- reinvestment income -

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

how did you figure out the answer?

it is C?? 79.4947 - Dinesh S

dinesh can you post your calculations?

I am going with B: \$76 PMT = -22.5 (4.5%/2 * 1000) PV = 0 i = 3.25% (6.5/2) n = 14 (Semiannual pay) FV = ? —> \$391 22.5 \* 14 = 315 (Gross amount of coupons) Reinvestment income required = \$391.02 - \$315 = \$76

florinpop, delhirocks this is what I did … 22.5 \* 14 = 315 (Gross Coupon Income) CF0 = 0 C01 = 22.5 (4.5/2*1000) F01 = 13 [14 -1 because you don’t get any interest on the 14th Coupon Payment] I = 3.25 (6.5/2) CPT -> NPV = 235.505 So the difference would be Interest income = 315 - 235.505 = 79.495 Don’t know if anything of this is correct… barthezz, what is the correct answer? - Dinesh S

I just dont know how correct it is to compare sum of cupons at different times with a future or present value first of all the bond has 7 years all togheter or was bought 3y ago and has 7 y to maturity? If it has a life of 7y isn’t the yield 6.5% already? thanks

Logic behind it is this: You are receiving \$22.5 every 6 months, which you are taking out as cash, you are not reinvesting them. Therefore, you will get the 6.5% return only if you reinvest those \$22.5 payments at 6.5%. So, just calculate the futyre value of those payments at 6.5%, and consider only the return generated by them. That is, their future value minus their sum (14*\$22.5), that’s the reinvestment income you need to have to get the 6.5% promised rate. So, in reality when it says you get a return of 6.5%, it is not really correct, unless you assume that you reinvest the payments you receive at the same rate . Dreary

B. Coupon Payments = 315 Yield of 6.5 == >888.94 (1.0325^14)= 1391 Face Value at Maturity = 1000 Reinvestment Income = 1391 – 1000 -315 = 76

Dinesh…I think you get coupon along with the last payment. So if its a 2 year semiannual pay Note @ 5%, its CF will be 50, 50, 50 & 1,050. dinesh.sundrani Wrote: ------------------------------------------------------- > florinpop, delhirocks this is what I did … > > 22.5 \* 14 = 315 (Gross Coupon Income) > > CF0 = 0 > C01 = 22.5 (4.5/2*1000) > F01 = 13 [14 -1 because you don’t get any interest > on the 14th Coupon Payment] > I = 3.25 (6.5/2) > CPT -> NPV = 235.505 > > So the difference would be Interest income = 315 - > 235.505 = 79.495 > > Don’t know if anything of this is correct… > barthezz, what is the correct answer? > > - Dinesh S

This is an interesting question. Agree with the answer B. barthezz can you give out the answer now?

sorry guys, was out of the house until now. the correct answer is B. congrats