# How to Calculate Dividends That Have Been Reinvested

by Ryan Menezes

A bond that matures after one year pays a fixed dividend at the end of that period. If it matures any sooner than that, as money market instruments do, you can then reinvest the dividends at the bond's coupon rate. As a result, the interest may be compounded several times with the year. During each maturation, the bond will yield a coupon that's a fraction of the stated annual yield. The total annual percentage yield will exceed the stated annual coupon due to the compounded returns.

1. Divide the number of days in a year by the bond's maturity. For example, if a bond assumes a financial year of 360 days, as many do by convention, and it matures after 45 days, divide 360 by 45, which yields 8, the number of times that the bond pays each year.

2. Divide the bond's coupon, which is its interest rate, by the number of times it pays out each year. For example, if you invest the returns from a bond with a 0.065 coupon, divide 0.065 by 8, yielding a periodic coupon of 0.008125.

3. Add 1 to the periodic rate. With this example, the result is 1.008125.

4. Raise this multiplier to the power of the number of times that the bond matures each year. 1.008125. raised to the power of 8, gives 1.0669.

5. Multiply this total multiplier by the bond's principal. For example,if the bond has a principal of \$10,000, \$10,000 multiplied by 1.0669 gives a total of \$10,669.

6. Subtract the bond's principal. In this case, this gives \$669. This is the value of the dividends after a year if you have reinvested them.

#### References

• "Bonds and Bond Derivatives"; Miles Livingston; 1999
• "Modeling Structured Finance Cash..."; Keith A. Allman; 2010

#### Resources

• "Fixed Income Mathematics"; Robert Zipf; 2003
• "Bond Markets: Analysis And Strategies"; Fabozzi; 2007