An investor owns a 3000$ par-value 12% bond with semiannual coupons. The bond wi

Question

An investor owns a 3000$ par-value 12% bond with semiannual coupons. The bond will mature at par at the end of fourteen years. The investor decides that a ten-year bond would be preferable. Current yield rates are 6% convertible semiannually. The investor uses the proceeds from the sale of the 12% bond to purchase an 8% bond with semiannual coupons, maturing at par at the end of ten years. Find the face value of the 8% bond.

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Explanation / Answer

Current Yield = 6%

Semi Annual Coupon = 12%*3000 *1/2 = 180

Current Price of 12% Bond = Semi Annual Coupon /(Current Yield/2)

Current Price of 12% Bond = 180/(6%/2)

Current Price of 12% Bond = 6000

Half Year YTM = rate(nper,pmt,pv,fv)

Nper  (indicates the semi annual period) = 14*2 = 28

PV (indicates the price) = 6000

PMT (indicate the semi annual payment) = 12%*3000 *1/2 = 180

FV (indicates the face value) = 3000

Rate (indicates YTM) = ?

Half Year YTM = rate(28,180,-6000,3000)

Half Year YTM = 1.563%

Purchase price of new bond = Proceed from 12% Bond

Purchase price of new bond = 6000

No of semi annual period = 10*2 = 20

Purchase price of new bond = Semi Annual Coupon*PVIFA(rate,nper) + Face Value*PVIF(rate,nper)

6000 = 8%*1/2*Face Value *PVIFA(1.563%,20) + Face Value*PVIF(1.563%,20)

6000 = Face Value*(4%* 17.0625 + 0.73331)

Face Value = 6000/1.41581

Face Value = $ 4237.86

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