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 Contributed Comments 12
| 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. |