Time Value of Money (TVM)

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. Introduction to Time Value of Money (TVM)

  • Definition: TVM is the concept that money available today is worth more than the same amount in the future due to its potential earning capacity.
  • Basis: TVM is based on the idea that money can earn interest or returns.

Real-World Example:
If you receive Rs. 100,000 today and invest it at 10%, after one year it becomes Rs. 110,000. Thus, receiving money today is more valuable.

2. Importance and Applications

  • Investment Analysis
  • Capital Budgeting
  • Loan Amortization
  • Retirement Planning
  • Business Valuation

3. Advantages of TVM

  • Helps in comparing investment opportunities
  • Assists in making informed decisions
  • Useful in financial planning and forecasting

Disadvantages

  • Assumes constant interest rates
  • Inflation and risk factors may not be fully considered

4. Concepts Related to TVM

a. Future Value (FV):

Future Value (FV) refers to the value of a sum of money at a specific point in the future, based on a particular interest rate or rate of return. It helps answer the question: "How much will my money be worth in the future if I invest it today?"

Formula for Future Value

  1. For a single lump sum:

FV=PV×(1+r)n

  • FV = Future Value
  • PV = Present Value (initial amount)
  • r = Interest rate per period
  • n = Number of periods
  • Key Uses of Future Value:
    • Retirement planning
    • Investment planning
    • Education savings
    • Business project evaluation

    Present Value (PV):

    Definition:
    Present Value (PV) is the current worth of a future sum of money or stream of cash flows given a specified rate of return (also called the discount rate). It reflects the idea that a specific amount of money today is worth more than the same amount in the future due to its earning potential.

    Formula:

    For a single future value:

    PV=FV(1+r)n

    Where:

    • PV = Present Value
    • FV = Future Value
    • r = Discount rate (interest rate per period)
    • n = Number of periods

  • Annuity – Definition, Importance, Types & Solved Examples

    1. Definition of Annuity

    An annuity is a series of equal payments or receipts made at regular intervals over a period of time. Each payment can occur weekly, monthly, quarterly, or annually.

    📌 Common real-life examples:

    • Loan repayments
    • Insurance premiums
    • Retirement pensions
    • Investment deposits

    2. Importance of Annuity

    1. Financial Planning: Helps in planning long-term savings or repayment strategies.
    2. Loan Structuring: Used in calculating fixed monthly loan payments.
    3. Retirement Security: Annuities provide predictable income for retirees.
    4. Business Analysis: Supports cash flow planning and project evaluation.

    3. Types of Annuity

    Type

    Description

    Ordinary Annuity

    Payments made at the end of each period (e.g., mortgage or loan)

    Annuity Due

    Payments made at the beginning of each period (e.g., rent, lease)

    Perpetuity

    Payments continue forever (e.g., preferred stock dividends)

    Deferred Annuity

    Payments start after a certain period (used in retirement planning)

    : Ordinary Annuity – Concept, Importance & Solved Questions

    ✅ 1. Definition of Ordinary Annuity

    An Ordinary Annuity is a series of equal payments made at the end of each period over a fixed amount of time. Each payment includes both interest and principal.

    🔹 Examples:

    • Monthly car loan payments
    • Home mortgage payments
    • Retirement pension received at the end of each year

    🧠 Key Point: In an ordinary annuity, payments occur at the end of each period, not the beginning.

    ✅ 2. Importance of Ordinary Annuity

    🔹 1. Financial Planning: Helps in planning for retirement, loans, insurance premiums, etc.
    🔹 2. Loan Management: Used by banks to calculate EMIs (Equal Monthly Installments).
    🔹 3. Investment Decisions: Investors evaluate fixed-return investment opportunities like bonds or pensions.
    🔹 4. Business Forecasting: Helps businesses in evaluating long-term cash flows and capital budgeting.

    ✅ 3. Formula for Ordinary Annuity




  • Annuity Due – Concept, Importance & Solved Questions

    1. Definition of Annuity Due

    An Annuity Due is a series of equal payments made at the beginning of each period over a fixed duration. Each payment includes both principal and interest.

    Examples:

    • Rent paid at the beginning of the month
    • Lease payments
    • Insurance premiums paid in advance

    📌 Key Point: Payments are made at the beginning of each period (unlike ordinary annuity where payments are made at the end).

    2. Importance of Annuity Due

    1. Financial Planning: Helps manage regular advance payments, such as rent or insurance.
    2. Real Estate: Lease/rent structures are often based on annuity due models.
    3. Insurance Sector: Premiums are paid in advance and modeled as annuity due.

    Business Forecasting: Useful in budgeting for recurring early-period payments.


  • Perpetuity – Concept, Importance & Solved Questions

    1. Definition of Perpetuity

    A Perpetuity is a type of annuity that provides an infinite series of equal payments made at regular intervals. These payments continue forever and do not have an end date.

    📘 Example:

    • Scholarships or pensions that pay indefinitely
    • Preferred stock dividends that continue forever

    2. Importance of Perpetuity

    1. Valuation of Financial Securities: Helps in valuing preferred shares and perpetual bonds.
    2. Endowments & Charities: Useful in calculating sustainable annual disbursements from permanent funds.
    3. Capital Budgeting: Assists in estimating the value of projects with indefinite cash flows.
    4. Simplified Models: Provides a simplified model in economic theory and financial planning.

      Compounding and Discounting – Concepts, Importance & Solved Examples

      1. Compounding

      Definition:

      Compounding refers to the process of calculating the future value of a present amount of money by applying interest over time. Interest is calculated on both the principal and accumulated interest from previous periods.

      Importance of Compounding:

      1. Investment Growth: Shows how savings/investments grow over time.
      2. Retirement Planning: Essential in calculating future retirement funds.
      3. Loan Projections: Helps determine how much interest will be paid on loans.
      4. Time Value of Money (TVM): Central concept for financial planning.

        2. Discounting

        Definition:

        Discounting is the process of finding the present value of a future amount of money. It helps determine how much a future cash flow is worth today.

        Importance of Discounting:

        1. Investment Decisions: Essential in Net Present Value (NPV) calculations.
        2. Loan Valuation: Helps in determining current loan worth.
        3. Business Valuation: Used to assess future income streams.
        4. Pricing Bonds and Securities: Used in financial markets.

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