Security Valuation: Stocks and the Bonds | FIN 3010, Study notes of Finance

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Chapter 5

Security Valuation - Stocks and Bonds

Introduction

Stocks and bonds are securities issued by companies to fund their operations. Stock issuance provides equity and bond issuance provides debt to the funding side of a firm’s balance sheet. A stock or equity is evidence of ownership and a bond is evidence of indebtedness. Stocks and bonds can be issued publicly or privately. The public (and often the private) issuance of securities usually requires the assistance of an investment banker. The investment banker will bring buyers and sellers of securities together, help price the issue, and assist in preparing the necessary regulatory filings. There are several important ideas you need to grasp in this chapter. Among the most important for you to understand are why stocks are so risky, the factors that influence a stock’s risk, and how the stock of a company is valued using perpetuity formulas. Stocks and bonds are financial assets and their values are the discounted value of the expected future cash flows. The discount rate is the return required for similar risk class investments. Stocks (Equity) A stock is a representation of ownership. Corporations are formed by states and they have infinite lives. Ownership is broken down into shares and this fractional ownership makes transferring ownership fairly easy (especially if a firm's stock is publicly traded). Stock investors are the first investors in a company and the last to receive their money. Stock investors have a residual claim on the cash flows (or assets) of a company after all other stakeholders receive their claims. When thinking of valuing a stock you must think in terms of constructing an expected cash flow series that is available to shareholders that deducts payments of all claims to stakeholders other than stockholders. Stock investors can also have a claim on all of the assets after paying all of the liabilities. A disadvantage of a corporation is that investors are taxed on the income the firm makes as well as the dividends paid to the individual investor. Ross, Westerfield and Jordan point out three reasons why stocks are more difficult to value than bonds^1 :  The Cash flows to stockholders are not known  Stocks have a perpetual life.  The required return is difficult to identify.

Characteristics of common stock:

(^1) Ross Westerfield and Jordan McGraw-Hill Irwin, 2003, New York, New York, Sixth Edition

A stock certificate is a representation of ownership. Most stock is held in “Street Name” at a brokerage firm. The brokerage firm sends all corporate correspondence through to the shareholder. The brokerage firm owns the stock in its name and credits your account with the stock. An investor can make money from a stock investment in two ways. These two ways are through dividends and capital gains. A dividend represents a return of cash (the shareholders’ money) back to the shareholder. A dividend stream then can be thought of as a cash flow stream that is available to shareholders that can be valued. Stock valuation models are often called dividend discount models but they are really cash flow valuation models. The phrase dividend discount model has confused many students because they are left wondering how to value a company that doesn’t pay a dividend and many companies pay low dividends or no dividend at all. Basically, dividend discount models are used in practice to value perpetual preferred stocks (no maturity) that have a constant dividend. In academics, dividend discount models are useful because they show the valuation of a never ending (perpetual) cash flow stream and since the formation of a business begins with the idea that it will live forever a formula for the valuation of a perpetual cash flow stream is useful. A financial asset’s value is the discounted value of the expected cash flows. Stocks and bonds are financial assets representing something intangible. Even though a single company might issue a stock and a bond the factors that influence the valuation and risk of stocks and bonds are different. Stocks (equity) are generally thought of as being more risky than bonds because ownership of a stock represents a claim on the cash a company can generate after paying the other claimants (bondholders, venders, taxes, employees, etc.). Stocks are more risky than bonds because bonds have a legal claim on the cash flows of a company ahead of stockholders. Investors looking for higher returns will invest in stocks because stocks historically offer a higher return than other asset classes such as bonds or money market instruments. Since stocks have a perpetual life, perpetuity formulas make sense when valuing stocks. Since perpetuity formulas assume a specific growth rate in cash flows available to shareholders be careful in practice using these formulas. This is because you shouldn’t assume that the growth rate in cash flows available to shareholders will remain constant except in the case of the valuation of a perpetual preferred stock with a fixed dividend. To value equities using a discounted cash flow model many stock analysts will forecast cash flows available to shareholders for five years and then assume a constant growth rate from that point into the future. Changes in the growth rate of cash flows expected earlier in the life of a company can have a significant impact on equity valuation and spreadsheet packages (that are used to model a firm’s cash flows) make the cash flow estimation process easier. The perpetuity formulas used in this chapter are for explanation purposes only. Don’t think stock valuation is as easy as plugging numbers into a formula. Experienced stock analysts must diligently estimate cash flows based on their knowledge of the company and they must diligently estimate the discount rate. If a company has thirty analysts following the stock there will be about thirty different stock valuations. When an analyst uses a stock valuation model the analyst is determining the value he or she thinks the stock is worth today. The price the analyst thinks the stock is worth today will

then be compared to the market price of the stock to determine if the stock is overvalued or undervalued. An analyst might put out a “buy” recommendation on a stock believed to be undervalued and a “sell” recommendation on a stock believed to be overvalued. All stocks have infinite maturities. This means that a company begins with the intention that it will be an ongoing concern with no fixed maturity date. All stocks are equally risky from the standpoint of maturity. Financial assets with longer maturities have higher risk. The risk of financial assets with longer maturities lies in the time value of money. Cash flows that are expected to be received further into the future are more sensitive to changes in the discount rate than cash flows that are expected to be received nearer to today. The price of a financial asset is the discounted value of the cash flows expected to be available to the holders of the financial asset. The discount rate (the cost of capital) is a reflection of the risk of the expected cash flow stream. Stocks are riskier than bonds so the discount rate is higher for stocks than bonds. The discount rate used to value stocks can be a complicated concept but it is basically the return required by shareholders. Changes in the discount rate occur due to volatility in the stock market (and how an individual stock tends to move with the stock market), the level of interest rates in general, the amount of financial leverage (debt) a company has on its balance sheet, and the volatility of the expected cash flow stream. One thing you will discover about valuation of financial assets is that assets with longer lives are more sensitive to changes in expected cash flows and changes in the discount rate used to value (discount) the cash flows. One of the most important factors influencing the volatility of a firm’s stock price is the expected growth rate of the company. Growth in sales, EPS, and cash flows available to shareholders (which all contribute to growth in the book value of shareholders’ equity) are key growth financial performance measures. The financial markets may focus on any of these measures at any time. When I refer to a firm’s growth rate I am referring to growth in the measure of financial performance that is important to the financial market at the time. Measures of financial performance that are important to the financial markets change over time. A change in a firm’s growth rate can have a profound influence on a firm’s stock price. If you hear in the financial press that a company’s growth rate is forecasted to slow this is usually bad news for the firm’s stock price. The issuance of public or private equity will increase the Common Stock account and Additional Paid in Capital account (APIC) in the Shareholders’ Equity section of a firm’s balance sheet. An increase in shareholders’ equity will strengthen a firm’s balance sheet but all companies prefer to strengthen their balance sheets by earning profits from operating and increasing the Retained Earnings account. A firm’s founders usually own a large percentage of a firm’s stock and they usually do not want to sell additional shares to outside investors because this action will dilute the percentage ownership interest of the founders. Stockholders may have preemptive rights that give them the opportunity to purchase additional shares that will maintain their percentage interest. Common shareholders usually have the right to vote their stock and shareholders usually have one vote for each share of stock. The Shareholders’ Equity account in a firm’s balance sheet represents the book value (the balance sheet value) of the equity when it was originally purchased by

ratio is like buying a high quality diamond. You pay for quality in everything in life and stocks are no different. There is a considerable difference between the quality of a stock and the quality of a diamond. A diamond’s quality will not change with time but a stock’s quality will change with time so a risk in buying a stock with a high P/E is that something happens to the company that slows its growth rate. Just like a diamond there are several indicators of quality for a stock. Some of the indicators of stock quality are a high growth rate in sales and free cash flow, a low level of debt on the balance sheet, conservative accounting practices that offer transparency, and a high return on the shareholders’ equity. A thoroughbred horse has a certain quality level but unlike a diamond you have to watch it. It might get into the wrong pasture, hit a barbed wire fence, and not be useful any more so you really must watch it. A stock must be watched so investors must continue to do a due diligence investigation to keep up with the company and its competitors. A firm’s management will prefer to issue equity when the stock price is high because this reduces the firm’s cost of equity capital. The cost of equity capital is the return required by shareholders and is a function of the risk perceived by shareholders. According to the principle of risk and return the higher the risk the higher the return required. In introductory finance classes I usually offer this example of how a high stock price reduces a firm’s cost of capital. Suppose Replay, Inc. needs $100,000,000 in funding to purchase plant and equipment to stay competitive and that the firm’s stock price is $100 per share. The firm’s current Net Income is $20,000,000 and there are 1,000,000 shares of common stock outstanding so EPS is $20.00. Replay, Inc. must issue $100,000,000 / $100 = 1,000,000 shares of common stock to finance the capital investment. With the price of Replay at $100 and EPS of $20.00 the P/E ratio of Replay is 5 before the stock issuance. Following the issuance of 1,000,000 shares of stock Replay has 2,000,000 shares of common stock outstanding. Assuming Net Income does not change EPS will be $20,000,000 / 2,000,000 = $10.00 = EPS. If the price of Replay’s stock remains at $100 per share and Net Income remains the same at $20,000,000 the P/E of replay will be $100 / $10.00 = 10 = P/E. The doubling of the P/E ratio shows the expectation that investors expect the capital investment project to pay off in the future. If Replay’s stock price is at $200 per share its P/E ratio is 10 prior to the stock issuance based on current earnings of $20,000,000 and 1,000,000 shares of common stock outstanding (EPS = $20 so $200 / $20.00 = 10 = P/E). Suppose the stock is sold at $200 per share to raise $100,000,000 to fund capital investment. Replay, Inc. must then issue $100,000,000 / $200 = 500,000 shares of common stock to finance the capital investment. Selling stock at a higher price means that to raise a certain amount of capital fewer shares must be sold and dilution of current shareholders’ interest will be lower than if stock is sold at a lower price. Following the issuance of stock at $200 per share the total number of shares outstanding is 1,500,000 and EPS will be $13.33 ($20,000, / 1,500,000 = $13.33 = EPS). Earnings Per Share are higher and the number of common shares outstanding are lower, all else remaining equal, if the company can issue stock at $200 per share instead of $100 per share. Issuance of fewer shares of common stock at a

higher price results in less dilution of the current shareholders’ interest in the company and less dilution in EPS. You can see from the example that selling stock at a higher price reduces the cost to current shareholders where the measurement of cost is in terms of dilution of ownership. Higher P/E ratios generally are associated with the expectation of higher growth in the future and a lower cost of equity capital.

Stock Valuation formulas

These formulas are special perpetuity formulas that incorporate different cash flow growth assumptions. If an investment analyst does some analysis to determine the price of a share of stock he or she will calculate P 0. P 0 is the price the analyst thinks the stock is worth today. P 0 is the price the analyst will compare to MP 0 , the market price of the stock, to determine if the stock is overvalued or undervalued. If P 0 is greater than MP 0 the analyst will recommend purchase of the stock. If P 0 is less than MP 0 the analyst will recommend sell of the stock. Equation 1 shows a formula for valuing a share of stock assuming that the cash flow stream expected at time 1 and beyond is not expected to grow. This is a discounted cash flow valuation formula that discounts a stream of infinite cash flows Dj of the same amount at a constant rate R. Definitions:  Dj is the cash flow expected at time period j.  P 0 is the price the analyst believes the stock is worth today.  R is the return required by investors that the analyst believes reflects the risk of the stock. R equals a dividend yield (D 1 / P 0 ) plus a capital gains yield (g). If the investment analyst believes the cash flows will grow at a constant rate g forever the formula used to value the stock is Equation 2.  g is the expected growth rate in the expected dividend or cash flows Dj. Equation 1 - No growth (in cash flows) stock valuation formula   

( 1 ) ( 1 )^2

2 1 1 1 0 R

D

R

D

R

D

R

D

P

Equation 2 - Constant growth (in cash flows) stock valuation formula. This is known as the Gordon Model   

0 2 2 0 1 1 1 0 0 R D g R D g R D g R g

D

P

The forecast of a firm’s earnings is crucial to the valuation of a firm’s equity. Investment analysts often relate the price per share of a firm to the earnings per share (EPS) of a firm. This relationship is referred to as the P/E ratio. Analysts can use either the current year’s EPS or the forecast of EPS for next year. The important thing here is to use the P/E for comparative purposes so be consistent in using either current year of next year’s forecast P/E. P/E = Price Per Share / EPS One simple way an analyst can use the P/E ratio to value a share of stock is to compare the P/E’s of similar firms in the same industry to the P/E of a particular security. Equation 4 – P/E method of valuing a company Peer company P/E * Current EPS = P 0 Suppose Killian Industries trades on the market today at $70 per share. If a firm’s (Killian Industries) current EPS are $4.00 and other firms in the same industry are trading at an average P/E of 16 the investment analyst can simply multiply Killian Industries’ EPS of $4.00 by the average P/E for other firms in the same industry to find a theoretical value for Killian’s stock. In this case the analyst thinks the stock of Killian Industries should be at $4.00 * 16 = $64. If the stock is trading higher than $64 per share the analyst might think the stock overvalued. An analyst looks at reasons for Killian Industries’ trading at a higher or lower multiple than other stocks in the industry. If Killian Industries’ management is not superior, if the firm has no dominant market position, if the firm has no proprietary product, if prospects for growth are limited, etc. the analyst may conclude that the firm is overvalued if its stock is trading higher than $64 per share. If Killian’s stock is trading less than $64 per share the analyst might think that the stock is undervalued unless the firm has poor management, no dominant market position, no prospect for growth, etc. This seems simple and it is. The process gets more complicated if the analyst uses next year’s forecast of EPS (and forward P/E ratios) to do the same thing. Of course in this case the analyst must forecast next year’s EPS and this is not simple. Generally speaking, stocks with low P/E’s are considered undervalued and stocks with high P/E’s are considered overvalued. But be careful, there are usually reasons why stocks have low P/E’s (for example, poor management). There are reasons why stocks have high P/E’s (proprietary products and high expected growth). Cisco Systems has traded at a high P/E for a long time. For several years Intel traded at a low P/E due to likely competition from other chip makers. Analysts often compare a stock’s P/E to the P/E of a broad stock market index. Stocks with higher growth prospects usually trade at higher P/E ratios. If a stock has a P/ E greater than the market P/E this might indicate that growth prospects are greater for this firm. P/E’s are usually higher in periods of low inflation and low interest rates and lower in periods of high interest rates.

Some analysts use a rule of thumb to determine an appropriate P/E for stocks. They subtract the current inflation rate from 20. Therefore, the higher the inflation rate the lower the P/E. Usually a high inflation environment is associated with a high interest rate environment and stocks usually do not like a high interest rate environment ( especially an inverted yield curve). Interest rates have a vast impact on stock prices. This happens in basically two ways. First, debt instruments that pay interest compete for the dollars of savers. If bonds pay higher interest rates investors are likely to buy bonds for the higher yield. Second, the required return on stocks must be higher than the required return on debt so if debt rates rise the required return on equity rises. Look in the Wall Street Journal at some firms you are familiar with and try to determine if their P/E is appropriate. Questions:

1. Assume Waxtronics stock is trading at $25 per share, has current EPS of $1.00, and a P/E of 25. Its peer group has a P/E of 30. Determine the price you think Waxtronics should be trading if its P/E is similar to peer companies. Answer: $1.00 * 30 = $30= 0 P^ ˆ . Are there reasons why the stock might not be undervalued? Answer: Yes. Growth can be slower than peers, management might not be performing, etc..
2. Assume Tsronics stock is trading at $40 per share, has current EPS of $1.00, and a P/E of 40. Its peer group has a P/E of 20. Determine the price you think Tsronics should be trading if its P/E is similar to peer companies. Answer: $1.00 * 20 = $20= 0 P^ ˆ . Are there reasons why the stock might be overvalued? Answer: Yes. Growth can be faster than peers, management might be better performing than peers, etc..

What is a stock split?

A stock split occurs when a firm’s stock price gets so high that a round lot ( shares) is viewed as unaffordable by the average investor. In a 2 for 1 split an investor who owned 100 shares of stock will now own 200 shares of stock. If the stock price is trading at $30 per share before the split the price should fall to $15 after the split. Therefore, investors will not be richer after the split. However, if the stock continues to increase the investor now makes $200 for each $1.00 increase in the price of the stock. So if a stock can keep splitting and also keep increasing this is a great deal for investors. But if the stock falls following a split each $1.00 decrease in the stock price is now $200. So stock splits can be good and they can be bad depending on what happens to the stock price after the split. A stock dividend is often paid by younger firms that do not have cash to pay the regular cash dividend. It has the effect of increasing the number of shares outstanding and thus (possibly) the liquidity of those shares. A stock dividend is frequently referred to as a capitalization of earnings.

A bond is a representation of funded indebtedness and is a liability of the funding side of a firm's balance sheet. Investing in bonds is less risky than investing in stocks because bond investors have a priority claim on a firm's assets ahead of stockholders. Investing in bonds involves taking on interest rate risk as well as credit risk. Interest rate risk is the risk that interest rates will change after a bond is purchased. Credit risk is the risk that a firm's financial health will deteriorate in the future. When you invest in bonds you must think in terms of a total return on the bond as the dollar interest received plus any capital gain or loss. If a firm issues funded debt substantial equity must exist on the firm's balance sheet and the company's income statement should be operating cash flow positive. The risk of a bond is generally lower than a stock because the expected cash flow stream to the bondholder remains fixed and not variable like a stock that pays dividends. Bond prices fluctuate and money can be lost on a bond by an investor even if a company remains sound. One of the main risks of bond investing is interest rate risk. This risk is somewhat embedded in stocks (the other financial asset) but is more directly related to bonds. Bond prices and interest rates vary inversely. If you buy a bond and interest rates rise the price of the bond will fall. You may continue to receive the interest from the bond but the bond’s value will be lower than the value at the time of purchase. If interest rates rise the bond’s value will decline. Bonds have many different maturities and so a bond’s maturity plays an important role in valuation and risk. Bonds with shorter maturities are less risky than bonds with longer maturities. When we work some problems later in the Chapter you will get a better feel for the maturity risk of a bond. Also, the bondholders’ claim on the company is ahead of stockholders in financial stress situations. Since bondholders may not receive their interest and principal back if a company moves into financial distress the likelihood that a company will fall into financial difficulty plays an important role in determining the risk of a bond. Bonds usually pay a fixed coupon rate of interest ( fixed at the time of issuance to the market yield (rate) on similar financial quality and maturity issues ) so the expected cash flow stream from the company to the bondholder will not change (unless the company defaults). If a bond's coupon rate is fixed at the yield on similar financial quality and maturity issues the bond will be sold at par. A bond's yield to maturity and coupon rate will be approximately equal at the bonds issuance. The discount rate used to value a bond is simpler than the discount rate used to value a stock. The discount rate on a bond is essentially the yield to maturity on similar financial quality and maturity bonds issued by other companies. A yield to maturity is an interest rate calculation that considers the rate of return an investor will receive by purchasing a bond at the market price and holding it to maturity. To obtain a good feel about the discount rate on a bond examine the yield to maturity on similar financial quality companies with bonds of the same maturity. When a bond is issued the issuing company pays a rating agency such as Standard & Poor's or Moody's to rate the firm's credit. A firm's credit rating is a measure of a firm's default risk. The rating agency will follow the company and put the company on credit watch alert if the firm's financial health deteriorates. A bond quote in the financial press includes the current yield, the volume of trading, and the closing price. The closing price of a bond in the financial press is quoted

as a percentage of par. A quote of 88 1/8 is associated with a price per each $1,000 face value bond of $881.25. The cash flows to bond investors are generally more certain than the cash flows to stock investors so stockholders require a higher return than bond investors. The cash flows to bond investors are the annuity payments associated with the coupon and the face value of the bond at maturity. A bond usually pays an annuity stream of coupon payments over a period of time and at maturity the company pays the face amount of the bond to investors. To value a bond find the present value of the annuity and add this to the present value of the maturity value. Bond valuation makes use of an annuity formula and a lump sum formula. Bonds backed by collateral (company assets) are referred to as mortgage bonds. If the company doesn’t pay the principal and interest on the bond (that is if the bond defaults) the bondholders might be repaid by selling the assets that back the bond. Since mortgage bonds have asset backing they are less risky than bonds with no asset backing. Bonds with no asset backing are referred to as debenture bonds. Mortgage bonds will carry a lower interest rate than debenture bonds due to the lower risk. Bonds can have features that tend to make them more attractive to investors and to the company issuing the bond. These features are attached at the issuance of a bond and are a result of the wants and needs of the suppliers and demanders of capital and the condition of the financial markets at the time of issuance. Preferred by issuing companies is the call feature. This is because a call feature gives the company the right to retire a bond prior to its stated maturity date. An issuing company will prefer a call feature to take advantage of a decline in interest rates following the bond’s issuance. For example, suppose a company issues a 20 year bond (20 years to maturity) with a 9% coupon rate, a $100,000,000 face amount, and a 5 year call feature. The bond will not be callable until five years have passed. This period of time where the bond is not callable gives bond holders some opportunity to enjoy the interest rate they expect and this period of time is determined in the capital markets. If interest rates decline to 5% after five years the company can save 400 basis points on $100,000,000 or $4,000,000 per year in interest costs if the bonds are refunded. To refund a bond issue is to issue new bonds to pay off an old bond issue. Convertible feature: The conversion feature of a bond makes the bond trade like a stock (in some situations). The conversion feature usually allows the holder of a bond to convert the bond to common stock. Firms usually issue convertible bonds at a time of high interest rates or low stock prices. The convertible bond is a way to fund the firm with debt and then have the debt converted to equity (stock). The conversion feature allows the bond to be converted into a certain number of shares of common stock. The conversion value of a bond is found by multiplying the conversion rate (number of shares the bond is convertible into) times the market price of the common stock. If a bond is convertible into 40 shares of common stock and the common stock is trading at $30 per share the convertible bond will be worth $30 * 40 = $1,200. $1,200 is the conversion value of the bond.

Since most bonds pay interest semiannually the Dollar Coupon is the semiannual dollar amount the investor receives each six months. Investors will receive the first of these coupon payments six months after the issuance of the bonds.  Dollar Coupon is the semiannual dollar amount. To find this amount multiply the face value of the bond by the annual coupon rate of the bond and divide by 2 semiannual periods in a year.  Face value at time zero is the original stated maturity.  r = The market rate of interest on similar financial quality and maturity bonds.  BP 0 is the price you think the bond should sell for today given your inputs. Important conceptual issue: The bond valuation formulas below find the value you think a bond should be trading for based on your inputs. You must compare the price you think a bond should be trading to the price of a bond in the marketplace. Equation 5 - The formula for pricing a bond Bond Value at time zero equals: (C x (1- (1/(1+r)t^ )) /r ) + Face Value / (1 + r )t Bond Value at time zero equals: Present value of the coupons + Present Value of the Face Amount The formula (1- (1/(1+r)t^ )) /r ) is the formula for the present value of an annuity. Written in Summation form the bond value equals:   

t j t t j j r Face Value r

C

Bond Value 1 0 ( 1 )

Some bond pricing questions. Assume the face value of the bonds is

1. Determine the price of a 4% coupon semiannual payment debenture due in 10 years assuming nominal annual yields on similar quality and maturity paper are at 2%. Answer $1,180.
2. Determine the price of a 4% coupon semiannual payment debenture due in 20 years assuming nominal annual yields on similar quality and maturity paper are at 2%. Answer $1,328.
3. Determine the price of a zero coupon debenture due in 10 years assuming semiannual bond equivalent annual yields on similar quality and maturity paper are at 4%. Answer $672.
4. Determine the price of a zero coupon debenture due in 20 years assuming semiannual bond equivalent annual yields on similar quality and maturity paper are at 4%. Answer $452. Bond problems are just time value of money problems with two parts. The first part is to discount the lump sum and the second part is to discount the annuity. To find the bond's price add the two parts. For Zero coupon bond problems the payment is zero.

5. Determine the price of a 4% coupon semiannual payment debenture due in 10 years assuming nominal annual yields on similar quality and maturity paper are at 6%. Answer $851.
6. Determine the price of a 4% coupon semiannual payment debenture due in 20 years assuming nominal annual yields on similar quality and maturity paper are at 6%. Answer $768.
7. Determine the price of a zero coupon debenture due in 10 years assuming semiannual bond equivalent annual yields on similar quality and maturity paper are at 2%. Answer $819. Pay attention to the detail in these problems.  What happens to bond prices when interest rates rise? When interest rates fall?  Are long-term bonds more price sensitive to interest rate changes?  Are low (or zero) coupon bonds more price sensitive to interest rate changes?  If your view of interest rates is a decline would you make more money in long- term bonds or short-term bonds? Answer long-term bonds.  If your view of interest rates is an increase would you lose less money in long- term bonds or short-term bonds? Answer long-term bonds.  If your view of interest rates is a decline would you make more money (in percentage terms) in high coupon or low coupon bonds? Answer: Take the 4% 10 year bond priced at a 2% yield the price is $1,180.45. The 4% 10 year bond priced at par is $1,000. The percentage increase in price is 18.450%. The zero coupon 10 year bond priced in a 4% (2% semiannual) rate environment is $672.97. The zero coupon 10 year bond priced in a 2% (1% semiannual) rate environment is $819.54. The percentage increase is ($819.54- $672.97) / $672. = 21.77%. Therefore, the zero coupon bond gives the investor a greater percentage price increase than the higher coupon bond. Yield Calculations There are many different yield calculations to consider. The current yield is the annual dollar coupon divided by the market price of the bond. A current yield does not consider any capital gain or loss on the bond if it is held to maturity. Equation 6 - Current Yield Dollar Amount of the coupon Current market price Current yield .... .. .

Answer Exercise 5 -1; approximately 10.84% Determine the current yield of this bond. $100 / $950 = Answer 10.53%

End of Chapter Questions - Bonds

Note: For all bond problems the par (maturity) value is $1,000.

1. Determine the price of a 6% coupon semiannual payment debenture due in 10 years assuming yields on similar quality and maturity paper are at 5%. Answer $1,077.
2. Determine the price of a 6% coupon semiannual payment debenture due in 10 years assuming yields on similar quality and maturity paper are at 7%. Answer $928.
3. Determine the price of a zero coupon debenture due in 10 years assuming semiannual bond equivalent yields on similar quality and maturity paper are at 6%. Answer $553.
4. Determine the price of a zero coupon debenture due in 10 years assuming semiannual bond equivalent yields on similar quality and maturity paper are at 5%. Answer $610.
5. Determine the price of a zero coupon debenture due in 10 years assuming semiannual bond equivalent yields on similar quality and maturity paper are at 4%. Answer $672.
6. Determine the price of a 6% coupon semiannual payment debenture due in 20 years assuming yields on similar quality and maturity paper are at 5%. Answer $1,125.
7. Determine the price of a 6% coupon semiannual payment debenture due in 20 years assuming yields on similar quality and maturity paper are at 7%. Answer $893.
8. Determine the price of a zero coupon debenture due in 20 years assuming semiannual bond equivalent yields on similar quality and maturity paper are at 6%. Answer $306.
9. Determine the price of a zero coupon debenture due in 20 years assuming semiannual bond equivalent yields on similar quality and maturity paper are at 5%. Answer $372. 10a. Determine the price of a zero coupon debenture due in 20 years assuming semiannual bond equivalent yields on similar quality and maturity paper are at 4%. Answer $452. b. What are some characteristics of bonds that make these securities fluctuate more in price. c. Examine your answers in problems 1 - 10. Now that you see what happens to bond prices when interest rates change explain how you can use this information to trade bonds in a changing rate environment. Class 11a. Determine the yield to maturity (use the formula on the formula sheet) of a debenture bond that has 10 years to maturity, pays a $100 annual coupon and is priced in the market at $950. Answer formula, 10.77% ; Answer Calculator, approximately 10.84% b. Determine the current yield of this bond. Answer 10.53% c. Why did the price of this bond fall? Class

12a. Determine the yield to maturity (use the formula on the formula sheet) of a debenture bond that has 10 years to maturity, pays a $100 annual coupon and is priced in the market at $1,150. Answer formula, 7.91% ; Answer Calculator, approximately 7.78% b. Determine the current yield of this bond. Answer 8.7% c. Why did the price of this bond rise? Class

13. Assume you are a bond portfolio manager for a major North Carolina bank and you will be placed in charge of a $10,000,000 portfolio of investment grade securities (BBB rating or higher). The bank employs a bond analyst who has recommended the following issues. By contract you must keep funds invested in long-term paper. Market rates are at 10%.  10% Mortgage bond Due in 10 years (Semiannual payment)  10% Mortgage bond Due in 20 years (Semiannual payment)  Zero Coupon Mortgage bond Due in 10 years (Compare to a Semiannual payment issue)  Zero Coupon Mortgage bond Due in 20 years (Compare to a Semiannual payment issue) Assuming your view of interest rates is a decline to 8%. Which bonds would you consider? Why? Answer: Price a 10%, 20 year bond at par $1,000 Price a 10%, 10 year bond at par $1, Price a 10%, 20 year bond at an 8% yield $1,197.92 Price a 10%, 10 year bond at an 8% yield $1,135. Percentage price rise = 19.79% Percentage price rise = 11.359% If you expect rates to fall you need to be invested in longer term bonds (the 20 year issue) because you will make more money ( in absolute dollar terms) and percentage terms. Since we know that we need to be invested in the longer term bond if we expect rates to decline let's find the percentage price change in the long-term zero coupon bond to determine if the change is greater than the price change of the 10% coupon issue. Price a 20 year, zero coupon bond at a 10% yield = $142. Price a 20 year, zero coupon bond at an 8% yield = $208. Percentage price rise = 46.57% If you expect rates to fall you need to be invested in lower coupon longer-term bonds (the zero coupon issue) because you will realize a greater percentage price rise.
14. Assume you are a bond portfolio manager for a major North Carolina bank and you will be placed in charge of a $10,000,000 portfolio of investment grade securities (BBB rating or higher). The bank employs a bond analyst who has recommended the following issues from which you can choose. By contract you must keep funds invested in long-term paper. Market rates are at 6% and the yield curve is flat. 6% Mortgage bond Due in 10 years (Semiannual payment) 6% Mortgage bond Due in 20 years (Semiannual payment) Zero Coupon Mortgage bond Due in 10 years (Compare to a Semiannual payment issue) Zero Coupon Mortgage bond Due in 20 years (Compare to a Semiannual payment issue) a) Assuming your view of interest rates is for rates to rise to 7%. Which bonds would you consider? Why? Answer: Price of 6% 20 year bond at par $1,000 Price of 6% 10 year bond at par $1, Price of 6% 20 year bond at a 7% yield $893.22 Price of 6% 10 year bond at a 7% yield $928. Percentage price decline = 10.68% Percentage price decline = 7.10% If you expect rates to rise you need to be invested in shorter term bonds ( the 10 year issue) because you will lose less money. Assume semiannual compounding on the zero coupon bonds even though they pay no interest