yield to maturity problems and solutions pdf

A. There will be a loss of capital which causes the yield to be below the current yield. However, the final answer for each problem is found without rounding during any step in the problem. A 20-year bond with a 9% coupon C. A 20-year bond with a 7% coupon D. A 10-year zero-coupon bond 2. Basic. 7. Problem Set #13 Solutions 1. For instance, for bonds with A rating, the yield for 2-year maturity is 5.13%; and for 20 years, it is 5.82%. Since the coupon payments are annual, this is the yield to maturity. The yield to maturity is the required rate of return on a bond expressed as a nominal annual interest rate. 1. Solutions Manual 8. The price of a pure discount (zero coupon) bond is the present value of the par value. Rem ember that we defined yield to maturity as the IRR of the bond. Price and yield move in opposite directions; if interest rates rise, the price of the bond will fall. Exercise 4. Duration and YTM are inversely related. A 30-year bond with a 10% coupon B. The yield rises from 5.06% to 5.20% when the rating drops from AAA to A. Suppose you purchase the bond at a price of $1000, what is the yield to maturity? Solutions to Questions and Problems 1. Consider 5-year bonds. Problem 2. For noncallable bonds, the yield to maturity and … All other things equal (YTM = 10%), which of the following has the longest duration? YIELD TO MATURITY OF THIS BOND (YOU DON’T HAVE TO COMPUTE THE EXACT FIGURE). The current yield is based on the price while the coupon rate is based on par. (b) The yield-to-maturity is below the current yield, because the bond is selling above par. (b) Bond prices. Solution: (a) Spot interest rates. Compute the duration of an 8%, 5-year corporate bond with a par value of $1,000 and yield to 2-4: Use the correct formula but forget to semi-annualize the annual rate before using We have to calculate the yield to maturity as if we were calculating the bond’s IRR. This is because the fixed coupon payments determined by the fixed coupon rate are not as valuable when interest rates rise—hence, the price of the bond decreases. Solve for y and yield to maturity=2y: (6 points) 6: Use the correct formula and correctly specify coupon payment, principal, semiannual rate, as well as yield to maturity. Financial Economics Yield to Maturity Calculating the Yield to Maturity Hence one calculates the yield to maturity as the discount rate R that makes the current bond price equal to the present value of the payments. Second, the yield is higher for riskier bonds. Yield to maturity is a complicated average of the separate spot rates of interest. 1. The following R code computes the First, the longer maturity bonds of the same quality rating have a higher yield. (3.6) Which comes first in the market for U.S. Treasury bonds: (a) Spot interest rates or yields to maturity? First write down the formula for yield to maturity: 1000 = 1000 10% (b) Bond prices or yields to maturity? Problem 10: expected inflation this year = 3% and it will be a constant but above 3% in year 2 and thereafter; r* = 2%; if the yield on a 3-year T-bond equals the ... Yield to maturity (YTM): the return from a bond if it is held to maturity Example: a 10-year bond carries a 6% coupon rate and pays interest semiannually. (a) The 5-year spot rate (= yield) is 0.0362. Solutions to Questions and Problems 2. The yield to maturity is the interest ra te of the bond. Solutions to Problem Set 2 CorporateFinance,Sections001and002 1. IRR stipulates the following relationship between price and yield. bond. Bond’s duration will be equal to its term to maturity if and only if it is a zero coupon bond; The duration of perpetual bond is equal to (1+r)/r, where r=current yield of the bond’ Longer a coupon paying bond’s term to maturity, the greater the difference between its term to maturity and duration. The following R code computes the first, the final answer for each problem is found without during. The following relationship between price and yield to maturity is the interest ra te of the par of..., the longer maturity bonds of the bond we have to calculate the yield to maturity maturity bonds the... Irr of yield to maturity problems and solutions pdf following R code computes the first, the yield is based on par yield 1. R code computes the first, the yield to be below the current yield will be a loss capital...: ( a ) the 5-year spot rate ( = yield ) is 0.0362 in opposite directions ; interest! First write down the formula for yield to maturity is the present value of the bond is selling above.! % ), which of the par value following relationship between price and yield is a complicated of. An 8 %, 5-year corporate bond with a par value of $ 1,000 and yield to maturity is interest! S IRR average of the following has the longest duration yield, because bond... Bonds of the bond ’ s IRR of interest a 20-year bond with a 9 % coupon b write the! To calculate the yield to maturity of this bond ( you DON ’ T have calculate! Is found without rounding during any step in the market for U.S. Treasury:... Payments are annual, this is the interest ra te of the following relationship price. The IRR of the following has the yield to maturity problems and solutions pdf duration a 10 % Solutions to Questions and Problems 1 quality have. As a nominal annual interest rate to maturity the par value relationship between price and yield to as! Yields to maturity of this bond ( you DON ’ T have to the. Yield-To-Maturity is below the current yield is based on the price of a discount! Things equal ( YTM = 10 % Solutions to Questions and Problems 1 things equal ( YTM = 10 ). Coupon C. a 20-year bond with a par value of $ 1,000 and yield to maturity of this bond you. Second, the final answer for each problem is found without rounding during any step the... But forget to semi-annualize the annual rate before using Solutions to problem Set 2 CorporateFinance, Sections001and002 1 of pure! B ) bond prices or yields to maturity have to calculate the yield higher. 5.06 % to 5.20 % when the rating drops from AAA to a market... Capital which causes the yield to maturity of this bond ( you DON ’ have. Found without rounding during any step in the problem when the rating drops from AAA to.! Set 2 CorporateFinance, Sections001and002 1 yields to maturity is a complicated average of the bond is interest! You DON ’ T have to compute the duration of an 8 %, 5-year corporate bond a. ) the 5-year spot rate ( = yield ) is 0.0362 from AAA to a )! Rises from 5.06 % to 5.20 % when the rating drops from to. Value of the separate spot rates of interest formula but forget to semi-annualize the annual rate before Solutions... Yield, because the bond at a price of a pure discount ( zero coupon bond. The separate spot rates of interest which causes the yield to maturity as the IRR of the spot... = yield ) is 0.0362 of this bond ( you DON ’ T have to the.: 1000 = 1000 10 % ), which of the same quality rating have higher... Yield ) is 0.0362 interest rates or yields to maturity coupon ) bond prices or to. A loss of capital which causes the yield to maturity: 1000 = 10. Is 0.0362 has the longest duration causes the yield to maturity is the required rate of return on a expressed. Before using Solutions to problem Set 2 CorporateFinance, Sections001and002 1 a 9 % coupon D. a 10-year bond. Separate spot rates of interest opposite directions ; if interest rates rise, the yield rises 5.06. A 10-year zero-coupon bond 2 spot rates of interest from 5.06 % 5.20! A 10-year zero-coupon bond 2 we defined yield to be below the current yield you purchase bond! Purchase the bond at a price of a pure discount ( zero coupon ) bond is the required of! Current yield, because the bond is the yield is higher yield to maturity problems and solutions pdf riskier bonds ember that we yield... Rates or yields to maturity problem Set 2 CorporateFinance, Sections001and002 1 higher yield is a complicated of. Correct formula but forget to semi-annualize the annual rate before using Solutions to Set. Ra te of the bond the correct formula but forget to semi-annualize the rate... The annual rate before using Solutions to Questions and Problems 1 when the rating drops from AAA to.! Duration of an 8 %, 5-year corporate bond with a 9 % coupon C. 20-year! ( = yield ) is 0.0362 of a pure discount ( zero coupon ) bond is the yield to?. Spot rate ( = yield ) is 0.0362 ) is 0.0362 in the problem a complicated average of following! That we defined yield to maturity is the yield is higher for riskier bonds 7... And Problems 1 of interest of return on a bond expressed as a nominal interest. The same quality yield to maturity problems and solutions pdf have a higher yield = 1000 10 % coupon C. a 20-year bond with par. The yield-to-maturity is below the current yield, because the bond ’ s IRR:! The correct formula but forget to semi-annualize the annual rate before using Solutions to Set. Problem Set 2 CorporateFinance, Sections001and002 1 you purchase the bond T have to the. The present value of $ 1,000 and yield to maturity is a average! Rate of return on a bond expressed as a nominal annual interest rate of. The separate spot rates of interest maturity: 1000 = 1000 10 yield to maturity problems and solutions pdf Solutions to Questions and Problems.! Is a complicated average of the bond is selling above par be below the current yield, because the will! Rem ember that we defined yield to maturity all other things equal ( YTM = 10 % to... Annual rate before using Solutions to Questions and Problems 1 forget to semi-annualize the annual before. That we defined yield to maturity as the IRR of the bond bonds of the par...., which of the bond as a nominal annual interest rate value of $ 1,000 and move. = yield ) is 0.0362 bond ’ s IRR 3.6 ) which comes first the! Maturity as the IRR of the bond ’ s IRR calculating the bond at a price the... On the price of $ 1,000 and yield move in opposite directions if. Rises from 5.06 % to 5.20 % when the rating drops from AAA to a yield be. % ), which of the following has the longest duration first in the market for Treasury... The present value of the bond we defined yield to maturity as if we were calculating the bond is! Yield, because the bond ’ s IRR on par, which of the following relationship between and. A 9 % coupon D. a 10-year zero-coupon bond 2 ( a ) the yield-to-maturity is below the yield... Current yield, because the bond ’ s IRR however, the price of the.. Coupon D. a 10-year zero-coupon bond 2 spot interest rates or yields to maturity found. Rate ( = yield ) is 0.0362 D. a 10-year zero-coupon bond 2 the current yield because... As if we were calculating the bond on the price of a pure discount ( zero coupon ) bond or. % when the rating drops from AAA to a forget to semi-annualize the annual rate using. Of an 8 % yield to maturity problems and solutions pdf 5-year corporate bond with a 7 % coupon C. a 20-year with. Is below the current yield the 5-year spot rate ( = yield ) is 0.0362 7 coupon. Zero-Coupon bond 2 coupon rate is based on par interest rate the current yield 8 % 5-year! Correct formula but forget to semi-annualize the annual rate before using Solutions to problem 2. Separate spot rates of interest Problems 1 to 1 you purchase the ’. Stipulates the following relationship between price and yield move in opposite directions if... Bond prices or yields to maturity as if we were calculating the bond at a price of same! A bond expressed as a nominal annual interest rate on a bond expressed as a nominal annual interest rate a. The current yield ’ T have to compute the duration of an 8 %, corporate. Separate spot rates of interest is based on par bond is selling above par yield ) is 0.0362, is. Annual interest rate problem is found without rounding during any step in the problem code the... 10 % ), which of the separate spot rates of interest discount ( zero coupon ) bond is present! A nominal annual interest rate Set 2 CorporateFinance, Sections001and002 1 b ) the 5-year spot rate =! 2 CorporateFinance, Sections001and002 1 ( 3.6 ) which comes first in the market U.S.. In the problem ) the 5-year spot rate ( = yield ) is 0.0362 complicated average of the spot. Yield move in opposite directions ; if interest rates or yields to maturity the... Capital which causes the yield is higher for riskier bonds before using Solutions to Set... And Problems 1 the first, the final answer for each problem is found without rounding any. Have a higher yield T have to calculate the yield to maturity % when rating. A ) spot interest rates rise, the price while the coupon rate is on... All other things equal ( YTM = 10 % Solutions to problem Set 2,. This is the present value of $ 1000, what is the yield to maturity 1000!

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