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7.2.3 Calculating Yield On Treasury Bill

Learn how to calculate the yield on a Treasury Bill (T-bill) which trades at a discount and matures at par. This guide provides the formula, detailed explanations, and an example calculation.

Overview

A Treasury bill (T-bill) is a very short-term security that trades at a discount and matures at par. No interest is paid in the interim. Instead, the return is generated from the difference between the purchase price and the sale price (if sold before maturity) or maturity value (if held to maturity). For tax purposes, the investor’s earnings from the T-bill are treated as interest income.

In this section, we will learn how to calculate the yield on a Treasury Bill using a simple formula.

Formula

The yield on a T-bill can be calculated using the following formula:

$$ \text{Yield} = \frac{(100 - \text{Price}) \times 365}{\text{Price} \times \text{Term}} \times 100 $$

Where:

  • Price is the purchase price of the T-bill.
  • Term is the number of days to maturity.

Detailed Breakdown of the Formula

  • (100 - Price): This part of the formula calculates the discount, which is the difference between the par (face) value of 100 and the price paid for the T-bill.
  • 365: This is the number of days in a year, used to annualize the yield.
  • Price: The price paid for the T-bill.
  • Term: The number of days remaining until the T-bill matures.
  • 100: This multiplication brings the result into a percentage format.

Example Calculation

Let’s calculate the yield on an 89-day T-bill purchased for a price of 99.5.

  1. Identify the values:

    • Price = 99.5
    • Term = 89 days
  2. Apply the formula:

    $$ \text{Yield} = \frac{(100 - 99.5) \times 365}{99.5 \times 89} \times 100 $$

    $$ \text{Yield} = \frac{0.5 \times 365}{99.5 \times 89} \times 100 $$

    $$ \text{Yield} = \frac{182.5}{8865.5} \times 100 \approx 2.061 $$

Thus, the yield is approximately 2.061%.

Frequently Asked Questions (FAQs)

1. What is a Treasury Bill (T-bill)?

A Treasury Bill, commonly referred to as a T-bill, is a short-term government security that trades at a discount and matures at par value. It pays no periodic interest, with the investor’s return generated from the difference between the buying price and the value at maturity.

2. How are T-bill gains taxed?

Investors’ earnings from T-bills are treated as interest income for tax purposes.

3. Why is the number 365 used in the formula?

The number 365 is used to annualize the yield, converting the return from the term of the bill to a yearly equivalent rate.

Key Takeaways

  • T-bill yield calculation is essential for understanding the return on these short-term investments.
  • The formula for yield takes into account the difference between the purchase price and maturity value, annualized over the time to maturity.
  • Yield on a T-bill is always represented as a percentage.

Glossary

  • T-bill: Short-term debt security issued by a government, traded at a discount to par value and redeemed at maturity for full face value.
  • Yield: Earnings generated and realized on an investment over a particular period, expressed as a percentage of the investment’s cost.
  • Par Value: The nominal or face value of a bond, share, or coupon as stated by the issuer.

Visual Representation

    graph TD
	  A[Start] --> B["Calculate Discount (100 - Price)"]
	  B --> C["Annualize (Multiply by 365)"]
	  C --> D["Divide by (Price * Term)"]
	  D --> E[Multiply by 100 to get percentage]
	  E --> F[Yield]

Assess and Solidify Your Understanding

Welcome to the Knowledge Checkpoint! At the end of each chapter, you’ll find 10 carefully curated quizzes designed to reinforce the key concepts covered. These questions will help you gauge your grasp of the material, identify areas that need further review, and ensure you’re on the right track towards mastering the content for the Canadian Securities certification exams. Take your time, think critically, and use these quizzes as a tool to enhance your learning journey.

Good luck!

📚✨ Quiz Time! ✨📚

🧐 Assess and Solidify Your Understanding

Welcome to the Knowledge Checkpoint! You’ll find 10 carefully curated quizzes designed to reinforce the key concepts covered. These questions will help you gauge your grasp of the material, identify areas that need further review, and ensure you’re on the right track towards mastering the content for the Canadian Securities certification exams. Take your time, think critically, and use these quizzes as a tool to enhance your learning journey. 📘✨

Good luck! 🍀💪

## Which type of security is a Treasury bill (T-bill)? - [x] A very short-term security that trades at a discount and matures at par - [ ] A long-term investment with periodic interest payments - [ ] A medium-term bond with variable interest rates - [ ] A high-yield bond with coupon payments > **Explanation:** T-bills are short-term securities that are sold at a discount and mature at face value. No periodic interest is paid; instead, the return is generated from the difference between the purchase price and the maturity value. ## How are earnings from T-bills treated for tax purposes? - [ ] As capital gains - [x] As interest income - [ ] As dividend income - [ ] As tax-free income > **Explanation:** The earnings from T-bills are treated as interest income for tax purposes, which is the difference between the purchase price and the sale price (or maturity value). ## What is the formula used to calculate the yield on a Treasury bill? - [ ] Yield = (Price - 100) / Price * 365 / Term * 100 - [ ] Yield = (Price + 100) / 365 * Term * 100 - [x] Yield = (100 - Price) / Price * 365 / Term * 100 - [ ] Yield = (Price - 365) / Term * 100 > **Explanation:** The correct formula to calculate the yield on a T-bill is: Yield = (100 - Price) / Price * 365 / Term * 100 ## What is the yield on an 89-day T-bill purchased at a price of 99.5? - [ ] 1.950% - [ ] 2.150% - [x] 2.061% - [ ] 2.250% > **Explanation:** Using the formula: Yield = (100 - 99.5) / 99.5 * 365 / 89 * 100, the yield is calculated to be approximately 2.061%. ## T-bills trade at a discount and mature at par. What does this mean? - [ ] They are purchased at a price higher than their face value and mature at the face value - [x] They are purchased at a price lower than their face value and mature at the face value - [ ] They are purchased at the face value and mature at a higher value - [ ] They are purchased and sold at the same price > **Explanation:** T-bills are bought at a discount to their face (or par) value and are redeemed at face value at maturity. The investor earns the difference. ## What is the term in the T-bill yield calculation formula referring to? - [ ] The interest rate - [ ] The maturity value - [ ] The principal amount - [x] The time period in days from purchase to maturity > **Explanation:** In the T-bill yield calculation formula, the term refers to the number of days from the purchase date to the maturity date. ## The yield on a T-bill is classified as what kind of yield? - [ ] Coupon yield - [ ] Dividend yield - [ ] Nominal yield - [x] Discount yield > **Explanation:** Since T-bills do not pay periodic interest but offer returns through the price discount, the yield is considered a discount yield. ## If a T-bill is sold before maturity, the yield is based on which prices? - [ ] Purchase price and par value - [ ] Maturity value and purchase price - [ ] Par value and sale price - [x] Purchase price and sale price > **Explanation:** If a T-bill is sold before maturity, the yield is based on the difference between the purchase price and the sale price. ## Which of the following statements is false regarding T-bills? - [ ] They are a form of short-term debt - [x] They provide regular interest payments - [ ] They are considered low-risk investments - [ ] They have a finite maturity term > **Explanation:** T-bills do not provide regular interest payments; returns are realized from the difference between the purchase price and the face value at maturity. ## The risk of a Treasury bill is typically considered: - [ ] Very high - [x] Very low - [ ] Moderate - [ ] High but mitigated by other factors > **Explanation:** T-bills are considered very low-risk investments due to their backing by the government and short maturity periods.

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Saturday, July 13, 2024