There is a puzzling thing that is bothering me regarding bonds and I would like to have some help. The following is the situation I am dealing with.
A 20-yr 8% bond has semi=annual coupons and a face amount of 100. It is quoted at a purchase price of 70.400. Smith purchases this bond and sells it to Jones in 5 yrs right after Smith receives his 10th coupon. Jones pays 112.225. Smith is able to reinvest his coupons at a bank that offers 6% nominal interest convertible semiannually.
I understand that the internal rate of return earned by Smith is equal to 19.0% because
$$70.4=112.225v^{10}_j+4a_{\overline{10}\rceil j}$$
has a solution $j \approx 9.5\%$
I also understand that Smith can reinvest his coupons which amounts to
$$4s_{\overline{10}\rceil j} \approx 45.86$$
at the time he sells his bond.
However, the average annual rate of return can be calculated fro
$$112.225+45.86 = 70.4(1+i)^5$$
where $i \approx 17\%$
This makes no sense to me. Why is it that Smith reinvested his money and the rate of return becomes smaller from 19% to 17%?
I would appreciate any help.
I think you should use:
$112.225+45.86=70.4(1+i)^9$
which gives approx. $9.4\%$ for half-yearly rate of return.
To be more accurate, the $6\%$ interest applies only on $9$ coupon deposits, since the bond is sold immediately after receiving the last ($10th$) coupon of $\$4$.