 # Annualized Return (Reinvestment Rate)

A 30-year 8% bond is purchased at par and held for 10 years. It is then sold at 98 for a YTM of 8.20%. The reinvestment rate on the coupons is 10%. The true annualized return on the bond over the 10-year period is closest to: A) 8% B) 8.2% C) 8.56% D) 10% I know the answer intuitively, but can someone do the math for me? Thanks

I’m not sure on this, but I’m giving it a shot: Start with: N=10*2=20 I/Y=10/2=5 PMT=8/2=4 PV=0 FV–>132.26 Then: FV=132.26+98=230.26 PV=-100 N=20 PMT=0 I/Y–>4.26*2=8.52% Closest to C.

Presuming this is a bond that pays semiannually: 1. find the FV of the coupons reinvested at 10%: N=20, I/Y=5, PV=0, PMT=80, CPT FV=1,322.64 2. Add to it the proceeds from the sale of the bond: 980 Total income generated by the initial 1,000 investment would be 2,302.64, make this your FV 3. Determine the annualized return: N=20, PV=-1,000, PMT=0, FV=2,302.64, CPT I/Y=4.25846~4.26% semiannual, that would be a bond equivalent of 8.52%, say C.

cheros16 Wrote: > I know the answer intuitively, but can someone do > the math for me? I think it’s good to do the math once but don’t waste your time performing calculations on the actual exam if you understand what the answer should be and can eliminate the other choices.

In this case, it cannot be 8% (because coupons are reinvested at 10%), and it cannot be 10% (because coupons are at 8% and the sale price is lower than the par value paid at the beginning), so neither A nor D are correct. You have a 50%-50% chance of guessing the right answer. Other than by calculus, I don’t see how one would get C over B.

8.2% YTM assumes that you can reinvest at 8.2%. Since you’re reinvesting at 10%, it must be > 8.2%.