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You are planning on buying $100,000 face value of Australian Commonwealth Government Bonds. The bonds mature...

You are planning on buying $100,000 face value of Australian Commonwealth Government Bonds. The bonds mature on 15 February 2022 and have a coupon rate of 4.75%. If your purchase will settle on 27 April 2012, and the quoted yield for the bond is 3.92%, what is the cash price of the bonds to the nearest dollar?

Solutions

Expert Solution

Price of bond = Present value of all coupon payments at yeild+present value of redemption price at yeild
Yeild = 3.92% or 0.0392
Redemption value=face value=$100,000
Coupon=$100,000*4.75%=$4750
calculation of Time to redemption
Period (in years) from 27th april 2012 to 15th feb 2013
= 294days/365 days a year
= 0.8055 year
period from 15 th feb 2013 to 15th feb 2022 = 9 years
Total time to redemption = 9years+0.8055year
= 9.8055 years
Price of the bond = [coupon*PVAF(yeild,time)]+PVF(Yeild,time)*redemption value
= [coupon*PVAF(3.92%,9.8055years)]+100,000*PVF(3.92%,9.8055yrs)
= (4750*8.0129)+(100,000*0.6859)
= 38061+68590
= $106,651
Cash price of bond is $106,651
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jeff jeffy answered 1 year ago
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