Suppose that a Detroit municipal bond was bought at issue for $5,000. Its maturity was ten years, the face value was $6,000 and the coupon rate was 5%. a) What was the initial yield to maturity? b) Suppose that in year 5 the coupon was cut to 2% and the face value was cut by $5,250 due to bankruptcy. What annual return did the bond holder experience? Is it greater than or less than the yield ot maturity? Why? c) If the bond holder could have sold in year four at a price of $5,100 (after receiving the year 4 coupon) would s/he have been better off than waiting until year 5 and experiencing the bankruptcy (as described in part b))? Explain.
a. The yield to maturity of the bond is calculated as =RATE(nper,pmt,pv.fv) where nper =10 years, pmt = 5%*6000 =$300, pv= purchase value =5000 and fv -face value =6000
The yield to maturity of the bond =RATE(10,300,-5000,6000) = 7.42%
b. Now, we calculate the price of the bond when there is bankruptcy =PV(rate,nper,pmt,fv) =PV(0.0742,5,120,750) =1010.94
Total return = 300*4+120 + 1010.94 -5000 = -2,669.06 .
prcentage return over 5 year period = -2669.06/5000 =-0.5338
Annualized (1-0.5338)^(1/5) -1 = -0.1415 = -14.15%
(c) If he had sold the bond in year 4, his YTM would be =RATE(6,300,-5100,6000) = 8.27%. So, he would have better better of since he ot a better return
Suppose that a Detroit municipal bond was bought at issue for $5,000. Its maturity was ten...
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