In the CFA exam, Net Present Value (NPV) and Internal Rate of Return (IRR) are two common topics. One should know that, during capital project evaluation, if NPV is used, we assume the cash inflow can be re-invested at the required rate of return while if IRR is used, we assume the cash inflow can be re-invested at IRR.

This is similar for bonds. The yield to maturity (YTM) calculated is based on the assumption that the cash inflows can be re-invested at the YTM. (And that’s why there is re-investment risk as the coupon payments may not be re-invested at YTM).

Therefore, you may be asked to calculate how much re-investment income is required in order to achieve the stated YTM. Don’t be sacred! Basically, it is just asking “what is the future value of the coupon payments after subtracting the coupon payments” or “how much extra cash you need to get at the end in order to have true YTM as stated”.

For example, if the bond is priced at $800 with par of $1000 and mature in 10 years with annual 10% coupon payment. What is the YTM and what is the re-investment income?

First, find the YTM:  [N] =10, [PV]= – 800, [PMT] = 100, [FV] = 1000, then [CPT][I/Y] gives YTM = 13.8%.

Now we want to find the FV of the payments, so put [PV]=0 and [CPT][FV] = -1915.5.

Ignore the –ve sign, then the “extra cash” generated from re-investment is 1915.5 – 10 * 100 = 915.

It means that you have to be able to reinvest the $1000 coupon payment (10 years X $1000 / per year) and get $915 extra cash at the end the bond life (10 years later) in order to have a true YTM = 13.8%!