Discount instruments are a type of debt securities that do not pay any interest or coupon to the investors. Instead, they are sold at a lower price than their face value and redeemed at their face value when they mature. The difference between the purchase price and the face value is the profit or return for the investor. For example, a discount instrument with a face value of $100 may be sold for $90 and redeemed for $100 at maturity. The investor earns $10 by holding the discount instrument.
Discount instruments are usually short-term securities that mature in less than a year. They are often issued by governments, corporations, or financial institutions to raise funds or manage liquidity. Some examples of discount instruments are Treasury bills, commercial paper, banker’s acceptances, and certificates of deposit. Discount instruments are considered low-risk investments because they have a fixed and predictable return and a low default risk.
The yield or interest rate of a discount instrument is calculated by dividing the difference between the face value and the purchase price by the face value and annualizing it. This is also known as the bank discount yield. For example, if a discount instrument with a face value of $100 is sold for $95 and matures in 180 days, the yield is:
(100 – 95) / 100 x (360 / 180) = 0.05 x 2 = 0.1 or 10%
The bank discount yield is not the same as the effective annual yield, which takes into account the compounding effect of reinvesting the return. The effective annual yield is higher than the bank discount yield. To compare the yields of different discount instruments, the effective annual yield is a more accurate measure.
Basic Theory:
A discount instrument is a financial product that is initially issued or purchased at a value below its face or par value. The difference between the face value and the purchase price represents the discount. Common examples of discount instruments include Treasury bills, zero-coupon bonds, and commercial paper.
The formula for calculating the discount on a financial instrument is as follows:
Discount = Face Value - Purchase Price
Procedures:
To calculate the discount on a financial instrument using Microsoft Excel, you can use the following steps:
- Open a new Excel spreadsheet.
- Label three columns: “Face Value,” “Purchase Price,” and “Discount.”
- Enter the face value and purchase price of the instrument in the respective cells.
- In the “Discount” column, use the formula:
=Face Value - Purchase Price.
Scenario:
Let’s consider a scenario where an investor purchases a Treasury bill with a face value of $10,000 at a discounted price of $9,500.
| Face Value | Purchase Price | Discount |
|---|---|---|
| $10,000 | $9,500 | =B2-C2 |
Now, input the formula in the Discount column cell (C2) as =B2-C2 to calculate the discount.
Calculation:
Discount = $10,000 – $9,500 = $500
Result:
In this scenario, the investor receives a $500 discount on the Treasury bill.
Other Approaches:
- Yield Function in Excel: Another way to approach discount instruments is by using the yield function in Excel.
- XIRR Function for Cash Flows: In cases where cash flows occur at irregular intervals, the XIRR function can be used to calculate the discount rate.
