to think about risk correctly. The Appendix discusses practical considerations when forecasting beta, including the time horizon, the index, the method used to extrapolate from past to future betas, and the treatment of outliers in the data.
Chapter 14: Capital Structure in a Perfect Market
Overview
In this chapter, the capital structure decision is examined in a setting of perfect capital markets in which all securities are fairly priced, there are no taxes or transactions costs, and the total cash flows of the firm’s projects are not affected by how the firm finances them.
14.1 Equity Versus Debt Financing
Table 14.1 presents a risky project that can be financed completely with equity, or with a portion of debt and the remainder in equity. Table 14.2 shows the return shareholders would get with equity alone under polar opposite economic scenarios—strong economy and weak economy. The expected return is 15%.
Next, the authors examine the case where the firm can raise part of the funding using debt. Modigliani and Miller discovered that the value of the firm in that situation would be the same as under the equity scenario, because of the increased riskiness of the firm’s equity. Table 14.5 illustrates this point, showing the increase in the risk premium on equity. As this example shows, leverage increases the risk of equity even when there is no default risk. Shareholders must be compensated for this increased risk—hence the increase in the risk premium.
14.2 Modigliani-Miller I: Leverage, Arbitrage, and Firm Value
This section shows how MM relates to the Law of One Price. A major result of MMs work is Proposition I:
MM Proposition I: In a perfect capital market, the total value of a firm is equal to the market value of the total cash flows generated by its assets and is not affected by its choice of capital structure.
Proposition I follows from the fact that, as long as the firm’s choice of securities does not change the cash flows generated by its assets, this decision will not change the total value of the firm or the amount of capital it can raise.
Table 14.6 shows how individuals can replicate levered equity using homemade leverage. Homemade leverage exists when investors use debt in their own portfolios to adjust the leverage decisions made by firms. Table 14.7 shows how investors can replicate unlevered equity by buying both the debt and equity of the firm.
The market value balance sheet is introduced, so that market value of equity is defined as market value of assets—market value of debt and other liabilities. The market value balance sheet includes all assets and liabilities—both tangible and intangible—and values them at current market values, rather than at historical costs.
The section also shows a leveraged recapitalization as an application of the preceding arguments.
14.3 Modigliani-Miller II: Leverage, Risk, and the Cost of Capital
This section begins with Proposition I and shows Proposition II.
MM Proposition II: The cost of capital of leered equity increases with the firm’s market value debt-equity ratio.
That is, the cost of capital of levered equity is equal to the cost of capital of unlevered equity plus a premium that is proportional to the market value debt-equity ratio.
The unlevered cost of capital (pretax WACC) is given in equation 14.6. As Figure 14.1 shows, the weighted average cost of capital is independent of capital structure. Figure 14.1 also has a data table that corresponds to the text example, showing there is no change in cost of capital.
Unlevered Cost of Capital (pretax WACC)
rU=( % of equity financing)rE + (% of debt financing)rD
rU = E / E + D(rE) + D / E + D (rD)
Equation 14.8 shows the unlevered beta as a weighted average of the equity beta and the debt beta. The authors solve for the equity beta in 14.9.
14.4 Capital Structure Fallacies
This section examines two incorrect arguments that are sometimes cited in favor of leverage: leverage increases equity value because it increases earnings per share, and issuing new equity results in dilution. First, although leverage often increases earnings per share, it also increases the risk of the equity. Example 14.9 illustrates this concept. Second, the authors show that, as long as shares are sold at a fair price, there is no such thing as dilution.
14.5 MM: Beyond the Propositions
The MM propositions were important in the field, not just for their findings, but for the way in which they taught finance researchers to reason. Proposition I was one of the first arguments to use the Law of One Price. The authors cite an excerpt from John Burr Williams’ 1938 book. They apply the concepts from that chapter to a conservation of value principle that states, “With perfect capital markets, financial transactions neither add nor destroy value, but instead represent a repackaging of risk.”
Chapter 15: Debt and Taxes
Overview
The motivation for this chapter is empirical observation of corporate capital structure. In particular, if capital structure is unimportant, why do we see consistent differences in capital structure across firms and industries? Also, why do managers spend time thinking about capital structure if it’s irrelevant?
This chapter focuses on the impact of taxes on the capital structure decision. The first part considers the benefits of debt in the presence of corporate taxes. Later, personal taxes are included to show their effect on the capital structure choice.
15.1 The Interest Tax Deduction
In this section the authors show the value of the interest tax shield. The interest tax shield is the additional amount that a firm would have paid in taxes if it did not have leverage. The interest tax shield is calculated as:
Interest Tax Shield = Corporate Tax Rate X Interest Payments
15.2 Valuing the Interest Tax Shield
This section of the chapter shows how to calculate the value of the levered firm.
The total vlue of the levered firm exceeds the value of the firm without leverage due to the present value of the tax savings from debt.
VL = VU + PV (Interest Tax Shield)
This formula (15.2) is a general formula—Example 15.2 shows the calculation for risk-free ten-year maturity debt. The analysis is extended to permanent debt with Equation 15.4.
Value of the Interest Tax Shield of Permanent Debt
PV of Tax Shield = τc x D
The authors then show the effect of taxes on the weighted average cost of capital, so that risk can be incorporated into the analysis.
Weighted Average Cost of Capital (After Tax) = Pretax WACC – Reduction Due to Interest Tax Shield
rWACC = E / E + D(rE) + D / E + D (rD)(1- τc)
15.3 Recapitalizing to Capture the Tax Shield
The authors first compute the value of the levered firm, then subtract the debt value to show the new value of equity. If the stock is repurchased at its pre-recapitalization rate, then the stock price will increase. The authors then use an arbitrage argument to explain that the company will not be able to repurchase at the previous price, and show how to calculate the new price. They conclude that, “When securities are fairly priced, the original shareholders of a firm capture the full benefit of the interest tax shield from an increase in leverage.”
Finally, the authors show how the leveraged recapitalization impacts the market value balance sheet in Table 15.2.
15.4 Personal Taxes
This section includes the consequences of the combination of personal and corporate taxes. Table 15.3 shows top federal tax rates in the United States over the last 34 years. Figure 15.3 is a visual aid to understanding how taxes are paid, so that Equation 15.7 can be derived fairly easily. Figure 15.4 shows the effective tax advantage of debt with and without personal taxes.
Equation 15.8 shows the adjustment that must be made in calculating the value of the levered firm in the presence of personal taxes. The final part of the section provides a discussion of the assumptions made to derive the results, and the impact of changes in those assumptions.
15.5 Optimal Capital Structure with Taxes
Figure 15.5 shows net external financing and capital expenditures by U.S. Corporations from 1975-2005. This chart indicates that most companies raise external capital using debt. However, market value of equity continues to increase as firms retain earnings, so that the market value debt to equity ratio is about 36% on average. Figure 15.7 shows debt as a fraction of firm value by industry and for the market. It is clear that there are large differences across industries.
There are several explanations for this difference. First, in order to receive tax benefits, a company must pay taxes. Table 15.4 shows that the optimal level of interest to pay, from a tax perspective, is the amount equal to EBIT. The consequences of regularly incurring interest charges that exceed EBIT are discussed in Chapter 16. When EBIT is uncertain, the tax savings declines for high levels of interest, as shown in Figure 15.8.
Growth will affect the optimal leverage ratio, even for firms with positive earnings. The higher the firm’s growth rate, the lower will be the optimal proportion of debt in the capital structure. In addition, when firms have other tax shields, taxable earnings will be reduced without incurring interest payments.
The chapter concludes with a discussion of the actual levels of leverage and interest as a percent of EBIT for U.S. companies. The conclusion is that, both in the United States and internationally (as shown by Table 15.5), firms tend to be under-leveraged. This observation motivates the discussion of costs of financial distress in Chapter 16.
Chapter 17: Payout Policy
Overview
This chapter shows that payout policy has similar constraints and motivations as capital structure. Dividend policy is shaped by market imperfections, such as taxes, agency costs, transaction costs, and asymmetric information, just as capital structure is. The chapter discusses why some firms pay dividends and some do not, and why some firms prefer share repurchases.
17.1 Distributions to Shareholders
This section describes the payment process for dividends. In addition, the authors briefly touch on stock splits and stock dividends, as well as special and liquidating dividends. The alternative processes for share repurchase (open market, tender offer, and targeted repurchase) are also described.
17.2 Comparison of Dividends and Share Repurchases
This section introduces a hypothetical company with a large amount of cash that will increase substantially and permanently in the next year. There are three alternative forms of payout: (1) pay a dividend, (2) repurchase shares, and (3) issue equity to pay a high dividend in order to keep the dividend payment steady. The analysis shows that, in a setting of perfect capital markets, there is no difference among the three alternatives. Table 17.1 shows the Modigliani and Miller Irrelevance theorem.
17.3 The Tax Disadvantage of Dividends
Because dividends are generally taxed at a higher rate (in the United States) than capital gains, dividends are tax disadvantaged. In fact, issuing equity to pay dividends returns shareholders less money than they put in.
Figure 17.4 shows the declining use of dividends over the past 30 years, and an increasing use of repurchases. Most notable is the trend away from any sort of dividend payout.
17.4 Dividend Capture and Tax Clienteles
This section quantifies the combined effects of dividend and capital gains taxes. Equation 17.3 gives the effective dividend tax rate. This rate will differ across investors. This section considers four different factors affecting investors—including income level, investment horizon, tax jurisdiction, and type of investor or investment accounts—and calculates the effective dividend tax rate for each. Table 17.3 summarizes payout preferences among different types of investor.
The dividend-capture theory states that absent transaction costs, investors can trade shares at the time of the dividend so that non-taxed investors receive the dividend. An implication of this theory is that investors in low tax brackets buy the stock just before the ex-dividend date to collect the dividend, then sell the stock shortly after. This contention is empirically supported by the observed increase in volume at that time.
17.5 Payout Versus Retention of Cash
This section explains how firms choose the amount to pay out to shareholders. It starts out with the Modigliani and Miller (1961) finding that, in perfect capital markets, the choice of payout versus retention is irrelevant. In reality, though, the firm must pay taxes on earnings from the funds retained; therefore, it is generally better to pay the funds out. Example 17.5 gives an example of the tax disadvantage to cash, while 17.6 shows the example in the context of Microsoft’s special dividend.
There are, however, issuance and financial distress costs if the firm pays out the funds that it could have used later. There are also agency costs associated with retaining cash, as discussed in Chapter 16, that arise if managers are tempted to spend excess cash on inefficient investments and perks. Firms should choose to retain cash for the same reasons as they use low leverage—to preserve financial slack.
17.6 Signaling with Payout Policy
Firms seldom vary the size of their dividend (they smooth dividends). If this is the case, then dividend choice will contain information regarding expectations of future earnings. This dividend signaling is similar to the use of leverage described in Chapter 16. Specifically, dividend changes may reflect managers’ views about a firm’s future earnings prospects.
Share repurchases may also signal information to the market. However, there are several differences between repurchases and cash dividends. First, the actual amount spent may be far less than the amount promised, and it may take several years to finish. Second, firms do not smooth repurchase activity. Third, the cost of a share repurchase depends on the market price of the stock. Because repurchasing shares that are overvalued is a negative-NPV project, managers who do a repurchase are signaling that their stock price is undervalued.
17.7 Stock Dividends, Splits, and Spin-Offs
The chapter closes with a definition of stock splits and dividends. The authors attempt to answer the question about why firms split their stock. They conclude that the goal is to keep the stock price within a range that will allow investors to more easily trade the stock, since fractional ownership of shares is not allowed. Figure 17.8 shows the distribution of stock prices in April of 2005.
Spin-offs are a different type of distribution. The company issues shares in a subsidiary in place of a special dividend. This action avoids transaction costs of paying dividends and the special dividend is not taxed as if it were cash. Instead, investors pay capital gains tax when they sell shares.
