What is the yield to maturity on a 10-year, 9 percent annual coupon, $

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 bonds coupon rate?What is the current yie
According to the given information,Years to maturity = 10Annual coupon rate = 9%Annual coupon payment = Face value of the bond * Annual coupon rate = $1000 * 9% = $90Face value of the bond = $1000Present value of the bond = $887CAlculating 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 = -1000Step4: 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 $1,134.20Years to maturity = 10Annual coupon rate = 9%Annual coupon payment = Face value of the bond * Annual coupon rate = $1000 * 9% = $90Face value of the bond = $1000Present value of the bond = $1,134.20CAlculating 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 = -1000Step4: 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 rateWhen the bond sells at a premium: Coupon rate > Current yield > YTMWhen the bond sells at par: YTM = Current yield = Coupon rate2) According to the given information,Years to callable bond = 5yrsAnnual coupon rate = 9%Annual coupon payment = Face value of the bond * Annual coupon rate = $1000 * 9% = $90Face value of the bond = $1090Present value of the bond = $887CAlculating 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 = -1090Step4: 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 $1,134.30Step1: 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 = -1090Step4: Click “OK” to get the desired value.The value comes to “7.26%”Therefore, the yield to maturity is 7.26%

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