I have two questions I am needing help with. 1. A 7% bond is selling to yield 4
ID: 2712578 • Letter: I
Question
I have two questions I am needing help with.
1. A 7% bond is selling to yield 4 and 1/2%. The bond pays interest semi annually and the investor who owns 10,000 worthof face value bonds would receive_____ the next time interest is paid. I know the answer is $350 but I dont know how to find that answer.
2. What would be the price of a 15 year bond that originally sold for 1,000 with a 10% semiannual coupon rate if yields on similar bonds are 8%? I know the answer is 1172.92 but how do you get this answer?
Thank you!
Explanation / Answer
1) The interest paid is the coupon interest paid which is coupon interest rate 7% paid semiannually on the Bond's Face value.The semiannual coupon interest paid =(7%/2) *10000=3.5% *10000=$350, we need to divide the coupon rate by 2 because the coupon rate is given in annual terms we need to get coupon rate in semiannual terms as we are paying coupon semiannually so divide the coupon rate by 2.
2)Let P =price of Bond=?, c=coupon on Bond, y be the current yield and FV= par value, T be time to maturity
c=coupon on Bond=(10%/2)*1000=5%*1000=50,y=8%,T=15,FV=1000 , total periods are double of T so we discount over total periods of 2T.
So P=(2c/y)(1-1/(1+y/2)2T)+FV/(1+y/2)2T (formula derived in note below)
Put above given values in this formula to get,
P=(2*50/.08)(1-1/(1.04)30)+1000/(1.04)30
P=(1250)(1-.308318668)+308.318668=864.601665+308.318668
P=1172.92
(note:
P=c/(1+y/2)1+ c/(1+y/2)2+........+c/(1+y/2)2T+FV/(1+y/2)2T
P=c{1/(1+y/2)1+ 1/(1+y/2)2+........+1/(1+y/2)2T}+FV/(1+y/2)2T
1/(1+y/2)1+ 1/(1+y/2)2+........+1/(1+y/2)2T GP with first term =1/(1+y/2)1 and common ratio=r=1/(1+y/2) and no of terms=2T
Sum of GP= first term*(1-r2T)/(1-r) = 1/(1+y/2)1 * (1-1/(1+y/2)2T)/(1-1/(1+y/2))
=1/(1+y/2)1 * (1-1/(1+y/2)2T)/(y/2*(1+y/2))= 1/(1+y/2)1 * (1-1/(1+y/2)2T)*(2*(1+y/2)/y)=(1-1/(1+y/2)2T)*(2/y)
So P=(2c/y)(1-1/(1+y/2)2T)+FV/(1+y/2)2T ).