# Fixed Income: Reinvestment income

Can anyone tell me how to calculate reinvestment income in fixed coupon bond? You help will be appreciable.

I think you take the individual coupon payments and discount them with individual spot rates. thats is reinvestiment income.

I haven’t got there yet but just guessing.

You’re trying to calculate the future value of a stream of cash flows: the coupon payments: use the cash flow buttons on your calculator:

PV = 0

PMT = coupon payment

i = reinvestment rate (per period)

n = number of coupon payments

Calculate FV.

Reinvestment income can make up a large portion of the return for a bond. Before beginning with calculations, it is important to understand the difference between total future dollars, which is equal to all the dollars an investor expects to receive and the total dollar return, which is equal to the dollars the investor will realize from the three sources of income for a bond (coupon payment, capital gain/loss, and reinvestment income.

We can explain it through a example:Let’s look at an investor that has \$96 to invest in a certificate of deposit (CD) that will mature in five years. The bank will pay 3% every six months, which equals a bond equivalent basis of 6%. The total future value of this investment today would be

96 x (1.03) to the tenth power = \$129.02

So the investment of \$96 for five years at 6% on a BEY will generate \$129.02 To further break it down: Total Future Dollars = 129.02 Return of Principle = 96.00 Total interest = 33.02 Now let’s turn to a bond that has a price of \$96, five-year maturity and with a coupon of 5% and YTM of 6%. As shown above an investor must generate \$129.02 to provide a yield of 6% or the total dollar return must be \$33.02. So with this bond, the sources of return are a capital gain of: \$4 (\$100 - \$96) and coupon interest of \$2.50 for ten periods or \$25. That equals \$29 without the reinvestment of the coupon payments. As we can see, this leads to a shortfall of \$4.02 when compared to the CD example above. This \$4.02 can be generated if the coupon payments are invested at a 3% semi-annual rate at the time it is paid. For the first payment the reinvestment income earned is: \$2.50 x (1.03) to 10 - 1 power - 2.50 = \$2.50 x (1.03) to 9th power = \$0.76. If you were to continue this effort, you would find the reinvestment income would equal \$4.02.

Thank you s2000 and edupristine. Now I know how to calculate reinvestment income.