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Fri 12 Nov, 2010 04:23 pm
Its a questions from Mishkin/Earkin's Fianncial Markets & inst. and ques is from the Bonds' chapter and goes like word to word.A 2-year $1,000 par zero-coupon bond is currently priced at $819.00. A 2-year $1,000 annuity is currently priced at $1,712.52. If you want to invest $10,000 in one of the two securities, which is a better buy?
My professor solves it likeWith PV = $819, FV = $1,000, PMT = 0 and N = 2, the yield to maturity on the two-year
zero-coupon bonds is 10.5% for the two-year annuities, PV = $1,712.52, PMT = 0,FV = $2,000 and N = 2 gives a yield to maturity of 8.07%. The zero-coupon bonds are the better buy.
My question when the second instrument is an annuity .Why is it being treated as PMT =0 and FV=2000.Its not a bullet maturity.
@eva mendes,
Shouldn't it be PMT = $1000 and FV = 0?
@engineer,
It's been since 1992 that I had that class, but I think it's stated correctly. Future value would be the maturity payout. The 0 payment and the 2 are in there just to accommodate the normal bond formula.
@roger,
Maybe I don't understand the meaning of "A 2-year $1,000 annuity is currently priced at $1,712.52." I thought that meant that each year, you would receive a payment of $1000 for two years, so PMT = 1000 and at the end of two years the annuity would be used up and the FV=0. I went to this
calculator and put in those values. I got a present value of $1,781.55, not what was in the problem. I must be reading it wrong but my understanding seemed to work with what the calculator was asking for.
@engineer,
I didn't pick up on the word annuity, and assumed a zero interest bond with a two year maturity.
@eva mendes,
yes eva your observations are correct
my observation is that the erroneous answer is lifted from a doc rather than something your professor solved
[DOC] M10_MISH1438_06_IM_C10.doc - mishkin_6e_531438_IM_ch10
@fobvius,
Even I think so.Bcoz If I treat this as a simple annuity where you are just paid back 1000 for 2 years. The YTM comes out to be some 11%. I wud have easily ignored my prof's solution but what bogs me is the author Mishkin solves the same way in one of his edition .This totally violates the time value of money if you treat 1000 each year and 2000 after 2 years as same.
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