Kilgore Natural Gas has a $1,000 par value bond outstandingthat pays 9 percent a

Question

Kilgore Natural Gas has a $1,000 par value bond outstandingthat pays 9 percent annual interest. the current yield to maturityon such bonds in the market is 12 percent. Compute the price of thebonds for these maturity rates: a) 30 years b) 15 years c) 1 year Kilgore Natural Gas has a $1,000 par value bond outstandingthat pays 9 percent annual interest. the current yield to maturityon such bonds in the market is 12 percent. Compute the price of thebonds for these maturity rates: a) 30 years b) 15 years c) 1 year

Explanation / Answer

a. We have N=30yrs, M=Maturity value of bond = 1000, Couponrate = 9%. So INT = 9%xM = 9%*1000 = 90, & Desired yield tomaturity Kd=12%
Value of Bond Vb = INT(PVIFA Kd,N) + M(PVIF Kd,N) Putting values we get Vb=90(PVIFA 12%,30) + 1000(PVIF 12%,30) ie Vb = 90*[1/Kd - 1/{Kd(1+Kd)^N}] +1000*(1/(1+Kd)^N ie Vb = 90*[1/12% - 1/{12%*(1+12%)^30}] +1000*(1/(1+12%)^30) ie Vb = 90*(1/12% - 0.2781) + 1000*0.03338 ie Vb = 90*8.0552 + 333.80 ie Vb= 1058.77 So value of Bond is 1058.77 when YTM is 12% & Maturityperiod is 30 Years
b. We have N=15yrs, M=Maturity value of bond = 1000, Couponrate = 9%. So INT = 9%xM = 9%*1000 = 90, & Desired yield tomaturity Kd=12%
Value of Bond Vb = INT(PVIFA Kd,N) + M(PVIF Kd,N) Putting values we get Vb=90(PVIFA 12%,15) + 1000(PVIF 12%,15) ie Vb = 90*[1/Kd - 1/{Kd(1+Kd)^N}] +1000*(1/(1+Kd)^N ie Vb = 90*[1/12% - 1/{12%*(1+12%)^15}] +1000*(1/(1+12%)^15) ie Vb = 90*(1/12% - 1.5225) + 1000*0.1827 ie Vb = 90*6.8109+ 182.70 ie Vb= 795.68 So value of Bond is 795.68 when YTM is 12% & Maturityperiod is 15 Years
c. We have N=1yrs, M=Maturity value of bond = 1000, Couponrate = 9%. So INT = 9%xM = 9%*1000 = 90, & Desired yield tomaturity Kd=12%
Value of Bond Vb = INT(PVIFA Kd,N) + M(PVIF Kd,N) Putting values we get Vb=90(PVIFA 12%,1) + 1000(PVIF 12%,1) ie Vb = 90*[1/Kd - 1/{Kd(1+Kd)^N}] +1000*(1/(1+Kd)^N ie Vb = 90*[1/12% - 1/{12%*(1+12%)^1}] +1000*(1/(1+12%)^1) ie Vb = 90*(1/12% - 7.4405) + 1000*0.8929 ie Vb = 90*0.8929 + 892.90 ie Vb= 973.26 So value of Bond is 973.26 when YTM is 12% & Maturityperiod is 1Years b. We have N=15yrs, M=Maturity value of bond = 1000, Couponrate = 9%. So INT = 9%xM = 9%*1000 = 90, & Desired yield tomaturity Kd=12%
Value of Bond Vb = INT(PVIFA Kd,N) + M(PVIF Kd,N) Putting values we get Vb=90(PVIFA 12%,15) + 1000(PVIF 12%,15) ie Vb = 90*[1/Kd - 1/{Kd(1+Kd)^N}] +1000*(1/(1+Kd)^N ie Vb = 90*[1/12% - 1/{12%*(1+12%)^15}] +1000*(1/(1+12%)^15) ie Vb = 90*(1/12% - 1.5225) + 1000*0.1827 ie Vb = 90*6.8109+ 182.70 ie Vb= 795.68 So value of Bond is 795.68 when YTM is 12% & Maturityperiod is 15 Years
c. We have N=1yrs, M=Maturity value of bond = 1000, Couponrate = 9%. So INT = 9%xM = 9%*1000 = 90, & Desired yield tomaturity Kd=12%
Value of Bond Vb = INT(PVIFA Kd,N) + M(PVIF Kd,N) Putting values we get Vb=90(PVIFA 12%,1) + 1000(PVIF 12%,1) ie Vb = 90*[1/Kd - 1/{Kd(1+Kd)^N}] +1000*(1/(1+Kd)^N ie Vb = 90*[1/12% - 1/{12%*(1+12%)^1}] +1000*(1/(1+12%)^1) ie Vb = 90*(1/12% - 7.4405) + 1000*0.8929 ie Vb = 90*0.8929 + 892.90 ie Vb= 973.26 So value of Bond is 973.26 when YTM is 12% & Maturityperiod is 1Years c. We have N=1yrs, M=Maturity value of bond = 1000, Couponrate = 9%. So INT = 9%xM = 9%*1000 = 90, & Desired yield tomaturity Kd=12%
Value of Bond Vb = INT(PVIFA Kd,N) + M(PVIF Kd,N) Putting values we get Vb=90(PVIFA 12%,1) + 1000(PVIF 12%,1) ie Vb = 90*[1/Kd - 1/{Kd(1+Kd)^N}] +1000*(1/(1+Kd)^N ie Vb = 90*[1/12% - 1/{12%*(1+12%)^1}] +1000*(1/(1+12%)^1) ie Vb = 90*(1/12% - 7.4405) + 1000*0.8929 ie Vb = 90*0.8929 + 892.90 ie Vb= 973.26 So value of Bond is 973.26 when YTM is 12% & Maturityperiod is 1Years

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