Now we can calculate the accrued interest using the following formula:. Note that bonds are priced as clean or dirty, depending on whether accrued interest is included.

## Bond Pricing

Most bonds are quoted at clean prices and transacted at dirty prices, which include the accrued interest. Advanced Bond Concepts: Introduction Advanced Bond Concepts: Bond Pricing Advanced Bond Concepts: Duration Advanced Bond Concepts: Convexity Advanced Bond Concepts: We can combine the bond price formula and the annuity model to arrive at the following formula, which requires us to also include the present value of the par value reached at maturity: Determine the number of coupon payments.

Determine the semi-annual yield. Enter the amounts into the formula: Determine the number of periods.

The required yield of zero-coupon bonds is usually based on a semi-annual coupon payment. As such, the number of periods will be doubled to 10 periods 5 X 2. Determine the yield.

Pricing Bonds Between Payment Periods So far, our pricing calculations have assumed that we are buying bonds where the next coupon payment is one payment period away. Each bond market has its own convention: The next coupon payment would be in 61 days: To entice investors to purchase the bond despite its lower coupon payments, the company has to sell the bond at less than its par value, which is called a discount.

Since the market price of bonds is so changeable, it is possible to make a profit in addition to that generated by coupon payments by purchasing bonds at a discount. The yield to maturity of a bond is the rate of return generated by a bond after accounting for its market price, expressed as a percentage of its par value. Considered a more accurate estimate of a bond's profitability than other yield calculations, the yield to maturity of a bond incorporates the gain or loss created by the difference between the bond's purchase price and its par value.

The coupon rate is often different from the yield. A bond's yield is more accurately thought of as the effective rate of return based on the actual market value of the bond.

### 2) Key Bond Characteristics

At face value, the coupon rate and yield equal each other. If you sell your IBM Corp.

Because coupon payments are not the only source of bond profits, the yield to maturity calculation incorporates the potential gains or losses generated by variations in market price. If an investor purchases a bond for its par value, the yield to maturity is equal to the coupon rate. If the investor purchases the bond at a discount, its yield to maturity is always higher than its coupon rate.

## When is a bond's coupon rate and yield to maturity the same?

Yield to maturity approximates the average return of the bond over its remaining term. A single discount rate is applied to all future interest payments to create a present value roughly equivalent to the price of the bond. Harrogath Apr 7th, GrahamDoddFisher Apr 7th, If I use the effective semi-annual rate for discounting I get the following. Smagician Apr 7th, 5: Just … wow!

PompeyCrassus wrote:. Simplify the complicated side; don't complify the simplicated side. PompeyCrassus Apr 8th, Smagician Apr 8th, 1: Harrogath Apr 8th, 2: Wait a sec, this is not the end of this post! Appreciate it. Smagician Apr 8th, 4: My pleasure, Harrogath.

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Harrogath Apr 9th, Thanks for your kind words S, and your support. Really appreciate it. Pass together. Email Address.