In: Finance
You are planning on buying $100,000 face value of Australian Commonwealth Government Bonds. The bonds mature on 15 February 2027 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 5.81%, what is the cash price of the bonds to the nearest dollar?
Price of bond | = | Present value of all coupon payments at yeild+present value of redemption price at yeild | |||||||||||
Yeild | = | 5.81% or 0.0581 | |||||||||||
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 2027 | = | 14 years | |||||||||||
Total time to redemption | = | 14 years+0.8055year | |||||||||||
= | 14.8055 years | ||||||||||||
Price of the bond | = | [coupon*PVAF(yeild,time)]+PVF(Yeild,time)*redemption value | |||||||||||
= | [coupon*PVAF(5.81%,14.8055years)]+100,000*PVF(5.81%,14.8055yrs) | ||||||||||||
= | (4750*9.7525)+(100,000*0.4334) | ||||||||||||
= | 46324.28+43338.09 | ||||||||||||
= | $89,662.37 | ||||||||||||
PVAF and PVF | For fraction time (9.8055 yrs) | Can be calculated using financial calculators or excel | |||||||||||
Cash price of bond is $89,662.37 | |||||||||||||
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