# Discount Yield Defined

The expected return is a measure of the rate of return on a bond for an investor, expressed as a percentage, and the expected return is used to calculate the return on municipal notes, commercial paper and treasury bills sold at a discount. The discount yield is calculated as (nominal value – purchase price)[/par value] * 360 / days until maturity, and the formula uses a month of 30 days and a year of 360 days to simplify the calculation.

### Break down the return on discounts

The discount return calculates the investor’s return on investment (ROI), which is generated by buying the investment at a discount and earning interest income. A Treasury bill is issued with a discount from face value (face value), as well as many forms of commercial paper and municipal notes, which are short-term debt securities issued by municipalities. US T-bills have a maximum maturity of six months (26 weeks), while T-bills and bonds have longer maturities.

### How to calculate the return on the discount

Suppose, for example, that an investor purchases a \$ 10,000 treasury bill with a \$ 300 discount on the face value (a price of \$ 9,700) and the security matures in 120 days. In this case, the return yield is (\$ 300 rebate)[/\$10,000 par value] * 360/120 days before maturity, i.e. a dividend yield of 9%.

### The differences between the discount yield and the increase

Securities sold at a discount use the discount yield to calculate the investor’s rate of return, and this method is different from discounting bonds. Bonds that use bond discounting can receive a nominal value, at a discount or premium, and the discounting is used to transfer the discount amount into bond income over the remaining life of the bond.

Suppose, for example, that an investor buys a corporate bond for \$ 1,000 for \$ 920 and that the bond matures in 10 years. Since the investor receives \$ 1,000 at maturity, the \$ 80 discount is bond income for the owner, as well as interest earned on the bond. The increase in bonds means that the \$ 80 discount is recognized in bond income over the 10-year term, and an investor can use a straight-line method or the effective interest method. Linear records the same dollar amount in bond income each year, and the effective interest method uses a more complex formula to calculate the amount of bond income.

### Factoring in a sale of securities

If a security is sold before the maturity date, the rate of return earned by the investor is different and the new rate of return is based on the sale price of the security. If, for example, the \$ 1,000 corporate bond purchased for \$ 920 is sold for \$ 1,100 five years after the date of purchase, the investor realizes a gain on the sale. The investor must determine the amount of the bond discount that is recognized in income before the sale and must compare it with the sale price of \$ 1,100 to calculate the gain.