Study Notes on Annuities and Bonds

Introduction to Annuity Calculations

  • Annuity Terms:

    • PMT: The periodic payment amount.

    • n: Number of periods (in years).

    • Rate: The interest rate per period.

    • Future Value (FV): The value of the annuity at future periods, often set to zero when calculating the present value.

Present Value Calculation

  • Setting Future Value to Zero:

    • The future value is set to zero to mean that there are no additional transactions beyond the repetitive payments of $2,500 over ten years.

    • Example scenario: a person continuously pays $2,500 for three years, implying future value cannot be zero; it's an operational method for calculating present value.

  • Excel Formula for Annuity:

    • Method:

    • Change PMT (e.g., $2,500) to negative for present value calculation to remain positive.

    • Result:

    • The calculated present value results to $16,775.20.

Timing of Payments

  • Payment Timing:

    • If payments are made at the beginning of each year, set the type in Excel to 1.

    • Alternative Calculation Methods:

    • Formula-based: Use the present value formula adjusting for the new type, and setting the PMT to negative.

    • Rule-based: Multiplying the present value of ordinary annuity by $(1 + r)$, where $r$ is the periodic interest rate.

Loan Payment Calculation

  • Loan Scenario:

    • Loan amount: $15,000 to be paid in equal annual amounts over five years at 14%.

    • Understanding Payment Frequency: Payments occur at the end of each year, needing to adjust the interest.

    • Importance of Loan Terms:

    • Clarifies payment schedule and signifies when the first payment occurs, ensuring it's at period "end".

  • Input Values:

    • Present Value = $15,000 (Positive cash inflow because it's received now).

    • Future Value = 0 (Loan to be fully paid off).

    • Rate = 14% (Annual rate).

    • NPER (Number of periods) = 5 years (Annual compounding).

Cash Flow Growth Calculation

  • Present Value of Growing Cash Flows:

    • Scenario: Expecting $1,000 growing at 8% annually at the interest rate of 10%.

    • The cash flow grows forever, which is a perpetuity, thus leading to issues defining the timeframe.

  • Growing Perpetuity Formula: Demonstrates that further details will be covered in advanced chapters.

Understanding Bond Investments

  • Definition of Bonds:

    • Bonds referred to as fixed income securities promise fixed coupon rate payments at regular intervals.

    • Fixed income securities are stable compared to equities, focused primarily on interest income rather than growth.

  • Bond Features:

    • Par Value or Face Value: The amount returned to bondholders at maturity (commonly $1,000 unless stated otherwise).

    • Coupon Interest Rate: The rate at which the bond issuer pays interest on the par value. - Fixed coupon rates offer predictable income.

    • Maturity: Time remaining until the bond matures, may vary.

  • Default Risk: Analysis of the likelihood a borrower will default on loan obligations, which directly impacts investor returns.

Co-Provision in Bonds

  • Call Provision:

    • Grants issuers the option to buy back the bond at a specific price before maturity under certain conditions.

    • Protects issuers from unfavorable interest rate changes by allowing refinancing.

  • Final Thoughts:

    • Understanding these principles is fundamental in handling financial instruments, particularly in developing future financial strategies to manage risks and returns effectively for both bonds and annuities.

  • Exam Preparation:

    • Importance of reviewing bonds' features, calculations, and understanding theoretical foundations leading to practical applications in real-world scenarios.