A 5 percent, semi-annual bond with a par value of 1000 matures in 10 years and is selling for 925.61 for a 6 percent yield to maturity. Over the life of the bond, the reinvestment income that must be earned in order to realize that 6 percent yield is closest to: A. $157.63 B. 171.75 C. 232.02 D. $ 246.04
B
Total cash flows from bond = 2.5%*1000*20 + 1000 = $ 1500 To get a 6% YTM you need 925.61*1.03^20 = 1671.75 difference is 171.75 => B
i also got B. 925.61*(1.03)^20-(1000+5*10) = 171.75
another way of doing this: the FV of the coupon payments is 671.7594, since N=20 I/Y=3 PMT=25 PV=0 FV=671.75 gross amount of coupons is: 25*20=500 Difference is 671.75-500= 171.75
a good one, bartheezz.
to nail this concept, here you go: it’s from schweser. posted this question a couple of days ago. 3 years ago, an investor purchased a $1000 face, 4.5% semiannual coupon bond with 7 years to maturity priced to yield at 6.5% for $888.94. The reinvestment income that must be generated over the life of the bond for the investor to realize a yield of 6.5% is closest to: a) $72 b) $76 c) $80 d) $83
Following your footsteps … barthezz 76.01 = Ans is C N=14 I/Y= 3.25 PMT=22.5 PV=0 FV=391.01 gross amount of coupons is: 22.5*14=315 Difference is 391.01-315= 76.01 - Dinesh S
or 888.94*(1.0325^14) - (1000 + 22.5*14) = 1391.02 - 1315 = 76.02
B. is correct since you arrive at the same number doing it the non-barthezz way as well.
highparkcfa Wrote: ------------------------------------------------------- > B. is correct since you arrive at the same number > doing it the non-barthezz way as well. non-barthezz way (shocked to see the exact same answer :-))) ) =888.94*(1.0325)^14 - (1000 +22.5*14) =888.94*1.5648 - 1315 =1391.0197- 1315 =76.0197 - Dinesh S
the are many roads leading to rome… or what is the correct saying? congrats to all. answer is b.
im not getting the right answers at all… for the first question, for example… as i see it, we’re only concerned with re-investment income… that is, income from reinvested coupons… now, there are only 19 coupons that provide reinvestment income (the final coupon is received on maturity, and so does not provide any reinvestmetn income)… so, the FV of coupon payments is 627.92 N=19 I/Y=3 PMT=25 Total coupons is (19*25)=475 therefore, REINVESTMENT income should be 152.92 ??? (which isnt one of the answers anyway) i dont understand why we include the final coupon if it doesnt provide ‘reinvestment’ income
the book says to use the entire 20 coupons… so with that it is 171.75. in fact the calculation shown is: A 5 percent, semi-annual bond with a par value of 1000 matures in 10 years and is selling for 925.61 for a 6 percent yield to maturity. Over the life of the bond, the reinvestment income that must be earned in order to realize that 6 percent yield is closest to: 925.61*1.03^20 - (1000+25*20) = 171.75 as barthezz has shown above.
ahhhh dont worry, i get why you have to use 20 coupons now… technically, you are only getting reinvestment income on 19 of those coupons, so technically, you should only calculate it with 19 coupons… BUT, when using the FV function on the calculator, by using N=19, its assuming the 19th payment was on maturity, thus receiving no interest… (maybe using BGN would fix that)… either way, by using N=20, the coupon received at maturity is cancelled out by the 20th coupon in the total coupon calculation…