# Bond Formulas

## Bond Formulas

Bond valuation is a technique for determining the theoretical fair value of a particular bond. Bond valuation includes calculating the present value of a bond’s future interest payments, also known as its cash flow, and the bond’s value upon maturity, also known as its face value or par value. Because a bond’s par value and interest payments are fixed, an investor uses bond valuation to determine what rate of return is required for a bond investment to be worthwhile. The present value of a bond is calculated by discounting the bond’s future cash payments by the current market interest rate.

For example, for small interest rate changes, the duration is the approximate percentage by which the value of the bond will fall for a 1% per annum increase in market interest rate. So the market price of a 17-year bond with a duration of 7 would fall about 7% if the market interest rate (or more precisely the corresponding force of interest) increased by 1% per annum.

The market price of a bond is determined using the current interest rate compared to the interest rate stated on the bond. The first part is the present value of the bond’s face value. The second part is the present value of the bond’s interest payments.

Bond valuation is the determination of the fair price of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Therefore, the value of a bond is obtained by discounting the bond’s expected cash flows to the present using an appropriate discount rate. In practice, this discount rate is often determined by reference to similar instruments, provided that such instruments exist. The formula for calculating a bond’s price uses the basic present value (PV) formula for a given discount rate.

Bond valuation, in effect, is calculating the present value of a bond’s expected future coupon payments. The theoretical fair value of a bond is calculated by discounting the present value of its coupon payments by an appropriate discount rate. It takes into account the price of a bond, par value, coupon rate, and time to maturity.

If it is less than the coupon rate, the present value is greater than the face value. If the two rates are the same, the present value is the same is the face value. Bond Value Calculator is an online investment planning tool programmed to calculate bond value, bond duration, interest payment present value and the ratio of Present to face value of payment. with respect to the given input values of face value, coupon interest rate, market interest rate and the maturity time. The bond valuation is used by investors to determine what rate of return is required for an investment in a particular bond to be worthwhile.

However, because interest is paid semiannually in two equal payments, there will be 6 coupon payments of \$35 each. Finally, the required rate of return (discount rate) is assumed to be 8%. This free online Bond Value Calculator will calculate the expected trading price of a bond given the par value, coupon rate, market rate, interest payments per year, and years-to-maturity.

## Bonds Payable Outline

YTM is the internal rate of return of an investment in the bond made at the observed price. It is also referred to as discount rate or yield to maturity. If the market rate is greater than the coupon rate, the present value is less than the face value.

Market Rate or Discount Rate – The market rate is the yield that could otherwise be received by buying another investment. Generally, this will be different than the actual coupon rate on a bond – see our bond yield to maturity calculator for more (this is essentially the inverse of this operation). The yield to maturity is the discount rate which returns the market price of the bond.

The investor computes the present value of the interest payments and the present value of the principal amount received at maturity. Assume that the market rate for similar bonds is 11 percent. Specifically, similar bonds (with similar credit rating, stated interest rate, and maturity date) are priced to yield 11 percent.

• Bond valuation, in effect, is calculating the present value of a bond’s expected future coupon payments.
• It takes into account the price of a bond, par value, coupon rate, and time to maturity.

## Understanding Bond Prices and Yields

Because the stated rate is 7 percent, the bond must be priced at a discount. The discount is amortized into income, which increases the yield to maturity. A zero-coupon bond makes no annual or semi-annual coupon payments for the duration of the bond. Instead, it is sold at a deep discount to par when issued.

If a bond’s coupon rate is less than its YTM, then the bond is selling at a discount. If a bond’s coupon rate is more than its YTM, then the bond is selling at a premium. If a bond’s coupon rate is equal to its YTM, then the bond is selling at par. Yield to maturity is the discount rate at which the sum of all future cash flows from the bond are equal to the price of the bond. The bond price can be calculated using the present value approach.

In the example shown, we have a 3-year bond with a face value of \$1,000. The coupon rate is 7% so the bond will pay 7% of the \$1,000 face value in interest every year, or \$70.

Duration is a linear measure of how the price of a bond changes in response to interest rate changes. It is approximately equal to the percentage change in price for a given change in yield, and may be thought of as the elasticity of the bond’s price with respect to discount rates.

## Calculating the Present Value of a 9% Bond in an 8% Market

The current yield is simpler measure of the rate of return to a bond than the yield to maturity. Current yield is measured as the ratio of the bond’s annual coupon payment to the bond’s market price.

The two main approaches here, Relative pricing and Arbitrage-free pricing, are discussed next. Hence, the value of a bond is obtained by discounting the bond’s expected cash flows to the present using an appropriate discount rate. A bond is a debt security that pays a fixed amount of interest until maturity. When a bond matures, the principal amount of the bond is returned to the bondholder. The present value (i.e. the discounted value of a future income stream) is used for better understanding one of several factors an investor may consider before buying the investment.

Now, suppose market interest rates rise, thereby causing bonds similar to yours to offer, say, an 8% coupon rate. If you were looking to sell your 7% bond, you would need to discount the price of your bond to the point where the buyer would achieve the same total return being offered by the bond paying 8%. If the yield to maturity for a bond is less than the bond’s coupon rate, then the (clean) market value of the bond is greater than the par value (and vice versa).

## A. Zero Coupon Bonds

Therefore when it comes to online calculation, this Bond Value calculator can assist you to select the best investment option available in the finance market. Let us take an example of a bond with semi-annual coupon payments. Let us assume a company ABC Ltd has issued a bond having the face value of \$100,000 carrying a coupon rate of 8% to be paid semi-annually and maturing in 5 years. Let us take an example of a bond with annual coupon payments. Let us assume a company XYZ Ltd has issued a bond having a face value of \$100,000 carrying an annual coupon rate of 7% and maturing in 15 years.