Chapter EightValuation of Known Cash Flows: BondsThis chapter contains 50 multiple choice questions, 18 short problems and 9 longer problems.Multiple Choice1. A ________ is a quantitative method used to infer an asset's value from market information about theprices of other assets and market interest rates.(a)fixed model(b)perpetual valuation model(c)valuation model(d)variable modelAnswer: (c)2.________ are examples of fixed-income securities.(a)Common stock and pension funds(b)Mortgages and pension annuities(c)Mutual funds and common stock(d)Preferred stock and common stockAnswer: (b)3.Consider a fixed-income security that promises to pay $150 each year for the next five years. Howmuch is this five-year annuity worth if the appropriate discount rate is 7% per year?(a)$534.74(b)$615.03(c)$802.50(d)$867.96Answer: (b)8-14.Consider a fixed-income security that promises to pay $120 each year for the next four years.Calculate the value of this four-year annuity if the appropriate discount rate is 6% per year.(a)$415.81(b)$508.80(c)$531.85(d)$629.06Answer: (a)5.The price of any existing fixed-income security ________ when market interest rates rise becauseinvestors will only be willing to ________ them if they offer a competitive yield.(a)rises; buy(b)rises; sell(c)falls; buy(d)falls; sellAnswer: (c)6. A fall in interest rates causes a ________ in the market value of a fixed-income security.(a)a rise(b)a fall(c)no change(d)it cannot be determined from the information givenAnswer: (a)7. A change in market interest rates causes ________ in the market values of all existing contractspromising fixed payments in the future.(a)a change in the same direction(b)a change in the opposite direction(c)no change(d)an unpredictable variationAnswer: (b)8-28.What happens to the value of a four-year fixed-income security promising $100 per year if the marketinterest rate rises from 5% to 6% per year?(a)A rise of 1% causes a drop of $4.87 in market value.(b)A rise of 1% causes a rise of $4.87 in market value.(c)A rise of 1% causes a drop of $8.09 in market value.(d)A rise of 1% causes a rise of $8.09 in market value.Answer: (c)9.What happens to the value of a four-year fixed-income security promising $100 per year if the marketinterest rate falls from 6% to 5% per year?(a)A fall of 1% causes a drop of $4.87 in market value.(b)A fall of 1% causes a rise of $4.87 in market value.(c)A fall of 1% causes a drop of $8.09 in market value.(d)A fall of 1% causes a rise of $8.09 in market value.Answer: (d)10.A zero-coupon bond is also known as ________.(a)a perpetual bond(b)a pure discount bond(c)a market rebate(d)an infinite bondAnswer: (b)11.The promised cash payment on a pure discount bond is called its ________.(a)face value(b)par value(c)fixed interest(d)both a and bAnswer: (d)8-312.What is the yield of a 1-year pure discount bond with a price of $850 and a face value of $1,000?(a)8.50%(b)9.09%(c)15.00%(d)17.65%Answer: (d)13.What is the yield of a 1-year pure discount bond with a price of $900 and a face value of $1,000?(a)5.26%(b)10.00%(c)11.11%(d)15.79%Answer: (c)14.Consider a four-year pure discount bond with a face value of $1,000. If its current price is $850,compute its annualized yield.(a)1.17%(b)4.15%(c)5.57%(d)17.60%Answer: (b)15.Consider a three-year pure discount bond with a face value of $1,000. If its current price is $900,compute its annualized yield.(a)1.036%(b)1.111%(c)3.57%(d)5.41%Answer: (c)8-416.Consider a five-year pure discount bond with a face value of $1,000. If its current price is $780, whatis its annualized yield?(a)5.09%(b)2.82%(c)1.28%(d)1.05%Answer: (a)17.A ________ obligates the issuer to make periodic payments of interest to the bondholder for the lifeof the bond and then to pay the face value of the bond when the bond matures.(a)pure discount(b)zero-coupon(c)perpetual bond(d)coupon bondAnswer: (d)18.The ________ of the bond is interest rate applied to the ________ of the bond to compute theperiodic payment.(a)coupon rate; face value(b)maturity rate; face value(c)coupon rate; price(d)maturity rate; priceAnswer: (a)19.For a bond with a face value of $1,000 and coupon rate of 11%, what is the annual coupon payment?(a)$100(b)$110(c)$1,000(d)$1,100Answer: (b)8-520.For a bond with a face value of $1,000 and a coupon rate of 9%, what is the annual coupon payment?(a)$90(b)$99(c)$1,000(d)$1,190Answer: (a)21.If the market price of a coupon bond equals its face value, it is also termed a ________.(a)par bond(b)premium bond(c)discount bond(d)zero-discount bondAnswer: (a)22.If the bond’s market price is higher than its face value, it is termed a ________.(a)par bond(b)premium bond(c)discount bond(d)zero-discount bondAnswer: (b)23.If the bond’s market price is lower than its face value, it is termed a ________.(a)par bond(b)premium bond(c)discount bond(d)zero-par bondAnswer: (c)8-624.If a bond selling for $850 has an annual coupon payment of $80 and a face value of $1,000, what isits current yield?(a)8.00%(b)9.41%(c)17.65%(d)27.05%Answer: (b)25.If a bond selling for $1,120 has an annual coupon payment of $110 and a face value of $1,000, whatis its current yield?(a)8.90%(b)9.82%(c)10.71%(d)11.00%Answer: (b)26.If a bond selling for $900 has an annual coupon payment of $80 and a face value of $1,000, what isits current yield?(a)8.00%(b)8.89%(c)11.00%(d)20.00%Answer: (b)27.The ________ is the discount rate that makes the present value of the bond’s stream of promised cashpayments equal to its price.(a)compound rate(b)yield to maturity(c)coupon rate(d)current yieldAnswer: (b)8-728.Suppose you are considering buying a one-year 11% coupon bond with a face value of $1,000 and acurrent price of $1,020. What is its yield to maturity?(a)8.82%(b)9.00%(c)10.78%(d)11.00%Answer: (a)29.Suppose you are considering buying a one-year 11% coupon bond with a face value of $1,000 and acurrent price of $1,050. What is its yield to maturity?(a)4.76%(b)5.71%(c)6.00%(d)10.48%Answer: (b)30.Suppose you are considering buying a five-year 11% coupon bond with a face value of $1,000 and acurrent price of $950. What is its yield to maturity?(a)5.62%(b)9.63%(c)11.58%(d)12.40%Answer: (d)31.Suppose you are considering buying a five-year 11% coupon bond with a face value of $1,000 and acurrent price of $1,100. What is its yield to maturity?(a)3.87%(b)8.47%(c)10.00%(d)13.62%Answer: (b)8-832.Suppose you are considering buying a six-year 10% coupon bond with a face value of $1,000 and acurrent price of $1,100. What are the current yield and yield to maturity of this bond?(a)CY = 11.00%; YTM = 12.23%(b)CY = 12.23%; YTM = 11.00%(c)CY = 7.85%; YTM = 9.09%(d)CY = 9.09%; YTM = 7.85%Answer (d)33.Suppose you are considering buying a seven-year 11% coupon bond with a face value of $1,000 and acurrent price of $950. What are the current yield and yield to maturity of this coupon bond?(a)CY = 12.10%; YTM = 11.58%(b)CY = 11.58%; YTM = 12.10%(c)CY = 9.92%; YTM = 10.45%(d)CY = 10.45%; YTM = 9.92%Answer: (b)34.Over time bond prices ________ their face value. Before maturity, bond prices can ________ a greatdeal as a result of changes in market interest rates.(a)diverge from; fluctuate(b)converge toward; flatten out(c)converge toward; fluctuate(d)diverge from; flatten outAnswer: (c)35.When the yield curve is not flat, bonds of the same ________ with different coupon rates have________ yields to maturity.(a)maturity, different(b)maturity, identical(c)callability, different(d)callability, identicalAnswer: (a)8-936.Bonds offering the same future stream of promised payments can differ in a number of ways, but thetwo most important are ________ and ________.(a)taxability, issue origin(b)type of issuer, default risk(c)type of issuer, taxability(d)taxability, default riskAnswer: (d)37.A ________ is one that gives the holder of a bond issued by a corporation the right to convert thebond into a pre-specified number of shares of common stock.(a)callable bond(b)convertible bond(c)stock bond(d)preferred bondAnswer: (b)38.A ________ is one that gives the issuer of the bond the right to redeem it before the final maturitydate.(a)callable bond(b)convertible bond(c)stock bond(d)preferred bondAnswer: (a)39.Five years ago, English and Co. issued 25-year coupon bonds with par value $1,000. At the time ofissuance, the yield to maturity was 6 percent and the bonds sold at par. The bonds are currently selling at 110 percent of their par value. Assuming that the coupon is paid annually, what is the current yield to maturity?(a)3.77%(b)5.18%(c)5.27%(d)5.46%Answer: (b)8-1040.Potemkin Corporation plans to raise $10,000,000 in funds by issuing zero coupon $1,000 par valuebonds with a 25 year maturity. Potemkin Corporation is able to issue these bonds at an after tax cost of debt of 12%. To the nearest whole number, how many bonds must Potemkin Corporation issue?(a)10,000 bonds(b)42,919 bonds(c)125,837 bonds(d)170,000 bondsAnswer: (d)41.Calculate the years to maturity for a bond based on the following information. The bond trades at$950, it has a par value of $1,000, a coupon rate of 11%, and a required rate of return of 12%.(a)8 years(b)12 years(c)15 years(d)16 yearsAnswer: (a)pute the current price of Walsingham bonds based on the following information. Walsinghambonds have a $1,000 par value, have 20 years remaining until maturity, a 12 percent coupon rate, anda yield to maturity of 10.5 percent.(a)$858.42(b)$982.47(c)$1,119.52(d)$1,124.41Answer: (d)pute the yield to maturity of Arundel bonds based on the following information. Arundel bondshave a $1,000 par value, 25 years remaining until maturity, an 11% coupon rate, and a current market price of $1,187.(a)4.55%(b)9.08%(c)9.27%(d)13.17%Answer: (b)8-1144.When prices of U.S Treasury strips are listed, principal from a Treasury bond is denoted by the letters________.(a)ci(b)tb(c)bp(d)npAnswer: (c)45.The ________ is the price at which dealers in Treasury bonds are willing to sell.(a)bid price(b)asked yield(c)ask price(d)maturity priceAnswer: (c)46.The ________ is the price at which dealers are willing to buy.(a)bid price(b)ask price(c)asked yield(d)maturity priceAnswer: (a)47.The bid price of a bond is always ________ the ask price.(a)greater than(b)less than(c)identical to(d)it varies from case to caseAnswer: (b)8-1248.The ________ of a bond price measures the sensitivity of the bond price to a change in the yield tomaturity.(a)callability(b)convertibility(c)immutability(d)elasticityAnswer: (d)49.Suppose you buy a 25-year pure discount bond with a face value of $1,000 and a yield of 6% per year.A day later market interest rates drop to 5% and so does the yield on your bond. What is theproportional change in the price of your bond?(a)a decrease of 26.74%(b)a decrease of 21.10%(c)an increase of 26.74(d)an increase of 21.20Answer: (c)50.Suppose you buy a 25-year pure discount bond with a face value of $1,000 and a yield of 6% per year.A day later market interest rates rise to 5% and so does the yield on your bond. What is the elasticityof the bond price to the change in the yield?(a)–0.62%(b)–1.27%(c)–1.60%(d)–2.67%Answer: (c)8-13Short Problems1.Consider a five-year fixed-income security which promises $120 per year. Calculate the value of thesecurity if the market interest rate rises from 5% to 6% per year.Answer:n i PV PMT Result5 5 ? $120 PV = $519.54n i PV PMT Result5 6 ? $120 PV = $505.48The price drops by $14.06.2.Consider a four-year fixed-income security which promises $120 per year. Calculate the value of thesecurity if the market interest rate falls from 7% to 6% per year.Answer:n i PV PMT Result4 7 ? $120 PV = $406.47n i PV PMT Result4 6 ? $120 PV = $415.81The price increases by $9.34.3.Discuss the general principles about the relation between prices and yields of coupon bonds.Answer:Principle #1: Par Bonds.If a bond's price equals its face value, then its yield equals its coupon rate.Principle #2: Premium Bonds.If a coupon bond has a price higher than its face value, its yield to maturity is less than its current yield, which is in turn less than its coupon rate.Principle #3: Discount Bonds.If a coupon bond has a price lower than its face value, its yield to maturity is greater than its current yield, which is in turn greater than its coupon rate.8-144.List some reasons why differences in the prices of fixed-income securities of a given maturity mayarise.Answer:Differences in the prices of fixed-income securities of a given maturity may arise due to differences in coupon rates, default risk, tax treatment, callability and convertibility.5.Explain why it is important to have a method for valuation of fixed-income contracts.Answer:(1) The parties to the contracts need to have an agreed-upon valuation procedure insetting the terms of the contracts at the outset.(2) Since market factors determining the value of fixed-income contracts change overtime, both buyers and sellers have to reevaluate them each time they are traded.6.Consider a five-year pure discount bond with a face value of $1,000. If its current price is $775,compute its annualized yield.Answer:n i PV FV Result5 ? –$775 $1,000 i = 5.23%7. A four-year bond has a coupon rate of 6% per year, a price of $950, and a face value of $1,000.Calculate its current yield and yield to maturity.Answer:Current yield = coupon/price= 60/950= 6.32%To calculate yield to maturity:n i = YTM PV FV PMT Result4 ? –$950 $1,000 $60 YTM = 7.49%8-158.What is the current price of a bond that has a coupon rate of 7%, a return rate of 8%, and a face valueof $1,000? Assume that this bond will mature in five years. Compare the current price of the bond against its face value.Answer:n i = YTM PV FV PMT Result5 8 ? $1,000 $70 PV = $960.07Because the price of the bond is below its face value, it is a discount bond.9. A five-year coupon bond has a coupon rate of 5%, a return rate of 6%, and a face value of $1,000.What is its current price and how does it compare to its face value?Answer:n i = YTM PV FV PMT Result5 6 ? $1,000 $50 PV = $957.88Because the price of the bond is below its face value, it is a discount bond.10.What is the yield to maturity of a five-year coupon bond with a current price of $850, a face value of$1,000, and coupon rate of 7%?Answer:n i = YTM PV FV PMT Result5 ? –$850 $1,000 $70 YTM = 11.07%11.Five years ago, English and Co. issued 30 year coupon bonds with a par value of $1,000. At the timeof issuance, the yield to maturity was 6 percent per year and the bonds sold at par. The bonds are currently selling at 85 percent of their par value. Assuming that the coupon is paid annually, what is the current yield to maturity?Answer:Five years ago, the bonds were issued at par, which means at the time yield to maturity equaled coupon rate. So the annual coupon is 0.06 x $1,000 = $60.For the current yield to maturity:n i = YTM PV FV PMT Result25 ? –850 1,000 60 YTM = 7.33%8-1612.Eisenstein Corporation plans to raise $100,000,000 in funds by issuing zero-coupon $1,000 par valuebonds with a 30-year maturity. Assuming that Eisenstein Corporation is able to issue these bonds at an after-tax cost of debt of 11%, how many bonds must Eisenstein Corporation issue?Answer:First, calculate the price of an Eisenstein bond:n i = YTM PV FV PMT Result30 11 ? 1,000 0 PV = $43.68The corporation wants to raise $100,000,000, so it must issue the following number of bonds:$100,000,000/$43.68 = 2,289,377 bonds13.Currently, an Eisenstein bond trades at $1,050 per bond and has a coupon rate of 10%. Assuming thebond matures at a $1,000 value, and the required rate of return is 9.5%, in how many years does an Eisenstein bond mature?Answer:n i = YTM PV FV PMT Result? 9.5 –1,050 1,000 0 n = 33pute the current price of Walsingham bonds based on the following information. Walsinghambonds have a $1,000 par value, 26 years remaining until maturity, a 13 percent coupon rate, and a current yield to maturity of 11 percent per year.Answer:n i = YTM PV FV PMT Result26 11 ? 1,000 0 PV = $1,169.6915.Health & US Corporation is a major pharmaceutical firm that has recently experienced a marketreevaluation. Currently, the firm has a bond issue outstanding with 18 years to maturity and a coupon rate of 9 percent, with interest paid annually. The required rate of return of this debt issue has risen to15 percent. Calculate the current price of this bond.Answer:n i = YTM PV FV PMT Result18 15 ? 1,000 90 PV = $632.328-1716.Calculate the coupon rate, current yield, and the yield to maturity for a bond that has $1,000 par value,pays a coupon of $85 annually, matures in 20 years, and has a current price of $985.25.Answer:Coupon rate = 85/1,000= 8.5% per yearCurrent yield = coupon/price= 85/985.25= 8.63%For yield to maturity:n i = YTM PV FV PMT Result20 ? –985.25 1,000 85 YTM = 8.66%17.Suppose you buy a 20-year pure discount bond with a face value of $1,000 and a yield of 7% per year.A day later, market interest rates rise to 8% and so does the yield of your bond. What is theproportional change in the price of your bond? What is the elasticity of the bond price to the change in the yield?Answer:n i = YTM PV FV PMT Result20 7 ? 1,000 0 PV = $258.42n i = YTM PV FV PMT Result20 8 ? 1,000 0 PV = $214.55The price of the bond decreased by $43.87, so the proportional decline in price is $43.87/$258.42 = 16.98%.Elasticity is % change in price over % change in YTM, or –16.98%/14.29% = –1.19.18.As of today, January 1, 2009, Flanders Corporation is holding $10,000,000 in long-term debt at parbonds. The bonds have a par value of $1,000, mature on January 1, 2019, and pay a 5 percent coupon.Calculate the current market value of Flanders’ debt, if the yield to maturity is 7 percent.Answer:Total number of bonds = $10,000,000/$1,000 = 10,000 bondsn i PV FV PMT Result10 7 ? 1,000 50 PV = $859.50The current market value = $859.50 x 10,000= $8,578,8008-18Longer Problems1.Consider the purchase of a 30-year pure discount bond with a face value of $1,000 and a yield of 7%per year. A week later the market interest rate rises to 8% and o does the yield on your bond.Calculate the proportional change in the price of the bond. What basic principle in valuation of known cash flows does this illustrate?Answer:n i PV FV Result30 7 ? $1,000 PV = $131.37n i PV FV Result30 8 ? $1,000 PV = $99.38The price drops by $31.99, so a rise of 1% in market interest rates results in a $31.99/$131.37 =24.35% drop in the price of the bond. The general principle illustrates is that a change in marketinterest rates causes a change in the opposite direction in the market value of the bonds.2.Suppose our want to know the price of a 15-year 8% coupon bond which pays interest annually. Theface value of the bond is $1,000.(a) You have been told the yield to maturity is 9%. What is the price? Assume coupons arepaid annually.(b) What is the price if coupons are paid semi-annually and the yield to maturity is 9% peryear?Answer:(a) If coupons are paid annually:n i PV FV PMT Result15 9 ? $1,000 $80 PV = $919.39(b) If coupons are paid semi-annually:n i PV FV PMT Result30 4.5 ? $1,000 $40 PV = $918.563. A media report recently stated that prices of 30-year treasury bonds increased substantially becauseinflation was falling and the Federal Reserve was not expected to increase interest rates. How would you describe this interpretation using discounted cash flow techniques?Answer:Inflation is a component of i, the required return on bonds, so when inflation decreases, idecreases and bond prices rise.8-194.Suppose you want to know the price of a 10-year 7% coupon bond which pays interest annually. Theface value of the bond is $1,000.(a) What is the price of this bond if the yield to maturity is 8%?(b) What is the current yield of this coupon bond?(c) What is the price of this bond if coupons are paid semi-annually and the yield to maturityis 8%?Answer:a. n i PV FV PMT Result10 8 ? $1,000 $70 PV = $932.90b. Current yield = coupon/price= 70/932.9= 7.5%c. n i PV FV PMT Result20 4 ? $1,000 $35 PV = $932.055.Suppose you buy a 30-year pure discount bond with a face value of $1,000 and a yield of 9% per year.A day later, market interest rates fall to 8% and so does the yield of your bond. What is theproportional change in the price of your bond? What is the elasticity of the bond price to the change in the yield?Answer:n i = YTM PV FV PMT Result30 9 ? 1,000 0 PV = $75.37n i = YTM PV FV PMT Result30 8 ? 1,000 0 PV = $99.38The price of the bond decreased by $24.01, so the proportional increase in price is $24.01/$75.37 = 31.86%.Elasticity is % change in price over % change in YTM, or 31.86%/–11.11% = –2.87.8-206.As part of a reorganization plan, a bankruptcy court has permitted a new indenture on an outstandingbond issue to be put into effect for Leicester Corporation, which recently filed for bankruptcy. It is known that the issue has $1,000 par value per bond, 15 years to maturity, and a coupon rate of 11 percent paid annually. The reorganization plan allows the following arrangement: In years 1 through 7, there will be no coupon paid (that is, coupon = $0). In years 8 through 15, regular couponpayments will resume. At maturity in year 15, the par value plus the sum of all coupon payments that were not paid during years 1 through 7 must be paid. However, no interest will be paid on thedeferred coupon payments. If the required rate of return is 18 percent, calculate the current price the Leicester bonds would sell for in the market.Answer:Coupon = 0.11 x 1000= $110 per yearThe present value of this cash flow stream, using a discount rate of 18%, is $288.62 per bond.8-217.The Dharma Corporation has recently experienced a market reevaluation. Currently, the firm has abond issue outstanding with 18 years to maturity, a face value of $1,000, and a coupon rate of 10 percent paid annually. The required rate of return on this debt issue has risen to 16 percent. Calculate the current price of this bond.Answer:n i = YTM PV FV PMT Result18 16 ? 1,000 100 PV = $650.928.Calculate the coupon rate, current yield, and the yield to maturity for a bond that has $1,000 par value,pays $95 interest annually, matures in 25 years, and has a current price of $1,087.75.Answer:Coupon rate = 95/1,000= 9.5% per yearCurrent yield = coupon/price= 95/1,087.75= 8.73%To calculate yield to maturity:n i = YTM PV FV PMT Result25 ? –1,087.75 1,000 95 YTM = 8.63%9.As of today, January 1, 2009, Gala Worldwide is holding $1,000,000 in long-term debt at par bonds.The bonds have a par value of $1,000, mature on January 1, 2029, and pay a 7 percent coupon.Cal culate the current market value of Flanders’ debt, if the yield to maturity is 8 percent.Answer:Total number of bonds = $100,000,000/$1,000 = 100,000 bondsn i PV FV PMT Result20 8 ? 1,000 70 PV = $901.85The current market value = $901.85 x 100,000= $90,185,0008-22。