CFA Level 1 Quantitative Methods: Time Value of Money

Overview

• Time Value of Money (TVM): Money accumulates value over time due to interest.
  • Concept taught since early education.
  • Known as compounding into the future.
• Learning Outcome Statements (LOS): Focus on interpreting, explaining, demonstrating, and calculating TVM.
• Emphasis on becoming familiar with financial calculators.

Basic Concepts

• Present Value (PV): Value today.
• Future Value (FV): Value at a future date.
• Interest Rate (r): The rate at which money grows.
• Compounding: Earning interest on interest.
• Interest Compounding Frequency: Annual, semi-annual, quarterly, etc.

Key Points

Simple Example

• Choice: $1,000 today vs. $1,000 in 5 years.
  • Choosing today’s amount allows for investment opportunities and accumulation due to positive interest rates.

Old Long Way Math vs. New Short Way Math

• Old method: Separate steps for calculating interest and adding it to the principal.
• New method: Combines steps using Time Value Factor (TVF).
  • Formula:
    • FV = PV (1 + r)^n
    • PV = FV / (1 + r)^n

Using Financial Calculators

• Steps for Calculation: Enter four variables to solve for the fifth one (PV, FV, n, i, PMT).
• Example: Different scenarios calculating FV, PV, interest rates, and annuity values.
• Best Practice: Always check calculator settings (decimals, payments per year).
• Key Inputs: Present value, future value, interest rate, number of periods.

Interest Rates Interpretation

• Required Rate of Return: Minimum return required to compensate for risk.
• Discount Rate: Used to discount future cash flows back to present value.
• Opportunity Cost: Value of the best foregone alternative.

Components of Interest Rates

• Real Risk-Free Rate: Compensation for time preference with no inflation.
• Inflation Premium: Adjustment for expected inflation.
• Default Risk Premium: Compensation for risk of borrower defaulting.
• Liquidity Premium: Compensation for asset’s illiquidity.
• Maturity Premium: Compensation for longer-term investments.

Effective Annual Rate (EAR)

• Adjusts nominal rates for compounding frequency.
• Formula: EAR: [(1 + (i/n))^n] - 1
  • Example: 10% nominal rate compounded quarterly yields 10.38% EAR.

Financial Mathematics

• Future Value Formula: FV = PV(1 + r)^n
• Present Value Formula: PV = FV / (1 + r)^n
• Adjust for multiple compounding periods:
  • r/m and nm where m = number of compounding periods per year.

Example Problems

• Calculations Using Timelines: Visual aid for understanding cash flow over periods.
• Ordinary Annuity: Payments at end of each period.
• Annuity Due: Payments at the beginning of each period.
• Use financial calculators to solve annuity problems by setting to Begin mode.

Visualizing with Timelines

• Unequal Cash Flows: Use timelines to visualize different payments and their present values.
• Timeline Example: Compute PV of a series of unequal cash flows.

Exam Tips

• Familiarize with steps leading to calculator outputs.
• Understand components of interest rates for good foundation.
• Ability to demonstrate and calculate TVM effectively and efficiently.