Question

Suppose that a 9-year bond with a face value of 1000 dollars pays semiannual coupons at a rate of 5.2 percent per half year. The issuer of the bond has the option to redeem it at the time of the 16th coupon for 2100 dollars, or at maturity for 2000 dollars. Find the price that will guarantee an investor a yield rate of at least 12.3 percent convertible semiannually, regardless of when the bond is redeemed.

Price when redeemed at 16th coupon:

Nper = 16
FV = 2100
PMT = 1000 * 5.2% = 52
Rate = 12.3%/2 = 6.15%

Bond price can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(6.15%,16,-52,-2100)
= \$1,328.30

Price when redeemed at 16th coupon = \$1,328.30.

Price when redeemed at maturity:

FV = 2000
Nper = 9 * 2 = 18
PMT = 52
Rate = 6.15%

Bond price can be calculated by using the following excel formula:
=PV(rate,nper,pmt,fv)
=PV(6.15%,18,-52,-2000)
= \$1,239.83

Price when redeemed at maturity = \$1,239.83

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