# How to Calculate Spot Rate From Government Bonds

by Pedro Carrasquillo ; Updated July 27, 2017Calculating the implied spot rate on a coupon paying government-issued bond is not a complicated calculation if you have all of the necessary information. The spot rate refers to the theoretical yield on a zero-coupon Treasury security. Coupon paying government bonds are a form of debt that pays a fixed amount of interest each year and makes a principal payment when the bond matures. The amount of return earned over the lifetime of a government ecurity is referred to as yield to maturity. To calculate the spot rate requires taking into account the present and future value of a bond's cash flow.

Establish the government bond's future value cash flow. Future value is the amount of cash at a specified date in the future that is equivalent in value to a specified sum today. For example, assume a $100 five-year U.S. Treasury Note that pays $1.50 in annual interest would have a future value of $107.50. To arrive at this future value add the $100 principal payment to the $1.50 annual interest payment you receive for each of the five years of the debt obligation without compounding the interest you receive- $100 + $1.50 +$1.50 + $1.50 + $1.50 + $1.50 = $107.50.

Establish the government bond's present value cash flow. Present value is the amount of cash today that is equivalent in value to a payment, or to a stream of payments, to be received in the future. To determine the present value, each future cash flow is multiplied by a present value factor. If you do not know the present value factor use a government zero-coupon bond, such as the current price of a U.S. Treasury STRIP, as a substitute for the government bond's present value you are analyzing. A U.S. Treasury STRIP is a government bond that can be subdivided into a series of zero-coupon bonds. A zero-coupon bond is a bond in which no periodic coupon is paid over the life of the bond. Instead, both the principal and the interest are paid at the maturity date. Make sure the government zero coupon bond and the regular government coupon bond you are analyzing have the same maturity date. You can view regular government coupon bonds and zero coupon bonds price data online at financial websites.

Divide the bond's future value by the bond's present value and then raise the resultant quotient to the power of one divided by the total number of bond payments. For example, assume a five-year U.S. Treasury Note that has a future value of $107.500, a present value of $93.262, and that makes a total of 10 payments over the course of five years since most government bonds usually make the annual payment in two installment payments per year. Under, these assumptions this future value to present value discounting calculation would be 1.014 [($107.50 ÷ $93.262)^(1 ÷ 10) = 1.014].

Subtract the bond's future value to present value discounted calculation by 1. For example, if you had calculated 1.014 as the bond's future value to present value discount you would subtract 1 from 1.014 to arrive at an adjusted value 0.014.

Multiply the adjusted value by the total number of government bond payments made in a single year to arrive at your government bond spot rate. For example, if you were analyzing a five-year U.S. Treasury Note that makes two payments per year you would multiply the adjusted value of 0.014 times 2 to arrive at your government spot rate of 0.028 or 2.8 percent.

#### References

- YieldCurve.com: Illustrating Spot and Forward Interest Rates
- Duke University Hypertextual Finance Glossary: Future Value
- Duke University Hypertextual Finance Glossary: Present Value
- Duke University Hypertextual Finance Glossary: Stripped Bond
- Duke University Hypertextual Finance Glossary: Yield to Maturity
- Duke University Hypertextual Finance Glossary: Zero-coupon Bond