(a) Price of Zero coupon bond P= FV/(1+r)^n Where FV is the face value (redemption value, r= YTM and n= number of periods (years in this case) to maturity.
Price of Zero Coupon bond in the given case= $1,000/(1+8.6%)^10 =$1,000/2.281908639 = $438.23
Price of 8.6% coupon bond is equal to Face value ie., $1,000 since the discount rate (YTM) and coupon rate are the same at 8.6%
Price of 10.6% coupon bond, using PV function of Excel is $1,130.64
Details of working as follows:
(b): After one year, term to maturity is 9 years. With the YTM remaining at 8.6%, prices will be as follows:
Zero coupon bond: $475.92
8.6% coupon Bond: $1,000
10.60% Bond: $1,121.88
Detailed working as follows:
(c) Holding period return (HPR) during one year period= [(P1-P0) + Interest earned]/P0 Where P0 and P1 are prices at the beginning and end of the period respectively
Zero coupon bond: P1= $475.92, P0= $438.23. Interest earned=Nil., HPR= [(475.92-438.23)/438.23]*100 = 8.60%
8.6% coupon bond= P1=$1,000 P0= $1,000 Interest earned= $86. HPR= (86/1000)*100 = 8.60%
10.6% coupon Bond: P1= $1,121.88 P0=$1,130.64 Interest earned= $106. HPR= [(1121.88-1130.64)+106/1130.64]*100
=[(-8.76+106)/1130.64]*100 = 8.60%
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