Question

Which $10,000 bond has the higher yield to maturity, a twenty year bond selling for $8,000 with a current yield of 20% or a one-year bond selling for $8,000 with a current yield of 10%?

Answer 1

What is the yield to maturity on a $10,000-face-value discount bond maturing in one yearthat sells for $9,523.81?5% = ($10,000 - $9,523.81) / $ 9,523.81 = $476.19 / $9,523.81 = 0.05.18.What is the yield to maturity (YTM) on a simple loan for $1,500 that requires arepayment of $15,000 in five years’ time?58.5%, derived as follows:The present value of the $15,000 payment five years from now is $15,000 / (1 +i)5,which equals the $1,500 loan. Thus 1500 = 15000 / (1 +i)5.Solving fori,(1 +i)5= 15000/1500, so that° = √105– 1 = 0.±8± = ±8.±%19.Which $10,000 bond has the higher yield to maturity, a twenty-year bond selling for$8,000 with a current yield of 20% or a one-year bond selling for $8,000 with a currentyield of 10%?The yield to maturity on the one-year bond is 0.35, or 35%. Recall, for long-term bonds,the yield to maturity is approximately the current yield. So on the 20-year bond it is about20% (the current yield): in fact, it is 20.13%.Not required: If you are interested, you can calculate the exact yield to maturity oncoupon bonds in Excel using the YIELD function. But three notes: 1. You need to enterthe Settlement date (start date) and Maturity date using the Date function (For the 20-yearbond, I choose 1/1/2016 and 1/1/2036. 2. For the rate, you enter thecoupon rate= C/Fnot the current yield = C/P. 3. You enter the price of the bond ($8,000) and theredemption (face value for us: $10,000)in units of 100: so Pr = 80 and Redemption =100. I have posted the Excel file on Moodle if you are interested.