Chapter 06Chapter 06Inputs are in BlueAnswers are in RedNOTE: Some functions used in these spreadsheets may require thatthe "Analysis ToolPak" or "Solver Add-In" be installed in Excel.To install these, click on the Office buttonthen "Excel Options," "Add-Ins" and select"Go." Check "Analysis ToolPak" and"Solver Add-In," then click "OK."

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3Quiz 3A bond with face value $1,000 has a current yield of 6% and a coupon rate of 8%.What is the bonds price?Face value$1,000.00Current Yield6%Coupon Rate8%Solution:Bond price$1,333.33note: current yield =coupon payment/bond price

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4Quiz 4A 6-year Circular File bond pays interest of $80 annually and sells for $950.What are its coupon rate and yield to maturity?Time6.00yearsInterest80.00Price950.00Solution:Coupon rate8.00%Using a financial calculator:Yield to maturity9.119%

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5Quiz 5A 6-year Circular File bond pays interest of $80 annually and sells for $950.If Circular File wants to issue a new 6-year bond at face value, what coupon rate must the bond offer?Time6.00yearsInterest80.00Price950.00Solution:In order for the bond to sell at par, the coupon rate must equal the yield to maturity.Using a financial calculator:Yield to maturity9.119%Hence the coupon rate must be9.119%

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6Quiz 6A bond has 8 years until maturity, a coupon rate of 8%, and sells for $1,100.a.What is the current yield on the bond?b.What is the yield to maturity?Time8.00yearsCoupon rate8%Price1,100.00Solution:a.Current yield=7.27%recall: current yield=coupon payment/bond priceput the kursor on the answer, klick on fx to see the functionargument =Rnta (perioder; betalning; nuvrde; slutvrde; typ)b.Using a financial calculator:Yield to maturity=6.3662%

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7Quiz 7General Matters outstanding bond issue has a coupon rate of 10%, and it sells ata yield to maturity of 9.25%. The firm wishes to issue additional bonds to the public at facevalue. What coupon rate must the new bonds offer in order to sell at face value?Coupon rate10%YTM9.25%Solution:Coupon rate on the new bonds=9.25%

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8Quiz 8Refer to Table 6.1 (below). What is the current yield of the 8.75% 2020 maturitybond? Why is this more than its yield to maturity?Table 6.1MaturityCouponBid PriceAsked PriceAsked Yield, %2012 May 151.375101:05101:060.782013 May 153.625106:31107:011.232014 May 154.75111:22111:231.72020 May 158.75144:17144:193.442025 Aug 156.875133:07133:113.942030 May 156.25128:25128:274.122040 May 154.375100:28100:294.32Coupon Rate8.75%Asked Price144.0019.00Solution:Current yield6.05%The current yield exceeds the yield to maturity on the bond because the bond is selling at apremium. At maturity the holder of the bond will receive only the $1,000 face value, reducingthe total return on investment

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9Practice Problem 9One bond has a coupon rate of 8%, another a coupon rate of 12%. Both bonds have 10-yearmaturities and sell at a yield to maturity of 10%. If their yields to maturity next year are still 10%,what is the rate of return on each bond? Does the higher coupon bond give a higher rate of return?Coupon rate - bond 18.00%Coupon rate - bond 212.00%Maturity10.00yearsYTM10.00%YTM next year10.00%Solution:Using a financial calculator:Bond 1:Rate of return=10.00%Bond 2:Rate of return=10.00%Both bonds provide the same rate of return.

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10Practice Problem 10A bond has 8 years until maturity, a coupon rate of 8%, and sells for $1,100.a.If this bond has a yield to maturity of 8% 1 year from now, what will its price be?b.What will be the rate of return on the bond?c.If the inflation rate during the year is 3%, what is the real rate of return on the bond?Time8.00yearsCoupon rate8%Price1,100.00YTM8%Inflation3%Solution:a.Bond Price=$1,000.00b.Bond Price$1,000.00Rate of return=-1.82%c.Rate of return-1.82%Real return=-4.68%

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11Practice Problem 11A General Electric bond carries a coupon rate of 8%, has 9 years until maturity, and sells at ayield to maturity of 7%.a.What interest payments do bondholders receive each year?b.At what price does the bond sell? (Assume annual interest payments.)c.What will happen to the bond price if the yield to maturity falls to 6%?Face value$1,000.00Time9.00yearsCoupon rate8%YTM7%YTM falls to6%Solution:a.Annual interest payments=$80.00b.Annual interest payments80.00Bond price=$1,065.15c.Annual interest payments80.00Bond price if YTM falls to 6%=$1,136.03

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12Practice Problem 12A 30-year maturity bond with face value of $1,000 makes annual coupon payments and has acoupon rate of 8%. What is the bonds yield to maturity if the bond is selling fora.$900.00?b.$1,000.00?c.$1,100.00?Face value$1,000.00Time30.00yearsCoupon rate8%Solution:Using a financial calculator:a.Yield to maturity=8.971%b.Yield to maturity=8.000%c.Yield to maturity=7.180%

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13Practice Problem 13A 30-year maturity bond with face value of $1,000 makes semi-annual coupon paymentsand has a coupon rate of 8%. What is the bonds yield to maturity if the bond is selling fora.$900.00?b.$1,000.00?c.$1,100.00?Face value$1,000.00Time30.00yearsCoupon rate8%Solution:Using a financial calculator:a.Yield to maturity=8.966%b.Yield to maturity=8.000%c.Yield to maturity=7.184%

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14Practice Problem 14Fill in the table below for the following zero-coupon bonds. The face value of each bondis $1,000.PriceMaturity (years)Yield to Maturity$300.0030.00$300.008%10.0010%Face value$1,000.00Solution:Price = $1,000/(1 + y)maturityPriceMaturity (years)Yield to Maturity$300.0030.004.095%$300.0015.648.000%$385.5410.0010.000%

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15Practice Problem 15Perpetual Life Corp. has issued consol bonds with coupon payments of $60. (Consols pay interestforever and never mature. They are perpetuities.) If the required rate of return on these bonds at thetime they were issued was 6%, at what price were they sold to the public? If the required returntoday is 10%, at what price do the consols sell?Coupon Payments$60.00Required rate of returnat the time of issue6%Current required rate of return10%Solution:PV of perpetuity = coupon payment/rate of returnPresent value=$1,000.00If the required rate of return is 10%, the bond sells for:Present value=$600.00

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16Practice Problem 16Sure Tea Co. has issued 9% annual coupon bonds that are now selling at a yield to maturity of10% and current yield of 9.8375%. What is the remaining maturity of these bonds?Face value$1,000.00Time30.00yearsCoupon rate9%Yield to maturity10%Current yield9.8375%Solution:Using a financial calculator:Remaining maturity=20.00years

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17Practice Problem 17Large Industries bonds sell for $1,065.15. The bond life is 9 years, and the yield to maturity is7%. What must be the coupon rate on the bonds?Face value$1,000.00Bond price$1,065.15Time9.00yearsYield to maturity7%Solution:Using a financial calculator:Coupon rate=8.00%

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18Practice Problem 18a.Several years ago, Castles in the Sand, Inc., issued bonds at face value at a yield to maturityof 7%. Now, with 8 years left until the maturity of the bonds, the company has run into hardtimes and the yield to maturity on the bonds has increased to 15%. What has happened to theprice of the bond?b.Suppose that investors believe that Castles can make good on the promised coupon payments,but that the company will go bankrupt when the bond matures and the principal comes due.The expectation is that investors will receive only 80% of face value at maturity. If they buy thebond today, what yield to maturity do they expect to receive?Face value$1,000.00Yield to maturity7%Years left8.00Yield to maturity increased to15%Face value received by the investors80%Solution:a.Price of bond=$641.01b.Price of bond$641.01Using a financial calculator:Yield to maturity=12.87%

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19Practice Problem 19You buy an 8% coupon, 10-year maturity bond for $980. A year later, the bond price is $1,200.a.What is the new yield to maturity on the bond?b.What is your rate of return over the year?Face value$1,000.00Coupon rate8%Time10.00yearsBond price980.00Bond price a year later1,200.00Solution:Using a financial calculator:a.Yield to maturity=5.165%b.Rate of return=30.61%

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20Practice Problem 20You buy an 8% coupon, 20-year maturity bond when its yield to maturity is 9%. A year later, theyield to maturity is 10%. What is your rate of return over the year?Face value$1,000.00Coupon rate8%Time20.00yearsbond price at t0Yield to maturity9%908.71 krYield to maturity next year10%bond price at t1832.70 krSolution:total return on investment on bond:(coupon payment + P1-P0)/ P0Using a financial calculator:0.4388%Rate of return=0.44%

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21Practice Problem 21Consider three bonds with 8% coupon rates, all selling at face value. The short-term bond has amaturity of 4 years, the intermediate-term bond has maturity 8 years, and the long-term bond hasmaturity 30 years.a.What will happen to the price of each bond if their yields increase to 9%?b.What will happen to the price of each bond if their yields decrease to 7%?Face value$1,000.00Coupon rate8%Short term bond maturity4.00yearsIntermediate-term bond maturity8.00yearsLong-term bond maturity30.00yearsYield (a)9%Yield (b)7%Solution:a., b.Price of Each Bond at Different Yields to MaturityMaturity of BondYield4 Years8 Years30 Years7%$1,033.87$1,059.71$1,124.098%$1,000.00$1,000.00$1,000.009%$967.60$944.65$897.26

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22Practice Problem 22A 2-year maturity bond with face value of $1,000 makes annual coupon payments of $80 andis selling at face value. What will be the rate of return on the bond if its yield to maturity atthe end of the year isa.6%?b.8%?c.10%?Face value$1,000.00Annual coupon$80.00Time2.00yearsSolution:a.Rate of return=9.89%b.Rate of return=8.00%c.Rate of return=6.18%

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23Practice Problem 23A bond that pays coupons annually is issued with a coupon rate of 4%, maturity of 30 years,and a yield to maturity of 7%. What rate of return will be earned by an investor who purchasesthe bond and holds it for 1 year if the bonds yield to maturity at the end of the year is 8%?Face value$1,000.00Coupon rate4%Time30.00yearsYield to maturity7%Yield to maturity by end of 1st year8%Solution:Rate of return=-5.43%

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24Practice Problem 24A bonds credit rating provides a guide to its risk. Long-term bonds rated Aa currently offer yields tomaturity of 7.5%. A-rated bonds sell at yields of 7.8%. If a 10-year bond with a coupon rate of 7% isdowngraded by Moodys from Aa to A rating, what is the likely effect on the bond price?Face value$1,000.00Coupon rate7%Time10.00yearsCurrent yield to maturity7.5%Yield of A rated bonds8%Solution:The bonds yield to maturity will increase from 7.5% to 7.8% when the perceived default riskIncreases.The bond price will fall:Initial price=$965.68New price=$945.83

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25Practice Problem 25Suppose that you buy a 1-year maturity bond for $1,000 that will pay you back $1,000 plus acoupon payment of $70 at the end of the year. What real rate of return will you earn if the inflationrate isa.2%?b.4%?c.6%?d.8%?Face value$1,000.00Annual coupon$70.00Time1.00yearSolution:a.Real rate of return=4.902%b.Real rate of return=2.885%c.Real rate of return=0.9434%d.Real rate of return=-0.926%

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26Practice Problem 26Suppose that you buy a 1-year maturity bond for $1,000 that will pay you back $1,000 plus acoupon payment of $70 at the end of the year and the inflation rate isa.2%?b.4%?c.6%?d.8%?Now suppose that the bond is a TIPS (inflation-indexed) bond with a coupon rate of 4%.What will the cash flow provided by the bond be for each of the four inflation rates? What will bethe real and nominal rates of return on the bond in each scenario?Face value$1,000.00Time1.00yearCoupon rate4%Solution:The principal value of the bond will increase by the inflation rate, and since the couponis 4% of the principal, the coupon will also increase along with the general level ofprices. The total cash flow provided by the bond will be:1,000 x (1 + inflation rate) + coupon rate x 1,000 x (1 + inflation rate)Since the bond is purchased for face value, or $1,000, total dollar nominal return istherefore the increase in the principal due to the inflation indexing, plus coupon income:Income = ($1,000 x inflation rate) + [coupon rate x $1,000 x (1 + inflation rate)]Finally: Nominal rate of return = income/$1,000a.Nominal rate of return=6.080%Real rate of return=4.00%b.Nominal rate of return=8.160%Real rate of return=4.00%c.Nominal rate of return=10.240%Real rate of return=4.00%d.Nominal rate of return=12.320%Real rate of return=4.00%

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27Practice Problem 27Suppose that you buy a 1-year maturity bond for $1,000 that will pay you back $1,000 plus acoupon payment of $70 at the end of the year and the inflation rate isa.2%?b.4%?c.6%?d.8%?Now suppose the TIPS bond in the previous problem is a 2-year maturity bond.What will be the bondholders cash flows in each year in each of the inflation scenarios?Face value$1,000.00Time2.00yearsCoupon rate4%Solution:First-Year Cash FlowSecond-Year Cash Flowa.$40.80$1,082.02b.$41.60$1,124.86c.$42.40$1,168.54d.$43.20$1,213.06

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28Challenge Problem 28Suppose interest rates increase from 8% to 9%. Which bond will suffer the greater percentagedecline in price: a 30-year bond paying annual coupons of 8% or a 30-year zero-coupon bond?Face value$1,000.00Interest rate 18.00%Interest rate 29.00%Time30.00yearsCoupon8.00%Solution:Coupon bondInitial price=$1,000.00New price=$897.26Price decline %=10.27%Zero-coupon bondInitial price=$99.38New price=$75.37Price decline %=24.16%Hence zero-coupon bond will suffer greater price decline.

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29Challenge Problem 29Consider two 30-year maturity bonds. Bond A has a coupon rate of 4%, while bond B has a couponrate of 12%. Both bonds pay their coupons semiannuallya.Construct an Excel spreadsheet showing the prices of each of these bonds for yields to maturityranging from 2% to 15% at intervals of 1%. Column A should show the yield to maturity(ranging from 2% to 15%), and columns B and C should compute the prices of the twobonds (using Excels bond price function) at each interest rate.b.In columns D and E, compute the percentage difference between the bond price and its valuewhen yield to maturity is 8%.c.Plot the values in columns D and E as a function of the interest rate. Which bonds price isproportionally more sensitive to interest rate changes?Face value$100.00Coupon rate bond A4.00%Coupon rate bond B12.00%Time30.00yearsYield to maturity8.00%-144.96 kr-119.69 krSolution:-100.00 krc.a., b.YieldPrice APrice B% Diff. (8%) A% Diff. (8%) B2%144.96324.78165%124%3%119.69277.21119%91%4%100.00239.0483%65%5%84.55208.1854%43%6%72.32183.0332%26%7%62.58162.3614%12%8%54.75145.250%0%9%48.40130.96-12%-10%10%43.21118.93-21%-18%11%38.93108.72-29%-25%12%35.35100.00-35%-31%13%32.3592.48-41%-36%14%29.8085.96-46%-41%15%27.6280.26-50%-45%The price of bond A is more sensitive to interest rate changes as reflected in the steeper curve.here you can see the higher the yield to maturity (IRR), the lower the bond price.

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29

% Diff. (8%) A% Diff. (8%) B

30

Price APrice B

Challenge Problem 30In Figure 6.7, we saw a plot of the yield curve on stripped Treasury bonds and pointed out thatstripped Treasury bonds:every coupon payment can be seen as a zero coupon bond with time to maturity of the coupon payment.bonds of different maturities may sell at different yields to maturity. In principle, when we are valuinga stream of cash flows, each cash flow should be discounted by the yield appropriate to its particularmaturity. Suppose the yield curve on (zero-coupon) Treasury strips is as follows:Time to MaturityYTM1 year4.00%25%355.50%6106%You wish to value a 10-year bond with a coupon rate of 10%, paid annually.a.Set up an Excel spreadsheet to value each of the bonds annual cash flows using this table ofyields. Add up the present values of the bonds 10 cash flows to obtain the bond price.b.What is the bonds yield to maturity?recall: Yield to maturity is internal rate of return (IRR, overall interest rate) earned by an investor who buys the bond today at the market price.Face value$1,000.00Coupon rate10.00%Time to maturity10.00yearsSolution:a., b.YearYTMCash Flow from BondPV of cash flow14.00%100.0096.153846153825.00%100.0090.702947845835.50%100.0085.161366418445.50%100.0080.721674330255.50%100.0076.513435384166.00%100.0070.49605404476.00%100.0066.505711362286.00%100.0062.741237134296.00%100.0059.189846353106.00%1,100.00614.2342546066Bond price (PV)=1302.4203736324YTM (RATE)=5.91%

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