A firm issues a $10 million bond with a 6% coupon rate, 4-year maturity, and annual interest payments when market interest rates are 7%. The initial book value of the bonds is: A. $9,400,000. B. $9,661,279. e. $10,000.000. D. $10,338.721. plz help…
B? Coupon rate is less than market rate, hence the bond will be selling at a discount. N - 4 I/Y - 7 PMT - 600,000 FV - 10,000,000 CTP PV = 9,661,278.87
Ya …but A or B?? C n D can be eliminated…by just reading question… plz help…
B is the answer. Ditchdigger2CFA explained it well. Milos
Thnx a lot…
There’s a better way to do the problem. Eliminate C and D immediately. Now to decide between A and B, imagine that it was a zero. Then it would have duration = 4 so a 1% change in yield would cause the bond to drop 4% to 9.6 M. Since it’s not a zero, it drops in value less so answer must be B. The same process lets you eyeball a problem and say, uh, I dunno, the bond drops 3.5% because the duration is less than a zero but not that much less. You can do the problem in 2 seconds and get on to the next one.
Amazing…Thanx a ton…
JoeyDVivre…i was not able to follow ur explanation…i know thats very dumb to say…but better safe then sorry !!! Agreed eliminate C and D …coz market yield > bond yield implies Bond price will fall down. To start with i got lost at this point…“imagine it was zero”…??? thanks for ur patience.
Bee Wrote: ------------------------------------------------------- > JoeyDVivre…i was not able to follow ur > explanation…i know thats very dumb to > say…but better safe then sorry !!! > > Agreed eliminate C and D …coz market yield > > bond yield implies Bond price will fall down. > > To start with i got lost at this > point…“imagine it was zero”…??? > > > thanks for ur patience. When you get to fixed income you’ll learn about calculating bond duration. Joey’s method didn’t even phase me as an option, but it worked a lot better. “Now to decide between A and B, imagine that it was a zero. Then it would have duration = 4 so a 1% change in yield would cause the bond to drop 4% to 9.6 M.” By definition zero coupon bonds have duration (aka interest rate risk) equal to their YTM. Since this is not a zero, the drop is not quite to 9.6M.
It makes much more sense now…!! Thank you ditchdigger2CFA…though its not crystal clear…but am sure it will make complete sense when i am done with fixed income section.
Joey … that is very smart approach to look at the problem … even after reading fixed income section many times and after passing L1 with >70% marks in all subjects I haven’t thought about this problem the way you sought the solution … thanks for adding a valuable technique to my arsenal … (you can never learn enough) Let me clarify joey’s answer a bit … zero coupon bonds have a duration equal to their maturity. In this case make an assumption as if it is a zero coupon bond. The maturity is 4 years so duration is also 4. Duration of 4 means 1% change in yield will move the price of bond by 4% in opposite direction. There is a 1% difference in yield (7% required by market and 6% coupon). If it were a zero coupon bond than its value must have been 9.6M, but it is a coupon bond so it must be little higher than that … so B will the correct answer. $9.4 M is not a possible answer by any means. Note: as explained in FSA textbook, to calculate book value of bonds we use the market rate at the time of issuance of bond. Market rates at any time in future are not used in BV calculation. If the problem would have added a lit confusion by mentioning current yield required by market, say, 8% than this additional information is only for adding confusion to problem.