Question

31. A coupon bond pays annual interest, has a par value of $1,000, matures in 12 years, has a coupon rate of 8%, and has a yield to maturity of 7%.

    1. 1) Calculate the price of the bond and the Current Yield.

    2. 2)   The Macaulay Duration for this bond is 8.29 years, then what is the

       Modified Duration?

    3. 3) Suppose you sell the bond at $1000 two years later. The reinvestment return

       during these two years is 6%. What is the realized compound return?

    4. 4) Suppose you purchase the bond three months after its issuance, what is the

       invoice price you need to pay?

    5. 5) Suppose the bond is embedded with a call provision, and your purchase

       price is the same with the price calculated in part 1). One year later, the bond is called by the issuer at $1050 due to the favorable interest rate. Calculate the Yield-to-Call.

Answer 1

1. Price of the bond using financial calculator

Feed N = 12

I/Y = 7

PMT = 80

FV = 1000

Compute PV we get 1079.43

Current Yield = Coupon / Full Price = 80 / 1079. 43 = 7.41%

2) Modified Duration = Macaulay Duration / (1+ YTM) = 8.29 / 1.07 = 7.75

3) Future value of coupons= 80 (1+ 6%)^1 + 80 = 164.80

Selling Price = 1000

Total Realised value after 2 years = 1164.80

Hence, PV (1+ R)^N = FV

1079.43 (1+R)^2= 1164.80

R = 3.88%

4) If we purchase bonds after 3 months, we need to pay accrued interest on the bonds over the flat price

Full Price = Flat Price + Accrued Int

= 1079. 43 * 80 * 3 / 12 = 1099.43

5) Amount received at end of 1 year = 1050 + 80 = 1130

Hence 1079.43 (1+R) = 1130

R = 4.68%

YTM call = 4.68%