## Proof Using Derivatives from Calculus

To show that the covariance is a marginal variance, add m, per dollar invested in the portfolio, of stock k to the portfolio and finance this purchase by borrowing m of a risk-free security with return rf which, being risk free, has zero variance and a zero covariance with the portfolio. If, prior to the addition of stock k, the portfolio had return Rp, the new portfolio return, R, is where rf is the risk-free return. Because the risk-free return is constant and has no effect on the variance,...

## What Are the Long Term Returns of IPOs

A series of papers Ritter (1991), Loughran, Ritter, and Rydqvist (1994), and Aggarwal and Rivoli (1990) have shown that the long-term return to investing in IPOs is surprisingly low. Examining the shareholder return to owning a portfolio of IPOs for up to five years after the companies went public, these studies find annual returns to be in the range 14This discussion is based on recent papers by Sherman (2001) and Ljungvist, Jenkinson, and Wilhelm (2000). Exhibit 3.5 Average Initial Returns of...

## Example 125 Creating Value by Rejecting a Positive NPV Project

Acme Industries is considering building a plant. After an initial investment of 100 million, the plant will be completed in one year and then have the series of annual cash flows shown in Exhibit 12.5. Acme's managers can decide to immediately invest the 100 million, or they can wait until next year to decide whether to build or not. If the project is built immediately, panel A in Exhibit 12.5 shows that after a year of startup procedures, next year's cash flow will be 10 million, but a...

## Exhibit 102 Net Present Value for Cash Flows in Example 1012 as a Function of Discount Rates

350 Part III Valuing Real Assets The previous material illustrated problems that arise with the internal rate of return method because of multiple internal rates of return in some cases and none in others. Additional problems exist when the term structure of riskless interest rates is not flat. In this case, there is ambiguity about what the appropriate hurdle rate should be. In general, long-maturity riskless bonds have different yields to maturity than short-maturity riskless bonds, implying...

## Implications of the Modigliani Miller Theorem for Hedging

To understand why a firm like Intel would want to change its risk exposure, we must first return to the Modigliani-Miller Theorem (see Chapter 14). This theorem states that in the absence of taxes and other market frictions, the capital structure decision is irrelevant. In other words, financial decisions cannot create value for a firm unless they in some way affect either the firm's ability to operate its business or its incentives to invest in the future. The Modigliani-Miller Theorem was...

## Allocating Capital and Corporate Strategy

After reading this chapter, you should be able to 1. Identify the sources of positive net present value. 2. Implement the real options approach to value projects, the options inherent in mines and vacant land, and the options to wait or to expand a project. Know the effect of these options on a firm's choice to diversify and select different production techniques from its competitors. 3. Use the ratio comparison approach to value real assets, and in the case of price earnings ratios, how to...

## The Costs of Going Public

It costs a lot of money to go public. An obvious cost is hiring an investment banker, attorneys, and accountants, but by far the largest expense is the underwriting fee. As Exhibit 1.7 in Chapter 1 shows, the total direct costs associated with taking a firm public are about 11 percent of the amount of money raised. While direct costs may be large, there exists an additional and equally important cost of going public. The price at which the investment banker sells the issue to the original...

## The Effect of Leverage on Price Earnings Ratios

To use the price earnings ratio method to make capital allocation decisions, it also is important to understand how leverage affects a firm's net income per share (EPS) and, consequently, its price earnings ratio. As this chapter will demonstrate shortly, an increase in leverage, holding the firm's operations and total value constant, will increase or decrease the firm's net income per share and price earnings ratio, depending on the relative sizes of the price earnings ratio and the reciprocal...

## How Chapter 11 Bankruptcy Mitigates Debt Holder Equity Holder Incentive Problems

This section discusses how some of the problems that arise because of the debt holder-equity holder conflict can be mitigated in a Chapter 11 bankruptcy. Consider again Lily Pharmaceuticals, described in Exhibit 16.1, which passed up a positive NPV investment because of the debt overhang problem. Recall that firms suffer from debt overhang when they have a substantial amount of existing debt with protective covenants that prevent them from issuing additional debt that is senior to the existing...

## The Cross Sectional Relation between Dividend Yields and Stock Returns

If a firm's dividend policy is determined independently of its investment and operating decisions, the firm's future cash flows also are independent of its dividend policy. In this case, dividend policy can only affect the value of a firm by affecting the expected returns that investors use to discount those cash flows. For example, if dividends are taxed more heavily than capital gains, then, as noted earlier, investors must be compensated for this added tax by obtaining higher pretax returns...

## How Dividend Policy Affects Expected Stock Returns

We have asserted that share repurchases provide a better method of distributing cash than dividends because most investors prefer capital gains income to an equivalent dividend taxed at a higher rate. Stocks with higher dividend yields, to compensate investors for their tax disadvantage, should thus offer higher expected returns than similar stocks with lower dividend yields. Firms with higher dividend yields, but equivalent cash flows, should then have lower values, reflecting the higher rates...

## How Taxes Affect Dividend Policy

Personal taxes on dividends can profoundly affect a firm's choice between paying dividends and repurchasing shares. Because the pretax proceeds from both strategies are equal, the only difference between the two methods of cash distribution is the amount of the tax liability generated by each. The Tax Disadvantage of Dividends. Exhibit 15.4 details the immediate tax consequences to an individual investor, if a firm chooses to distribute 100 million in the form of a dividend versus distributing...

## Exhibit 152 Selected Dividend Yields and Payout Ratios 1993 and 1999

Dividend Yield Payout Ratio Dividend Yield Payout Ratio Dividend Yield Payout Ratio Dividend Yield Payout Ratio Note These ratios were calculated with data taken from COMPUSTAT. Note These ratios were calculated with data taken from COMPUSTAT. The Miller-Modigliani Dividend Irrelevancy Theorem In their classic article, Miller and Modigliani (1961) examined a firm that wanted to distribute a fixed amount of cash to its shareholders either by repurchasing shares or by paying a cash dividend. The...

## Intuition for Hedging with a Maturity Mismatch in the Presence of a Constant Convenience Yield

We summarize the results of this section as follows Result 22.2 Long-dated obligations hedged with short-term forward agreements need to be tailed if the underlying commitment has a convenience yield. The degree of the tail depends on the convenience yield earned between the maturity date of the forward instrument used to hedge and the date of the long-term obligation. When hedging with futures, a greater degree of tailing is needed (see Result 22.1). Result 22.2 derives from the fact that a...

## Example 119 Valuation with the Risk Free Scenario Method

The McGirwin Company is evaluating a project with a one-year life that has an uncertain cash flow at the end of the first year. Its managers estimate that the project will generate a cash flow of 100,000 at the end of year 1 under a scenario where all securities are expected to earn the risk-free return of 5 percent per year. What is the present value of this risky project For what costs should the project be accepted or rejected Answer 100,000 is the certainty equivalent of the future cash...

## Sources of Takeover Gains

Section 20.2 categorized takeovers according to the sources of takeover gains. This section examines the various sources in more detail. Result 20.1 summarizes the four main sources of takeover gains that were discussed briefly. Result 20.1 The main sources of takeover gains include We discuss each of these sources in turn. Tax laws change substantially from year to year and differ from country to country. As a result, we can provide only a brief overview of the relevant tax issues in this...

## Changes in Corporate Governance

A number of changes took place between the mid-1980s and the early 1990s that made managers more responsive to the interests of shareholders. These include a more active takeover market, an increased usage of executive incentive plans (e.g., stock options) that increase the link between management compensation and corporate performance, and more active institutional shareholders (for example, CALPERS) who have demonstrated a growing tendency to vote against management.4 The active role of...

## The Investment Choices Managers Prefer

An important premise of this chapter is that there are significant benefits associated with controlling a large corporation, and that top executives prefer investments that enhance and preserve those benefits. As discussed below, a firm's investment choice can affect control benefits in a number of ways. 10The authors of this study noted that, in many cases, individuals purchase large blocks of shares in closed-end funds and improve the fund's value either by forcing managers to liquidate the...

## Accounting Implications of the Financing of a Merger or an Acquisition

If a merger is financed with an exchange of stock, it may qualify for pooling of interests accounting treatment. This means that the items on the balance sheets of the two firms are added together, and the merged firm's reported income would simply be the sum of the income of the two separate firms. For example, if Alpha has a book value of 3 million and Beta has a book value of 2 million, then the merged firm, AlphaBeta, will have a book value of 5 million. If an acquisition is made with cash,...

## Example 98 Computing the Value of a Complex Perpetuity

What is the value of a perpetuity with payments of 2 every half-year commencing one-half year from now if r 10 percent per year Answer Examine the cash flows of the payoffs, outlined in the following table This can be viewed as the sum of two perpetuities with annual payments, outlined below Perpetuity 2 is worth 2 r or 20. The first perpetuity is like the second perpetuity except that each cash flow occurs one-half period earlier. Let us discount the payoffs of perpetuity 1 to year .5 rather...

## Operating Leases and Capital Leases

As Chapter 2 discussed, an operating lease is an agreement to obtain the services of an asset for a period that generally represents only a small part of the asset's useful life. For example, one might lease a car for three years. At the end of this period, the lease may or may not be extended. In a financial lease (also known as a capital lease), the lease agreement extends over most of the asset's useful life. The decision to enter into an operating lease generally relates to the transaction...

## Exhibit 162 Applied Textronics Cash Flows

Year 2 40 million 60 million in favorable state To illustrate this possibility, consider the case of Applied Textronics, which has debt obligations that are due both next year and in two years. The firm has a debt obligation of 100 million due next year and 40 million due the following year. The firm is considering two equally costly mutually exclusive projects A short-term project that generates positive cash flows next year and zero cash flows thereafter. A long-term project with positive...

## Relaxing the Modigliani Miller Assumptions

To understand why firms hedge, we must reevaluate the assumptions underlying the Modigliani-Miller Theorem and ask which assumptions are likely to be unrealistic. Our method for understanding why firms hedge is thus similar to the method employed in Chapters 14 through 19 to understand the firm's capital structure choice, and we draw heavily from the analysis in those chapters. The assumptions of the theorem imply that investors as well as corporations have access to hedging instruments with no...

## Financial Synergies

A common argument in support of diversification is that lowering the risk of a firm's stock increases its attractiveness to investors and thereby reduces the firm's cost of capital. However, both the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT) suggest that investors are unlikely to be willing to pay a premium for the reduced risk of a diversified firm, since they can easily form a well-diversified portfolio on their own by holding the stocks of a number of...

## How Does Hedging Increase Expected Cash Flows

The rest of this chapter will examine various ways that firms can increase their expected cash flows by implementing risk management programs. The primary benefits of hedging are related to taxes and to other market frictions discussed in Parts IV and V. Specifically, we will discuss the following benefits associated with hedging 1. Hedging can decrease a firm's expected tax payments. 2. Hedging can reduce the costs of financial distress. 3. Hedging allows firms to better plan for their future...

## Exhibit 145 Debt Equity Trade Offs for a Distribution Company and a Pharmaceutical Company

Return to new shareholders (10 of 14,000) Tax shields subtracted earlier for tax purposes Cash flows available to original shareholders When evaluating whether to issue debt or equity, the firms take into account the following information Therefore, rD (12 ) > E (10 ) > (1 - Tc)rD (7.92 ). Exhibit 14.5 illustrates how the capital structure choices of Prodist and Pharmcorp affect the cash flows to the original shareholders of each firm, assuming that the firms held no previous debt. Exhibit...

## Exercises

Small firms currently hedge less than large firms. Why is this Do you expect smaller firms to start hedging more in the future Explain. 21.2. Why is it harder to hedge currency risks in countries with volatile inflation rates 21.3. Whistler Resorts is a Canadian ski resort just north of Vancouver, British Columbia. Discuss the resort's exposure to exchange rate risk. 21.4. It is now much easier to hedge risks than it was in the past. How should this affect a firm's optimal capital...

## Adverse Selection Theory

Consider a health insurance company offering two different policies. One policy is very expensive, but it pays 100 percent of all of your medical bills. The second policy is much less expensive, but it pays only 80 percent of your medical bills. How do you expect individuals to choose between the two policies Most economists predict that individuals will not randomly select between the policies. Rather, we will observe what economists call adverse selection. In the health insurance example,...

## Debt and Predation

A firm's leverage ratio will also affect the strategies of its competitors. Specifically, a highly leveraged firm might be especially vulnerable to predation from more conservatively financed competitors.15 In other words, a competitor might purposely lower its prices in an attempt to drive the highly leveraged firm out of business. This could be to the competitor's advantage in the long run if doing so bankrupts its more highly leveraged rival forcing it to exit the market. 15Bolton and...

## The Effect of Inflation on the Tax Gain from Leverage

Recall that the last part of equation (14.5b) had an expression for the yearly savings associated with increased leverage. Note that r D (1 - TD) - (1 - Tc)(1 - TE) , the tax gain, increases as the interest rate on corporate debt increases. Although interest rates for corporate borrowers can change for a number of reasons, the most notable cause is a change in the expected rate of inflation. If investors expect inflation to be high, nominal borrowing costs will also be high, reflecting the...

## Defining and Interpreting Convexity

Convexity is a measure that determines how secure an investor should feel about a perfectly hedged portfolio (for example, whether an electronic feed of bond prices requires constant monitoring or whether the investor can relax and do other things). If the convexity of a hedged portfolio is zero, even fairly large changes in interest rates over a short time span should not alter the value of the portfolio drastically. If the convexity is large, constant monitoring of the bond prices might be a...

## Formulas Relating Duration to DV01

The relation between duration and DV01 is straightforward if the 01 in DV01 is defined as a continuously compounded rate. In this case, DV01 is the product of -.0001 and the derivative of the value of the bond with respect to a shift in the bond's continuously compounded yield that is Equation (23.6) implies that duration is the derivative of the percentage change in the value of the bond with respect to the (continuously compounded) yield to maturity that is Solving either of the last two...

## Example 146 The Effect of Corporate Taxes and Personal Taxes on the Tax Gain from Leverage

In 2000 the maximum personal income tax rate was 40 percent, the maximum corporate tax rate was 35 percent, and the rate on capital gains was 20 percent. Using these tax rates, what is the tax gain from leverage Answer From equation (14.6) Tg 1 - (.65 X .8) .6 .133. The preceding example illustrates that personal taxes can significantly reduce the tax advantage of debt. Tg will be further reduced if one accounts for the fact that capital gains can be deferred as well as taxed at a rate lower...

## Example 122 Valuing a Copper Mine with a Shutdown Option

Penny Copper Mining's Brazilian mine will produce 75 million pounds of copper one year from now if economic conditions are favorable. Penny's managers forecast two possible outcomes for copper prices then 0.50 per pound if demand is low and 0.90 per pound if demand is high. The year 1 forward price is currently 0.60 per pound, implying that a forward contract has a negative future cash flow of - 0.10 per pound next year if demand is low and a positive future cash flow of 0.30 per pound if...

## How an Individual Investor Can Undo a Firms Capital Structure Choice

The proof of the Modigliani-Miller Theorem described in the last section implicitly assumes that firms with identical cash flows but different capital structures exist. An alternative interpretation of the Modigliani-Miller Theorem is that, under its assumptions, a firm's shareholders are indifferent to a change in its capital structure. This is illustrated in Example 14.2. 2Chapters 16-19 examine how the financing mix affects a firm's investment choices and the efficiency of its operations....

## Example 232 Estimating Bond Price Changes with DV01

Its yield is currently 8.0 percent. Estimate the change in the value of the bond position if the yield drops to 7.9 percent. Answer Using equation (23.2), a drop of 10 basis points gives a price increase of Note from equation (23.2) that if the DV01 is zero, the change in the price for a small change in yield is zero. We will discuss how to use this insight for interest rate hedging shortly. DV01s of Various Bond Types and Portfolios Bonds with long maturities...

## The Dollar Value of a One Basis Point Decrease DV01

Once corporate managers have measured the interest rate risk exposure of a corporation or project, they can reduce the risk exposure of equity holders by acquiring or issuing bonds, the values of which move in an opposite direction from the value of the corporation or project as interest rates change. To implement a strategy like this, the financial manager needs to acquire familiarity with the tools of interest rate risk management. One of the most important tools for understanding the...

## Exhibit 167 Liquidation Proceeds for Emruss

Hence, if the firm were financed entirely with equity, equity holders would choose to have the firm liquidated immediately. Emruss's capital structure consists of both debt and equity. The debt, described in Exhibit 16.6, includes a 1,000,000 senior debt obligation due next year with a 150,000 coupon payment due immediately. In addition, Emruss has borrowed money from a venture capitalist to whom it owes 200,000 which is due next year. The debt to the venture...

## Example 1018 Multiple IRRs from Mutually Exclusive Projects

Reconsider Example 10.6, where NASA must select one of three commercial projects for the next space shuttle mission. Each of these projects has industrial spin-offs that will pay off in the next two years. The cash flows, net present values, and internal rates of return of the projects are described on the following page. Answer The net present value criterion indicates that project B is the best project, even though it has the lowest IRR. The internal rate of return criterion fails because the...

## Assumptions Sales Expenses Financing Dividends and Interest Rates

Most important number in your list of assumptions is the sales forecast, since this will drive many of the other items on the income statement and the balance sheet. There is no one method of sales forecasting that is right for all firms. A good analyst looks not only at trends based on past performance but also examines the firm's plans for future products, the competitive position of the firm relative to its competitors, and general trends affecting the industry such as the attraction of...

## How the Costs Imposed on Stakeholders Affect the Capital Structure Choice

To understand why nonfinancial stakeholders are concerned about a firm's financial health, it is first important to understand why there might be a connection between the firm's financial health and the decisions a firm might make that affect its stakeholders.3 Consider first the firm's liquidation decision. 3The arguments in this subsection are based on the theoretical work in Titman (1984). Chapter 17 Capital Structure and Corporate Strategy The Connection between Bankruptcy and Liquidation....

## Growth Opportunities Are Usually the Source of High Betas

The previous subsection observed that when a firm's value is largely generated by its perceived ability to develop new profitable projects more commonly referred to as growth opportunities or growth options, one must be cautious about using it as a comparison firm for a project, even one of its own. Consider Wal-Mart, for example. The value of this firm's assets can be regarded as the value of the existing Wal-Mart outlets in addition to the value of any outlets that Wal-Mart may open in the...

## The Junk Bond Market and Financial Innovation

The junk bond market also has been a driving force for innovative security design. Once the junk bond market took off, many innovations followed. Instead of straight bonds with high coupons, firms began to issue bonds with special features and embedded options. Thus, they created Zerfix bonds (short for zero and fixed coupons), a deferred coupon bond that consisted of an initial zero coupon followed by a fixed coupon after three to seven years. Zerfix bonds were intended to help the issuing...

## Incentives Information and Corporate Control

Up to this point, we have explored financial strategies that firms can employ to enhance the value of their shares. In reality, however, financial managers do not always make the decisions that maximize the stock prices of their firms. To understand how financial decisions actually are made, we have to understand how managerial incentives can differ from shareholder incentives. Part V takes a closer look at how managers actually make financial decisions. Chapter 18 examines managerial...

## What Determines a Managers Incentive to Be Shortsighted

The tendency of managers to implement strategies with better long-term payoffs increases as the weight that managers place on maximizing the current or near-term stock price declines. To understand this, consider again Example 19.2 and assume that management places a 75 percent weight on the year 1 value of the firm and a 25 percent weight on its intrinsic value, implying that the weighted average payoff from the long-term strategy (.75 X 440 million + .25 X 840 million) is 540 million, which...

## What Determines Factor Betas

Consider how the stock prices of General Motors (GM), an automobile manufacturer, and AMC Entertainment, Inc. (AMC), a chain of movie theaters, react differently to factors. Auto sales are linked highly to overall economic activity. Therefore, the returns to holding GM stock should be very sensitive to changes in industrial production. In contrast, movie attendance is not as related to the business cycle as car purchases, so AMC should prove less sensitive to this factor. Hence, GM should have...

## Example 82 Generating Arbitrage Profits When There Is a Violation of Put Call Parity

Assume that a one-year European call on a 45 share of stock with a strike price of 44 sells for c0 2 and a European put on the same stock (S0 45), with the same strike price ( 44), and time to expiration (one year), sells for p0 1. If the one-year, risk-free interest rate is 10 percent, the put-call parity formula is violated, and there is an arbitrage opportunity. Describe it. Answer PV(K) 44 1.1 40. Thus, c0 - p0 1 is less than S0 - PV(K) 5. Therefore, buying a call and writing a put is a...

## Example 113 Finding a Comparison Firm from a Portfolio of Firms

Assume that AOL-Time Warner is interested in acquiring the ABC television network from Disney. It has estimated the expected incremental future cash flows from acquiring ABC and desires an appropriate beta in order to compute a discount rate to value those cash flows. However, the two major networks that are most comparable, NBC and CBS, are owned by General Electric and Viacom respectively which have substantial cash flows from other sources. For these comparison firms, the table below...

## Estimating Beta from Scenarios The Certainty Equivalent Method

Hypothetical examples like Example 11.6 can illustrate the problem of using scenarios with the risk-adjusted discount rate method. In analyzing a real-world project, however, financial managers face a significant challenge whenever projects are mutually exclusive and it is difficult to identify a comparison tracking portfolio. Managers do not know the true PV unless they know the beta computed using a base cost that makes the project a zero-NPV investment. However, they cannot know this true...

## Discounting Cash Flows to Equity Holders versus Discounting Total Cash Flows

The Unitron project was a positive NPV project as traditionally defined. However, the cash flows to the firm's stockholders, after financing the project, are always negative, so it follows that the net present value of the project must be negative from the 8In reality, regulations exist to prevent a firm from expropriating wealth from the firm's debt holders by paying out all its cash as a liquidating dividend. However, lenders still must be aware of the incentive of equity holders to pay out...

## Summary and Conclusions

A good portion of this chapter focused on using the real options approach to value projects with strategic options. This approach requires making a number of simplifying assumptions that may not be particularly realistic (for example, the assumption that cash flows evolve along a binomial tree). As a result, one should consider the calculated values as rough estimates rather than as exact quantities. Nevertheless, though the pricing of strategic options is still an inexact science, the methods...

## Key Concepts

Result 14.1 (The Modigliani-Miller Theorem.) Assume (1) a firm's total cash flows to its debt and equity holders are not affected by how it is financed (2) there are no transaction costs and (3) no arbitrage opportunities exist in the economy. Then the total market value of the firm, which is the same as the sum of the market values of the items on the right-hand side of the balance sheet (that is, its debt and equity), is not affected by how it is financed. Result 14.2 Assume (1) a firm's...

## Example 134 Using the APV Method with the Certainty Equivalent Method

Emruss Ltd. is considering the purchase of a mold to make a new, improved dish drainer. The mold costs 150,000 and lasts five years, after which it has zero salvage value. Analysts estimate the expected unlevered cash flows to be 50,000 per year for the next five years and zero thereafter. The certainty equivalent cash flows, which tend to decline with the horizon when the expected cash flows are constant, are given in the table below Year 1 Year 2 Year 3 Year 4 Year 5 45 40 35 30 25 The mold...

## The Reluctance to Liquidate Problem

One of the most difficult decisions a firm must make is whether to remain in business. It must decide whether to continue to operate or to dismantle the business and sell its property and equipment for its liquidation value. Like the investment decision, the liquidation decision is affected by how much debt the firm has outstanding. In addition, the decision to liquidate can be affected by the firm's bankruptcy status. Liquidation Costs versus Bankruptcy Costs. Liquidation costs are the...

## Example 115 Estimating Betas with Scenarios

The Adonis Travel Agency wishes to estimate the present value of next year's cash flow from the purchase of 10 new airline reservation computers, at a cost of 10,000 per computer. The new computers, which are faster than the current ones at the agency, are expected to increase the number of reservations that each agent can handle. For simplicity, assume that the additional cash flows associated with the increase in booking capacity are all received one year from now. The size of the increase is...

## Example 87 Valuing an American Call Option on a Dividend Paying Stock

Even though, in reality, Chiron does not pay dividends, assume for illustrative purposes that it does and that the values above each node in Exhibit 8.8 represent the price process for 15If investors know that the price of the stock will drop by less than the dividend amount, buying the stock just before it goes ex-dividend and selling just after it goes ex-dividend means a loss equal to the drop in the stock price, which is more than offset by the dividend received. If the stock drops by more...

## Dividend Policy and Investment Incentives

The argument in the last subsection assumed that investors could correctly infer the firm's investment expenditures even though the investments are not directly observable. This assumption requires that investors understand the investment opportunities of the firm as well as the degree of emphasis that managers place on maximizing the firm's current share price versus maximizing the firm's intrinsic value. If investors know management's incentives and understand the firm's investment...

## Distribution Policy in Frictionless Markets

As we discuss later in this chapter, the dividend choice is closely related to the capital structure choice and, like the capital structure choice, is strongly influenced by market frictions like taxes and transaction costs. Before considering how market frictions affect dividend policy, we examine a simple case where there are no transaction costs and no taxes, and where the dividend choice conveys no information to investors.3 The analysis of this case serves as a useful benchmark for...

## Example 171 The Trade Off between Tax Gains and the Effect of Debt on Product Prices

Suppose that Apple produces computers at a cost of 2,000 and sells them for 2,400. This 400 profit margin on each computer generates large taxable earnings for Apple. Apple is considering a large increase in financial leverage that will increase the firm's probability of bankruptcy from zero to 10 percent, but will save the firm 58 million per year in taxes as a result of the interest tax deduction, given its 40 percent corporate tax rate. Although this is a financial decision, the financial...

## Options

After reading this chapter, you should be able to 1. Explain the basic put-call parity formula, how it relates to the value of a forward contract, and the types of options to which put-call parity applies. 2. Relate put-call parity to a boundary condition for the minimum call price and know the implications of this boundary condition for pricing American call options and determining when they should be exercised. 3. Gather the information needed to price a European option with (a) the binomial...

## Example 154 The Decision to Purchase Stock Before or After the ExDividend Date

Trevtex Corporation plans to pay a dividend of 1 per share. Tomorrow is the ex-dividend date, so investors who purchase the stock tomorrow will not receive the dividend. Assume Trevtex is selling for 20.00 per share today and is expected to sell for 19.20 per share tomorrow. Should an investor with a 33 percent marginal tax rate, who is not taxed on capital gains, purchase the stock today and receive the dividend or should the investor wait one day and purchase it without the dividend Answer...

## How Hedging Improves Decision Making

The Disney discussion suggests that an active risk management program can improve management's decision-making process by reducing the profit volatility of individual business units. Less volatile profits for a company's business units provide management at the firm's central headquarters with better information about where to allocate capital and which managers are the most deserving of promotions. Using Futures Prices to Allocate Capital. Firms with sophisticated risk management groups have...

## Bank and Privately Placed Debt

Recall that debt financing can cause either debt overhang or asset substitution, depending upon the circumstances. Bond covenants that affect the firm's ability to issue debt that is senior to existing debt can affect the firm's tendency to experience these problems. As noted in Section 16.2, the ability to issue debt that is senior to existing debt eliminates the debt overhang problem, but it also increases the asset substitution problem. The use of bank debt may be advantageous because it...

## The Ratio Comparison Approach

A popular way that investment bankers and analysts value firms, projects, or assets is to compare them with other traded firms, projects, or assets. One of the best examples of this occurs in the field of real estate. The standard discounted cash flow method often is used to value real estate, but it is not the principal method. For example, most commercial real estate is valued relative to comparable real estate that recently sold. A building should sell for 20 million if it has twice the...

## Example 1316 When Discounting Riskless Cash Flows at a Risk Free Rate Is Wrong

Anna Kramer, a recent Wharton graduate, is evaluating a project for Unitron that is virtually risk-less and returns 12 percent per year. Given that the risk-free borrowing rate is currently at 10 percent, she recommends to her supervisor that the company undertake the project because 14Alternatively, we could have a) used a formula that substitutes the risk-premiums of levered and unlevered assets for betas in equation (13.7) to unlever the equity expected returns associated with the comparison...

## Cross Sectional Tests of the CAPM

In the early 1970s, extensive tests were conducted to determine if the CAPM was consistent with the observed distribution of the returns of NYSE-listed stocks. One of the earliest procedures used to test the CAPM involved a two-step approach. First, betas were estimated with a set of time-series regressions, one for each security. (In a time series regression, each data observation corresponds to a date in time for example, the returns on IBM stock and the S& P 500 in January 2001 might be...

## Example 142 Undoing Elcos Capital Structure Change

Elco is considering a change in its capital structure. Before the change, the firm's stock sells for 100 per share, and the firm has 1,000 shares outstanding. The firm also is financed with riskless zero-coupon debt maturing in one year, and having a current market value of D 10,000. Stanley Kowalski currently owns 100 shares of Elco stock (10 percent of its equity). In the absence of a capital structure change, Stanley's payoff next year will equal .1 X - (1 + rD) 10,000 .1X - (1 + rD) 1,000...

## Example 173 Borrowing Costs and Product Quality

Handy Andy Cookies has earned a reputation for producing the best chocolate-chip cookies in the business and, as a result, is able to charge a premium price. The value of maintaining this reputation is clear. Lowering quality will save the firm money and boost profits by 20 million next year, but in later years, as the company's reputation erodes, profits will fall dramatically. Andy calculates that if the firm loses its reputation, it will lose 4 million per year over a nine-year period before...

## Example 2311 Using Immunization Techniques to Lock In a Payoff

The 10 million portfolio in Example 23.10 is a pension portfolio, which currently has a duration of five years. Half the portfolio's market value consists of identical maturity zero-coupon bonds. The remainder consists of 5 million (market value) of the 2-year straight-coupon bonds from Example 23.6. These bonds have a duration of 1.89 years and an 8 percent yield, compounded semiannually. a. What is the maturity of the zero-coupon bonds in the portfolio b. How should the manager rebalance the...

## Example 79 Using Risk Neutral Probabilities to Value Derivatives

Apply the risk-neutral probabilities of .87 and .13 from Example 7.8 to the cash flows of the derivative of Example 7.6 and discount the resulting risk-neutral expected value at the risk-free rate. See Exhibit 7.9 for the numbers to use in the example. Answer .87( 331.75) + .13( 106.75) yields a risk-neutral expected future value of 302.50, which has a discounted value of 302.50 1.1 275. Relating Risk-Neutral Valuation to the Tracking Portfolio Method. It is indeed remarkable, but not...

## Example 138 Computing the After Tax Cost of Debt and WACC When Default Is Unlikely

The financing of United Technologies (UT) consists of 20 percent debt and 80 percent equity. With so little debt, the firm is able to borrow at the risk-free rate of 8 percent per year. The interest expense is tax deductible and the corporate tax rate is 34 percent. Assuming that the CAPM holds, the expected return of the market portfolio is 14 percent, and the beta of the firm's equity is 1.2, what is the WACC of United Technologies Answer Using the CAPM, UT's cost of equity is The firm's cost...

## Example 117 Computing the Cost of Capital

Each share of Hot Shot Computer Corp (HSCC), a wholly owned subsidiary of Novel, Inc., first seen in Example 11.1, has a cash flow beta (b) of 10.91 when computed against the tangency portfolio. One year from now, this subsidiary has a .9 probability of being worth 10 per share and a .1 probability of being worth 20 per share. The risk-free rate is 9 percent per year. The tangency portfolio has an expected return of 19 percent per year. What is the present value of HSCC, assuming no dividend...

## Maturity Risk and Hedging in the Presence of a Constant Convenience Yield

To understand the hedging of long-dated commitments with shorter-maturing futures and forwards, it is necessary to link the risk of each commitment and hedging instrument to the risk of holding the commodity. For example, assuming that oil has a convenience yield of 2 percent per year, the forward commitment to buy a barrel of oil 10 years from now is equivalent in risk to a position in pur chased today. Similarly, a commitment to buy oil one year from now is equivalent in risk to a position in...

## How Management Incentive Problems Hurt Shareholder Value

The Armand Hammer and Occidental Petroleum example in the chapter's opening vignette provides a poignant case of how management incentive problems can affect shareholder wealth. Although the Hammer episode is an extreme example of the extent to which shareholder wealth can be destroyed by a self-interested manager, share prices tend to respond favorably when entrenched executives leave their positions unexpectedly. Articles in Newsweek and The Wall Street Journal provide several examples of...

## The Incentives of a Firm to Take Higher Risks The Case of Unistar

Consider Unistar, a startup firm that plans to manufacture memory chips and has borrowed the money to build a factory. Unistar's managers now have to decide on one of two designs for the production process. Although the two processes look nearly identical to the firm's bankers and each costs 70 million, Unistar's management knows that process 2 involves much more risk than process 1. Debt holders are aware of the two alternatives and can forecast the possible payoffs of each, but they cannot...

## Example 161 How Bankruptcy Affects Borrowing Costs

Westlake Corporation would like to borrow 1 million for one year. There is a 90 percent chance that the loan will be repaid in full and a 10 percent chance that the firm will be bankrupt at the end of the year. In the event that the firm is bankrupt, its assets can be sold for 600,000. However, the legal costs of seizing Westlake's assets will cost the bank 100,000. How much will a bank charge for the loan if it prices loans to companies like Westlake to earn, on average, 10 percent How is the...

## How Hedging Affects Debt Holders and Equity Holders

Previous chapters described how equity can be viewed as a call option on the firm's value. To the extent that hedging reduces volatility without increasing firm value, it reduces the value of this option, transferring value from equity holders to debt holders. From an equity holder's perspective, the value-maximizing benefits of hedging may be reduced, and possibly even reversed, by this transfer. The actions of managers to hedge in these circumstances certainly would not endear them to these...

## Example 185 The Information Conveyed from Adopting a Performance Based Compensation Plan

Consider the CEOs of two firms, Jack and Peggy. The two firms currently have stocks priced at 20 per share. Jack has favorable proprietary information that leads him to believe that his firm's stock is really worth 30 per share. Peggy has unfavorable proprietary information that leads her to believe that her firm's stock is worth only 15 per share. Both CEOs are considering 648 Part V Incentives, Information, and Corporate Control proposals that would lower their fixed salary in exchange for...

## References and Additional Readings

The Relationship between Return and Market Value of Common Stocks. Journal of Financial Economics 9 (1981), pp. 3-18. Basu, Sanjay. The Relationship between Earnings Yield, Market Value, and Return for NYSE Common Stocks Further Evidence. Journal of Financial Economics 12 (1983), pp. 129-56. Black, Fischer. Capital Market Equilibrium with Restricted Borrowing. Journal of Business 45 (1972), pp. 444-55. Black, Fischer Michael C. Jensen and Myron Scholes. The Capital Asset Pricing...

## Example 126 Valuing the Option to Increase a Plants Capacity

Acme Industries is considering building a plant. The plant will generate cash flows two years from now, as described in Exhibit 12.6. The cash flows from the plant will be 200 million following two good years (point D), 150 million following one good and one bad year (point E), and 100 million (point F) following two bad years. The initial cost of the plant is 140 million (point A). After one year, however, if the state of the economy looks good, the firm has the option to double the plant's...

## Risk Free or Zero Beta Returns

Most academic studies of the CAPM have used short-term Treasury bill returns as proxies for the risk-free return. However, as Black, Jensen, and Scholes (1972), among others, have noted, this rate seems to be lower than the typical average return of a zero-beta risky stock. An alternative is to use the zero-beta expected return estimate that comes from fitting the intercept in the risk-expected return equation to all stocks. Interestingly, the risk-free rate employed in derivative securities...

## Valuing Vacant Land

Vacant land has value because it represents an option to turn the vacant land into developed land. For example, a particular plot of land may be developed into condominiums, an office building, or a shopping mall. In the future, the developer will have an incentive to develop the property for the use that maximizes the difference between the value of the project's future revenues and its construction costs. However, the best possible future use for the land may not be known at the present time....

## How Managerial Incentives Affect Financial Decisions

After reading this chapter, you should be able to 1. Distinguish between managerial incentives and shareholder incentives. 2. Understand how the differences between manager and shareholder incentives affect the ownership structure, capital structure, and investment policies of firms. 3. Describe ways to design compensation contracts that minimize manager-shareholder incentive problems. Armand Hammer founded and ran Occidental Petroleum until his death in 1990 at the age of 92. Although he is...

## Investing in Risky Projects

After reading this chapter you should be able to 1. Estimate the cost of capital with the CAPM, APT, and dividend discount models. 2. Understand how to implement the comparison approach with the risk-adjusted discount rate method and know its shortcomings. 3. Understand when to use comparison firms and when to use scenarios to obtain present values. 4. Discount expected future cash flows at a risk-adjusted rate and know when to discount the certainty equivalent at a risk-free rate. 5. Identify...

## Example 135 Using the APV Method with the Real Options Approach

Reconsider Example 12.6, which featured Acme Industries, a company with the option to expand its plant's capacity during good times. The initial cost of the plant was 140 million and the cost of the expansion was an additional 140 million. The risk-free rate was 5 percent per period. Assume the following For tax purposes, Acme will expense at year 2 (when the project's income is realized), both the 140 million initial cost and, provided it expands capacity, the additional 140 million in...

## Capital Structure and Corporate Strategy

After reading this chapter you should be able to 1. Describe how a firm's financial situation is likely to affect its sales and its ability to attract employees and suppliers. 2. Understand how financial distress can benefit some firms by inducing employees, suppliers, and governments to make financial concessions to the firm. 3. Explain how a firm's financial condition affects the way its competitors price their products. 4. Describe how the past profitability of a firm affects its current...

## The Benefits of Financial Distress with Committed Stakeholders

The last section emphasized that when stakeholders commit resources to doing business with a firm, they are effectively betting on the long-term viability of that firm. If the firm does well, the stakeholders will do well if the firm does poorly, the stakeholders are likely to be hurt financially. Hence, in a competitive market, the terms of trade between the firm and the stakeholders are determined in part by the viability of the firm's future prospects. This section examines how debt affects...

## Guide to the Valuation of Synergies

Valuing acquisitions draws upon the techniques for evaluating real investment projects described in Chapters 9 to 13. However, acquisitions tend to be much larger than the capital investments that firms typically undertake, so firms should go into more depth in their valuation. They should evaluate a variety of scenarios and consider the various embedded options that exist in most firms see Chapter 12 . We suggest that acquiring firms take the following steps to evaluate prospective targets....

## Bankruptcy Costs and Debt Holder Equity Holder Conflicts

After reading this chapter you should be able to 1. Understand the effect of direct bankruptcy costs on borrowing rates and capital structure choices. 2. Describe the factors contributing to the conflicts of interest between debt holders and equity holders. 3. Explain how debt can cause equity holders to take on projects that are too risky and to pass up positive NPV projects. 4. Identify various situations in which debt holders and equity holders may disagree on the liquidation decision. 5....

## Example 123 Valuing Vacant Land

An investor owns a lot that is suitable for either six or nine condominium units. The per unit construction costs of the building with six units are 80,000 and with nine units 90,000. Construction costs are the same whether construction takes place this year or next. The current market price of existing comparable condominiums is 100,000 per unit. Their per year rental rate is 8,000 per unit net of expenses , and the risk-free rate of interest is 12 percent per year. If market conditions are...

## The Shortsighted Investment Problem

A popular topic for financial journalists since the late 1980s is the perceived shortsightedness of American businesses. A common claim was that shortsightedness was worsened by the increased use of debt financing by some firms highly leveraged firms prefer projects that pay off quickly since short-term projects allow them to meet their near-term debt obligations more easily. By extending the analysis in the preceding subsection, we can see how future debt obligations can make firms...

## Exhibit 141 Slicing the Cash Flows of the Firm

Slicing the pie doesn't affect the total amount available to debt holders and equity holders. Slicing the pie doesn't affect the total amount available to debt holders and equity holders. The size of the debt slice can affect the size of the slice going to government. The size of the debt slice can affect the size of the wasted slice. The size of the debt slice can affect the size of the slice going to government. The size of the debt slice can affect the size of the wasted slice....

## Example 103 Ranking Projects

Suppose that it is possible to adopt any two of the four positive NPV projects from Example 10.2. Which two should be selected Answer Projects A and C have the two largest positive NPVs and thus should be adopted. The last subsection considered the possibility of having mutually exclusive projects because of physical constraints. Among those was the possibility that some important input was in short supply, perhaps land available for building a manufacturing facility or managerial time. This...

## How Taxes Affect Financing Choices

After reading this chapter, you should be able to 1. Understand that in the absence of taxes, transaction costs, and other market frictions, capital structure can affect firm values only when the debt-equity choice affects cash flows the Modigliani-Miller Theorem . 2. Explain how corporate taxes provide incentives for firms to use debt financing as well as how they affect the decision to buy or lease capital assets. 3. Understand why personal taxes provide an incentive for firms to use equity...

## Exercises for Appendix 10A

A zero-coupon bond maturing two years from now has a yield to maturity of 8 percent annual compounding . Another zero-coupon bond with the same maturity date has a yield to maturity of 10 percent annual compounding . Both bonds have a face value of 100. a. What are the prices of the zero-coupon bonds b. Describe the cash flows to a long position in the 10 percent zero-coupon bond and a short position in the 8 percent zero-coupon bond. c. Are the cash flows in part b indicative of...

## Project Evaluation with the Net Present Value Rule

This subsection shows why the NPV rule, adopt the project when NPV is positive, is sensible. Below, we show that the NPV rule is consistent with the creation of wealth through arbitrage. Arbitrage and NPV. Adopting a project at a cost less than the present value of its future cash flows that is, positive NPV means that financing the project by selling short this tracking portfolio leaves surplus cash in the firm today. Since the future cash that needs to be paid out on the shorted tracking...

## Example 163 Interest Rate Changes Risk Incentives and Credit Rationing

The Little Cook Corporation is choosing between project T, which introduces a traditional triple patty greasy hamburger, and project E, which introduces a healthy, low-fat emu burger. Project T costs 100 million used for marketing, training of cooks, and so forth and yields cash flows for the next year of 115 million with certainty. Project E also costs 100 million but, because of the controversial nature of the meat, has only a limited probability of success. The marketing experts at Little...

## Example 43 Computing Portfolio Weights for a Portfolio of Many Stocks

Describe the weights of a 40,000 portfolio invested in four stocks. The dollar amounts invested in each stock are as follows Amount 20,000 - 5,000 0 25,000 Answer Dividing each of these investment amounts by the total investment amount, 40,000, gives the weights x-, .5 x2 -.125 x3 0 x4 .625 For an arbitrary number of assets, we represent securities with algebraic notation see Exhibit 4.1 . To simplify the language of this discussion, we refer to the risky assets selected by an investor as...

## Example 1110 Multiperiod Valuation with the Risk Free Scenario Method

Omegatron, a game software company, wants to value the cash flows of its new Doombo game at years 5 and 10. Assume the following Cash flow forecast errors are noise that is, they are distributed independently of everything. The year 5 cash flow of Doombo has an expected value of 39 million if its five-year stock return, with dividends reinvested in Doombo stock, is 30 percent over the five years. The year 10 cash flow of Doombo has an expected value of 80 million if an investment in its stock...

## The Tangency Portfolio and Optimal Investment

So far, this chapter has studied how to invest optimally by looking at the portfolios formed only from risky stocks. Generally, whenever an additional asset is added to the set of investments that can be held in a portfolio, the feasible set of the mean-standard deviation diagram expands. The risk-free asset is no exception, but it is notable for the manner in which it changes the shape of the feasible set and the efficient frontier. Chapter 4 indicated that portfolios of a risk-free investment...