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Chapter 8 Bond Valuation and Risk Outline Bond Valuation Process Impact of the Discount Rate on Bond Valuation Impact of the Timing of Payments on Bond Valuation Valuation of Bonds with Semiannual Payments Relationships between Coupon Rate, Required Return, and Bond Price Explaining Bond Price Movements Factors That Affect the Risk-free Rate Factors That Affect the Credit (Default) Risk Premium Summary of Factors Affecting Bond Prices Implications for Financial Institutions Sensitivity of Bond Prices to Interest Rate Movements Bond Price Elasticity Duration Bond Investment Strategies Used by Investors Matching Strategy Laddered Strategy Barbell Strategy Interest Rate Strategy Valuation and Risk of International Bonds Influence of Foreign Interest Rate Movements Influence of Credit Risk Influence of Exchange Rate Fluctuations International Bond Diversification European Debt Crisis Key Concepts 1. Explain the logic behind how bond prices are affected by interest rates. 2. Use the bond valuation equations to explain how the sensitivity of bond prices to interest rate movements is a function of bond characteristics (such as maturity and coupon rate). 3. Explain the common strategies that are used to invest in bonds. POINT/COUNTER-POINT: Does Governance of Firms Affect the Prices of Their Bonds? POINT: No. Bond prices are primarily determined by interest rate movements and therefore are not affected by the governance of the firms that issued bonds. COUNTER-POINT: Yes. Bond prices reflect the risk of default. Firms that impose more effective governance may be able to reduce their default risk and therefore increase the price of the bond. WHO IS CORRECT? Use the Internet to learn more about this issue and then formulate your own opinion. ANSWER: A bond’s price is based on the investor’s required rate of return, and investors may accept a lower return on bonds issued by firms that are subject to a higher degree of governance. Thus, governance can affect the price of the firm’s bonds. Questions 1. Bond Investment Decision. Based on your forecast of interest rates, would you recommend that investors purchase bonds today? Explain. ANSWER: Based on the forecast of increasing interest rates, investors should carefully consider whether to purchase bonds today. Here's a breakdown of factors to consider: 1. Interest Rate Risk : When interest rates rise, the value of existing bonds typically decreases. This is because newly issued bonds offer higher yields, making existing bonds less attractive in comparison. Therefore, investors who purchase bonds today may face the risk of a decline in bond prices if interest rates continue to rise. 2. Yield to Maturity : Despite the potential for price declines, investors may still find value in bonds if the yield to maturity is sufficiently attractive. If the yield on a bond compensates investors for the risk of rising interest rates and provides an acceptable return relative to other investment options, purchasing bonds may still be a viable strategy. 3. Investment Horizon : Investors should consider their investment horizon when making bond investment decisions. If they plan to hold the bonds until maturity and are primarily interested in collecting coupon payments, short-term fluctuations in bond prices due to interest rate movements may have less significance. 4. Portfolio Diversification : Bonds play an essential role in a diversified investment portfolio, providing stability and income generation. Even in a rising interest rate environment, bonds can still serve as a hedge against equity market volatility and provide steady income streams. 5. Alternative Investments : Investors should evaluate alternative investment options in light of the forecasted interest rate environment. Depending on their risk tolerance and investment objectives, they may consider allocating funds to assets less sensitive to interest rate movements, such as dividend-paying stocks, real estate, or inflation-protected securities. In conclusion, the decision to purchase bonds today depends on various factors, including the investor's risk tolerance, investment horizon, and portfolio objectives. While rising interest rates pose challenges for bond investors, bonds can still play a valuable role in a diversified investment portfolio. Investors should carefully assess the potential risks and rewards of bond investments in the context of the forecasted interest rate environment and their individual financial goals. 2. How Interest Rates Affect Bond Prices. Explain the impact of a decline in interest rates on: a. An investor’s required rate of return. ANSWER: An investor’s required rate of return should decrease. b. The present value of existing bonds. ANSWER: The present value of existing bonds should increase. c. The prices of existing bonds. ANSWER: The prices of existing bonds should increase. 3. Relevance of Bond Price Movements. Why is the relationship between interest rates and bond prices important to financial institutions? ANSWER: Most financial institutions maintain a portfolio of bonds or mortgages that provide fixed payments over time. Because the market values of these securities are very sensitive to interest rate movements, financial institutions must understand the relationship between interest rates and security prices. 4. Source of Bond Price Movements. Determine the direction of bond prices over the last year and explain the reason for it. ANSWER: If prices of existing bonds have increased, this is normally because interest rates have declined. If prices of existing bonds have decreased, this is normally because interest rates have increased. A thorough answer would identify factors that caused the interest rates to change. 5. Exposure to Bond Price Movements. How would a financial institution with a large bond portfolio be affected by falling interest rates? Would it be affected more than a financial institution with a greater concentration of bonds (and fewer short-term securities)? Explain. ANSWER: The market value of the financial institution’s bond portfolio will increase. A financial institution that has a greater concentration of bonds would be even more favorably affected because the market value of its portfolio would be more sensitive to interest rates. 6. Comparison of Bonds to Mortgages. Since fixed-rate mortgages and bonds have similar payment flows, how is a financial institution with a large portfolio of fixed-rate mortgages affected by rising interest rates? Explain. ANSWER: A financial institution with a large portfolio of fixed-rate mortgages is adversely affected by rising interest rates, because the market value of its mortgage portfolio is reduced. 7. Coupon Rates. If a bond’s coupon rate were above its required rate of return, would its price be above or below its par value? Explain. ANSWER: When a bond’s coupon rate is above the required rate of return, the price of the bond would be above its par value because the coupons provide more than the return required. 8. Bond Price Sensitivity. Is the price of a long-term bond more or less sensitive to a change in interest rates than to the price of a short-term security? Why? ANSWER: The price of a long-term bond is more sensitive to a given change in interest rates than the price of a short-term security. The long-term bond provides fixed payments for a longer period of time. Consequently, it will provide these fixed payments, whether interest rates decline or rise. The benefit of fixed payments during a period of falling interest rates is more pronounced for longer maturities. The same is true for the disadvantage of fixed payments during a period of rising rates. 9. Required Return on Bonds. Why does the required rate of return for a particular bond change over time? ANSWER: The required rate of return on a bond changes because of a change in interest rates, or a change in the risk of the bond. 10. Inflation Effects. Assume that inflation is expected to decline in the near future. How could this affect future bond prices? Would you recommend that financial institutions increase or decrease their concentration in long-term bonds based on this expectation? Explain. ANSWER: Since lower inflation normally causes a decline in interest rates (other things being equal), financial institutions would benefit if they increase their concentration of long-term bonds before this occurs. 11. Bond Price Elasticity. Explain the concept of bond price elasticity. Would bond price elasticity suggest a higher price sensitivity for zero-coupon bonds or high-coupon bonds that are offering the same yield to maturity? Why? What does this suggest about the market value volatility of mutual funds containing zero-coupon Treasury bonds versus high-coupon Treasury bonds? ANSWER: Bond price elasticity measures the percentage change in a bond’s price in response to a percentage change in interest rates. The percentage change in the price (as measured by present value) of the zero-coupon bonds would be more sensitive to interest rate movements than the high-coupon bonds. Thus, a mutual fund containing zero-coupon bonds would likely have a more volatile market value over time. 12. Economic Effects on Bond Prices. An analyst recently suggested that there will be a major economic expansion that will favorably affect the prices of high-rated fixed-rate bonds, because the credit risk of bonds will decline as corporations improve their performance. Assuming that the economic expansion occurs, do you agree with the conclusion of the analyst? Explain. ANSWER: The decline in the credit risk will result in slightly lower bond premiums, which would favorably affect the price if other things are held constant. However, the major economic expansion will likely result in higher interest rates, which could cause a major decline in bond prices. The interest rate effect on the bond prices will likely overwhelm the risk premium effect. 13. Impact of War. When tensions rise or war erupts in the Middle East, bond prices in many countries tend to decline. What is the link between problems in the Middle East and bond prices? Would you expect bond prices to decline more in Japan or in the United Kingdom as a result of the crisis? (The answer is tied to how interest rates may change in those countries.) Explain. ANSWER: The crisis led to an anticipated shortage of oil, which can fuel inflation. Those countries that rely on imported oil would be most affected. Since Japan imports all of its oil while the United Kingdom is self-reliant, Japan’s inflation was more susceptible to the crisis. Therefore, Japan’s bond prices would be expected to experience a greater decline (which they did). 14. Bond Price Sensitivity. Explain how bond prices may be affected by money supply growth, oil prices, and economic growth. ANSWER: Any factors that affect inflationary expectations may affect interest rate expectations and therefore affect the demand for bonds. Higher oil prices, excessive money supply growth, and strong economic growth contribute to higher inflationary expectations. Thus, interest rates would be expected to increase under these conditions (holding other factors constant), the demand for bonds would decline, and bond prices would decline. Lower oil prices or a weak economy could reduce inflationary expectations and result in an increased demand for bonds, causing bond prices to rise. 15. Impact of Oil Prices. Assume that oil-producing countries have agreed to reduce their oil production by 30 percent. How would bond prices be affected by this announcement? Explain. ANSWER: Reduced oil production implies higher oil prices, higher interest rates, and lower bond prices. Thus bond portfolio managers would sell bonds immediately causing immediate downward pressure on the bond prices. 16. Impact of Economic Conditions. Assume that breaking news causes bond portfolio managers to suddenly expect much higher economic growth. How might bond prices be affected by this expectation? Explain. Now assume that breaking news causes bond portfolio managers to suddenly anticipate a recession. How might bond prices be affected? Explain. ANSWER: Higher economic growth places upward pressure on interest rates and downward pressure on bond prices. As bond portfolio managers sell their bonds based on this expectation, there is immediate downward pressure on bond prices. A recession tends to imply a reduced demand for loanable funds and therefore lower interest rates and higher prices of existing bonds. As bond portfolio managers purchase bonds to capitalize on this expectation, there is immediate upward pressure on bond prices. Advanced Questions 17. Impact of the Fed. Assume that the bond market participants suddenly expect the Fed to substantially increase the money supply. a. Assuming no threat of inflation, how would bond prices be affected by this expectation? ANSWER: Without the threat of inflation, an increase in the money supply could reduce interest rates and bond prices would increase. Thus, bond portfolio managers would purchase more bonds now, causing immediate upward pressure on bond prices. b. Assuming that inflation may result, how would bond prices be affected? ANSWER: If inflation increases, interest rates will likely increase, and prices of existing bonds will decline. Therefore, bond portfolio managers would sell bonds now, causing immediate downward pressure on bond prices. c. Given your answers to (a) and (b), explain why expectations of the Fed’s increase in the money supply may sometimes cause bond market participants to disagree about how bond prices will be affected. ANSWER: Some bond market participants may expect that the Fed’s actions will cause higher inflation (and therefore higher interest rates), and therefore expect bond prices to decline. Other bond market participants may expect that the Fed’s actions will not cause higher inflation, and therefore expect bond prices to increase. 18. Impact of the Trade Deficit. Bond portfolio managers closely monitor the trade deficit figures, because the trade deficit can affect exchange rates, which can affect inflationary expectations and therefore interest rates. a. When the trade deficit figure is higher than anticipated, bond prices typically decline. Explain why this reaction may occur. ANSWER: A higher trade deficit figure signals the possibility of continued high trade deficits, which would place downward pressure on the dollar. If the dollar weakens, U.S. inflation may rise, and U.S. interest rates may rise. Thus, bond portfolio managers sell bonds, placing downward pressure on bond prices. b. On some occasions, the trade deficit figure has been very large, but the bond markets did not respond to the announcement. Assuming that no other information offset the impact, explain why the bond markets may not have responded to the announcement. ANSWER: If the large trade deficit was already anticipated by the market, the announcement does not offer any additional information. Therefore, the market does not react. Existing bond prices already reflect the market’s expectations. 19. International Bonds. A U.S. insurance company purchased British 20-year Treasury bonds instead of U.S. 20-year Treasury bonds because the coupon rate was 2 percent higher on the British bonds. Assume that the insurance company sold the bonds after five years. Its yield over the five-year period was substantially less than the yield it would have received on the U.S. bonds over the same five-year period. Assume that the U.S. insurance company had hedged its exchange rate exposure. Given that the lower yield was not because of default risk or exchange rate risk, explain how the British bonds could have generated a lower yield than the U.S. bonds. (Assume that either type of bond could have been purchased at the par value.) ANSWER: If British interest rates increased or remained constant while U.S. interest rates declined, the U.S. bonds could have been sold at a much higher price than British bonds. Thus, while default risk and exchange rate risk are not relevant in this case, the interest rate risk had different effects on the two types of bonds. 20. International Bonds. The pension fund manager of Utterback (a U.S. firm) purchased German 20-year Treasury bonds instead of U.S. 20-year Treasury bonds. The coupon rate was 2 percent lower on the German bonds. Assume that the manager sold the bonds after five years. The yield over the five-year period was substantially more than the yield it would have received on the U.S. bonds over the same five-year period. Explain how the German bonds could have generated a higher yield than the U.S. bonds for the manager, even if the exchange rate is stable over this five-year period. (Assume that the price of either bond was initially equal to its respective par value). Be specific. ANSWER: The German interest rates could have declined while U.S. interest rates increased, so that the value of the German bonds was higher than the value of U.S. bonds after five years. Even if interest rates in both countries moved in the same direction, the German bonds could have generated a higher yield. If both interest rates increased, the U.S. interest rates could have increased to a higher degree. If both interest rates decreased, the U.S. interest rates could have decreased by a smaller degree. 21. Implications of a Shift in the Yield Curve. Assume that there is a sudden shift in the yield curve, such that the new yield curve is higher and more steeply sloped today than it was yesterday. If a firm issues new bonds today, would its bonds sell for higher or lower prices than if it had issued the bonds yesterday? Explain. ANSWER: A higher and steeper yield curve implies that long-term bond yields have increased. The firm would have to sell the bonds for lower prices to entice investors with a high yield today. 22. How Bond Prices May Respond to Prevailing Conditions. Consider the prevailing conditions for inflation (including oil prices), the economy, the budget deficit, and the Fed’s monetary policy that could affect interest rates. Based on prevailing conditions, do you think bond prices will increase or decrease during this semester? Offer some logic to support your answer. Which factor do you think will have the biggest impact on bond prices? ANSWER: Bond prices may respond to prevailing conditions in various ways, particularly in response to factors such as inflation, economic growth, the budget deficit, and the Federal Reserve's monetary policy. Let's analyze the potential impact of these factors on bond prices during the semester: 1. Inflation (including oil prices) : Higher inflation expectations can lead to higher interest rates, as investors demand higher yields to compensate for the erosion of purchasing power. When interest rates rise, bond prices typically decrease, as existing bonds with lower coupon rates become less attractive compared to newly issued bonds with higher yields. Conversely, if inflation remains low or moderates, bond prices may experience less downward pressure. 2. Economic Growth : Strong economic growth prospects can also contribute to higher interest rates, as central banks may tighten monetary policy to prevent overheating and inflationary pressures. Again, higher interest rates tend to result in lower bond prices. Conversely, if economic growth falters or remains sluggish, central banks may maintain accommodative monetary policies, which could support bond prices. 3. Budget Deficit : A widening budget deficit can increase the supply of government debt, putting downward pressure on bond prices. When there is excess supply of bonds in the market, prices may decrease to attract buyers. Conversely, efforts to reduce the budget deficit or fiscal discipline may support bond prices by reducing the supply of government debt. 4. Federal Reserve's Monetary Policy : The Federal Reserve's monetary policy decisions, particularly changes in the federal funds rate and asset purchase programs, can significantly influence bond prices. If the Fed signals a hawkish stance by raising interest rates or tapering its asset purchases, bond prices may decline. Conversely, if the Fed maintains or adopts a dovish stance by keeping interest rates low and continuing asset purchases, bond prices may be supported. Considering these factors, the prevailing conditions suggest that bond prices may face downward pressure during the semester, particularly if inflationary pressures persist, economic growth accelerates, and the Federal Reserve takes steps to normalize monetary policy. Of these factors, the Federal Reserve's monetary policy decisions are likely to have the biggest impact on bond prices, as they directly influence interest rates and market expectations. Investors should closely monitor developments in inflation, economic growth, fiscal policy, and the Fed's actions to assess the direction of bond prices and adjust their investment strategies accordingly. 23. Interaction Between Bond and Money Markets. Assume that you maintain bonds and money market securities in your portfolio, and you suddenly believe that long-term interest rates will rise substantially tomorrow (even though the market does not share the same view), while short-term interest rates will remain the same. a. How would you rebalance your portfolio between bonds and money market securities? ANSWER: Based on your expectations, bond prices will decline. You should rebalance your portfolio by selling bonds and purchasing more money market securities. b. If the market suddenly recognizes that long-term interest rates will rise tomorrow, and that they respond in the same manner as you, explain how the demand for these securities (bonds and money market securities), supply of these securities for sale, and prices and yields of these securities will be affected. ANSWER: Bond prices will decline, while the prices of money market securities will rise as investors rebalance their portfolios. Consequently, the yield offered on bonds will rise, and the yield offered on money market securities will decline. c. Assume that the yield curve is flat today. Explain how the slope of the yield curve will change tomorrow in response to the market activity. ANSWER: The yield curve will become upward-sloping because the yield offered on bonds will rise, while the yield offered on money market securities will decline. 24. Impact of the Credit Crisis on Risk Premiums. Explain how the prices of bonds were affected by a change in the risk-free rate during the credit crisis. Explain how bond prices were affected by a change in the credit risk premium during the credit crisis. ANSWER: The risk-free rate declined, which placed upward pressure on bond prices. However, the credit risk premium increased, which placed downward pressure on bond prices. 25. Systemic Risk. Explain why there are concerns about systemic risk in the bond and other debt markets. Also explain how the Financial Reform Act of 2010 was intended to reduce systemic risk. ANSWER: Systemic risk refers to the potential collapse of the entire market or financial system. Many financial institutions rely heavily on debt to fund their operations, and they are interconnected by financing each other's debt positions. If some of these financial institutions cannot repay their debt, they may create cash flow problems for those other financial institutions from which they borrowed funds. In addition, if they took positions in derivative securities to offer insurance to another party in case of debt default, they may suffer major losses. The Financial Reform Act of 2010 resulted in the creation of the Financial Stability Oversight Council, consisting of heads of agencies that oversee key participants in the debt markets. This council is responsible for identifying risks in the U.S. financial system, and making regulatory recommendations that could reduce these risks. Interpreting Financial News Interpret the following comments made by Wall Street analysts and portfolio managers. a. “Given the recent uncertainty about future interest rates, investors are fleeing from zero-coupon bonds.” Zero-coupon bonds are most sensitive to interest rate movements; investors who were concerned about an increase in interest rates sold their holdings of zero-coupon bonds. b. “Catrell Insurance Company invests heavily in bonds, and its stock price increased substantially today in response to the Fed's signal that it plans to reduce interest rates.” Some of Catrell’s assets are long-term bonds, which increase in value when interest rates decrease. The stock valuation is influenced by the increase in the market value of its assets. c. “Bond markets declined when the Treasury flooded the market with its new bond offering.” If the Treasury issues new bonds, the supply of bonds may exceed the demand, causing a decline in the price of bonds. That is, the yields to be offered on any new bonds must be raised to attract buyers. Managing in Financial Markets As an investor, you plan to invest your funds in long-term bonds. You have $100,000 to invest. You may purchase highly rated municipal bonds at par with a coupon rate of 6 percent; you have a choice of a maturity of 10 years or 20 years. Alternatively, you could purchase highly rated corporate bonds at par with a coupon rate of 8 percent; these bonds also are offered with maturities of 10 years or 20 years. You expect that you will not need the funds for five years. At the end of the fifth year, you will definitely sell the bonds since you will need to make a large purchase at that time. a. What is the annual interest you would earn (before taxes) on the municipal bond? On the corporate bond? You would earn $6,000 per year on the municipal bond, or $8,000 on the corporate bond. b. Assume that you are in the 20 percent tax bracket. If the level of credit risk and the liquidity for the municipal and corporate bonds are the same, would you invest in the municipal bond or the corporate bond? Why? Invest in the corporate bond. The after-tax annual interest earned on the corporate bond is $6,400 (computed as $8,000 [1.20]). This exceeds the $6,000 after-tax annual interest on a municipal bond. c. Assume that you expect all yields paid on newly issued notes and bonds (regardless of maturity) to decrease by a total of 4 percentage points over the next two years, and to increase by a total of 2 percentage points over the following three years. Would you select the 10-year maturity or the 20-year maturity for the type of bond you plan to purchase? Why? Select the 20-year bond as long as you are confident about your expectations. The general level of interest rates in five years should be lower than today, which should increase the value of your bond. The value of the 20-year bond will be more sensitive than the value of the 10-year bond, and therefore should experience a higher increase in value by the time you need to sell the bond. The expected interest rate at the end of the fifth year is crucial to your decision. Even though the interest rates were expected to rise over the third, fourth, and fifth years, the general level of interest rates was expected to be lower at the end of the fifth year than when you first purchased the bonds. Problems 1. Bond Valuation. Assume the following information for an existing bond that provides annual coupon payments: Par value = $1,000 Coupon rate = 11% Maturity = 4 years Required rate of return by investors = 11% a. What is the present value of the bond? ANSWER: PV of Bond = PV of Coupon Payments + PV of Principal = $110(PVIFAi = 11%,n = 4) + $1,000(PVIFi = 11%,n = 4) = $110(3.1024) + $1,000(.6587) = $341 + $659 = $1,000 b. If the required rate of return by investors were 14 percent instead of 11 percent, what would be the present value of the bond? ANSWER: PV of Bond = PV of Coupon Payments + PV of Principal = $110(PVIFAi = 14%,n = 4) + $1,000(PVIFi = 14%,n = 4) = $110(2.9137) + $1,000(.5921) = $321 + $592 = $913 If the required rate of return by investors were 9 percent, what would be the present value of the bond? ANSWER: PV of Bond = PV of Coupon Payments + PV of Principal = $110(PVIFAi = 9%,n = 4) + $1,000(PVIFi = 9%,n = 4) = $110(3.2397) + $1,000(.7084) = $356 + $708 = $1,064 2. Valuing a Zero-Coupon Bond. Assume the following information for existing zero-coupon bonds: Par value = $100,000 Maturity = 3 years Required rate of return by investors = 12% How much should investors be willing to pay for these bonds? ANSWER: PV of Bond = PV of Coupon Payments + PV of Principal = $0 + 100,000(PVIFi = 12%,n = 3) = $100,000(.7118) = $71,180 3. Valuing a Zero-Coupon Bond. Assume that you require a 14 percent return on a zero-coupon bond with a par value of $1,000 and six years to maturity. What is the price you should be willing to pay for this bond? ANSWER: PV of Bond = PV of Coupon Payments + PV of Principal = $0 + 1,000(PVIFi = 14%,n = 6) = $1,000(.4556) = $455.60 4. Bond Value Sensitivity to Exchange Rates and Interest Rates. Cardinal Company, a U.S.-based insurance company, considers purchasing bonds denominated in Canadian dollars, with a maturity of six years, a par value of C$50 million, and a coupon rate of 12 percent. The bonds can be purchased at par by Cardinal and would be sold four years from now. The current exchange rate of the Canadian dollar is $0.80. Cardinal expects that the required return by Canadian investors on these bonds four years from now will be 9 percent. If Cardinal purchases the bonds, it will sell them in the Canadian secondary market four years from now. The exchange rates are forecast as follows: Year Exchange Rate of C$ 1 $0.80 2 0.77 3 0.74 4 0.72 5 0.68 6 0.66 Refer to earlier examples in this chapter to determine the expected U.S. dollar cash flows to Cardinal over the next four years. Refer to Chapter 3 to determine the present value of a bond. ANSWER: PV of C$ C$6,000,000 C$56,000,000 Cash Flows = (1 + .09)1 + (1 + .09)2 in 4 years = C$5,504,587 + C$47,134,080 = C$52,638,667 Year 1 2 3 4 C$ cash flows C$6,000,000 C$6,000,000 C$6,000,000 C$6,000,000 anticipated +C$52,638,667 Forecasted exchange rate of C$ $0.80 $0.77 $0.74 $0.72 U.S. $ cash flows anticipated $4,800,000 $4,620,000 $4,440,000 $42,219,840 b. Does Cardinal expect to be favorably or adversely affected by the interest rate risk? Explain. ANSWER: Cardinal Co. will be favorably affected if Canadian interest rates decline as expected because the bonds will sell for a higher price at the end of the fourth year as a result. c. Does Cardinal expect to be favorably or adversely affected by exchange rate risk? Explain. ANSWER: Cardinal Co. is adversely affected by the exchange rate movements, because a weaker Canadian dollar over time results in less U.S. dollar cash flows to be received. 5. Predicting Bond Values. (Use the chapter appendix to answer this problem.) Bulldog Bank has just purchased bonds for $106 million that have a par value of $100 million, three years remaining to maturity, and an annual coupon rate of 14 percent. It expects the required rate of return on these bonds to be 12 percent one year from now. a. At what price could Bulldog Bank sell these bonds for one year from now? ANSWER: PV of Bonds One PV of Remaining Year from Now = Coupon Payments + PV of Principal = $14,000,000(PVIFAi = 12%,n = 2) + $100,000,000(PVIFi = 12%,n = 2) = $14,000,000(1.6901) + $100,000,000(.7972) = $23,661,400 + $79,720,000 = $103,381,400 b. What is the expected annualized yield on the bonds over the next year, assuming they are to be sold in one year? ANSWER: $106,000,000 = ($14,000,000 + $103,381,400)(PVIFi = ?,n = 1) .903 = (PVIFi = ?,n = 1) i = between 10% and 11% 6. Predicting Bond Values. (Use the chapter appendix to answer this problem.) Sun Devil Savings has just purchased bonds for $38 million that have a par value of $40 million, five years remaining to maturity, and a coupon rate of 12 percent. It expects the required rate of return on these bonds to be 10 percent two years from now. a. At what price could Sun Devil Savings sell these bonds for two years from now? ANSWER: PV of Bonds PV of Remaining in 2 Years = Coupon Payments + PV of Principal = $4,800,000(PVIFAi = 10%,n = 3) + $40,000,000(PVIFi = 10%,n = 3) = $4,800,000(2.4869) + $40,000,000(.7513) = $11,937,120 + $30,052,000 = $41,989,120 b. What is the expected annualized yield on the bonds over the next two years, assuming they are to be sold in two years? ANSWER: $38,000,000 = $4,800,000(PVIFAi = ?,n = 2) + ($41,989,120)(PVIFi = ?,n = 2) By trial and error, i = about 17%. This can also be done with some calculators. c. If the anticipated required rate of return of 10 percent in two years is overestimated, how would the actual selling price differ from the forecasted price? How would the actual annualized yield over the next two years differ from the forecasted yield? ANSWER: If the required rate of return is overestimated, then the actual selling price will be higher than what is forecasted. Therefore, the annualized yield will be higher than what is forecasted. 7. Predicting Bond Values. (Use the chapter appendix to answer this problem.) Spartan Insurance Company plans to purchase bonds today that have four years remaining to maturity, a par value of $60 million, and a coupon rate of 10 percent. Spartan expects that in three years, the required rate of return on these bonds by investors in the market will be 9 percent. It plans to sell the bonds at that time. What is the expected price it will sell the bonds for in three years? ANSWER: PV of Bonds PV of Remaining in 3 Years = Coupon Payments + PV of Principal = ($6,000,000 + $60,000,000)(PVIFi = 9%,n = 1) = $66,000,000(.9174) = $60,548,400 8. Bond Yields. (Use the chapter appendix to answer this problem.) Hankla Company plans to purchase either (1) zero-coupon bonds that have ten years to maturity, a par value of $100 million, and a purchase price of $40 million, or (2) bonds with similar default risk that have five years to maturity, a 9 percent coupon rate, a par value of $40 million, and a purchase price of $40 million. Hankla can invest $40 million for five years. Assume that the market’s required return in five years is forecasted to be 11 percent. Which alternative would offer Hankla a higher expected return (or yield) over the five-year investment horizon? ANSWER: The PV of zero-coupon bonds five years from now is based on the PV of the par value to be received 5 years after that point in time: PV of Zero- Coupon Bonds = $100,000,000(PVIFi = 11%,n = 5) = $100,000,000(.5935) = $59,350,000 The discount rate at which the anticipated cash flows from the zero-coupon bonds will equal today’s price is: $40,000,000 = $59,350,000(PVIFi = ?,n = 5) (PVIFi = ?,n = 5) = .6740 i = about 8% The second alternative offers a yield to maturity of 9 percent, which exceeds the yield to maturity of about 8 percent on the zero-coupon bonds. 9. Predicting Bond Values. (Use the chapter appendix to answer this problem.) The portfolio manager of Ludwig Company has excess cash that is to be invested for four years. He can purchase four-year Treasury notes that offer a 9 percent yield. Alternatively, he can purchase new 20-year Treasury bonds for $2.9 million that offer a par value of $3 million and an 11 percent coupon rate with annual payments. The manager expects that the required return on these same 20-year bonds will be 12 percent four years from now. a. What is the forecasted market value of the twenty-year bonds in four years? ANSWER: PV of 20-Year PV of Remaining Bonds as of 4 = Coupon Payments + PV of Principal Years from Now = $330,000(PVIFAi = 12%,n = 16) + $3,000,000(PVIFi = 12%,n = 16) = $330,000(6.9740) + $3,000,000(.1631) = $2,301,420 + $489,300 = $2,790,720 b. Which investment is expected to provide a higher yield over the four-year period? ANSWER: Ludwig could achieve a yield of 9 percent on the Treasury notes with certainty. By discounting the cash flow resulting from the alternative investment (20-year bonds) over the four-year investment horizon at 9 percent, we can determine whether the bonds offer a higher or lower yield. The PV of the bonds as of today using a 9 percent discount rate is: = $330,000(PVIFAi = 9%,n = 4) + $2,790,720(PVIFi = 9%,n = 4) = $330,000(3.2397) + $2,790,720(.7084) = $1,069,101 + $1,976,946 = $3,046,047 Since Ludwig would pay less today for these bonds than the present value estimated here, this implies that the yield to maturity on the bonds exceeds 9 percent. Therefore, the bonds offer a higher yield. 10. Predicting Bond Portfolio Value. (Use the chapter appendix to answer this problem). Ash Investment Company manages a broad portfolio with this composition: Years Present Remaining Par Value Market Value to Maturity Zero-coupon bonds $200,000,000 $ 63,720,000 12 8% Treasury bonds 300,000,000 290,000,000 8 11% corporate bonds 400,000,000 380,000,000 10 $733,720,000 Ash expects that in four years, investors in the market will require an 8 percent return on the zero-coupon bonds, a 7 percent return on the Treasury bonds, and a 9 percent return on corporate bonds. Estimate the market value of the bond portfolio four years from now. ANSWER: PV of Zero-Coupon Bonds in 4 Years = $200,000,000(PVIFi = 8%,n = 8) = $200,000,000(.5403) = $108,060,000 PV of Treasury Bonds in 4 Years = $24,000,000(PVIFAi = 7%,n = 4) + $300,000,000(PVIFi = 7%,n = 4) = $24,000,000(3.3872) + $300,000,000(.7629) = $81,292,800 + $228,870,000 = $310,162,800 PV of Corporate Bonds in 4 Years = $44,000,000(PVIFAi = 9%,n = 6) + $400,000,000(PVIFi = 9%,n = 6) = $44,000,000(4.4859) + $400,000,000(.5963) = $197,379,600 + $238,520,000 = $435,899,600 PV of Portfolio in 4 Years = $108,060,000 + $310,162,800 + $435,899,600 = $854,122,400 Valuing a Zero-Coupon Bond. a. A zero-coupon bond with a par value of $1,000 matures in 10 years. At what price would this bond provide a yield to maturity that matches the current market rate of 8 percent? ANSWER: PV PV PV = $463.19 b. What happens to the price of this bond if interest rates fall to 6 percent? ANSWER: PV PV PV = $558.39 c. Given the above changes in the price of the bond and the interest rate, calculate the bond price elasticity. ANSWER: 12. Bond Valuation. You are interested in buying a $1,000 par value bond with 10 years to maturity and an 8 percent coupon rate that is paid semiannually. How much should you be willing to pay for the bond if the investor’s required rate of return is 10 percent? ANSWER: PV = C(PVIFA k = 5%, n = 20) + FV(PVIFk = 5%, n = 20) PV = 40(12.4622) + 1,000(0.3769) PV = $875.39 13. Predicting Bond Values. A bond you are interested in pays an annual coupon of 4 percent, has a yield to maturity of 6 percent and has 13 years to maturity. If interest rates remain unchanged, at what price would you expect this bond to be selling 8 years from now? Ten years from now? ANSWER: PV = C(PVIFAk = 6%, n = 5) + FV(PVIFk = 6%, n = 5) PV = 40(4.2124) + 1,000(0.7473) PV = $915.796 PV = C(PVIFAk = 6%, n = 3) + FV(PVIFk = 6%, n = 3) PV = 40(2.6730) + 1,000(0.8396) PV = $946.52 Sensitivity of Bond Values. a. How would the present value (and therefore the market value) of a bond be affected if the coupon payments are smaller and other factors remain constant? ANSWER: The bond would have a lower present value, since the future cash flows would be smaller. b. How would the present value (and therefore the market value) of a bond be affected if the required rate of return is smaller and other factors remain constant? ANSWER: The bond would have a higher present value, since the cash flows would be discounted at a lower discount rate. 15. Bond Elasticity. Determine how the bond elasticity would be affected if the bond price changed by a larger amount, holding the change in the required rate of return constant. ANSWER: The bond elasticity would be higher, meaning that there is a greater sensitivity of bond prices to a change in required rates of return. This would occur for bonds with longer terms to maturity. 16. Bond Duration. Determine how the duration of a bond be affected if the coupons were extended over additional time periods. ANSWER: The longer the coupon payments are extended, the greater is the duration, because the investor is more exposed to changes in the required rate of return. 17. Bond Duration. A bond has a duration of 5 years and a yield to maturity of 9 percent. If the yield to maturity changes to 10 percent, what should be the percentage price change of the bond? ANSWER: First compute the modified duration of the bond: Next, compute the percentage price change of the bond if the yield increases to 10 percent: Consequently, the bond should decrease in price by 4.59%. 18. Bond Convexity. Describe how bond convexity affects the theoretical linear price-yield relationship of bonds. What are the implications of bond convexity for estimating changes in bond prices? ANSWER: Bond convexity illustrates that the price-yield relationship is not linear, but convex. This is particularly pronounced for bonds with low coupons and long maturities. From a bond pricing perspective, bond convexity leads to estimation errors in the price change of a bond, although the effect is negligible for small yield changes. Specifically, using modified duration to estimate the percentage price change of a bond yields to an underestimation of bond price increases when yields drop and an overestimation of bond price decreases when yields increase. Flow of Funds Exercise Interest Rate Expectations, Economic Growth, and Bond Financing Recall that if the economy continues to be strong, Carson Company may need to increase its production capacity by about 50 percent over the next few years to satisfy demand. It would need financing to expand and accommodate the increase in production. Recall that the yield curve is currently upward sloping. Also recall that Carson is concerned about a possible slowing of the economy because of potential Fed actions to reduce inflation. It needs funding to cover payments for supplies. It is also considering the issuance of stock or bonds to raise funds in the next year. a. At a recent meeting, the Chief Executive Officer (CEO) stated his view that the economy will remain strong, as the Fed’s monetary policy is not likely to have a major impact on the interest rates. So he wants to expand the business to benefit from the expected increase in demand for Carson’s products. The next step would be to determine how to finance the expansion. The Chief Financial Officer (CFO) stated that if Carson Company needs to obtain long-term funds, the issuance of fixed-rate bonds would be ideal at this point in time because he expects that the Fed’s monetary policy to reduce inflation and will cause long-term interest rates to rise. If the CFO is correct about future interest rates, what does this suggest about the future economic growth, the future demand for Carson’s products, and the need to issue bonds? If the Fed’s monetary policy causes higher interest rates, the economic growth will be reduced and the demand for Carson’s products would be adversely affected. Thus, it may not need to issue bonds. b. If you were involved in the meeting described here, what do you think needs to be resolved before deciding to expand the business? There should be a clear conclusion about the Fed’s impact on interest rates. If the CEO is correct about the Fed’s monetary policy not affecting interest rates, then the economy should stay strong, and Carson should pursue expansion. However, the CFO’s argument for financing with long-term fixed rates should be questioned, because the CEO’s view of the Fed’s monetary policy conflicts with the CFO’s view. Both officers cannot be correct. c. At the meeting described here, the Chief Executive Officer (CEO) stated the following: “The decision to expand should not be dictated by whether interest rates are going to increase or not. Bonds should be issued only if the potential increase in interest rates is attributed to a strong demand for loanable funds rather than the Fed’s reduction in the supply of loanable funds.” What does this statement mean? If interest rates rise as a result of the Fed’s actions, its monetary policy is intended to slow economic growth as a means of reducing inflation. In this case, Carson should not expand because it will not be able to fully utilize its production capacity. However, if the interest rates rise because of a strong demand for loanable funds, that reflects a strong economy, which should result in a strong demand for Carson’s products. In this case, Carson should expand. Solution Manual for Financial Markets and Institutions Jeff Madura 9781133947875, 9781305257191, 9780538482172
