6 Lycan Inc has 82 coupon bonds on the market that have 10 years left to maturity The bonds make annual payments and have a par value of 1000 If the YTM on these bonds is 102 what is the current bond price ID: 1029925
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1. Class Problems – Chapter 6Lycan, Inc. has 8.2% coupon bonds on the market that have 10 years left to maturity. The bonds make annual payments and have a par value of $1,000. If the YTM on these bonds is 10.2%, what is the current bond price?F(1 + YTM)tBond Value = C *+1(1 + YTM)t1 -YTM$1,000(1.102)10Bond Value = $82 *+1(1.102)101 -.102= $82 * 6.0921 +$1,0002.6413C = 8.2% * $1,000 = $82; YTM = 10.2%; t = 10 years; F = $1,000= $499.55 + $378.60 = $878.151
2. Volbeat Corporation has bonds on the market making annual payments, with 17 years to maturity, a par value of $1,000, and a price of $956, the bonds yield 9.1%. What must the coupon rate be on the bonds?F(1 + YTM)tBond Value = C *+1(1 + YTM)t1 -YTM$1,000(1.091)17$956 = C *+1(1.091)171 -.091$956 = C * 8.4890 + $227.50Bond Value = $956; YTM = 9.1%; t = 17 years; F = $1,000Coupon rate =2$956 - $227.50 = C * 8.4890$728.50 / 8.4890 = C$85.82 = C $85.82$1,000= 8.58%Barnes Co. has bonds on the market making annual payments, with 15 years to maturity, a par value of $1,000, and a price of $971, the bonds yield 8.3%. What must the coupon rate be on the bonds?F(1 + YTM)tBond Value = C *+1(1 + YTM)t1 -YTM$1,000(1.083)15$971 = C *+1(1.083)151 -.083$971 = C * 8.4049 + $302.39Bond Value = $971; YTM = 8.3%; t = 15 years; F = $1,000Coupon rate =$971 - $302.39 = C * 8.4049$668.61 / 8.4049 = C$79.55 = C $79.55$1,000= 7.95%
3. Hardwell Inc. issued 14-year bonds one year ago at a coupon rate of 6.9%. The bonds make semi-annual payments. If the YTM of these bonds is 5.5%, what is the current dollar price assuming a $1,000 par value?F(1 + YTM/2)2t+1(1 + YTM/2)2t1 -(YTM/2)$1,000(1 + .055/2)26Bond Value = $69/2 *+1(1 + .055/2)261 -(.055/2)= $34.50 * 18.4023 +$1,0002.0245C = 6.9% * $1,000 = $69; YTM = 5.5%; t = 13 years; F = $1,000= $634.88 + $493.94 = $1,128.823Bond Value = C/2 *
4. You find a zero coupon bond with a par value of $10,000 and 24 years to maturity. If the YTM on this bond is 4.6%, what is the price of the bond? Assume semi-annual compounding periods.F(1 + YTM/2)2tBond Value == $10,000 / 2.9787YTM = 4.6%; t = 24 years; F = $1,0004$10,000(1 + .046/2)48Bond Value == $3.357.14If you invest $3,357.14 today, how much will you have in 24 years if you earn 4.6% interest compounded semi-annually?FV = $3,357.14 * (1 + .023)48 FV = PV * (1 + r)t PV = $3,357.14; r = 2.3% (semi-annual rate); t = 48 (semi-annual period) = $10,000.00Bond Pricing with Semi-Annual Coupons
5. PS 1 - Prufrock, Inc. has 7.9% coupon bonds on the market that have 6 years left to maturity. The bonds make annual payments and have a par value of $1,000. If the YTM on these bonds is 9.9%, what is the current bond price?F(1 + YTM)tBond Value = C *+1(1 + YTM)t1 -YTM$1,000(1.099)6Bond Value = $79 *+1(1.099)61 -.099= $79 * 4.3681 +$1,0001.7619C = 7.9% * $1,000 = $79; YTM = 9.9%; t = 6 years; F = $1,000= $345.08 + $567.56 = $912.64PS 2 - Guetta Enterprises issued 17-year bonds one year ago at a coupon rate of 7.3%. The bonds make semi-annual payments. If the YTM of these bonds is 5.3%, what is the current dollar price assuming a $1,000 par value?F(1 + YTM/2)2t+1(1 + YTM/2)2t1 -(YTM/2)$1,000(1 + .053/2)32Bond Value = $73/2 *+1(1 + .053/2)321 -(.053/2)= $36.50 * 21.3953 +$1,0002.3093C = 7.3% * $1,000 = $73; YTM = 5.3%; t = 16 years; F = $1,000= $780.93 + $433.03 = $1,213.96Bond Value = C/2 *