### CFA Practice Question

Consider a situation where an investor wants to invest in a semi-annual coupon-paying bond maturing 13 years from now with a face value of \$1,000,000 and a coupon payment of \$6,423. The corresponding YTM is said to be 6.981%. What should the price of the bond be today?
A. \$518,417
B. \$581,417
C. \$511,217
Explanation: When coupons are received twice per year, the value of the coupon bond can be specified as follows: P = C([1-{1 / (1+[YTM / 2])t}]/[YTM / 2]) + F / (1+[YTM / 2])t, where P = bond value, C = semi-annual coupon payment, t = number of semi-annual periods until maturity, YTM = yield to maturity, and F = face value. Here, C = \$6,423, t = 26, YTM = 0.06981, and F =\$1,000,000. It follows that: P =6,423 x ([1 - 1/{1+. 06981 / 2}26] / [.06981 / 2]) + 1,000,000 / (1+. 06981 / 2)26 = \$518,417.

User Comment
quincy n=26, pmt=6.423, i=3.49, fv=1000, pv=518.474
Xocrevilo Note that the coupon payment quoted is already on a semi-annual basis.
copus It is not clear that the coupon is already quoted on a semi annual basis, however, if you divide the coupon by 2, you come up with an answer of 464,115 which is not one of the options. If option c had been (none of the above), this would have been a tricky question.
apiccion Thanks Xocrevilo. I didn't catch that one.
scancubus Good thing that they mention that its already semi-annual, along with everything else being annual. It definately wouldn't be this clear in the real world, so I can understand their reasoning.
kellyyang yes, made a mistake with coupon pmt. Tricky one!
jonnyp Having a hard time understanding how you know to put 6.423 as pmt?
cslau83 my BAII Plus got 514981 instead...
cslau83 Accidentall set C/Y = 2 ... my bad
Polagaro OMG i was 15 minutes with this one, i was assuming que coupon was annual and didn´t understand why i wasn´t able to solve something so easy. Tricky one!
GBolt93 Did the exact same thing. now kicking myself for missing something so easy.
Lambo83 What the hell is the equation articulated in the answer explanation? Don't get it and never seen it before.