ch10 Intro to Finance

Chapter Ten: Bonds and Stocks: Characteristics and Valuations

Chapter 10Bonds and Stocks: Characteristics and Valuations

CHAPTER PREVIEW

A natural application of the time value of money principles is stock and bond valuation. Students are familiar with the financial markets from news reports. This chapter allows them to learn some of the influences on stock and bond values. We first review bond characteristics, the global nature of the bond market, and show how to interpret the price quotes found in many newspapers. The basics of equity securities are reviewed next. The second half of the chapter discusses valuation principles for bonds, stocks, and risk. It also discusses how to compute rates of return.

LEARNING OBJECTIVES

Identify the major sources of external long-term financing for corporations. Describe major characteristics of corporate bonds. Identify the reasons why investors seek stocks for an investment vehicle. Describe major characteristics of preferred stock and common stock. Describe the process for issuing dividends by a firm. Explain how financial securities are valued in general and specifically for bonds and stocks.

Learning Extension: Calculate rates of return.

CHAPTER OUTLINE

I. LONG-TERM EXTERNAL FINANCING SOURCES FOR BUSINESSES

II. DEBT CAPITALA. Who Buys Bonds?B. Bond CovenantsC. Bond RatingsD. Bondholder SecurityE. Time to MaturityF. Income from BondsG. Global Bond MarketH. Reading Bond Quotes

III. CORPORATE EQUITY CAPITALA. Common Stock B. Preferred StockC. Reading Stock QuotesD. Innovation in Common Stock

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IV. DIVIDENDS AND STOCK REPURCHASESA. How Do Firms decide on the Dollar amount of Dividends?B. Stock Dividends and Stock SplitsC. Share Repurchases

V. VALUATION PRINCIPLES

VI. VALUATION OF BONDSA. Determining a Bond’s Present ValueB. Calculating the Yield to MaturityC. Risk in Bond Valuation

1. Credit Risk2. Interest Rate Risk3. Reinvestment Rate Risk4. Risks of Nondomestic Bonds

VII. VALUATION OF STOCKSA. Valuing Stocks with Constant DividendsB. Valuing Stocks with Constant Dividend Growth RatesC. Risk in Stock Valuation

VIII. VALUATION AND THE FINANCIAL ENVIRONMENTA. Global Economic InfluencesB. Domestic Economics InfluencesC. Industry and Competition

IX. SUMMARY

LEARNING EXTENSION: ANNUALIZING RATES OF RETURN

I. Holding Period Returns

II. Annualized Rates of Return

LECTURE NOTES

I. LONG-TERM EXTERNAL FINANCING SOURCES FOR BUSINESSES

Internal financing sources arise from a firm’s cash flow, roughly defined as net income plus depreciation. External long-term financing is obtained from the capital markets by selling debt and equity claims. The relative use of internal and external funds varies over the business cycle.

Table 10.1 presents data on the absolute and relative use of securities used to raise external financing.

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Most financial claims sold to the public are debt claims. This occurs for several reasons:1. Firms prefer to use internal equity (e.g., retained profits) rather than external equity.2. It is cheaper to borrow funds than sell equity.3. Bonds mature; equity does not.

Both bonds and stock can be sold to the public or in a private placement. For large firms, global markets exist for selling these claims. There are four reasons why more and more firms are raising funds outside of the U.S.:1. If firms have overseas plants or factories, it may make financial sense to raise funds in

the country in which the plant is built (to hedge cash flows and to mitigate political risk).

2. Financing costs may be lower overseas. 3. Securities issued outside of the U.S. can avoid the costly and time-consuming SEC

approval process.4. In order to find sufficient buyers for large bond offerings, issuers seek access to global

capital markets.

(Use Discussion Questions 1 through 3 here.)

II. DEBT CAPITAL

Much of this section entails introducing students to various terms associated with bonds. This can be made livelier by circulating (or showing them on an overhead projector) copies of various “tombstone ads” from The Wall Street Journal to show students how some of the terms are used.

Debt issued in the U.S. is in registered form. Typical corporate bonds have a $1,000 face or par value, a set maturity date, and pay coupons twice a year. The bond contract between the issuer and investors is called the indenture and is overseen by a trustee. Covenants help protect investors. Firms usually pay to have the bonds rated by an outside agency to evaluate their credit risk. The bond rating will be affected by the firm’s ability to pay timely interest and principal and the bond’s security provisions, i.e., whether it is collateralized, is a mortgage bond, equipment trust certificate, debenture, or subordinated debenture. Some bonds may contain other features; they may be convertible, callable, putable, extendible, or they may have a sinking fund requirement. Newer innovations in bonds include asset securitization (issuing bonds whose coupon and principal payments arise from another existing cash flow stream; e.g., mortgages, credit card receivables, auto loans, and royalties) and inflation-protected securities. Securities in the global bond market include Eurodollar bonds, which are dollar-denominated bonds sold outside of the United States, and Yankee bonds, which are dollar-denominated bonds that are issued in the U.S. by a foreign issuer. Bond ratings provide information about an issuer’s ability to service its debt. Bond covenant provide rules the issuer must follow; they generally provide protection for investors. Bonds can differ on the degree of security they offer investors, factors that affect their time to

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maturity, and how they pay income to investors. The global bond market provides greater access to financial capital than can be expected in any one domestic market.


III. CORPORATE EQUITY CAPITAL

Equity ownership is indicated by possessing a stock certificate, although some investors prefer to keep their certificates in street name. Equity securities fall into two classes:1. Common stock provides for a residual claim on profits after debt and preferred

shareholders have been paid their claims.2. Preferred stock generally carries a specified dividend, expressed either as an absolute

dollar amount or as a percent of par. Preferred stock can be convertible, callable, or cumulative.

(Use Discussion Questions 22, 23, 28 and 29 here.)

IV. DIVIDENDS AND STOCK REPURCHASESIncome to shareholders comes in the form of dividends that are declared by the firm’s board of directors. Beginning students of finance or business will find the process of (in their mind) getting “free money” from a corporation interesting. After all, without a legal contract (as with bonds) why give the firm’s money to shareholders? This section, though largely descriptive, can lead to good discussions on why firms pay dividends, the process for determining the amount of dividends, and the differences between cash dividends, stock dividends and stock splits, and share repurchases. Class discussion can be helped by finding, on the internet or financial periodical, announcements by firms of dividend declarations or share repurchases.

(Use Discussion Questions 24, 31, and 32 here).

V. VALUATION PRINCIPLES

Introduces the general principle that value arises from discounting expected future cash flows.

(Use Discussion Question 13 here.)

VI. VALUATION OF BONDS

Applies valuation principles to determining the price of a straight bond price = PV(expected future cash flows)

= PV(coupon payments) + PV(principal)Bonds selling below par value are discount bonds; bonds with prices above par value

are premium bonds. Bond prices and interest rates are inversely related; when one rises, the other must fall, by nature of the discounting process. If a bond’s price is known, its

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yield to maturity can be found by using an approximation formula. An exact answer can be found by using a financial calculator or spreadsheet. When coupons are paid semiannually, care must be taken to compute interest rate, r. Recalling the discussion from Chapter 9, the yield to maturity on a bond is computed as an effective interest rate (EAR):

YTM = (1 + r)2 – 1 or

r = (1 + YTM)1/2 – 1

Bonds can be risky investments. Their cash flows, returns, and market prices are affected by credit risk, interest rate risk, and reinvestment rate risk. U.S. investors of non-U.S. bonds are subject to political risk and exchange rate risk.

(Uses Discussion Questions 14 through 21 here.)

VII. VALUATION OF STOCKS

The price of a share of stock today is the present value of future expected dividends, regardless of the length of a particular investor’s holding period. Stock valuation formulas are presented for stocks with constant dividends (such as preferred stock), a constant dividend growth rate, and a two-stage dividend growth model. As they represent a residual claim on earnings and assets, stock investments are riskier than bond investments.

The price of a stock is affected by the size of the dividend, future growth in the dividend, the level of interest rates, expected inflation, and the level of perceived risk in the investment.

(Use Discussion Questions 25 through 27, 30, 33 through 35 here.)

VIII. VALUATION AND THE FINANCIAL ENVIRONMENT

We estimate present value by using future expected cash flows and discount rates. This section introduces several economic influences on stock and bond valuation that may affect a firm’s cash flows or how investors want to discount those cash flows.

Two major global influences can affect cash flows and discount rates: 1) the condition of overseas economies, as they can be a source of demand for home country exports; 2) changes in exchange rates can affect the cash flows that firms receive and can influence, as we saw in Chapter 6, the level of home country interest rates.

Domestic economic conditions affect personal spending, business investment, and the returns that investors will require on their investments. Some industries are more sensitive to changes in economic factors than others. The level and type of competition in an industry and a firm’s market position will influence its future cash flows and discount rate.


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SUPPLEMENTARY MATERIAL

Based upon how you which to teach your course, you may find the topics below of interest to you and your students. It is set-up on separate pages for easy copying and distribution to your students.PROCESS OF ISSUING CASH DIVIDENDSAs dividend payments are not “automatic” in the sense of bond interest, there is a process to be followed. First, the firm’s board of directors—who oversee the firm’s managers and who are to make decisions for the benefit for the firm’s common shareholders1—must declare that a cash dividend will be paid. On this declaration date they will announce the amount of the dividend per share that will be paid on the distribution date to those who own stock as of the date of record. The time line of this process is shown in Figure IM10.1.

margin definition:declaration datethe date the board of directors announces that a dividend is declared, or is forthcoming distribution datedate on which the dividend is to be paid to shareholdersdate of recordthose owning the stock on this date will receive the declared dividend on the distribution date

The board declares that a dividend will be paid on the declaration date, for example March 1. The announcement will include information on the amount of the dividend and when the dividend will be paid (the distribution date, which is May 1 in Figure IM10.1). The board will also announce the date of record, dividends will only be paid to those who own shares of the firm’s stock on this date. In Figure 8.3 shows the date of record as April 2.

margin definition:ex-dividend datetwo working days before the date of record, trades on and after this trade do not include the right to receive the declared dividend

We learned earlier that stock trades are processed in “T+3”, that is, it takes up to three days before a stock purchase or sale is recorded. Thus, our time line needs one more date: the ex-dividend date. The ex-dividend date is two working days before the date of record. Stock trades on or after the ex-dividend date will not include the expectation of the dividend. In our timeline, assuming that April 2 falls on a Wednesday, the ex-dividend date will be two working days before, that is, Monday March 31. Anyone wanting to purchase shares in order to receive the dividend needs to purchase them before March 31.

What should happen to the stock price on the ex-dividend date? If there were no other influences, we would expect the price of the stock to fall by an amount equal to the dividend. If stock is trading for $27.50 with a declared quarterly dividend of $0.30, we expect the price to fall to

1 The board of directors is discussed more fully in Chapter 11 Business Organization and Financial Data.

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$27.20 on the ex-dividend date.

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Declaration Ex-Dividend Date of Distribution Date Date Record Date

March 1 March 31 April 2 May 1

Figure IM10.1 Time line for declaring and issuing a cash dividend---------------------------------------------------------------------------------------------------------

Why do some firms offer stock dividends or do stock splits? Since they have no value effects, the impact is mainly psychological. Stock dividends are a way to make investors think they are receiving something of value when in reality they are not. Some practitioners believe there is an optimal range for a stock price. Prices that are “too high” will scare away investors because of the large capital investment needed to purchase shares. Prices that are “too low” make the stock appear speculative. Stock dividends and splits can reduce/increase market prices to keep them within an optimal range of $20-$80. But many successful firms have stock prices far exceeding this range; in 2007 Google stock was selling for over $500 a share and Berkshire Hathway A shares have traded at over $100,000 a share. Stocks with low prices (say less than $5 a share) do have a stigma of being lower quality, speculative issues and some have done reverse splits to raise their stock price. But research studies show what we intuitively know: there is no shareholder value created in splits, reverse splits, and stock dividends.

TWO-STAGE GROWTH MODELSThe assumption of a smooth constant growth rate over time may not be true for some firms. The firm and industry life cycle is such that a period of fast and variable growth is followed by a period of slower, more consistent growth. And cyclical firms will have growth rates that fluctuate with the business cycle. One way to address this reality is to use a two-stage growth model. The model assumes supernormal growth will occur for the firm over a short period of time, after which “normal” and relatively constant growth will occur.2 To value these stocks, we

2 Some use a three-stage growth model in which a period of supernormal growth is followed by a period of above-normal but declining growth rates until a sustainable constant growth rate is

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use:

P0 = [D0(1 + g)]/(1 + rs) + [D0(1 + g)2]/(1 + rs)2 _ … _ (IM10-1)[D0(1 + g)n]/(1 + rs)n + Pricen/(1 + rs)n

That is, we estimate the dividends for each year of the n-year supernormal growth period and compute their present value; we add to this the present value of the stock price in year n. The year n price is estimated by the constant dividend growth model; since dividends are expected to grow at a consistent rate after year n we find their value as of year n and discount it back to the present. Without the notation of equation IM10-1, the process is:

1. Estimate the dividends for each year of the supernormal growth period;2. Since constant growth begins in year n + 1, find the price of the stock in year n using the Gordon model;3. Sum the present value of the dividends in each of the supernormal growth years and the present value of the stock price in year n.

As an example, let’s assume Kraham Corporation’s stock is in a growth period; dividends are expected to grow 20 percent annually for the next three years, at which time the firm will grow at a “normal” rate of 7 percent. If investors require a 10 percent return on their investment in a stock with Kraham’s risk and the firm just paid a dividend of 50 cents a share, what is a fair price for the stock?

The first step is to estimate the dividends in the supernormal growth period. With a current dividend of $0.50 and 20 percent growth, these dividends are:

YEAR DIVIDEND 1 (0.50)(1 + 0.20) = $0.60 2 (0.60)(1 + 0.20) = $0.72 3 (0.72)(1 + 0.20) = $0.86

The second step is to estimate the stock price in year 3. After year 3 the dividends are expected to grow at a normal growth rate of 7 percent. Using the constant dividend growth model, we find

Pn = Dn+1/(rs - g) = P3 = D4/(rs - g) = $0.86(1 + 0.07)/(0.10 - 0.07)= 0.92/0.03 = $30.67

The third and final step of the process is to sum the present values of the supernormal growthdividends and the year-3 price at the 10 percent required rate of return for Kraham stock. We have:

P0 = $0.60/(1.10) + $0.72/(1.10)2 + $0.86/(1.10)3 + $30.67/(1.10)3 = $24.83

According to the two-stage model, investors should be willing to pay $24.83 a share for Kraham

achieved.

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Corporation stock.

A simple spreadsheet design can incorporate the inputs and calculations for this three-year supernormal growth stock.

Using this spreadsheet, if we change the supernormal growth assumption (cell B5) to 30 percent, the stock should trade at $31.55 a share. Or, leaving the growth rate assumption at 20 percent, if we change the long-term dividend growth to only 5 percent (cell B7), the stock should sell for $15.42.

DISCUSSION QUESTIONS AND ANSWERS

1. Describe the relationship between internal and external financing in meeting the long-term financial needs of a firm.Internal financing takes place as retained earnings and internally generated cash flows such as depreciation are committed to operating assets. Some firms, either because of very high internal cash generation or slow growth, may depend entirely upon internal financing. Other firms may have to go to the markets with great frequency to meet their capital needs. Thus, the internal versus external financing relationship is dependent on the availability of retained earnings versus the size of plant and equipment investments.

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2. What are the major sources of long-term funds available to business corporations? Indicate their relative importance.Internally generated funds arise from the firm’s retained cash profits and depreciation. External funds are obtained from debt (e.g., bonds) and equity (preferred stock, common stock) markets. Such debt and equity claims can be sold to the public or can be privately placed. Businesses raise more funds from debt than equity; more common stock is issued than preferred. Banks loans are an important source of intermediate-term funds.

3. Why would firms raise capital in markets other than their domestic or home market?There are four reasons why a firm would raise funds outside of its domestic market. First, if the firm has overseas factories or facilities it may make good financial sense to raise funds in the country in which the facility exists. Second, financing rates are sometimes lower outside the home market. Third, if the U.S. is the home market, raising funds outside of the U.S. eliminates the costly and sometimes lengthy SEC approval process. Fourth, the size of some issues suggests going outside the home market in order to find a sufficient number of buyers.

4. Can bonds be purchased only by large institutional investors? Explain.No. Although institutions such as pension funds, life insurance firms, and mutual funds make up much of the market for debt, individual investors can purchase corporate and Treasury bonds. The Treasury Direct program is designed to help individuals purchase Treasury securities. Corporate debt can be purchased by individuals via brokers; some corporate issues (Smart Notes, medium-term notes, or direct access notes) are marketed directly to the retail investor.

5. How does a TIPS bond differ from the typical U.S. Treasury security?The typical U.S. Treasury note or bond pays the same coupon interest over its life and has a par value which is unchanging. TIPS (Treasury inflation-protected security) have a coupon payment and par value which rises with inflation. The stated interest rate on a TIPS is the real interest rate; the coupon income the investor received increases above the real rate by the rate of inflation.

6. Describe what is meant by bond covenants.Covenants impose additional restrictions (negative covenants) or duties (positive covenants) on the firm. Examples of positive covenants include maintaining a minimum level of working capital and submitting audited financial statements to bondholders. Examples of negative covenants include restrictions on the amount of a firm’s debt or limits on dividends.

7. What are bond ratings?Bond ratings are purchased by a firm issuing bonds in order to have a third party (the bond rating agency) evaluate the credit or default risk of a bond issue. The ratings inform the markets of the safety of the issue. The raters assess both the ability of the issuer to make timely interest and principal payments as well as the collateral and covenants specified in the bond indenture.

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8. Briefly describe the types of bonds that can be issued to provide bondholder security.Examples include collateralized bonds (backed by securities such as mortgages or credit card receivables), mortgage bonds (backed by property, plant, or equipment), and equipment trust certificates (backed by rolling stock, such as railroad cars or airplanes).

9. What is meant by the following terms: convertible bonds, callable bonds, putable bonds, and Eurodollar bonds?Convertible bonds can be changed or converted, at the investor’s option, into a specified number of common shares. Callable bonds can be redeemed prior to maturity at par value plus a call premium at the issuer’s option. Putable bonds allow the investor to force the issuer to redeem the bonds prior to maturity. Eurodollar bonds are dollar-denominated bonds that are sold outside the U.S.

10. Why are investment-grade bonds given that name? Why are “junk bonds” also known as “high-yield bonds”?Bonds rated BBB or higher are called “investment-grade” as institutional investors such as pension plans have historically limited their bond investments to higher-rated bonds. “Junk bonds”, those with ratings below investment-grade, have higher yields due to their higher risk—so they are sometimes called “high-yield” bonds.

11. Why might a firm want to maintain a high bond rating? What has been happening to bond ratings in recent years?There are two reasons why a firm might want to maintain a high bond rating. First was the prestige associated with having a high bond rating. Such firms are thought of being financially stable, well-managed, and might attract a number of institutional and individual investors. Second, a high bond rating saves the firm money by allowing it to have lower interest expenses on its bond debt.Over time, the stigma associated with high-yield or junk debt has diminished. Interest is tax-deductible whereas dividends are not; firms have issued debt to fund stock repurchase programs. Over time the percentage of investment-grade debt has fallen and the percentage of “junk” debt has risen.

12. Why might an investor find a zero-coupon bond an attractive investment?Many bond investors have long-term time horizons before the invested funds are needed (to pay for a child’s college education, personal retirement, or other financial goals). Such investors will not spend the bond’s coupon interest when it is received; they will re-invest it in other securities. When regular bonds are purchased by these investors, they face the risk of not knowing what the return will be on the re-invested coupons over the life of the bond. Interest rates may rise, fall, or cycle up and down over the life of the investment. Zero coupon bonds eliminate this uncertainty by, in essence, locking in the return (the difference between the price paid and the par value) when the bond is purchased. Since interest is taxed annually—although it is not received until maturity—zero coupon bonds are best suited for tax-deferred investments such as IRAs and 529 college savings plans.

13. Briefly describe how securities are valued.Future cash flows are estimated. The security’s value or price is the present value of these cash flows, discounted at an appropriate discount rate.

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14. Describe the process for valuing a bond.Determining the value of a bond is a three-step process:

First, we must find the present value of the coupon payments. The annual coupon payment is the coupon rate multiplied by the par value. If interest is paid semiannually, this amount is divided in half and the resulting amount is paid every six months. The time horizon is the number of years, until maturity, for a bond with annual coupon payments and the number of years, times two, for a bond with semiannual coupons. The discount rate is the periodic rate, determined by whether the yearly rate is quoted on a nominal (APR) basis or effective yield (EAR) basis.

Second, the present value of the par value is computed, using the same number of periods and periodic rate as that used for the coupons.

Third, the sum of the present value of the coupons and the present value of the par value is the price of the bond.

15. What is meant by the “yield to maturity” on a bond?It is the return on a bond investment if the bond is held to maturity, if all the coupon payments are reinvested at the yield to maturity, and there are no taxes to be paid.

16. Briefly describe the types of risk faced by investors in domestic bonds. Also indicate the additional risks associated with nondomestic bonds.Domestic bond risks include credit or default risk, interest rate risk, and rollover risk. Credit risk is the chance of not having timely payment of interest or principal. Interest rate risk is characterized by the “seesaw effect”—changes in interest rates in one direction lead to changes in bond prices in the opposite direction. Reinvestment or rollover risk is the risk that interest rates may fall, harming the returns earned on reinvested coupons or principal.

Nondomestic bond investors have at least two other risks: exchange rate risk (fluctuating exchange rates lead to varying U.S. dollar cash returns) and political risk (blocked currencies, social unrest in the foreign country).

17. What risk does a zero-coupon bond address?Reinvestment rate risk as there are no intermediate cash flows to reinvest in other securities.

18. According to the behavior of interest rates in Figure 10.5, were investors more concerned or less concerned about risk over the 2002-2006 time period? Explain.The narrowing (spread become smaller) between the Baa corporate bonds and Treasury bonds shows investors were becoming less concerned about risk over this time frame. Similarly, the spread or risk premium between Aaa corporates and Treasuries fell. Falling risk premiums as indicated in this part of the figure implies less investor concern about risk.

19. What does it mean with the horizon spreads in Figure 10.7 dip below the X-axis? Why do some feel that this was not to be the case in 2006?When horizon spreads are negative the yield curve is invested—that is, long-term bond rates are less than shorter term bond rates. This typically happens before a recession begins, when short-term rates are rising because of inflationary pressures at the time. Some experts feel, however, that the inverted yield curve in 2006 does not predict a soon-coming recession. They argue that easy monetary policy, both in the U.S. and world-wide created a great deal

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of liquidity in the financial markets. Indeed, in 2006 and early 2007 there was no sign of a restrictive monetary policy by the Fed and credit spreads (see Figure 7.3) remained low. If investors feared a soon-coming recession, credit spreads would widen due to a flight to quality.

20. How do you think credit spreads behave over the course of the economic cycle?Credit spreads are a risk premium between high-quality (low credit risk) bonds such as Treasuries or AAA-rated corporate bonds and lower-quality (higher credit risk) bonds such as BBB- or Baa-rated corporates. In periods of economic growth and rising optimism, spreads will narrow as investors will not be as concerned about risk and will be willing to seek higher yields in higher credit risk bonds. As economic uncertainty rises, however, over an economic slowdown or political uncertainty, there will be a “flight to quality.” Investors will prefer the perceived safety of lower credit risk securities and credit spreads will widen. In general, we expect spreads to narrow in periods of economic growth and to widen in periods of slower economic growth.

21. What is a “flight to quality”? Under what economic conditions might we see this?A flight to quality occurs when investors become nervous about future economic conditions. Less willing to take risks, they pull their funds from higher-risk investments and place them in securities that are perceived to be safer such as high-quality corporate bonds, federal agencies, and Treasury securities. This can be precipitated by fears of a coming recession, political uncertainty in a country, or economic uncertainty caused by, for example, rising oil prices, inflation, or widespread labor strikes. Higher credit risk securities will be perceived to have a much greater chance of default as we enter a recession so investors will opt for safer securities.

22. Why study stocks if the net amount of stock issues is negative?First, they are a source of new financing for new and growing firms. Both private and public equity can be issued to meet the needs of such firms. For investors in general, equity investing is the best means available for participating in the returns (and risks) of corporate wealth creation—share prices will reflect expectations and results in terms of profitability, market share growth, and managerial decisions.

23. Why should investors consider common stock as an investment vehicle if they have a long-term time horizon?An analysis of returns on an after-tax, after-inflation basis shows that common stocks have earned positive returns over time. Other securities, such as Treasury bonds, have lower after-tax returns while others (such as T-bills have lost money after calculating real, after-tax returns.

24. Why does dividend income growth exceed that of bond income growth over a period of time?Dividends can grow along with a company—rising sales and profits can lead to increases in dividends paid to increases in payments to the firm’s owners—its common shareholders. Bonds have contractually determined payments (coupon interest) which are typically fixed during the bond’s life. Coupon rates will rise and fall with the general trend of interest rates as new bond issues are sold but except for convertible bonds (which comprise a small

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fraction of all bond issues) they do not participate in a firm’s growth in cash flows over time.

25. What is a capital gain? Is it taxed the same way as dividends?A change in an asset’s price results in a capital gain (if its price rose) or a capital loss (if its price fell). Unlike dividends, capital gains are not taxable until the asset is sold and the gain is “realized.” Capital gains tax rates (per the 2010 tax code) are lower than ordinary income tax rates but are similar to those paid on qualifying dividends.

26. “Taxes on capital gains can be deferred.” Explain what is meant by this statement.If you buy a stock any increase in the price of that stock is not taxed until the stock is sold. Year-by-year increases in value are not taxable each year (and neither do any losses reduce taxable income). Only when the asset is sold does the gain (or loss) become “realized” and taxes are owed. If the asset is not sold, the tax implications of any gains or losses are postponed—or deferred.

27. Explain how a capital loss on the sale of a firm’s stock can affect an investor’s taxes.If an investor sells an asset at a capital loss, the loss can be deducted from any capital gain before taxes are calculated. This has the potential effect of reducing or eliminating any tax on the investor’s capital gains. Suppose stock A is sold with a long-term capital gain of $1,000 and stock B is sold with a long-term capital loss of $600. The net long-term capital gain for the investor will be $1,000 - $600 = $400. The investor will pay tax, at either the 5% or 15% marginal rate, on the $400 net long-term capital gain. If the investor had total long-term capital losses of $1,000, the net long-term capital gain would be zero and no capital gains taxes would be owed.

28. What is a round lot of common stock?A round lot equals 100 shares. Commissions are lower when an investor trades in terms of round lots. For high-priced issues (such as Berkshire Hathaway) a round lot will comprise 10 shares.

29. Describe some of the characteristics of common stock.Common stock represents ownership in the firm. Common shareholders can vote for the firm’s board of directors and other major issues as allowed by the firm’s charter. Common stock has a residual claim on the firm’s assets and earnings in case of bankruptcy. Some of the firm’s profits may be distributed to common shareholders if dividends are declared by the board of directors. The dividend can increase, decrease, remain stable, or be eliminated.

30. List and briefly explain the special features usually associated with preferred stock.Preferred stock carries a fixed dividend, expressed either as a dollar amount or as a percent of par value. They have a preference over common shareholders with respect to earnings and assets in case of bankruptcy. Shareholders have no voting rights, except in certain circumstances if dividends are missed. It may be cumulative (all dividends in arrears must be paid before common shareholders receive dividends) or non-cumulative. Preferred stock can be convertible into shares of common stock or callable by the issuer.

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31. How do firms decide how much of their earnings to distribute as dividends?There are several methods firms use. One is to maintain a target dividend payout ratio (dividends per share divided by earnings per share) over time.

Investors like predictability—so the board of directors will refrain from changing the dollar amount of dividends per share by large, unsustainable amounts. If the firm does have excess cash it decides to return to shareholders it can declare a special dividend or initiate a share repurchase program.

In addition to the sustainability of the level of dividends, other considerations include growth opportunities facing the firm (should it reinvest in itself or distribute funds to shareholders); the cost of other financing sources such as debt; tax rates on dividends; and legal considerations (a firm cannot issue dividends if doing so reduces its equity below the stock’s par value or if it will violate a bond or loan indenture in some manner.

32. Explain how an investor may view a stock dividend, a stock split, and a stock repurchase plan with regards to the value of his stock holdings.Stock dividends and stock splits should have no impact on firm value; they are little more than accounting entries adjusting the number of shares outstanding by the firm and the number of shares owned by an investor. A share repurchase plan is viewed positively as the firm is using funds to reduce the amount of shares outstanding. Under the laws of supply and demand this will increase the stock price above what it would be otherwise. Any gains from stock price increases are deferred until an investor’s shares are sold.

33. Describe the process for valuing a preferred stock.Since the cash dividends of a preferred stock are similar in nature to a perpetuity, they can be valued using the perpetuity relationship. This is usually done by dividing the periodic dividend by the preferred shareholders’ required rate of return.

34. Describe the process for valuing a common stock when the cash dividend is expected to grow at a constant rate. As long as the expected growth rate is less than the common shareholders’ required rate of return, the Gordon model or constant dividend growth model can be used. Today’s stock price is estimated by dividing next year’s expected dividend (which is this year’s dividend increased by the growth rate) divided by the difference between the shareholders’ required return and the dividend growth rate.

35. Discuss the risks faced by common shareholders that are not related to the general level of interest rates.As stockholders have a lower priority than bondholders on a firm’s cash flows and assets, any risk (poor management decisions, adverse change in exchange rates, competitive pressures, new products) that reduces cash flows or the value of a firm’s assets is primarily borne by a firm’s shareholders. Ethical lapses by management will harm a firm’s stock price. In addition, as the constant-growth model shows, much of a firm’s stock value is due to

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expectations of future growth. If growth expectations change due to economic or product market factors, the value of the stock will fall.

36. Under what economic forecast would you believe an auto manufacturer would be a good investment? A computer manufacturer?As the sales of auto manufacturers are typically related to the stage of the business cycle, an economic forecast of continued growth (business cycle upswing) may make an auto manufacturer an attractive investment. Other helpful economic signs include, for firms with large overseas sales, forecasts of higher growth in overseas economies and a weaker dollar. Higher growth overseas may help stimulate auto exports from the U.S. A weaker dollar will allow the auto manufacturer to a) increase dollar cash flows from sales, and/or b) lower prices (in terms of the foreign currency) without harming U.S. dollar cash flows.

A desirable economic forecast for a computer firm is similar to that of an auto manufacturer. Rising levels of income and sales associated with periods of economic growth will stimulate demand for computers, for homes, offices and for increased technology in the assembly line for manufacturing firms. Similarly, overseas sales may be assisted by robust overseas economic growth and a weaker dollar.

37. Discuss how changes in exchange rates can affect the outlook for both global and domestic firms.Changing exchange rates may affect sales both at home and abroad. If overseas suppliers or labor are used, changing exchange rates may affect costs as well. In general, a weakening home currency helps increase home currency cash flows from sales. For example, a weakening dollar (and a stronger euro) will help U.S.-based firms as euro sales are converted into more dollars as the stronger euro can purchase more dollars. A weaker dollar can help domestic firms, too, as it may cause imports to rise in price as firms raise dollar prices in order to maintain their home-currency cash flows. If a firm has a large expense presence overseas, a weakening currency can lead to higher expenses (for labor or supplies), thus hurting profitability.

Interest-rate sensitive firms may be affected by stronger or weaker home currencies if the changing level of exchange rates puts pressure on home country interest rates. A weakening home currency may lead to higher domestic interest rates.

38. What can looking at data on inventories tell us about the condition of the economy? Data on business expansion or investment plans? Firms produce inventories to sell; if sales rise, inventories will fall. To maintain an appropriate level of supplies and finished product, the firm may have to increase orders of raw materials, pay overtime or hire additional workers, and increase production. Thus, falling inventories may indicate growing consumer demand and continued economic growth. Rising inventories can indicate a weakening economy; lower sales accompanied by rising inventories may lead to supply cutbacks and worker layoffs.

Business plans to expand or invest in plant and equipment are good signs for future economic growth. Businesses invest in themselves based upon the outlook for future sales and profitability. This investment will, in turn, help supplier firms, construction firms, and will keep workers fully employed. Cutbacks in business investment are an indication of slower economic growth or recession.

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39. Is industry competition good or bad if you are looking for attractive stock investments?Firms that have some advantage over their rivals may be attractive stock investments. With a competitive advantage, firms can maintain profitability through higher prices, higher sales volumes, or lower expenses. Firms that can protect themselves against revenue-lowering price competition or expense-raising non-price competition may be good investments if they are attractively priced.

40. Give examples of firms you believe have been successful over time because they are industry leaders in quality; they are the low-cost producer; they are innovative; they offer superior customer service.The answer to this question depends upon when it is being answered as firm’s fortunes do rise and fall over time. At the time of this writing, examples of quality leaders include General Electric, Cisco, and Honda; examples of low-cost producers are Vanguard (mutual funds), Wal-Mart and UPS; examples of historically innovative firms are 3M and some pharmaceutical firms such as Merck and Johnson & Johnson; examples of firms offering superior customer service may include FedEx, Virgin Atlantic airlines, and Merrill Lynch.

41. Energy prices are forecast to go higher. How would this affect your decision to purchase the stocks and bonds of a) ExxonMobil? b) American Airlines? c) Ford? d) Archer Daniels Midland, a food processor? The investment decision will be affected by the current prices of these firm’s securities and the expected affect of higher energy prices on the firm’s profits and cash flows. a) ExxonMobil: as an oil exploration, drilling, refining and distribution firm, they will benefit as their sales revenues may rise while the costs of drilling and refining oil should remain relatively constant. b) American Airlines is a large consumer of energy—it consumes huge amounts of jet fuel. Their profits will fall due to higher fuel prices. c) Ford may experience a shift in sales by energy conscious consumers from higher-profit margin trucks and SUVs to lower-margin passenger cars, thus reducing profits. d) Archer Daniels Midland will likely face a profit squeeze, too. As a food processor, they purchase items from the agricultural sector, which uses a great deal of energy in the farming, fertilizing, and transportation process (thus, their raw materials prices may raise). In addition, they will face higher costs as the process of converting agricultural products into food items is energy-intensive.

PROBLEMS AND ANSWERS1. Compute the annual interest payments and principal amount for a Treasury Inflation-

Protected Security with a par value of $1,000 and a 3-percent interest rate if inflation is 4 percent in year 1, 5 percent in year 2, and 6 percent in year 3.

After the first year, the par value rises by the inflation rate of 4% to become $1000 (1.04) = $1040. The annual coupon interest will be 3% of par, 0.03 x $1040 = $31.20. In the second year, the par value rises by another 5%: (1.05)($1040) = $1092. The second year’s coupon interest is 3% of this new par value: 0.03 x $1092 = $32.76, and similarly in year 3 with its inflation rate of 6%: new par value = (1.06)($1092) = $1,157.52; interest = 0.03 x $1157.52 = $34.73

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Par value $1,000 Interest rate 3%

Annual couponYear Inflation Par value Interest1 4% $1,040.00 $31.202 5% $1,092.00 $32.763 6% $1,157.52 $34.73

2. Judy Johnson is choosing between investing in two Treasury securities that both mature in five years and have par values of $1,000. One is a Treasury note paying an annual coupon of 5.06 percent. The other is a TIPS which pays 3 percent interest annually.

a. If inflation remains constant at 2 percent annually over the next five years what will be Judy’s annual interest income from the TIPS bond? From the Treasury note?

Judy’s annual interest from the Treasury note is a constant 5.06% of par, or 0.0506 x $1000 = $50.60. For the TIPS, the year 1 interest is based on the bond’s par value and 2% inflation. At the end of year 1, the par value will be 1.02 x $1000 = $1020 and its interest payment will be 3% of this par value: 0.03 x $1020 = $30.60. This annual interest income will increase by the 2% annual inflation rate during years 2-5 as seen in the following table.

Par value $1,000 Treasury note 5.06% interest rateTIPS 3.00% interest rate

Treasury note TIPSAnnual coupon Annual coupon

YearPar

value interestinflatio

n Par value Interest1 $1,000 $50.60 2% $1,020.00 $30.602 $1,000 $50.60 2% $1,040.40 $31.213 $1,000 $50.60 2% $1,061.21 $31.844 $1,000 $50.60 2% $1,082.43 $32.475 $1,000 $50.60 2% $1,104.08 $33.12

TOTAL RECEIPTS $1,000 $253.00 $1,104.08 $159.24

b. How much interest will Judy receive over the five years from the Treasury note? From the TIPS?

Treasury note: Judy receives interest of $50.60 annually; over five years, this total 5 x

$50.60 = $253.00.TIPS: Summing the interest payments computed in part a), Judy expects to receive interest

payments of $159.24 over five years.

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c. When each bond matures, what par value will Judy receive from the Treasury note? The TIPS?

The Treasury note has a par value of $1,000, which she received at maturity. The TIPS par value changes according to the cumulative change in the price level of the five years. If inflation is 2-percent annually, the par value on the TIPS will be $1,104.08 as shown in the previous table. It can also be computed by compounding 2% inflation annually on the initial $1000 par value: $1,000 x (1.02)5 = $1,000 x 1.10408 = $1,104.08.

d. After five years, what is Judy’s total income (interest + par) from each bond? Should she use this total as a way of deciding which bond to purchase?

Treasury note: Over five years, Judy will receive $253 in interest (from part a) plus $1000 par value for a total of $1253.TIPS: Over five years, Judy will receive $159.24 in interest (from part a) plus $1,104.08 par value (from part c) for a total of $1263.32.No, comparing total funds received over the five-year time to maturity is not a good way to evaluate the bonds. By summing the funds over time, the effect of the time value of money is ignored. An appropriate procedure would consider time value of money.

3. Using the regular Treasury note of problem 2;

a. What is its price if investors’ required rate of return is 6.09 % on similar bonds? Treasury notes pay interest semiannually.

With a time to maturity of five years and coupons paid semiannually, the number of periods is 5 x 2 = 10; the periodic rate is the semiannual rate which compounds to 6.09%:(1 + r)2 – 1 = 0.0609. Solving for r, the periodic rate is 3.00 percent.The note’s coupon rate from problem 2 is 5.06%. The semiannual coupon income is 0.0506 x $1000 divided by 2, or $25.30.Using the tables with an interest of 3% and 10 periods yields the following results:PV of coupon interest annuity = $25.30 x 8.530 = $215.81PV of par value = $1,000 x 0.744 = $744.00The price of the Treasury bond will be $744.00 + $215.81 = $959.81Using a financial calculator, the answer is: $959.91

b. Erron Corporation wants to issue five-year notes but investors require a credit risk spread of three percentage points. What is the anticipated coupon rate on the Erron notes?

Erron’s notes will have a higher required return because of higher default or credit risk. The expected required rate of return on the five-year Erron notes equals the five-year Treasury note rate + credit risk premium = 6.09 % + 3% = 9.09%. When debt securities are issued, they are usually issued at a coupon rate close to the current market’s required rate of return on securities of similar maturity and risk. Thus, we expect Erron’s note coupon rate to be close to 9.09%.

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4. Assume a $1,000 face value bond has a coupon rate of 8.5 percent paid semiannually and has an eight-year life. If investors are willing to accept a 10.25 percent rate of return on bonds of similar quality, what is the present value or worth of this bond?

The periodic interest rate is the value of r such that (1+r)2 – 1 = 0.1025; r = 0.05 or 5%. The semiannual coupon is $85/2 = $42.50; the number of periods is 8 years x 2 or 16 periods.Price = $42.50 × PVIFA(5%, 16) + $1,000 × PVIF(5%, 16) = $42.50(10.838) + $1,000(0.45811) = $918.72The Excel command for computing this is =PV(0.05, 16, 42.5, 1000).

5. a. By how much would the value of the bond in Problem 4 change if investors wanted an 8-percent rate of return?The periodic interest rate is the value of r such that (1+r)2 – 1 = 0.08; r = 0.03923 or 3.923%. Price = $42.50 × PVIFA(3.923%, 16) + $1,000 × PVIF(3.923%, 16) = $42.50(11.719) + $1,000(.54027) = $1,038.32The Excel command for computing this is =PV(0.03923, 16, 42.5, 1000)Difference in price = $1,038.32 – $918.72 = $119.60 higher

b. A bond with the same par value and coupon rate as the bond in Problem 4 has 14 years until maturity. If investors will use a 10.25 percent discount rate to value this bond, by how much should its price differ from the bond in Problem 4?The periodic rate is the same as in problem 4, 5 percent. The number of periods is 14 x 2 or 28.Price of 14 year bond = $42.50 × PVIFA(5%, 28) + $1,000 × PVIF(5%, 28) = $42.50(14.898) + $1,000(.25509) = $888.26The Excel command for computing this is =PV(0.05, 28, 42.5, 1000)Difference in price = $918.72 – 888.26 = $30.46 lower

6. The Garcia Company’s bonds have a face value of $1,000, will mature in 10 years, and carry a coupon rate of 16 percent. Assume interest payments are made semiannually.

a. Determine the present value of the bond’s cash flows if the required rate of return is 16.64 percent.The periodic interest rate is the value of r such that (1+r)2 – 1 = 0.1664; r = 0.08 or 8%. The semiannual coupon is $160/2 = $80; the number of periods is 10 years x 2 or 20 periods.Price = $80 × PVIFA(8%, 20) + $1,000 × PVIF(8%, 20) = $80(9.818) + $1,000(.21455) = $1,000The Excel command for computing this is =PV(0.08, 20, 80, 1000)

b. How would your answer change if the required rate of return is 12.36 percent?The periodic interest rate is the value of r such that (1+r)2 – 1 = 0.1236; r = 0.06 or 6%. Price = $80 × PVIFA(6%, 20) + $1,000 × PVIF(6%, 20) = $80(11.470) + $1,000(.31180) = $1,229.40The Excel command for computing this is =PV(0.06, 20, 80, 1000).

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7. Judith, Inc. bonds mature in 8 years and pay a semi-annual coupon of $55. The bond’s par value is $1,000.

a. What is their current price if the market interest rate for bonds of similar quality is 9.2%?

Assuming the first cell is cell A1 the spreadsheet template on page 185 of the text can be used to solve this; a financial calculator, using the inputs below, can also be used.

Computing Bond Price using EAR (effective annual rate)Coupon Rate 8.00%Number of years until maturity 8.00Number of coupon payments per year 2.00Par Value $1,000.00 Market rate 9.20% (EAR)

Compute periodic interest rate: 4.50% equals [(1 + B7)^(1/B5)] minus 1Compute number of periods: 16.00 equals B4 * B5Compute coupon cash flow: $55.00 Given

Bond price $1,112.48 equals -PV(B9, B10, B11, B6, 0)

b. A change in Fed policy increases market interest rates 0.50 percentage points from their level in part a. What is the percentage change in the value of Judith, Inc. bonds from their value in part a?




Bond price $1,084.17 equals -PV(B9, B10, B11, B6, 0)Percentage change: -2.54%

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c. Better profits for Judith, Inc. reduces the market interest rate for its bonds to 9.0%. What is the percentage change in the value of Judith, Inc. bonds from the answer in part b?




Bond price $1,124.10 equals -PV(B9, B10, B11, B6, 0)Percentage change: 3.68%

8. Kamins Corporation has two bond issues outstanding, each with a par value of $1,000. Information about each is listed below. Suppose market interest rates rise 1 percentage point across the yield curve. What will be the change in price for each of the bonds? Does this tell us anything about the relationship between time to maturity and interest rate risk?

Bond A: 5 years to maturity, 8% coupon, market interest rate is 9%

Bond B: 12 years to maturity, 8% coupon, market interest rate is 9%

Assuming the first cell in each analysis is cell A1, the spreadsheet template on page 185 of the text can be used to solve this; a financial calculator, using the inputs below, can also be used.

Problem 8--original Bond AComputing Bond Price using EAR (effective annual rate)Coupon Rate 8.00%Number of years until maturity 5.00Number of coupon payments per year 2.00Par Value $1,000.00 Market rate 9.00% (EAR)

Compute periodic interest rate: 4.40% equals [(1 + B7)^(1/B5)] minus 1Compute number of periods: 10.00 equals B4 * B5Compute coupon cash flow: $40.00 equals (B3 *B6)/B5

Bond price $967.95 equals -PV(B9, B10, B11, B6, 0)

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Problem 8--Bond A with higher market rateComputing Bond Price using EAR (effective annual rate)Coupon Rate 8.00%Number of years until maturity 5.00Number of coupon payments per year 2.00Par Value $1,000.00 Market rate 10.00% (EAR)


Bond price $931.59 equals -PV(B9, B10, B11, B6, 0)Percentage change: -3.76%

Problem 8--original Bond BComputing Bond Price using EAR (effective annual rate)Coupon Rate 8.00%Number of years until maturity 12.00Number of coupon payments per year 2.00Par Value $1,000.00 Market rate 9.00% (EAR)



Problem 8--Bond B with higher market rateComputing Bond Price using EAR (effective annual rate)Coupon Rate 8.00%Number of years until maturity 12.00Number of coupon payments per year 2.00Par Value $1,000.00 Market rate 10.00% (EAR)


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Based upon these answers, longer time to maturity results ingreater bond price volatility for the same percentage pointchange in the market interest rate.

9. Billon Corporation has two bond issues outstanding, each with a par value of $1,000. Information about each is listed below. Suppose market interest rates rise 1 percentage point across the yield curve. What will be the change in price for each of the bonds? Does this tell us anything about the relationship between coupon rate and interest rate risk?

Bond A: 10 years to maturity, 0% coupon, market interest rate is 9.62%.

Bond B: 10 years to maturity, 10% coupon, market interest rate is 9.62%.






Compute periodic interest rate: 5.18% equals [(1 + B7)^(1/B5)] minus 1Compute number of periods: 20.00 equals B4 * B5

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Compute coupon cash flow: $0.00 equals (B3 *B6)/B5




Bond price $1,038.41 equals -PV(B9, B10, B11, B6, 0)




Based upon these answers, a lower coupon rate results ingreater bond price volatility for the same percentage pointchange in the market interest rate.

10. Koppen Corporation has two bond issues outstanding, each with a par value of $1,000. Information about each is listed below. Suppose market interest rates rise 1 percentage point across the yield curve. What will be the change in price for each of the bonds? Does this tell us anything about the relationship between frequency of cash flows and interest rate risk?

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Bond A: This bond is a Eurobond. It has 10 years to maturity, pays a 7% coupon, and the market interest rate is 11.3%.

Bond B: This is a issued in the U.S. It has 10 years to maturity, pays a 7% coupon, and the market interest rate is 11.3%.








Problem 10--original Bond BComputing Bond Price using EAR (effective annual rate)Coupon Rate 7.00%Number of years until maturity 10.00Number of coupon payments per year 2.00Par Value $1,000.00

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Market rate 11.30% (EAR)






Based upon these answers, less frequent coupon payments (once/yearrather than twice/year) result in greater bond price volatility for the same percentage pointchange in the market interest rate.

11. BVA Inc. has two bond issues outstanding, each with a par value of $1,000. Information about each is listed below. Suppose market interest rates rise 1 percentage point across the yield curve. What will be the change in price for each of the bonds? Does this tell us anything about the relationship between initial yield to maturity and interest rate risk?

Bond A: 12 years to maturity, pays a 7% coupon, and the market interest rate on this BB-rated bond is 12.36%.

Bond B: 12 years to maturity, pays a 7% coupon, and the market interest rate on this A-rated bond is 10.25%.


Problem 11--original Bond AComputing Bond Price using EAR (effective annual rate)Coupon Rate 7.00%

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Number of years until maturity 12.00Number of coupon payments per year 2.00Par Value $1,000.00 Market rate 12.36% (EAR)









Problem 11--Bond B with higher market rateComputing Bond Price using EAR (effective annual rate)

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Coupon Rate 7.00%Number of years until maturity 12.00Number of coupon payments per year 2.00Par Value $1,000.00 Market rate 11.25% (EAR)



Based upon these answers, the lower market interest rate results in greater bond price volatility for the same percentagepoint change in the market interest rate.

12. What is the approximate yield to maturity (use formula 10-3) and the exact yield to maturity (use a calculator) for the following bonds? Assume these are bonds issued in the U.S.

For each of these problems, since we were not told otherwise, we will assume a par value of $1,000 and semi-annual coupon payments.

a. 10 years to maturity, 6% coupon rate, current price is $950.

Approximate YTM = $60 + ($1000 – 950)/10 = $65/$975 = 6.67%

($1000+950)/2

Financial calculator (N=20, PMT=30, FV=1000, PV= -950): YTM = 6.81% [(1.03347)2 – 1]

b. 16 years to maturity, 0% coupon rate, current price is $339.

Approximate YTM = $0 + ($1000 – 339)/16 = $41.3125/$669.5 = 6.17%

($1000+339)/2

Financial calculator (N=30, PMT=0, FV=1000, PV= -339): YTM = 6.99%

c. 25 years to maturity, 8.5% coupon rate, current price is $1030.

Approximate YTM = $85 + ($1000 – 1030)/25 = $83.8/$1015 = 8.26%

($1000+1030)/2

Financial calculator (N=50, PMT=42.5, FV=1000, PV= -1030): YTM = 8.38% [(1.041078)2 – 1]

13. On Thursday, the following bond price quotation appears in the newspaper. Interpret each item that appears in the quote and compute its current yield.

Last Last Est Est $ Vol

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Company (Ticker) Coupon Maturity Price Yield Spread UST (000’s)Wal-Mart StoresWMT 4.550 May 1, 2013 99.270 4.649 47 10 66,830

The ticker symbol (WMT)—stock trading ticker symbol for Wal-Mart stock.Coupon rate is 4.550 percent; with a $1,000par value, Wal-Mart pays interest of 0.04550 x

1,000 = $45.50 per year or $22.75 every six months.The bond matures and par value payment is due on May 1, 2013. The closing price of the bond is 99.270 percent of par or $992.70; since the quote appears in

Thursday’s paper, this is the closing price on Wednesday.

Current yield is found by dividing the annual coupon interest by the current price. This equals $45.50/$992.70 = 4.58 percent.

“Last Yield” represents the bond’s yield to maturity, 4.649. It differs from the current yield as it incorporates both the coupon interest and the difference in current priced par value.

“Estimated Spread” is the difference between the yield to maturity on the Wal-Mart bond and a similar maturity U.S. Treasury bond. The spread is 47 basis points (0.47%) from the yield to maturity on Treasury security that matures in 10 years, as seen by the number under the “UST” column. Since the Wal-Mart bond has a yield to maturity of 4.649 percent the 10-year Treasury security must have a yield to maturity of about 4.649% - 0.47% = 4.179 percent.

The “Vol” column represents actual bond trading volume in thousands of dollars. The market value (quantity traded times last price) of the trading volume is $66,830,000. With a last price of $992.70, the approximate number of this type of Wal-Mart bond that traded is $66,830,000/$992.70 = 67,321.

14. Perusing the corporate bond quotations, you write down some summary information: Last Last Est Est $ VolCompany (Ticker) Coupon Maturity Price Yield Spread UST (000’s)Wal-Mart StoresWMT 4.550 10 years 99.270 4.649 47 10 66,830Wal-Mart StoresWMT 4.125 8 years 99.554 4.200 2 10 50,320Liberty Media L 5.700 10 years 102.750 5.314 112 10 26,045Ford Motor Credit F 7.250 8 years 107.407 6.012 183 10 22,863

a. Which company is the riskiest? Why?Which company is riskiest is a matter of opinion or additional research; the bond listings do not give information on a firm’s level of risk, only on a bond issue’s risk.

b. Which bond has the highest default risk? Why?The bond with the highest default is the Ford Motor bond; it was the highest spread relative to a similar U.S. Treasury bond.

c. Why would Wal-Mart have two bonds trading at different yields?

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Part of the reason for the difference in yields could be the time to maturity, as the bond with the shorter time to maturity has the lower yield. Another reason could be the two bond issues may have different covenants or bond ratings so credit risk differs.

d. Compute the current yield for each of the four bonds.Wal-Mart 10 years $45.50/$992.70 = 4.58%Wal-Mart 8 years $41.25/$995.54 = 4.14%Liberty Media 10 years $57.00/$1027.50 = 5.55%Ford Motor Credit 8 years $72.50/$1074.07 = 6.75%

e. Compute yield to maturity for each of the four bonds. Wal-Mart 10- year bond: 4.64%Wal-Mart 8-year bond: 4.23%Liberty Media 10-year bond: 5.35%Ford Motor Credit 8-year bond: 6.10%

15. You run across the following bond quotation on a Friday. Maturity AskedRate Mo/Yr Bid Asked Chg. Yld7.500 Nov 24 131:06 131:07 -9 5.04

a. What kind of security is it? This is the quote we see in the newspapers for a Treasury security; specifically, a Treasury bond as it matures (in November 2024) more than 10 years from now. If it matured less than 10 years from now it would be a Treasury note; less than 1 year from now, it would be a Treasury bill.

b. Interpret the information that is contained in the quote.Rate: The coupon rate for the bond is 7.500 percent of par value, meaning that a $1000 par value bond will pay $75of interest annually in two semiannual payments of $37.50.Maturity: The bond matures in November 2024.Bid: The bid price, or the price received by investors selling bonds, is 131 6/32 percent of par, or $1,311.875.Ask: The ask price, or the price paid by investors purchasing the bonds, is 131 7/32 of par or $1,312,1875. The bid-ask spread represents dealer profit, or $0.3125 per $1000 par value bond. Spreads are often an indicator of how liquid a security is; the narrower the bid-ask spread, the greater the liquidity (and, usually, the greater the trading volume). Chg: The change in price from the previous day was –9/32 of a percentage point. Asked yld: The yield to maturity, based on the asked price, is 5.04 percent.

c. Suppose a corporate bond with the same time to maturity has a credit-risk spread of 250 basis points. What should be the yield to maturity for the corporate bond?

A credit-risk spread of 250 basis points, or 2.50 percentage points, means the corporate bond’s yield to maturity will be 5.04% + 2.50% = 7.54%

16. A $1,000 face value bond issued by the Dysane Company currently pays total annual interest of $79 per year and has a 13-year life.

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a. What is the present value, or worth, of this bond if investors are currently willing to accept a 10 percent annual rate of return on bonds of similar quality if the bond is a Eurobond?As a Eurobond, coupon interest is paid on an annual basis:Price = $79 × PVIFA(10%,13) + $1,000 × PVIF (10%,13) = $79(7.103) + $1,000(.290) = $851.14\

b. How would your answer in Part a change if the bond is a U.S. bond?Coupon interest is paid semiannually, so

Periodic rate r = (1.10)1/2

– 1 = 0.0488 or 4.88%; n = 13 × 2 = 26Price = $39.50 × PVIFA(4.88%,26) + $1,000(4.88%,26) = $39.50(14.555) + $1,000(.290) = $864.92

c. How would your answer in Part b change if, one year from now, investors only required a 6.5 percent annual rate of return on bond investments similar in quality to the Dysane bond?

Periodic rate r = (1.065)1/2

– 1 = 0.0320 or 3.20% n = 12 × 2 = 24Price = $39.50 × PVIFA(3.20%,24) + $1,000 × PVIF(3.20%,24) = $39.50(16.576) + $1,000(.470) = $1,124.75

d. Suppose the original bond can be purchased for $925. What is the bond’s yield to maturity?Calculator solution: 925 press PV; 1000 press FV; 79 press PMT; 13 press N; Compute %iSolution: 8.90%

17. a. You own a two-bond portfolio. Each has a par value of $1000. Bond A matures in 5 years, has a coupon rate of 8 percent, and has a annual yield to maturity of 9.20 percent. Bond B matures in 15 years, has a coupon rate of 8 percent and has an annual yield to maturity of 9.20 percent. Both bonds pay interest semiannually. What is the value of your portfolio? What happens to the value of your portfolio if each yield to maturity rises by one percentage point?

For Bond A: the periodic interest rate is the value of r such that (1+r)2 – 1 = 0.092; r = 0.045 or 4.5%. The semi-annual coupon is $80/2 = $40; the number of periods is 5 years x 2 or 10 periods.

Price = $40 × PVIFA(4.5%,10) + $1,000 × PVIF(4.5%,10) = $40(7.913) + $1,000(0.64393) = $960.45

The Excel command for computing this is =PV(0.045, 10, 40, 1000).

For Bond B: the periodic interest rate is the value of r such that (1+r)2 – 1 = 0.092; r = 0.045 or 4.5%. The semi-annual coupon is $80/2 = $40; the number of

periods is 15 years x 2 or 30 periods.

Price = $40 × PVIFA(4.5%,30) + $1,000 × PVIF(4.5%,30) = $40(16.289) + $1,000(0.26700) = $918.56

The Excel command for computing this is =PV(0.045, 30, 40, 1000).

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The total value of the portfolio (Bond A + Bond B) $960.45 + $918.56=$1,879.01.

If the yield to maturity on each bond rises by one percentage point, the periodic interest rate is the value of r such that (1+r)2 – 1 = 0.0102; r = 0.04976 or 4.976%.

New value of bond A: Price = $40 × PVIFA(4.976%,10) + $1,000 × PVIF(4.976%,10) = $40(7.731) + $1,000(0.61531) = $924.55 New value of bond B: Price = $40 × PVIFA(4.976%,30) + $1,000 × PVIF(4.976%,30) = $40(15.414) + $1,000(0.23296) = $849.52

New portfolio value = $924.55 + $849.52 = $1,774.07

b. Rather than own a 5-year bond and a 15-year bond, suppose you sell both of them and invest in two 10-year bonds. Each has a coupon rate of 8 percent paid semiannually and has a yield to maturity of 9.20 percent. What is the value of your portfolio? What happens to the value of your portfolio if the yield to maturity on the bonds rises by one percentage point?

For the 10-year bonds, the periodic interest rate is the value of r such that (1+r)2 – 1 = 0.092; r = 0.045 or 4.5%. The semiannual coupon is $80/2 = $40; the number of periods is 10 years x 2 or 20 periods. Price = $40 × PVIFA(4.5%,20) + $1,000 × PVIF(4.5%,20)

= $40(13.008) + $1,000(0.41464) = $934.96 The Excel command for computing this is =PV(0.045, 20, 40, 1000).

Since both bonds are identical, the value of the portfolio is 2x $934.96 = $1,869.92.

If the yield to maturity on each bond rises by one percentage point, the periodic interest rate is the value of r such that (1+r)2 – 1 = 0.0102; r = 0.04976 or 4.976%.

New value of the bonds: Price = $40 × PVIFA(4.976%,20) + $1,000 × PVIF(4.976%, 20) = $40(12.488) + $1,000(0.37860) = $878.12 Since both bonds are identical, the value of the portfolio is

2x $878.12 = $1,756.24.

c. Based upon your answers to parts a) and b), evaluate the price changes between the two portfolios. Were the price changes the same? Why or why not?

Effect of a 1-percent increase in the yield to maturity:

Five and 15-year bond portfolio: The portfolio value fell from $1,879.01 to $1,774.07, a total of $104.94 or 5.58 percent.

Two ten-year bond portfolio: The portfolio value fell from $1,869.92 to $1,756.24, a total of $113.68 or 6.08 percent.

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Although the average portfolio bond time-to-maturity was 10 years in both portfolios, the changes in portfolio values were not the same. This is because present values weight earlier cash flows more heavily than later cash flows. This is easily seen by comparing the present value of the $1,000 par value when the yield to maturity is 9.2 percent:

Time to maturity 5 years 10 years 15 years Present value of $1,000 $643.93 $414.64 $267.00 The average of the 5- and 10-year present values is ($643.93 + $267.00)/2 =

$455.47; this is greater than the 10-year present value of $414.64.

18. A bond with a par value of $1000 has a coupon rate of 7 percent and matures in 15 years. Using a spreadsheet program, graph its price versus different yields to maturity, ranging from 1 percent to 20 percent. Is the relationship between price and yield linear? Why?Semi-annual coupons = $35; number of periods = 15 x 2 = 30A spreadsheet can be used to find the value of a bond with yields to maturity in different cells, ranging from 1 percent to 20 percent. The Chart Wizard in Excel can be used to plot the bond prices and yields. The relationship between price and yield to maturity is not linear as the present value equations require the use of exponents.The present value decreases more sharply the higher the yield we use for discounting.

19. Global Cycles (GC) offers investors a DRIP program. An investor purchases 100 shares of GC at a price of $20 per share on January 2. How many shares will the investor own on December 31 if the following dividends are paid and the investor participates in the DRIP program (assume the firm allows fractional shares and accounts for them up to three decimal places)? If the stock’s price is $27.50 on December 31 what is the value of her investment in GC?

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March 1: dividend paid of $0.50 per share; stock price is $21June 1: dividend paid of $0.50 per share; stock price is $22.5September 1: dividend paid of $0.55 per share; stock price is $19December 1: dividend paid of $0.55 per share; stock price is $25

March 1: total dividends received are $0.50/share x 100 shares = $50. The investor is able to purchase shares equal to $50/$21 = 2.381 shares. The total number of shares owned is now 100 + 2.381 = 102.381.

June 1: total dividends received are $0.50/share x 102.381 shares = $51.19. The investor is able to purchase shares equal to $51.19/$22.5 = 2.275 shares. The total number of shares owned is now 102.381+ 2.275 = 104.656.

September 1: total dividends received are $0.55/share x 104.656 shares = $57.56. The investor is able to purchase shares equal to $57.56/$19 = 3.030 shares. The total number of shares owned is now 104.656 + 3.030 = 107.686.

December 1: total dividends received are $0.55/share x 107.686 shares = $59.23. The investor is able to purchase shares equal to $59.23/$25 = 2.369 shares. The total number of shares owned is now 107.686 + 2.369 = 110.055.

On December 31: value of the stock holding = $27.50 x 110.055 = $3,026.51.

20. If a stock’s earnings per share is $2.00 what will be the dividend per share if the payout ratio is 40%? If the following year’s earnings per share is $2.10 what will the payout ratio be if the firm wants to maintain dividend growth of 8 percent?

Dividend = earnings per shares x payout ratio = $2.00 x 0.40 = $0.80.

At 8% dividend growth the next year’s dividend will be $0.80 x 1.08 = $0.86 (rounded to the nearest penny).If dividends per share = $0.86 and earnings per share is $2.10, the dividend payout ratio is: $0.86 / $2.10 = 0.41 or 41%

21. You purchased 200 shares of H2O Corporation stock at a price of $20. Consider each of the following announcements separately. What will the price of the stock be after each change? How many shares will you own? What will be the total value of your holdings (value of stock plus any income)?

a. The firm announces a 10 percent stock dividend.Your current wealth in the stock of the company is 200 shares x $20 = $4,000.After the 10% stock dividend the number of shares you own rises 10% to 220 shares but the market price of the stock will fall by 10% to about $18.18 so your wealth in the stock will remain at $4,000. In the case of stock dividends no new wealth is created so value of holdings before the stock dividend will equal the value of the holdings after the stock dividend.

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b. The firm announces a 2-for-1 stock splitYour current wealth in the stock of the company is 200 shares x $20 = $4,000.After the 2-for-1 stock split the number of shares you own rises 400 shares but the market price of the stock will fall by half to $10 so your wealth in the stock will remain at $4,000. In the case of stock splits no new wealth is created so value of holdings before the stock split will equal the value of the holdings after the stock split.

c. The firm announces a $0.50 per share dividend (in your answer use the price of the stock on the ex-dividend date).

Your current wealth in the stock of the company is 200 shares x $20 = $4,000.You will receive income (dividends) of $0.50 x 200 shares = $100.The value of the stock will fall by $0.50 on the ex-dividend date from $20 to $19.50 per share. This occurs as the firm has distributed assets totaling $0.50/share to its shareholders.After the dividend the number of shares you own remains at 200 shares but the market price of the stock will be $19.50 so the value of your stock investment is 200 shares x $19.50/share = $3,900. Adding the $100 dividends received to this amount, the value of your holdings (stock plus dividends) is $4,000. In the case of dividends no new wealth is created, it is only transferred. The value of holdings (stock + cash) before the dividend will equal the value of the holdings after the dividend (ignoring taxes).

d. The firm announces it will repurchase 10 percent of its shares; you do not offer to sell any of your shares.

Your current wealth in the stock of the company is 200 shares x $20 = $4,000.A 10% reduction in the number of shares outstanding will, all else equal, increase the stock’s price by about 10% to approximately $22/share. As kept your holdings, their value is approximately 200 shares x $22/share = $4,400, an increase in value of 10%.

22. The Fridge-Air Company’s preferred stock pays a dividend of $4.50 per share annually. If the required rate of return on comparable quality preferred stocks is 14 percent, calculate the value of Fridge-Air’s preferred stock.Price = Dp /r = $4.50/.14 = $32.14

23. The Joseph Company has a stock issue that pays a fixed dividend of $3.00 per share annually. Investors believe the nominal risk-free rate is 4 percent and that this stock should have a risk premium of 6 percent. What should be the value of this stock?

Regarding of whether students consider this to be preferred or common stock, the fact that the dividend growth rate is zero results in the same answer. The required return is the risk-free rate plus the risk premium: 4% + 6% = 10% so the value of the stock will be $3 / 0.10 = $30.00.

24. The Lo Company earned $2.60 per share and paid a dividend of $1.30 per share in the year just ended. Earnings and dividends per share are expected to grow at a rate of 5 percent per year in the future. Determine the value of the stock:

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a. if the required rate of return is 12 percent.P = D1/(r – g) = $1.30(1.05)/(.12 – .05) = $19.50

b. if the required rate of return is 15 percent.P = $1.30(1.05)/(.15 – .05) = $13.65

c. given your answers to Parts a and b, how are stock prices affected by changes in investor’s required rates of return?Higher required rates of return lead to lower prices.

25. The French Thaler and Company’s stock has paid dividends of $1.60 over the past 12 months. Its historical growth rate of dividends has been 8 percent but analysts expect the growth to slow to 5 percent annually for the foreseeable future.

a. Determine the value of the stock if the required rate of return on stocks of similar risk is 15 percent.

The growth rate of importance in this problem is the future expected growth rate of 5 percent rather than the historical growth rate. Using the constant dividend growth model, the value of the stock should be: D0 (1 + g) / (r – g) = $1.60 (1.05) / (0.15 – 0.05) = $1.68 / 0.10 = $16.80.

b. If analysts believe the risk premium on the stock should be reduced by 2 percentage points, what is the new required rate of return on French Thaler and Company stock? But how much should its price change from the answer you computed in part a?

A reduction in the risk premium of 2 percentage points means the required rate of return on the stock should now be 15% minus 2% or 13%. Its stock price should be:D0 (1 + g) / (r – g) = $1.60 (1.05) / (0.13 – 0.05) = $1.68 / 0.08 = $21.00.Which is a price increase of $4.20 or $4.20/$16.80 = 25%

26. Mercier Corporation’s stock is selling for $95. It has just paid a dividend of $5 a share. The expected growth rate in dividends is 8 percent.

a. What is the required rate of return on this stock? r = (D1/P) + g = $5(1.08)/$95 + .08 = .137 or 13.7%

b. Using your answer to Part a, suppose Mercier announces developments which should lead to dividend increases of 10-percent annually. What will be the new value of Mercier stock? P = D1/(r – g) = $5(1.10) /(.137 – .10) = $148.65

c. Again using your answer to Part a, suppose developments occur that leave investors expecting that dividends will not change from their current levels into the foreseeable future. Now what will be the value of Mercier stock? P = D1/(r – g); g = 0 P = $5/.137 = $36.50

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d. From your answers to Parts b and c, how important are investors’ expectations of future dividend growth to the current stock price?Growth expectations are very important in determining stock price. Higher growth expectations lead to higher stock prices.

27. The common stock of RMW Inc. is selling at $88 a share. It just paid a dividend of $4. Investors expect a return of 15 percent on their investment in RMW Inc. From this information, what is the expected growth rate of future dividends?P = D1/(r – g) = 88 = 4(1 + g)/(.15 – g)13.2 – 88g = 4 + 4g9.2 = 92g.10 = g Growth rate is 10%.

28. Lerman Company has preferred stock outstanding. It pays an annual dividend of $10. If its current price is $70, what is the discount rate investors are using to value the stock?P = Dp /r = $70 = $10/r r = .143 or 14.3%

29. Interpret the following stock price quote. In addition, what is Sizzler’s approximate earnings per share? What was the stock’s closing price the previous day?YTD 52 weeks Yld Vol Net% CHG Hi Lo Stock Sym Div % PE 100s Last Chg+17.3 7.13 5.00 Sizzlr SZ .16 2.7 25 844 6 –0.25YTD % change: Since January 1, the stock has risen in value by 17.3%. 52 week Hi/Lo: Over the past year (52 weeks), Sizzler’s stock price has ranged from $5 to $7.13.Div: In the past 12 months, $.16 per share in dividends has been paid.Yld % (dividend yield is dividend/closing price): .16/6 = .0266 or 2.7%. PE: (ratio of price to earnings per share).Approximate eps: P/E = 25 = 6/eps = 25 eps = $0.24. Vol 100s (trading volume in hundreds): 84,400 shares were traded.Last: Day’s closing price, or last trade price, was $6.00.Net change: (change in closing price from the previous trading day).The previous day’s close was $6.25 per share as the day’s close of $6 was $0.25 less than the prior day.

30. Ritter Incorporated just paid a dividend of $2 per share. Its management team has just announced a technological breakthrough that is expected to result in a temporary increase in sales, profits, and common stock dividends. Analysts expect the firm’s per-share dividends to be $2.50 next year, $3 in two years, and $3.50 in three years. After that, normal dividend growth of 5 percent is expected to resume. If shareholders expect a 15-percent return on their investment in Ritter, what should the firm’s stock price be?Find present value of dividends in Years 1, 2 and 3:

PV1–3 = $2.50/1.15 + $3/(1.15)2 + $3.50/(1.15)

3 = 6.74

Value of stock in Year 3:P3 = D4/(r – g) = $3.50(1.05)/(.15 – .05) = $36.75

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Present Value of Year 3 price = $36.75/(1.15)3 = $24.16

Price = present value of future expected dividends = $6.74 + $24.16 = $30.90

31. Tough times have hit the retail store chain of Brador, Inc. Analysts expect its dividend of $1.00 a share to fall by 50 percent next year and another 50 percent the following year before it returns to its normal growth pattern of 3 percent a year. If investors expect a return of 18 percent on their investments in Brador stock, what should its current stock price be?Find present value of dividends in Years 1 and 2:

PV1–2 = $0.50/1.18 + $0.25/(1.18)2 = $0.60

Value of stock in Year 2:P2 = D3/(r – g) = $0.25(1.03)/(.18–.03) = $1.72

Present value of Year 2 = stock price = $1.72/(1.18)2 = $1.24

Price = present value of future expected dividends = $0.60 + $1.24 = $1.84

32. JW Corp has a dividend of $0.50. The dividend is expected to grow at a 6% rate over time. Based on the stock’s risk, investors require an 11-percent rate of return.

a. Using the constant dividend growth model, what should the stock’s price be?

Value of stock: P0 = D1/(r – g) = $0.50(1.06)/(.11 – .06) = $10.60

b. Estimate the firm’s dividends for the next 10 years and find their present value. What proportion of the stock’s price is based upon dividends which are expected to occur more than 10 years into the future?

Sum of dividends

in year 1 – 10 = $3.91;

proportion of stock price based on dividends after year 10: 1 – ($3.91/$10.60) = 0.631 or 63.1 percent

c. What proportion of the firm’s price is based upon dividends which are expected to occur more than five years into the future?

Sum of dividends in year 1 – 5 = $2.18 Proportion of stock price based on dividends after year 10: 1 – ($2.18/$10.60) = 0.794 or 79.4 percent

33. A firm’s dividends are expected to grow 20 percent a year for the next five years and then trend downward by 3 percent a year until they stabilize at a constant growth rate of 5

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Year 1 2 3 4 5Dividend 0.5300 0.5618 0.5955 0.6312 0.6691PV (dividend) 0.4775 0.4560 0.4354 0.4158 0.3971

Year 6 7 8 9 10Dividend 0.7093 0.7518 0.7969 0.8447 0.8954PV (dividend) 0.3792 0.3621 0.3458 0.3302 0.3154


percent. The current dividend is $0.80 a share and the stock’s required rate of return is 13 percent. What should its current price be? If these growth expectations come to pass, what will its price be four years from now? Eight years from now?

Calculations for the current stock price follow (based on a spreadsheet, PV calculations could be rounded to the nearest penny or tenth of a penny).

Year 1 2 3 4 5Growth rate 20 20 20 20 20Dividend 0.96 1.152 1.382 1.659 1.991PV(dividend) 0.8495575 0.902185 0.9580725 1.0174222 1.0804483

Year 6 7 8 9 10Growth rate 17 14 11 8 5Dividend 2.329 2.655 2.947 3.183 3.342PV(dividend) 1.1186943 1.1285942 1.1086191 1.0595652 0.9845517

Price yr 10 = 43.865418PV price 10= 12.922241

Price yr 0= 23.129951

The current price is the sum of the present values of the estimated dividends in years 1-10 plus the present value of the price in year 10; it equals $23.13.

The year 10 price is $3.342*(1.05)/(.13-.05) or $43.86. The present value of the stock price in year 10 is $43.86/(1.13)10 = 12.92. Adding this present value of the sum of the year 1-10 present values gives a current price of $23.13.

The spreadsheet can be adopted to estimate year 4 and year 8 prices. To estimate the price in year 4, we start with the year 5 dividend and discount it back one year, to year 4. Continuing this process and finding the present value of the year-10 price gives us

Year 1 2 3 4 5Growth rate 20 20 20 20 20Dividend 0.96 1.152 1.382 1.659 1.991PV(dividends) as of year 4: 1.7616425

Year 6 7 8 9 10Growth rate 17 14 11 8 5Dividend 2.329 2.655 2.947 3.183 3.342

Price yr 10 43.865418PV(dividends) as of year 4: 1.8240015 1.8401431 1.8075742 1.727593 1.6052856

PV year 10 price as of year 4 21.069373

Price yr 4 1.635613

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Similarly, the spreadsheet can be adapted to find the stock’s year-8 price, which equals the present value (as of year 8) of the year-9 dividend, the year-10 dividend, and the stock’s price in year 10: $2.82 + $2.62 + $34.35 = $39.79.

SUGGESTED QUIZ

1. Why is the volume of debt issues consistently larger than the volume of equity issues?

2. Define or discuss briefly:a. Indenture b. Debenturec. Mortgage bonds d. Putable bonds e. Yankee bonds

3. Find the price of a bond that matures in 12 years, has a $1,000 par value, pays coupons semiannually with a coupon rate of 9 percent. The yield to maturity on the bond is 11 percent.

SolutionThe annual coupon is 9% × $1,000 = $90; it is paid as $45 every six months. The number of periods is 12 years × 2 = 24. The periodic rate is (1.11)1/2 – 1 or 0.0536 or 5.36 percent. Using a financial calculator, the price is $885.38.

4. Shareholders of UOI Corp. have a required return of 14 percent and expect UOI’s dividend to grow at 5 percent annually. This year’s dividend was $2.00.

a. What is the price of the stock today?b. Holding all else constant, suppose UOI management announces a dividend freeze;

dividends will be held constant into the foreseeable future. What will be the new price of UOI stock?

Solution a. Using the constant dividend growth model, today’s price is P0 = D1/(r – g) = $2.00

(1.05)/(.14 – .05) = $23.33.b. The stock should now be priced as a perpetuity, or using the constant growth model with

g equal to zero: P0 = D0 /r = $2.00/.14 = $14.29

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Learning Extension 10a Annualizing Rates of Return

The dollar return on a single financial asset held for a specific time, or holding period, is given byDollar return = Income received + price changeThe percentage return is simply the dollar return divided by the initial price of the stock:

Percentage Return = dollar return initial price

Percentage returns should be annualized to put investments with varying holding periods on an equivalent basis.

PROBLEM AND ANSWER

1. Given the information in the text, compute annualized returns.Asset Income Price Change Initial Price Time Period

A $ 2 $ 6 $ 29 15 monthsB 0 10 40 11 monthsC 50 70 30 7 yearsD 3 –8 20 24 months

a. Total return = $2 + $6 = $8 Percentage return = $8/29 = 0.276Annualized return = (1.276)12/15 – 1 = 0.215 or 21.5%

b. Total return = $0 + $10 = $10 Percentage return = $10/40 = 0.25

Annualized return = (1.25)12/11

– 1 = 0.276 or 27.6%c. Total return = $50 + $70 = $120 Percentage return = 120/30 = 4.0

Annualized return = (1 + 4)1/7 – 1 = 0.258 or 25.8%d. Total return = $3 + $ –8 = $ –5 Percentage return = –5/20 = –.25

Annualized return = (1 + –.25)1/2 – 1 = –0.134 or –13.4%

2. Given the information below, compute annualized returns

Asset Purchase Price Current Price Income Received Time Period

A $ 20 $ 26 $ 2 75 weeksB 15 18 0.40 3 monthsC 150 130 0 2 yearsD 3.50 3.00 0.20 8 months

a. Total return = ($26 – 20) + $2 = $8 Percentage return in decimal form = $8/20 = 0.40Annualized return = (1.40)1/(75/52) – 1 = 0.263 or 26.3%

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b. Total return = ($18 – 15) + $0.40 = $3.40 Percentage return in decimal form= $3.40/15 = 0.227Annualized return = (1.227)

1/0.25 – 1 = 1.267 or 126.7%

c. Total return = ($130 – 150) + $0 = $-20 Percentage return in decimal form= -20/150 = -0.133Annualized return = (1 - 0.133)1/2 – 1 = -0.069 or -6.9%

d. Total return = ($3.00 – 3.50) + $0.20 = $-0.30 Percentage return in decimal form= $–0.30/3.50 = –0.086Annualized return = (1 + –.086)1/(8/12) – 1 = –0.126 or –12.6%

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ch10 Intro to Finance