Module 3: The Concept of Time Value of Money

Module Overview

  • Title: Financial Decision Making Module 3: The Concept of Time Value of Money

  • Prepared by: Wahseem Soobratty

Module Objectives

  • Understand and apply the concept of time value of money.

  • Calculate present and future values, both with and without annuities.

  • Explore debt management methods of finance.

  • Prepare loan repayment schedules to determine total interest paid.

Time Value of Money (TVM)

Key Concepts

  • Definition: The principle that money available today is worth more than the same amount in the future due to earning capacity.

  • Example Scenario:

    • $1,000 today can be invested to grow to $1,610 in five years at an interest rate of 10%.

    • $1,000 today has greater purchasing power than $1,000 in the future due to inflation.

Factors Affecting TVM

  1. Interest Rates

    • The amount earned from investments over time.

  2. Inflation

    • Reduces future purchasing power of money.

Analyzing Cash Flows

  • Investment Decisions:

    • Question posed: Would you invest $45,000 to receive $20,000 annually for three years?

    • Money has a time value: $20,000 received later is worth less than $20,000 received sooner.

Cash Flow Timing

  • Cash flows from different years cannot simply be aggregated. Each cash flow must be converted into a common scale (Present Value) to compare accurately.

  • Present Value (PV):

    • Represents what future cash amounts are worth today.

    • Example: $500 in four years has a present value of $367.51 at an 8% interest rate.

Present Value Calculation

  • Formula to Calculate PV:[PV = \frac{FV}{(1 + i)^n}]

    • Where:

      • FV = Future Value

      • i = Interest Rate

      • n = Number of Years

  • Example Calculation: For $161 received in five years at a 10% interest rate:

    • [PV = \frac{161}{(1 + 0.10)^5} = 100 ]

Annuities

  • Definition: A series of equal cash flows received over time.

  • PV Calculation of Annuity:[PV = \frac{FV1}{(1 + i)^1} + \frac{FV2}{(1 + i)^2} + \frac{FV3}{(1 + i)^3}]

    • Example: To fund a $5 million program annually for three years at 10% interest:

    • Calculate present values for each year:

      • PV1 = $5,000,000/(1.1)^1 = $4,545,454

      • PV2 = $5,000,000/(1.1)^2 = $4,132,231

      • PV3 = $5,000,000/(1.1)^3 = $3,756,574

    • Total PV = $12,434,259

Using Discount Tables

  • Discount tables simplify the calculations for various cash flows.

  • Example:

    • For one cash flow use Table 1, for series of equal cash flows (annuity) use Table 2.

    • Discount factor for three equal payments at 10%: 2.4869

Calculating Loan Repayments

  • From PV to FV:

    • Known present value (loan amount), calculate future value (total repayments).

    • Example 1: Loan of $10,000 at 3% for 3 years

      • Using discount factor = 2.8286:

        • [FV = \frac{10,000}{2.8286} = 3,535.32 ]

        • Total payments = $3,535.32 x 3 = $10,605.96; Total interest = $605.96

Loan Repayment Examples

  • Example 2: Biannual repayments of a loan

    • Loan amount = $10,000, Interest = 3% annually (1.5% biannually), 6 periods.

    • Total payments will differ due to more frequent compounding.

  • Example 3: Monthly repayments

    • Loan amount = $10,000, Interest = 3% annually (0.25% monthly), 36 periods.

Loan Schedules

  • A complete loan schedule can be compiled using repayment and interest calculations for each period.

    • Example details including opening balance, interest, repayments, reduction in principal, and closing balance for each year.

Acknowledgements

  • Content is adapted from ACCT1002 prescribed textbook by Wahseem Soobratty.

Conclusion

  • Understanding the time value of money is critical for making informed financial decisions and effectively managing debt.