Question

Rick bought a 25-year bond when it was issued by Macroflex Corporation 10 years ago. The bond has a $1,000 face value and a coupon rate equal to 7 percent and the coupon is paid every six months. If the yield on similar-risk investments is 5 percent,

a) What is the current market value (price) of the bond?

b) Suppose interest rate levels rise to the point where such bonds now yield 9 percent. What would be he price of Macroflex bond?

c) At what price would Macroflex bonds sell if the yield on them was 7 percent?

d) What do you observe regarding the relationship between interest rate (YTM) bond's price?

e) What do you observe regarding the relationship between coupon, YTM and the bond's price?

**Please show your work so I can understand it**

Answer 1

Number of Years = 15*2 = 30
Coupon = 7%*1000/2 = 35
YTM semiannual = 5%/2 = 2.5%
a) Price of Bond = PV of Coupons + PV of par Value = 35*(1-(1+2.5%)^-30)/2.5% +1000/(1+2.5%)^30 = 1209.30

b) YTM semiannual = 9%/2 = 4.5%
Price of Bond = PV of Coupons + PV of par Value = 35*(1-(1+4.5%)^-30)/4.5% +1000/(1+4.5%)^30 =837.11

c)  YTM semiannual = 7%/2 = 3.5%
Price of Bond = PV of Coupons + PV of par Value = 35*(1-(1+3.5%)^-30)/3.5% +1000/(1+3.5%)^30 =1000

d) Higher the YTM lower is the price.

e) If Coupon rate is less than YTM then the bond is sold at discount and price is less than par value.
If Coupon rate is greater than YTM then the bond is sold at premium and price is more than par value.

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