Question

d) The company is planning to issue 10-year semi-annual coupon bonds with a coupon rate of 6% and a face value of $1,000. The effective annual yield to maturity of investors is expected to be 8% per annum. Calculate the required number (expressed in integer) of semi-annual coupon bonds to raise $20 million.

e) Alternatively, XYZ Ltd is looking into issuing 15-year zero-coupon bonds with a face value of $1,000. The desired nominal yield to maturity of investors is expected to be 8% compounded semi-annually. Calculate the required number (expressed in integer) of zero-coupon bonds to raise $20 million.

Answer 1

d) Number of Periods =10*2 =20
Semi annual coupon =6%*1000/2 =30
Semi annual YTM =(1+Effective annual Yield)^(1/2)-1 =(1+8%)^(1/2)-1 =3.92304845413265%
Price of Bonds =PV of Coupons+PV of Par value
=30*((1-(1+3.92304845413265%)^-20)/3.92304845413265%)+1000/(1+3.92304845413265%)^20=873.695564358936
Number of bonds =20,000,000/873.695564358936 =22891.27
So bonds to be raised 22892

e) Number of Periods =15*2 =30
Price of Bond =Face Value/(1+r)^n =1000/(1+8%/2)^30=308.31866797342
Number of zero coupon bonds =20000000/308.31866797342=64867.95 or 64868