Time Value of Money (TVM)
. 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
- 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
- Retirement
planning
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
- Financial
Planning: Helps in planning long-term savings or repayment strategies.
- Loan
Structuring: Used in calculating fixed monthly loan payments.
- Retirement
Security: Annuities provide predictable income for retirees.
- 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
- Loan
repayments
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
- Financial
Planning: Helps manage regular advance payments, such as rent or
insurance.
- Real
Estate: Lease/rent structures are often based on annuity due models.
- Insurance
Sector: Premiums are paid in advance and modeled as annuity due.
Business Forecasting: Useful in budgeting for recurring early-period payments.
- Rent
paid at the beginning of the month
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
- Valuation
of Financial Securities: Helps in valuing preferred shares and
perpetual bonds.
- Endowments
& Charities: Useful in calculating sustainable annual
disbursements from permanent funds.
- Capital
Budgeting: Assists in estimating the value of projects with indefinite
cash flows.
- 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:
- Investment
Growth: Shows how savings/investments grow over time.
- Retirement
Planning: Essential in calculating future retirement funds.
- Loan
Projections: Helps determine how much interest will be paid on loans.
- 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:
- Investment
Decisions: Essential in Net Present Value (NPV) calculations.
- Loan
Valuation: Helps in determining current loan worth.
- Business
Valuation: Used to assess future income streams.
- Pricing
Bonds and Securities: Used in financial markets.
- Investment
Decisions: Essential in Net Present Value (NPV) calculations.
- Investment
Growth: Shows how savings/investments grow over time.
- Scholarships
or pensions that pay indefinitely