What is the yield to maturity on a 10-year, 9 percent annual coupon, $1,000 par
ID: 2666324 • Letter: W
Question
What is the yield to maturity on a 10-year, 9 percent annual coupon, $1,000 par value bond that sells for $887.00? That sells for $1,134.20? What does the fact that a bond sells at a discount or at a premium tell you about the relationship between r and the bond's coupon rate?What is the current yield, the capital gains yield, and the total return in each case in the preceding question?
Suppose that the bond described is callable in five years at a call price equal to $1,090.00. What is the yield to call (YTC) on the bond if its market value is $887.00? What is the YTC on the same bond if its current market price is $1,134.30?
Explanation / Answer
According to the given information, Years to maturity = 10 Annual coupon rate = 9% Annual coupon payment = Face value of the bond * Annual coupon rate = $1000 * 9% = $90 Face value of the bond = $1000 Present value of the bond = $887 CAlculating the yield to maturity using excel sheet: Step1: Go to excel and click "insert" to insert the function. Step2: Select the "Rate" function as we are finding the yield to maturity in this case. Step3: Enter the values as Nper = 10; PMT = -90; PV = 887; FV = -1000 Step4: Click "OK" to get the desired value. The value comes to "10.91%" Therefore, the yield to maturity is 10.9% The current yield is calculated as Current yield = Annual coupon payment / Current price of the bond = $90 / $887 = 10.15% The capital gains yield is calculated as CApital gains yield = (Current selling price - Original selling price) -------------------------------------------- Original selling price = ($887 - $1000) / $1000 = -0.113 or -11.3% The total return is calculated as Total return = Current yield + CApital gains yield = 10.15% - 11.3% = -1.15% Now, computing the Yield to maturity when the Present value is $1,134.20 Years to maturity = 10 Annual coupon rate = 9% Annual coupon payment = Face value of the bond * Annual coupon rate = $1000 * 9% = $90 Face value of the bond = $1000 Present value of the bond = $1,134.20 CAlculating the yield to maturity using excel sheet: Step1: Go to excel and click "insert" to insert the function. Step2: Select the "Rate" function as we are finding the yield to maturity in this case. Step3: Enter the values as Nper = 10; PMT = -90; PV = 1134.20; FV = -1000 Step4: Click "OK" to get the desired value. The value comes to "7.08% Therefore, the yield to maturity is 7.08% The current yield is calculated as Current yield = Annual coupon payment / Current price of the bond = $90 / $1134.20 = 7.9% The capital gains yield is calculated as CApital gains yield = (Current selling price - Original selling price) -------------------------------------------- Original selling price = ($1134.20 - $1000) / $1000 = 0.1342 or 13.42% The total return is calculated as Total return = Current yield + CApital gains yield = 7.9% + 13.42% = 21.32% The relation of yield to price is when the price goes up, the yield to maturity comes down and when the price comes down the yield goes up. There is an inverse relation betwee the yield and the price of the bond. The relation between the YTM, current yield and Coupon payment is shown as below: When the bond sells at a discount: YTM > Current yield > Coupon rate Years to maturity = 10 Annual coupon rate = 9% Annual coupon payment = Face value of the bond * Annual coupon rate = $1000 * 9% = $90 Face value of the bond = $1000 Present value of the bond = $1,134.20 CAlculating the yield to maturity using excel sheet: Step1: Go to excel and click "insert" to insert the function. Step2: Select the "Rate" function as we are finding the yield to maturity in this case. Step3: Enter the values as Nper = 10; PMT = -90; PV = 1134.20; FV = -1000 Step4: Click "OK" to get the desired value. The value comes to "7.08% Therefore, the yield to maturity is 7.08% The current yield is calculated as Current yield = Annual coupon payment / Current price of the bond = $90 / $1134.20 = 7.9% The capital gains yield is calculated as CApital gains yield = (Current selling price - Original selling price) -------------------------------------------- Original selling price = ($1134.20 - $1000) / $1000 = 0.1342 or 13.42% The total return is calculated as Total return = Current yield + CApital gains yield = 7.9% + 13.42% = 21.32% The relation of yield to price is when the price goes up, the yield to maturity comes down and when the price comes down the yield goes up. There is an inverse relation betwee the yield and the price of the bond. The relation between the YTM, current yield and Coupon payment is shown as below: When the bond sells at a discount: YTM > Current yield > Coupon rate When the bond sells at a premium: Coupon rate > Current yield > YTM When the bond sells at par: YTM = Current yield = Coupon rate 2) According to the given information, Years to callable bond = 5yrs Annual coupon rate = 9% Annual coupon payment = Face value of the bond * Annual coupon rate = $1000 * 9% = $90 Face value of the bond = $1090 Present value of the bond = $887 CAlculating the yield to maturity using excel sheet: Step1: Go to excel and click "insert" to insert the function. Step2: Select the "Rate" function as we are finding the yield to maturity in this case. Step3: Enter the values as Nper = 5; PMT = -90; PV = 887; FV = -1090 Step4: Click "OK" to get the desired value. The value comes to "13.63%" Calculating the yield to maturity when the present value of the bond is $1,134.30 Step1: Go to excel and click "insert" to insert the function. Step2: Select the "Rate" function as we are finding the yield to maturity in this case. Step3: Enter the values as Nper = 5; PMT = -90; PV = 1134.30; FV = -1090 Step4: Click "OK" to get the desired value. The value comes to "7.26%" Therefore, the yield to maturity is 7.26% Years to callable bond = 5yrs Annual coupon rate = 9% Annual coupon payment = Face value of the bond * Annual coupon rate = $1000 * 9% = $90 Face value of the bond = $1090 Present value of the bond = $887 CAlculating the yield to maturity using excel sheet: Step1: Go to excel and click "insert" to insert the function. Step2: Select the "Rate" function as we are finding the yield to maturity in this case. Step3: Enter the values as Nper = 5; PMT = -90; PV = 887; FV = -1090 Step4: Click "OK" to get the desired value. The value comes to "13.63%" Calculating the yield to maturity when the present value of the bond is $1,134.30 Step1: Go to excel and click "insert" to insert the function. Step2: Select the "Rate" function as we are finding the yield to maturity in this case. Step3: Enter the values as Nper = 5; PMT = -90; PV = 1134.30; FV = -1090 Step4: Click "OK" to get the desired value. The value comes to "7.26%" Therefore, the yield to maturity is 7.26% Step1: Go to excel and click "insert" to insert the function. Step2: Select the "Rate" function as we are finding the yield to maturity in this case. Step3: Enter the values as Nper = 5; PMT = -90; PV = 1134.30; FV = -1090 Step4: Click "OK" to get the desired value. The value comes to "7.26%" Therefore, the yield to maturity is 7.26%Related Questions
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