CH-7 The Valuation and Characteristics of Bonds – Practical Financial Management : Book Guide

CHAPTER 7 THE VALUATION AND CHARACTERISTICS OF BONDS FOCUS The discussion of bonds is presented in two parts. First we concentrate on understanding the calculations associated with pricing bonds including consideration of call provisions and convertibles. After that we take a close look at the nature of the bondholder-issuer relationship and the institutional characteristics of the bond instrument. Since leasing is increasingly an alternative to debt, a detailed treatment of lease financing is included after the treatment of bonds. PEDAGOGY The chapter begins with a general introduction to valuation that establishes an exact definition of the relationship between the price of a security and its return. Then, before beginning bond calculations, we go through a careful illustration of just why interest rate changes drive bond prices. This background helps to avoid confusion later on. TEACHING OBJECTIVES In this chapter, students should: 1. Gain an understanding of the basis for valuation of traditional and convertible debt securities. 2. Develop the ability to calculate bond prices and yields. 3. Learn a few of the basic institutional characteristics of bonds. 4. Develop and understanding of leasing as an alternative to debt. OUTLINE I. THE BASIS OF VALUE A financial asset's value is the present value of its future cash flows. A. Investment Investment is using a resource to improve the future. B. Return Return as the discount rate that makes the present value of a security's cash flows equal to its price. II. BOND VALUATION A bond allows one organization to borrow from many lenders at one time. A. Bond Terminology and Practice A little vocabulary, term, coupon rate etc. B. Bond Valuation - Basic Ideas Why bond prices adjust to interest rate changes. C. Determining the Price of a Bond The time line representation of a bond's cash flows. Treatment as two simultaneous time value problems, an annuity and an amount. The bond pricing formula, examples. Solving bond problems with a financial calculator. D. Maturity Risk Revisited Maturity risk as interest rate induced price variation which depends on term. E. Finding the Yield at a Given Price The iterative technique for finding yield at a given price. F. Call Provisions The nature and purpose of calls. Modifying the pricing approach if a call is expected. The refunding decision. G. Risky Issues Some hidden call provisions that can hurt unwary investors. III. CONVERTIBLE BONDS Definitions and terminology, the effect of conversion, convertibles as deferred stock purchases. A. Advantages Why companies issue and investors buy convertibles. B. Forced Conversion Limiting the cost of conversion equity. C. Valuation of Convertibles. The larger of value as bond and stock, the time premium, calculations. D. Dilution The effect of convertibles on earnings per share. IV. INSTITUTIONAL CHARACTERISTICS OF BONDS A. Registration, Transfer Agents, and Owners of Record Basic ideas and definitions. B. Kinds of Bonds Debentures, secured, convertible, subordinated, etc. The nature and purpose of each. C. Bond Ratings - Assessing Default Risk The reasons for ratings and what they mean. The symbols used by S&P and Moody's. D. Bond Indentures - Controlling Default Risk The indenture as a limit on management's risk taking. Sinking funds. V. LEASING A. The Development of Leasing in business. The effect on balance sheets, misleading results. B. FASB 13 The response of the accounting profession, disclosure. C. Operating and Financing Leases Rules for classifying leases. D. Financial Statement Presentation –Lessees An asset and an offsetting obligation, calculations. E. The Lessor’s Perspective The return implicit in the lease. F. Residual Values The effect of the residual assumption on payments and returns. G. Lease versus Buy Analyses Detailed calculations and technique. H. The Advantages of Leasing No money down, the risk of obsolesce, liquidity, etc. I. Leveraged Leasing Overview of tax based leasing. DISCUSSION QUESTIONS 1. What is valuation, and why are we interested in the results? Answer: Valuation is a systematic process through which we determine the price at which a security should sell. Since the value of securities is based on the future cash flows that come from owning them, valuation involves determining the present value of those flows. Securities don't always trade for the intrinsic values we calculate for them. This means valuation is a method of identifying potential bargains. 2. Contrast real assets and financial (paper) assets. What is the basis for the value of each? Answer: Real assets are tangible things like cars and houses that provide services like transportation and shelter. The value of real assets is based on the services they provide. Financial assets are pieces of paper that provide no services in themselves. However, they give their owners claims to cash flows expected in the future. The value of financial assets is based on receiving those future cash flows. 3. How can two knowledgeable people come to different conclusions about the value of the same security? Can this happen if they have access to the same information? Answer: A security's value is based on the present value of an estimate of its future cash flows. That, in turn, is largely based on an estimate of the issuing company's future financial performance. It is a fact of human nature that people from different opinions of the future based on the same knowledge of the past and present. In other words, different people interpret the same events differently. This leads to differing valuations even when the same information is available to everyone. In addition, people have different opinions about the appropriate interest rate used in present value calculations. 4. Describe the nature of a bond. Include at least the following ideas. Answer: A bond represents a debt relationship between the investor (lender) and the issuing company (borrower). In contrast, stock represents ownership of a share of the issuing company. A bond issue is a device through which one organization simultaneously borrows from many lenders under one agreement. Each bond represents a share of the loan. An investor is said to "buy" a bond even though he or she is actually lending money. The amount of the loan represented by a bond is denominated (printed) on its face. This principal amount, known as the bond's "face value," is repaid on a designated "maturity" date at the end of the bond's "term." Until maturity, the investor receives only interest, usually paid twice a year at the bond's "coupon rate" which is also printed on the face of the bond. Since no principal is repaid until maturity, bonds are said to be "non-amortized" debt. The payment of interest and principal to bondholders has a higher legal priority than the payment of dividends to stockholders. Therefore, bonds are said to be less risky than stocks of the same company. Conflicts between stock and bondholders exist, because the rewards of risky ventures accrue to stockholders, but the penalties for failure can also hurt bondholders. Hence stockholders are more inclined to support risk taking than bondholders. 5. What is a call provision? Why do companies put them in bonds? Define: call-protected period and call premium/penalty Answer: A call provision is a clause in a bond contract that allows the issuing company to pay the debt off early. Calls are usually exercised when interest rates have fallen substantially and the bond's debt can be reissued at a lower rate. They also allow companies to escape indentures that may have become restrictive. Call provisions generally require that bondholders receive an additional payment if the call is exercised to compensate for the loss of the original high interest rate. The payment is known as the call premium (to the bondholder) or penalty (to the issuer). There's also generally a protected period at the beginning of the bond's life when it can't be called. 6. Two interest rates are associated with pricing a bond. Name and describe each. How are they used? Describe a third rate not used in pricing. Answer: The coupon rate is the rate at which the bond pays interest on its face value. It is used to calculate the dollar amount of interest payments. The bond's yield is the current market rate offered by bonds of similar risk and term. It is used to take the present value of the bond's future interest and principal payments. The current yield is the annual interest payment divided by the current price of the bond. 7. If bonds pay fixed interest rates, how can they be sold year after year on the secondary market? Include the idea of how yields adjust to changing market interest rates. Answer: The interest actually paid by a bond is constant from year to year, but the return on an investment in the bond as seen by a new buyer varies as its price changes. The prices of old bonds adjust continually to keep their yields competitive with newly issued bonds. They can therefore be traded during their entire lives, but not at face value. 8. Why do bonds have indentures? Answer: Bonds are generally less risky investments than the stock of the same company. However, a bond can become more risky if the issuing company is run recklessly or takes on riskier projects. Indentures are contractual conditions required by lenders (bond buyers) that control the way management can run the company in an effort to limit risk. 9. Describe bond pricing as two time-value-of-money problems. Answer: A bond's price is the present value of its future cash flows, including periodic interest payments and a single payment returning principal at maturity. The interest payments constitute an annuity, since they are constant in amount and regular in timing. Therefore, the present value of a bond's cash flows is conveniently separable into an annuity problem to handle the interest payments and an amount problem to handle the return of principal. 10. What is the relationship between bond prices and interest rates? Verbally describe how this relationship comes about. How can we use this relationship to estimate the value of a bond? Answer: Bond prices and interest rates vary inversely with one another (but not in direct proportion). The relationship arises because investors often need to sell old bonds in the secondary market where interest rates change regularly. In order to stay competitive with newly issued bonds, an old bond has to offer a market yield to a new buyer. The only way it can do that is through a price change, since bond interest payments are fixed. We can roughly estimate a bond's price by looking at the difference between the current interest rate and the bond's coupon rate. If that difference is large, and the bond has a long time until maturity, we can guess that the percentage price change will be in the neighborhood of the percentage interest rate change. 11. What is interest rate or price risk? Why is it sometimes called maturity risk? Explain fully. Answer: Bond prices vary inversely with interest rates. If an investor buys a bond and interest rates rise, its market price falls. Therefore, an investor who has to sell the bond while rates remain high suffers a loss due to a price change induced by an interest rate change. The possibility of such a loss is called interest rate or price risk. The phenomenon also depends on the maturity of the bond, because the prices of long-term bonds change more in response to interest rate changes than the prices of short-term bonds. This connection leads to the term maturity risk. 12. What causes maturity risk? In other words, why do long-term bonds respond differently to interest rate changes than short-term bonds? (Hint: Think about how the present value formulas work.) Answer: A bond's future cash flows are discounted to their present values by dividing by (1+k)i where i varies from 1 to the bond's term of n periods. The sensitivity of (1+k)i to changes in k depends on the value of i. The larger is i, the more (1+k)i changes due to a given change in k. In a long-term bond many of the cash flows are discounted by factors with large exponents. In a short-term bond, the exponents are all small. Therefore, a change in k affects a long-term bond relatively more than a short-term bond. 13. Using words only, describe the process of finding a bond's yield at a given selling price. Answer: The technique is iterative. We begin by making an educated guess at the yield based on the relation between the bond's selling price and its face value. Then we evaluate the price implied by that yield and compare it to the actual selling price. If the two are different we make another guess at the yield and repeat the process. We continue until a yield is found that results in a price that's very close to the selling price. Successive guesses aren't random, but are based on the inverse relationship between prices and yields. 14. Under what conditions is a bond almost certain to be called at a particular date in the future? How does this condition affect its price? Answer: A bond issued at a high coupon rate is likely to be called if interest rates drop substantially. If the drop occurs during the call-protected period, the call is likely at the end of that period. Under these conditions the call limits price increases induced by interest rate declines, because it makes above market interest payments unlikely after the call-protected period. 15. How and why do sinking funds enhance the safety of lenders? Answer: The principal repayment required when a bond issue matures is typically many times the annual interest paid during the issue's life. That means a borrowing company that has easily funded interest payments can be unable to come up with enough cash to repay principal when it's due. In extreme cases this can cause the borrower to fail and never repay the full amount of principal. A sinking fund usually prevents this from happening by forcing the borrower to put aside money for principal repayment over an extended period so that it is available at the bond's maturity. 16. What, in general, is meant by off balance sheet financing? Answer: Off balance sheet financing occurs when a company has the use of an asset without showing it or the source of the funds that acquired it on the balance sheet. Operating leases are the most common form of off balance sheet financing. 17. Describe the feature of financial reporting that made leasing popular before FASB 13. Answer: Before FASB 13, if a firm used an asset technically owned by someone else, it didn’t have to capitalize the asset on its balance sheet. It also didn’t have to show a liability for funds used to acquired it. This was important because liabilities cause a firm’s financial ratios to deteriorate. Leasing let lessees use assets owned by lessors without showing any obligation to make lease payments on their balance sheets. That was attractive, because it made lessee’s financial statements look stronger than they would have had the firms borrowed money to purchase the assets. 18. What argument was made against adopting FASB 13? (One line answer.) Answer: Footnote disclosure of leases is sufficient. 19. There’s a fundamental difference between the rules one, two, and four for qualifying an operating lease and rule three. What is it? Answer: Rules one, two, and four identify installment sales (time payment sales) masquerading as leases. Rule three is aimed at identifying the transfer of economic ownership within a real lease. 20. Just what is placed on the balance sheet in a financing lease? Answer: A figure representing the value of the asset and a liability representing what the lessee is obligated to pay for that asset in the future. Both are usually taken as the present value of the committed future lease payments. This assumes that the lessor would not transfer the asset for a committed stream of payments worth much less than the market value of the asset. 21. In leases with no residuals, lessors calculate the lease payments they must charge as if the lease was a loan. How does the presence of a residual change the calculation? Answer: The residual reduces the amount the lessor must recover from lease payments making the payments lower. This is accomplished by subtracting the present value of the residual from the lessor’s beginning investment in the equipment before calculating payments. 22. Why are residuals important in negotiations between lessees and lessors? Answer: There’s a tradeoff between the residual assumed in the lease and the payment required to give the lessor its target return. And residuals are notoriously difficult to predict with any accuracy. Hence arguing for a higher residual can be a way to lower payments without lowering the lessor’s planned return. 23. Depreciation is a noncash charge. Why then is it important in Lease-Buy analysis? (Very short answer.) Answer: Depreciation is tax deductible and therefore saves taxes which are cash outlays. 24. Leasing is generally more expensive than borrowing to buy, and FASB 13 has reduced the availability of off balance sheet financing. Why then is leasing popular? Answer: Leasing offers a number of conveniences not usually available from borrowing to buy. These include: • Little or no down payment • Fewer restrictions on the lessee’s activities • Easier credit when the lessor is also the equipment manufacturer • The risk of obsolescence may be transferred to the lessor • It can be possible to tax deduct the cost of land • Funds tied up in real estate may be freed up through a sale and leaseback • Leveraged leases allow unprofitable companies to indirectly enjoy the tax advantages of ownership 25. Leveraged leases offer tax advantages to unprofitable companies. a. Why are they called leveraged? b. Briefly, how do they work? Answer: a. Leveraged leases are so called because the lessor borrows most of the money to purchase the leased asset. I.e., the lessor’s purchase is leveraged. They are also called tax leases. b. In a leveraged lease the lessor is permitted to depreciate the leased asset for tax purposes as well as to tax deduct interest on the debt used to acquire it. Those tax advantages lower the lessor’s cost. The lessor then passes much of that saving on to the lessee through lower lease payments. Thus the lessee indirectly enjoys the tax advantages of ownership. BUSINESS ANALYSIS 1. You're an analyst in the finance department of Flyover Corp., a new firm in a profitable but risky high-tech business. Several growth opportunities have presented themselves recently, but the company doesn't have enough capital to undertake them. Stock prices are down, so it doesn't make sense to try to raise new capital through the sale of equity. The company's bank won't lend it any more money than it already has, and investment bankers have said that debentures are out of the question. The treasurer has asked you to do some research and suggest a few ways in which bonds might be made attractive enough to allow Flyover to borrow. Write a brief memo summarizing your ideas. Answer: Flyover's problem is that the firm is perceived as too risky for debt investors. Two approaches might help. These involve lowering the risk of new debt and making the existing level of risk more acceptable. The risk in new bonds could be lowered by: 1. Securing the bonds with owned assets (e.g., a mortgage bond secured by real estate). 2. Agreeing to subordinate future debt. 3. Providing a restrictive indenture limiting the risk in future undertakings. 4. Providing a sinking fund for principal repayment. The current level of risk might be made acceptable by: 1. Including a convertible feature. 2. Issuing the new bonds in the junk bond market 2. The Everglo Corp., a manufacturer of cosmetics, is financed with a 50-50 mix of debt and equity. The debt is in the form of debentures, which have a relatively weak indenture. Susan More money, the firm's president and principal stockholder, has proposed doubling the firm's debt by issuing new bonds secured by the company's existing assets and using the money raised to attack the lucrative but very risky European market. You're Everglo's treasurer, and have been directed by Ms. More money to implement the new financing plan. Is there an ethical problem with the president's proposal? Why? Who is likely to gain at whose expense? (Hint: How are the ratings of the existing debentures likely to change?) What would you do if you really found yourself in a position like this? Answer: Yes, there is an ethical problem. The proposal will seriously erode the position of the existing bondholders. Notice that the existing bonds are unsecured debentures meaning that in the event of failure, they depend on the firm's general pool of assets for repayment. The proposal would take the firm's existing assets out of the general pool and pledge them to new creditors thus weakening the security of old creditors. Further, the company would probably be perceived as considerably more risky under the new plan. That means the rating of its existing bonds will drop which means the market prices of those bonds will fall. Hence, the firm becomes more risky, but old bondholders can't get out without taking an immediate loss. The reward for bearing all this risk is the potential profit from the European market. However, bondholders won't share in this profit because, their returns are limited to interest and principal repayment. The stockholders (principally the president) get the benefits of success, but are sharing the risk with the old bondholders. This constitutes an abuse of the bondholders by the stockholder- manager of the firm. An ethical financial executive would try his or her best to dissuade the president from this course of action. How far a person will go to resist such pressure is a question of individual conscience. 3. You're the CFO of Nildorf Inc., a maker of luxury consumer goods that, because of its product, is especially sensitive to economic ups and downs. (People cut back on luxury items during recessionary times.) In an executive staff meeting this morning, Charlie Suave, the president, proposed a major expansion. You felt the expansion would be possible if the immediate future looked good, but were concerned that spreading resources too thin in a recessionary period could wreck the company. When you expressed your concern, Charlie said he wasn't worried about the economy, because the spread between AAA and B bonds is relatively small, and that's a good sign. You observed, however, that rates seem to have bottomed out recently and are rising along with the differential between strong and weak companies. After some general discussion, the proposal was tabled pending further research. Later in the day, Ed Slide rule, the chief engineer came into your office and asked, "What in the world were you guys talking about this morning?" Prepare a brief written explanation for Ed. Answer: Ed, Charlie and I were talking about the way certain financial statistics are used as indicators of the near term health of the economy. In general, low interest rates imply good times, and that's what we've been experiencing recently. Beyond that however, the spread between the rates demanded of risky and stable borrowers is an economic indicator. In good times risky companies can borrow at rates close to those offered to stable firms. That's because risky firms don't tend to fail much more often than stable companies in good times. However, when times are tough, risky firms tend to go bankrupt far more frequently than stable companies. That means lenders demand a big interest rate differential for risky borrowers in recessionary times. This effect is so pronounced that the spread between the yields on the bonds of high (AAA) and low (B) rated companies is taken as an indicator of near term economic conditions. A small spread, usually coupled with low rates, implies prosperity while a large spread coupled with high rates implies recession. Charlie was quite correct in saying that the spread has recently indicated prosperity. However, I'm concerned that there's an increasing trend in both rates and the spread. This could mean that things are turning down and we're in for a recession. That's critical because the nature of our products is such that we do very well in good times but exceptionally badly during recessions. That means committing to an expansion during a recessionary period could be fatal. 4. Paliflex Corp. needs new capital, but is having difficulty raising it. The firm’s stock price is at a ten year low, so selling new equity means giving up an interest in the company for a very low price. The debt market is tight and interest rates are unusually high, making borrowing difficult and expensive. In fact, it isn’t certain that anyone will lend to Paliflex because it’s a fairly risky company. On the other hand, the firm’s long-term prospects are good, and management feels the stock price will recover within a year or two. Ideally management would like to expand the company’s equity base, so it can borrow more later on, but at the moment the stock price is just too low. Suggest a capital strategy that addresses both the short and long-run explaining why it is likely to work. Answer: A convertible bond may solve both Paliflex’s short run need for capital and its long run need for equity. Since the company’s stock has good long-term prospects a convertible feature will be valuable, and may induce investors to accept lower than market interest rates. If things are so bad that no one will lend to Plaflex, a convertible may sweeten the deal enough to prompt an investor it to extend credit. In the longer run if the stock price goes up, convertible debt will eventually become equity at a conversion price substantially above the stock’s current market value. In effect, a convertible bond will be a deferred sale of equity. The convertible should be issued with a call feature to force conversion if necessary. 5. You’ve just joined Sea Craft Inc., a manufacturer of fiberglass boats, as its CFO. When you took the job you knew that the company was not in the best of financial condition. Profits are adequate, but the firm is carrying substantial debt. To make matters worse, the company’s largest fiberglass molding machine is almost completely worn out and needs to be replaced. Sea Craft can’t pay for a new machine out of operating profit, and the owner, Sam Alston, doesn’t want to sell any new stock which would dilute his interest. You’ve looked into borrowing money to acquire the machine, and can get a deal with practically no down payment and a favorable interest rate through some banking contacts. But Sam is concerned about taking on more debt. He would like to sell the company and retire, but he’s afraid that a heavier debt load will depress the price he might get. You agree that his concern is well founded. Sam rushed into your office this morning with what he described as a great idea. He’d read an article that said just about anything could be leased, and knew that Sea Craft already leased a number of copying machines. On his way to see you he stopped into the accounting department and found that neither the copying equipment nor any associated liability was on Sea Craft’s balance sheet. Storming into your office he declared, “Leasing the molding machine is going to solve my debt problems! You’re supposed to be the financial expert, why didn’t you think of it? Why do I have to think of everything? Get on this quick! I want to see a lease deal on my desk by the end of the week.” Before you could answer, he rushed out for a meeting with the marketing department. Prepare a tactful memo to Sam explaining a little more about leasing and why it may not be as wonderful for Sea Craft as he thinks. Write the memo for a reader who is not a financial person, i.e., avoid using technical jargon like FASB, capitalize, equity, annuity, and present value. Talking about financing, balance sheets, assets and debt is ok. Answer: Sam: Leasing sounds like a good way to avoid showing long-term debt on our balance sheet, and at one time it was. It’s called off balance sheet financing. Unfortunately, it doesn’t work for large assets like the molding machine anymore. In 1976 the accounting profession promulgated a rule saying that if a lease transfers an asset in such a way that the lessee effectively becomes the owner, that lessee has to show the asset on its balance sheet along with a “lease obligation” that financial analysts treat as debt. Leases like that are called financing leases, because they represent an alternate method of financing equipment. Short-term leases, like those on copying machines aren’t treated that way, because the lease term is less than the machine’s life, and the lease payments account for less than its full value. That means the lessor generally sells or re-leases the equipment to someone else after the initial lease is over. These arrangements are called operating leases and do provide a modest amount of off balance sheet financing. Unfortunately, we couldn’t get an operating lease on a molding machine, because any lessor who buys one for us will insist on a long term, financing lease. That’s because the molding machine is a specialized piece of equipment that wouldn’t be readily saleable or re-leasable to anyone else if we didn’t want it after an initial short-term lease. But even if we could get an operating lease on the mold, it probably wouldn’t help much. Off balance sheet financing won’t keep a sophisticated analyst from recognizing the lease and the fact that it’s effectively debt. That’s because all leases have to be disclosed in footnotes to the financial statements. Anyone interested in buying the company is sure to have a financial expert scrutinize the books, so the lease and the fact that it’s effectively debt will certainly be disclosed to the potential buyer. The bottom line is that leasing won’t make us look any better, and is generally a good deal more expensive than purchasing with borrowed money. PROBLEMS The first two problems involve annual compounding. In the remaining problems, assume all bonds pay interest semiannually unless otherwise indicated. Finding the Price of a Bond: Concept Connection Example 7-1 (page 293) 1. A bond that pays 10% interest compounded annually on a $1,000 face value will mature in 20 years. The interest rate is now 12%. What should the bond’s market price be? Solution: 2. A $1,000 par value, 30 year bond is 5 years old. It pays interest once a year at an annually compounded coupon rate of 12% The market is returning 8% on comparable bonds. What is the bond’s market price? Solution: 3. The Altoona Company issued a 25-year bond 5 years ago with a face value of $1,000. The bond pays interest semiannually at a 10% annual rate. a. What is the bond's price today if the interest rate on comparable new issues is 12%? b. What is the price today if the interest rate is 8%? c. Explain the results of parts a and b in terms of opportunities available to investors. d. What is the price today if the interest rate is 10%? e. Comment on the answer to part d. Solution: c. In part a the interest rate has risen above the coupon rate. Therefore an investment equal to the bond's face value would earn more if placed in newly issued bonds. That means the bond's price has to decrease below face value to keep its yield competitive with new issues. In part b the bond offers more than new issues costing $1,000. Therefore, its price can increase above $1,000 and still remain competitive. d. $1,000. e. A bond will always sell at par value when the interest rate is equal to its coupon rate. 4. Calculate the market price of a $1,000 face value bond under the following conditions. 5. What is the current yield on each of the bonds in the previous problem. Solution: a. $120.00/$1,153.72 = .104 = 10.4% b. $70.00/$816.00 = .086 = 8.6% c. $90.00/$1,385.95 = .065 = 6.5% d. $140.00/$1,515.95 = .092 = 9.2% e. $50.00/$859.23 = .058 = 5.8% 6. The Sampson Company issued a $1,000 bond 5 years ago with an initial term of 25 years and a coupon rate of 6%. Today’s interest rate is 10%. a. What is the bond’s current price if interest is paid semiannually as it is on most bonds? b. What is the price if the bond’s interest is paid annually? Comment on the difference between a and b. c. What would the price be if interest was paid semiannually and the bond was issued at a face value of $1,500? Solution: 7. Fix-It Inc. recently issued 10-year, $1,000 par value bonds at an 8% coupon rate.. a. Two years later, similar bonds are yielding investors 6%. At what price are Fix-Its bonds selling? b. What would the bonds be selling for if yields had risen to 12%? c. Assume the conditions in part a. Further assume interest rates remain at 6% for the next 8 years. What would happen to the price of the Fix-It bonds over that time? Solution: 8. The Mariposa Co. has two bonds outstanding. One was issued 25 years ago at a coupon rate of 9%. The other was issued 5 years ago at a coupon rate of 9%. Both bonds were originally issued with terms of 30 years and face values of $1,000. The going interest rate is 14% today. a. What are the prices of the two bonds at this time? b. Discuss the result of part a. in terms of risk in investing in bonds. Solution: b. The old bond has a shorter remaining life (term, maturity) than the new bond. Its price is therefore less sensitive to the change in the market interest rate from 9% to 14%. We say the old, short-term bond has less maturity risk than the new, long-term bond. 9. Longly Trucking is issuing a 20-year bond with a $2,000 face value tomorrow. The issue is to pay an 8% coupon rate, because that was the interest rate while it was being planned. However rates have increased suddenly and are expected to be 9% when the bond is marketed. What will Longly receive for each bond tomorrow? Solution: PB = PMT [PVFAk,n] + FV [PVFk,n] PB = $80 [PVFA4.5,40] + $2,000 [PVF4.5,40] = $80 (18.4016) + $2,000 (.1719) = $1,815.93 10. Daubert, Inc. planned to issue and sell at par 10-year, $1,000 face value bonds totaling $400 million next month. The bonds have been printed with a 6% coupon rate. Since that printing, however, Moody’s downgraded Daubert’s bond rating from Aaa to Aa. This means the bonds will have to be offered to yield buyers 7%. How much less than it expected will Daubert collect when the bonds are issued. Ignore administrative costs and commissions. Solution: The bonds will sell for PB = PMT[PVFAk,n] + FV[PVFk,n] k = 3.5 n = 20 PB = $30[14.2124] + $1,000[.5026] = $928.97 Daubert planned to sell $400,000,000 / $1,000 = 400,000 bonds. Hence selling the same number will bring 400,000 x $928.97 = $371,588,000 which is $28,412,000 less than the $400 million originally expected. Calculator Solution: n = 20; I/Y = 3.5; PMT = 30; FV = 1,000 CPT PV = $928.93 11. Tutak Industries issued a $1,000 face value bond a number of years ago that will mature in eight years. Similar bonds are yielding 8%, and the Tutak bond is currently selling for $1,291.31. Compute the coupon rate on this bond. (In practice we generally aren’t asked to find coupon rates.)(Hint: Substitute and solve for the coupon payment.) Solution: PB = PMT [PVFAk,n] + FV [PVFk,n] $1,291.31 = PMT(11.6523) + $1,000(.5339) from which PMT = $65 Then $65 / $1,000 = 6.5% per semiannual period or 13% per year Calculator Solution: n = 16; I/Y = 4; PV = 1,291.31; FV = 1,000 CPT PMT = $65.00 12. John Wilson is a conservative investor who has asked your advice about two bonds he is considering. One is a seasoned issue of the Capri Fashion Company, which was first sold 22 years ago at a face value of $1,000, with a 25-year term, paying 6%. The other is a new 30-year issue of the Gantry Elevator Company that is coming out now at a face value of $1,000. Interest rates are now 6%, so both bonds will pay the same coupon rate. a. What is each bond worth today? (No calculations should be necessary.) b. If interest rates were to rise to 12% today, estimate without making any calculations what each bond would be worth. c. Calculate the prices in part b to check your estimating ability. If interest rates are expected to rise, which bond is the better investment? d. If interest rates are expected to fall, which bond is better? Are long-term rates very likely to fall much lower than 6%? Why or why not? (Hint: Think about the interest rate model of Chapter 5 and its components.) Solution: a. $1,000 b. The new bond has a long maturity, so guess that doubling in the interest rate will result in a more or less proportionate price decrease, say to one half of the original par value, $500. The old bond has a relatively short maturity, so arbitrarily guess that the price change will be less than half of the change in the new bond's price, say a drop of $200 to a price of $800. c. PB = PMT [PVFAk,n] + FV [PVFk,n] Old: PB = $30 [PVFA6,6] + $1,000 [PVF6,6] = $30 (4.9173) + $1,000 (.7050) = $852.52 New: PB = $30 [PVFA6,60] + $1,000 [PVF6,60] = $30 (16.1614) + $1,000 (.0303) = $515.42 d. If rates fall, prices will increase. The new bond's price will increase more, however, because of its longer maturity. That might create an opportunity for a capital gain if John is able to sell the bond. Long-term rates on corporate bonds are unlikely to fall too much below 6%. Recall from Chapter 5 that in theory interest rates are the sum of a pure rate, an estimate of inflation, and several risk factors. The pure rate is between 2% and 4%, and inflation doesn't go much below 3% even in the best of times. Adding a percent or two for risk makes it hard to visualize a long-term rate much below 6%. The experience of the early 2000s, however, shows us that theory doesn’t always work. In early 2012 long term corporate rates were in the neighborhood of 4.5%. Finding the Yield at a Price: Concept Connection Example 7-3 (page 298) 13. Smithson Co.'s Class A bonds have 10 years to go until maturity. They have a $1,000 face value and carry coupon rates of 8%. Approximately what do the bonds yield at the following prices? a. $770? b. $1,150? c. $1,000? Solution: A series of iterations leads to the following approximate solutions for a. and b. c. 8%, because a bond sells at its face value when it yields the coupon rate. 14. Hoste Corp. issued a $1,000 face value 20-year bond seven years ago with a 12% coupon rate. The bond is currently selling for $1,143.75. What is its yield to maturity (YTM)? Solution: PB = PMT[PVFAk,n] + FV[PVFk,n] $1,143.75 = $60PMT[PVFAk,26] + $1,000[PVFk,26] Trial and error results in k = 5% PB = $60(14.3752) + $1,000(.2812) = $1,143.75 Hence the market interest rate is (5x2=) 10%. Calculator Solution: n = 26; PV = (1,143.75); PMT = 60; FV = 1,000 CPT I/Y = 5.00% 15. Pam Smith just inherited a $1,000 face value K-S Inc. bond from her grandmother. The bond clearly indicates a 12% coupon rate, but the maturity date has been smudged and can’t be read. Pam called a broker and determined that similar bonds are currently returning about 8% and that her bond is selling for $1326.58. How many more interest payments can Pam expect to receive on her inherited bond? (Hint: Use an iterative approach, but solve for n rather than k.) Solution: PB = PMT[PVFAk,n] + FV[PVFk,n] $1,326.58 = $60[PVFA4,n] + $1,000[PVF4,n] Trial and error yields n = 27 $1,326.58 = $60[16.3296] + $1,000[.3468] Calculator Solution I/Y = 4; PV = 1,326.58; PMT = 60; FV = 1000 CPT n = 27 16. Ernie Griffin just purchased a 5-year zero coupon corporate bond for $680.60 and plans to hold it until maturity. Assume Ernie has a marginal tax rate of 25%. a. Calculate Ernie’s after-tax cash flows from the bond for the first two years. Assume annual compounding. b. Describe in words the difference in cash flows between owning Ernie’s bond and a 5-year U.S. savings bond for the same amount. (Hint: See the Insights box on page XXX for this problem.) Solution: a. A zero coupon bond pays no interest so Ernie has simply invested a sum at interest to be repaid in five years. PB = 0[PVFAk,n] + FV[PVFk,n] = FV[PVFk,n] $680.60 = $1,000[PVFk,5] [PVFk,5] = $680.60/$1,000 = .6806 From which Appendix A-2 yields k = 8% Although no interest is actually paid, tax is due on the interest earned each year on corporate zero coupon bonds. In the first year interest will be $680.60 x .08 = $54.45 and Ernie will pay $54.45 x .25 = $13.61 in tax. In the second year his principal will grow to $680.60 + $54.45 = $735.05 and his tax will be $735.08 x .08 x .25 = $14.71. These taxes will be cash outflows. Ernie won’t have an inflow until the bond pays off in the fifth year or he sells the bond. b. Although savings bonds are zero coupon bonds, the government doesn’t make bond holders pay tax on the accrued interest until they’re cashed in, so there is no negative cash flow associated with them. Pricing a Likely to be Called Bond – Example 7.4 (page XXX) Problems 17 through 19 refer to the bonds of the Apollo Corporation, all of which have a call feature. The call feature allows Apollo to pay off bonds any time after the first 15 years, but requires that bondholders be compensated with an extra year's interest at the coupon rate if such a payoff is exercised. 17. Apollo's Alpha bond was issued 10 years ago for 30 years with a face value of $1,000. Interest rates were very high at the time, and the bond's coupon rate is 20%. The interest rate is now 10%. a. At what price should an Alpha bond sell? b. At what price would it sell without the call feature? Solution: a. The Alpha bond is likely to be called, so its price should be calculated using the call formula: PB(call) = PMT [PVFAk,m] + CP [PVFk,m] where m = (15-10)  2 = 10 CP = $1,000 + $200 = $1,200 so PB(call) = $100 [PVFA5,10] + $1,200 [PVF5,10] = $100 (7.7217) + $1,200 (.6139) = $1,508.85 b. PB = $100 [PVFA5,40] + $1,000 [PVF5,40] = $100 (17.1591) + $1,000 (.1420) = $1,857.91 18. Apollo’s Alpha-1 bond was issued at a time when interest rates were even higher. It has a coupon rate of 22%, a $1,000 face value, an initial term of 30 years, and is now 13 years old. Calculate its price if interest rates are now 12%, compare it with the price that would exist if there were no call feature, and comment on the difference. Solution: The rather significant difference of $370.87 represents an amount that the call feature saves an issuing company forced to borrow when interest rates are extremely high. 19. Apollo's Beta bond has just reached the end of its period of call protection, has 10 years to go until maturity and has a face value of $1,000. Its coupon rate is 16%, and the interest rate is currently 10%. Should Apollo refund this issue if refunding costs a total of 8% of the value of the debt refunded plus the call penalty? (Hint: See The Refunding Decision, page 306.) Solution: The cost of not refunding is the present value of the future cash flows to be paid out until maturity, which is also the current price of the bond Another way to look at the refunding issue is to say that the interest payments under the old bond are $160 per year for ten years. If a new bond is issued at 10%, the interest will be $100 a year. The interest saved is then $60 per year for ten years. Assuming semiannual payments and compounding at 10% we have PV (Savings) = PMT [PVFAk,n] = $30 (PVFA5,20) = $30 (12.4622) = $373.88 The cost of this saving is the sum of the call penalty and the cost of refunding. These add to $240. 20. Snyder Mfg. issued a $1,000 face value 30-year bond 5 years ago with an 8% coupon. The bond is subject to call after 10 years, and the current interest rate is 7%. What call premium will make a bondholder indifferent to the call? (Hint: Equate the formulas for the bond’s price with and without the call.) Solution: Risky Issues (page 306) 21. Your friend Marvin is excited because he believes he’s found an investment bargain. A broker at Quick Cash Investments has offered him an opportunity to buy a bond issued by Galveston Galleries Inc. at a very attractive price. The 30 year bond was issued ten years ago at a face value of $1,000, paying a coupon rate of 8%. Interest rates have risen recently driving bond prices down, but most economists think they’ll fall again soon driving prices back up. That makes Marvin and his broker think this bond may be a real money maker if he buys now, holds for a year or two, and then sells. The bonds of companies that were similar to Galveston at the time its bond was issued are now yielding 12%. Galveston’s bond is selling at $300 which the broker claims is a fantastic bargain. Marvin knows you’re a finance major and has asked your opinion of the opportunity. How would you advise him? Solution: First calculate the price at which the bond should sell given the yield on seemingly similar bonds. Using a financial calculator we have: n = 40, I/Y = 6, PMT = 40, FV = 1,000 Answer: PV = 699.07 Hence, the bond’s market price based on interest rate changes alone should be $699.07. The fact that it’s selling for less than half of that price probably means the issuing company is in financial trouble. It’s likely that Galveston Galleries is in jeopardy of defaulting on the issue or has already done so . Since the bond has some value, traders must still believe there’s a chance of recovery, but the investment opportunity is extremely risky. Marvin shouldn’t invest without understanding what he’s getting into and doing some research to learn more about Galveston and its prospects. Basics of Investing in Convertible Bonds: Concept Connection Example 7-5 (pages 307) 22. Pacheco Inc. issued convertible bonds 10 years ago. Each bond had an initial term of 30 years, had a face value of $1,000, paid a coupon rate of 11%, and was convertible into 20 shares of Pacheco stock, which was selling for $30 per share at the time. Since then the price of Pacheco shares has risen to $65 and the interest rate has dropped to 8%. What is the least that each of the bonds is worth today? Comment on the function of the bond valuation procedure for convertibles Solution: Each bond is worth at least the higher of its value as stock or its value as a bond. As stock each bond is worth 20 shares $65 = $1,300 As a bond each is worth PB = PMT[PVFAk,n] + FV[PVFk,n] = $55[PVFA4,40] + $1,000[PVF4,40] = $55(19.7928) + $1,000(.2083) = $1,088.60 + $208.30 = $1,296.90 Hence, under current conditions the conversion option gives the bond a slightly higher minimum value than the value of an otherwise identical but unconvertible bond. In general the valuation of a convertible as a bond provides a floor for the value of the security which may be higher if the price of the stock rises considerably. 23. Jake Cornwall just bought a $1,000 par value, 8% coupon rate, 30 year bond of the Pristine Corp. Interest rates had risen somewhat between the time the coupon rate was set and the bond was issued, so Jake got it at a discount paying only $950. The bond is convertible into 50 shares of stock at a conversion price of $20 per share. Similar Pristine Corp bonds without the conversion feature carry 10% coupon rates and are also selling at $950. Pristine’s stock is selling at $15 per share. The company consistently pays an annual dividend of $1 per share. Calculate the following at the end of one year. a. The return on Jake’s investment if the stock’s price rises to $25 per share, Jake exercises the conversion and sells immediately. b. The one year return on Jake’s investment if he had invested in Pristine’s ordinary bonds (no conversion) and interest rates at the end of the year were the same as they were when he purchased the bond. c. Jake’s one year return if he had invested in the company’s stock. d. What would the returns on the three investments have been if the stock’s price hadn’t moved? e. What would the returns on the three investments have been if the stock’s price had declined to $12 and interest rates were the same as on the day he purchased the bond? f. What would the return on Jakes investment have been if Pristine had forced conversion at a stock price of $23 a few days before the end of the year? g. Comment on the effect of the forced conversion on investors. Solution: g. The forced conversion limits the convertible investor’s participation in stock price appreciation. In this case the difference between Jake’s return with and without the forced transaction is $100 or 10.5%. The difference becomes available to Pristine if it offers new stock for sale. A call feature makes convertibles less attractive than they initially seem to be. Calculating the Conversion Premium and Dilution: Concept Connection Examples 7.6 and 7.7 (pages 311 and 314) 24. The Maritime Engineering Corp sold 1,500 convertible bonds two years ago at their $1,000 par value. The 20-year bonds carried a coupon rate of 8% and were convertible into stock at $20 per share. At the time, the firm’s stock was selling for $15, and similar bonds without a conversion feature were yielding 10%. Maritime’s stock is now selling for $25. The firm does not pay dividends. a. Calculate the return on investment from buying the bond when it was issued, exercising the conversion today, and immediately selling the stock received. b. What would the return on an investment in Maritime’s stock have been? c. What was the conversion premium of the bond at the time it was issued? d. Last year Maritime had Net Income of $4.5 million and 3 million shares outstanding. The company’s marginal tax rate was 34%. Compute Maritime’s basic and diluted EPS. Solution: 25. Lindstrom Corp. reported earnings after tax of $2,160,000 last year along with basic EPS of $3.00. All of Lindstrom’s bonds are convertible, and if converted, would increase the number of shares of the firm’s stock outstanding by 15%. Lindstrom is subject to a total effective tax rate of 40% and has a TIE of 10. Compute Lindstrom’s diluted earnings per share. Solution: First find the numbers of shares outstanding before and after conversion Before conversion we have EPS = Net Income / shares 3 = 2,160,000 / shares shares = 720,000 The after conversion Shares = 720,000 x 1.15 = 828,000 Next calculate Lindstrom’s interest expense, all of which will be saved if the bonds convert. Do this by working up the income statement starting with Net Income Net Income = EBT x (1 – T) EBT = Net Income / (1 – T) = $2,160,000 /.6 = $3,600,000 By definition EBT = EBIT – Interest from which EBIT = EBT + Interest Substitute this expression for EBIT into the definition of TIE TIE = EBIT / Interest TIE = (EBT + Interest) / Interest Next substitute numerical values for TIE and EBT into this expression, and solve for Interest 10 = ($3,600,000 + Interest) / Interest Interest = $400,000 The after tax impact of which is $400,000 x (1-T) = $400,000 x .6 = $240,000 and Diluted EPS = (Net Income + Interest saved after tax)) / new number of shares = ($2,160,000 + $240,000) / 828,000 = $2,400,000 / 828,000 = $2.90 per share 26. Harvester Inc. has net income of $75,000,000 and 15,000,000 shares of common stock outstanding. Several years ago it issued 10,000, 8% coupon, 30 year convertible debentures at a par value of $1,000. The conversion price was set at $25, the price of the stock at the time was about $18. The company is taxed at a total effective rate of 35% and regularly pays an annual dividend of $0.50 per share. The bond issue included a call feature with a call premium of two years coupon interest and a 5 year period of call protect which has now past. Management thought the stock price would increase steadily over the next few years and anticipated a quick conversion into equity but that hasn’t happened. The stock is now selling for $30 and management is considering a call hopefully to force conversion. a. Calculate Harvester’s Basic and Fully Diluted EPS. b. What is annual the cash flow impact on the company of conversion of all the bonds? c. Evaluate a bondholders’ position at this time. Why haven’t they converted? d. Will a call force conversion? Why? That is, what is difference in value for each bond between conversion and call? e. Why does management prefer conversion to call? (Words only.) Solution: a. Basic EPS EPS = Net Income / # of shares = $75M / 15M = $5.00 Fully Diluted EPS Interest saved by conversion = 10,000 bonds x $1,000 x .08 = $800,000 Interest savings after tax = $800,000 (1 - .35) = $520,000 Net Income adjusted for conversion = $75,520,000 New shares per bond at conversion = $1,000 / $25 = 40 Total new shares from conversion = 40 x 10,000 = 400,000 Shares outstanding adjusted for conversion = 15,400,000 Fully Diluted EPS = $75,520,000 / 15,400,000 = $4.90 b. Cash Flow Impact = After Tax Interest Savings – Additional Dividends Additional dividends = New Shares x $0.50 = 400,000 x $0.50 = $200,000 Cash Flow Impact = $520,000 - $200,000 = $320,000 Improvement c. Each bond pays annual interest of $80. Conversion would change that into a dividend stream of 40 shares x $0.50 = $20. Conversion would also give the bondholder a one-time gain of ($30 - $25) x 40 = $200. But bondholders know that if the stock continues to increase in value that gain will be larger. Hence it makes sense to defer the gain while maintaining the larger annual income associated with holding the bond rather than stock. d. Yes. If a call is issued bondholders are forced to choose between converting or accepting the call price, which for each bond is [$1,000 + 2($80)] = $1,160. On the other hand converting a bond gives the bondholder 40 shares worth $30 each for a total of $1,200. The difference is $40 per bond. Hence a rational investor will convert. e. The company prefers conversion because it doesn’t require any cash outflow. The call would require paying out ($1,160 x 10,000=) $11,600,000. Historical Development of Leasing (page 322) 27. Caruthers Inc. is a small manufacturing firm and has the following summarized balance sheet. The firm is interested in acquiring a fleet of ten company cars for its sales staff. The cars have an economic life of seven years, but Caruthers plans to keep them for only three because it doesn’t want its salespeople driving around in old vehicles. The cars cost $20,000 each, and Caruthers is considering borrowing to purchase them. a. Restate Caruthers’ balance sheet after the loan is made. b. Calculate the firm’s debt ratio now and immediately after the loan is made. c. Comment on the change in part b. (Words only.) d. Suggest a solution and explain why it will qualify for accounting treatment that will avoid the problem highlighted in part b. (Words only.) Solution: c. If the firm borrows this much money, its debt ratio will deteriorate to a dangerous level. 80% debt is very high for a non-financial company. Equity investors will be concerned and may bid its stock down if it is traded. Lenders will probably be unwilling to lend more for any reason. d. Caruthers may be able to lease the cars over three years, treat the lease as an operating lease, and avoid putting anything on its balance sheet. The lease will qualify as operating because its three year term is less that 75% of the cars’ economic life of seven years. 28. Henderson Engineering Ltd. just leased a computer aided design system for five years with annual payments of $12,000 payable at the end of each year. The lease contains a provision that allows Henderson to purchase the machine at its fair market value as used equipment when the lease expires. Industry data indicate that systems like these normally last for about eight years. Henderson could have purchased the machine for $50,000 with money borrowed at 9%. Does Henderson have to capitalize the lease on its balance sheet? Why? Solution: The issue is whether the lease qualifies as an operating lease. If it does, capitalization can be avoided. The first three qualifications are obviously met. Title doesn’t automatically transfer at the lease’s end, the purchase option is at fair market value so it’s not a bargain, and the lease’s five year term is less than 75% of the machine’s expected eight year economic life. To evaluate the fourth rule we have to calculate the present value of the lease payments at the firms borrowing rate, and compare the result to 90% of the $50,000 fair market value of the asset at the beginning of the lease. The present value of payments is PVA = $12,000[PVFA9,5] = $12,000(3.8897) = $46,676. And 90% of the fair market value is: $50,000 x .90 = $45,000. Since $46,676 is more than $45,000 the lease fails the fourth test and cannot be treated as an operating lease. It is therefore a financing lease and must be capitalized. Accounting for a Financing Lease: Concept Connection Example 7-8 (page 326) 29. Taunton Manufacturing Inc. is a machine shop in Taunton Massachusetts. The firm recently leased a drill press for a 20-year term at payments of $9,000 per year payable at year-end. No residual value was assumed in the lease, which is clearly a financing lease. Taunton can borrow at 8%, and will depreciate the press straight line over 20 years. Shortly before the lease became effective Taunton’s balance sheet was as follows: Answer the following questions working in whole dollars but present balance sheet accounts rounded to the nearest $1,000. a. Construct Taunton’s balance sheet showing the capitalized lease and the related lease obligation. b. Calculate the firm’s debt ratio before and after the lease, and comment on the difference. c. (Optional) Reconstruct the balance sheet at the end of the first year assuming the other accounts remain the same. Solution: After the lease it is debt ratio = (current liabilities + lease obligation + long term debt)/total assets = ($25 + $88 + $95)/$438 = $208/$438 = 47.5% Comment: The lease causes an increase in Taunton’s debt ratio but the result is probably not bad enough to jeopardize the company’s survival. It might make further borrowing more difficult and expensive, but not impossible. c. First year depreciation on the press is Depreciation = $88,363/20 = $4,418 Leased Press: Ending balance = Beginning balance - depreciation = $88,363 - $4,418 = $83,945 The lease obligation account is treated as a loan at 8% Interest = $88,363 x .08 = $7,069 Obligation reduction = Lease payment - interest = $9,000 - $7,069 = $1,931 New obligation balance = Beginning balance – Obligation reduction = $88,363 - $1,931 = $86,432 New balance sheet. Calculating Lease Payments and Returns: Concept Connection 7-9 (page 329) 30. Wings Inc. is a commuter airline that serves the Boston area. Wings plans to lease a new plane through Nantucket Capital Inc. The lease term is fifteen years, and no residual value is expected at its end. a. What monthly lease payment must Nantucket charge to earn a 12% return on its investment if the plane Wings wants costs $1.5 million? b. What would Nantucket’s return be if it agreed to accept annual payments of $200,000? Solution: a. PVA = PMT[PVFAk,n] $1,500,000 = PMT[PVFA1,180] $1,500,000 = PMT(83.3217) PMT = $18,003 b. PVA = PMT[PVFAk,n] $1,500,000 = $200,000[PVFAk,15] [PVFAk,15] = $1,500,000/$200,000 = 7.5000 Reference to table A-4 shows the answer to be about 10.25%. A calculator gives an exact solution of 10.247%. Residual Values: Concept Connection Example 7-10 (page 331) 31. Suppose Wings and Nantucket of the last problem agree to assume a $300,000 residual value for the plane at the end of the lease. How much will wings have to pay monthly to give Nantucket its 12% return? Solution: First take the present value of the residual at the rate implicit in the lease PV = FV[PVFk,n] = $300,000[PVF1,180] = $300,000(.1668) = $50,040 Subtract that from the initial investment $1,500,000 - $50,040 = $1,449,960 And find the required annuity payment PVA = PMT[PVFAk,n] $1,449,960 = PMT[PVFA1,180] $1,449,960 = PMT(83.3217) PMT = $17,402 Lease vs. Buy Analysis Concept Connection Example 7-11 (page 332) 32. Paxton Sheet Metal Works Inc. is about to acquire a new stamping press that costs $400,000. It is considering purchasing the asset with money it can borrow at 10% repayable in annual, yearend installments over six years. It has also been offered an opportunity to lease the machine for payments of $86,500 per year payable at year end, also over six years. The machine is depreciable for tax purposes over six years according to the following schedule (This is the actual tax schedule for five year life assets, a “half year convention” takes a half year’s depreciation in the first and last years; see page 405.) The lease contains a purchase option at its end at fair market value which is estimated to be $100,000. It also stipulates that Paxton will be responsible for paying for maintenance, taxes and insurance. Paxton’s marginal tax rate is 30%. Conduct a lease/buy analysis to determine which option is preferable from a purely financial point of view. Solution: Purchase cash flows are as follows ($000) The present value of the lease cash flows at 7% is PVA = PMT[PVFA7,6] = -$60,500(4.7665) = -$288,373 And the present value of the ending purchase is: PV = FV6[PVF7,6] = -$100,000(.6663) = -$66,630 Hence the present value of cash outflows associated with leasing is PV = -$288,373 -$66,630 = -$355,003 So, from a purely financial standpoint, purchasing with borrowed money is better than leasing. COMPUTER PROBLEMS (BONDS) 33. You are a securities salesperson. Many of your clients are elderly people who want very secure investments. They remember the days when interest rates were very stable (before the 1970s) and bond prices hardly fluctuated at all regardless of their terms. You've had a hard time convincing some of them that bonds, especially those with longer terms, can be risky during times when interest rates move rapidly. Use the BONDVAL program to make up a chart to help illustrate your point during discussions with your clients. People generally make bond investments because they’re considered stable and safe. That’s generally true with respect to the interest income that comes from owning bonds. But there’s another risk you should consider. The only way you can get out of a bond before it matures is to sell it at a market price that depends on the interest rate at the time of sale. Unfortunately that can lead to big losses. Let’s look at the table above to see how. Imagine that you bought two 3% bonds when the interest rate was 4%. Suppose one had only a year to go until maturity while the other had 25 years to go. You'd pay $990 and $843 respectively for the bonds as indicated in the first and fourth columns of the top row. Now imagine that the interest rate increases to 10%. Both bonds lose value as their prices drop to those along the fourth row. Notice that your one-year bond loses only $55 as it drops to 94.4% of its original value. On the other hand, your long-term issue loses $522 as it drops to 42.8% of the price you paid for it. Since interest rates are currently at record lows, it’s likely that they’ll increase over the next few years, so long term bonds should be avoided. 34. Use BONDVAL to find the YTM of the following $1,000 par value bonds. Solution Manual for Practical Financial Management William R. Lasher 9781305637542