Question

•Company Z has issued bonds with a par value of $1000, 20 years to maturity, and a coupon rate of 4%. The bond makes semiannual payments. The yield to maturity (YTM) is 6% per annum.

•What is the current price of the bond?

•What is the effective annual yield on this bond?

•Is this a discount or a premium bond? Discuss.

•If the market interest rate increases, what happens to this bond price. Discuss.

•If this bond would sell at par what could you tell about the YTM?

Please show the formulas

Answer 1

Semi annual YTM =6%/2 =3%
Number of Periods = 20*2 =40
Par value = 1000
Coupon = 4%*1000/2 = 20

Price of the bond =PV of Coupons + PV of par Value = 20*(1-(1+3%)^-40)/3% +1000/(1+3%)^40 = 768.85

Effective annual Yield =(1+Semiannual yield)^2-1 =(1+3%)^2-1 =6.09%

This is discount bond because price of bond is less than par value. This happen when coupon rate is less than YTM.

If market rate increases then bond price decreases. This is because higher the YTM lower the bond price. Bond price is inversely related to interest rate.

If bond would sell at par then YTM and coupon rate should be same. YTM = Coupon rate when bond is sold at par.