Time Value of Money
1. Definition
Time Value of Money (TVM) is the concept that money available today is worth more than the same amount in the future due to its potential earning capacity. This core principle underlies all financial decisions and valuation methods.
Simple Statement: ₹100 today > ₹100 after 1 year
2. Why Money Has Time Value
2.1 Earning Potential
Money today can be invested to earn returns.
Example:
₹10,000 today invested @ 10% per year
After 1 year: ₹10,000 + ₹1,000 interest = ₹11,000
Therefore:
₹10,000 today = ₹11,000 after 1 year
2.2 Inflation
Purchasing power decreases over time.
Example:
Today: ₹100 can buy 5 notebooks @ ₹20 each
After 1 year (5% inflation): Same ₹100 can buy only 4.76 notebooks @ ₹21 each
Real value decreases due to inflation
2.3 Risk and Uncertainty
Future is uncertain; money in hand is certain.
Preference: Bird in hand orth two in the bush.
3. Key Concepts
3.1 Present Value (PV)
Definition: Current worth of future sum of money.
Formula:
PV = FV / (1 + r)^n
Where:
- PV = Present Value
- FV = Future Value
- r = Interest rate (discount rate)
- n = Number of periods
Question: What is ₹11,000 received after 1 year worth today if interest rate is 10%?
Solution:
Given:
FV = ₹11,000
r = 10% = 0.10
n = 1 year
Formula:
PV = FV / (1 + r)^n
PV = ₹11,000 / (1 + 0.10)^1
PV = ₹11,000 / 1.10
PV = ₹10,000
Answer: ₹10,000
3.2 Future Value (FV)
Definition: Worth of current sum after a specified time period.
Formula:
FV = PV × (1 + r)^n
Where:
- FV = Future Value
- PV = Present Value
- r = Interest rate
- n = Number of periods
Question: If you invest ₹10,000 today @ 10% for 1 year, how much will you have?
Solution:
Given:
PV = ₹10,000
r = 10% = 0.10
n = 1 year
Formula:
FV = PV × (1 + r)^n
FV = ₹10,000 × (1 + 0.10)^1
FV = ₹10,000 × 1.10
FV = ₹11,000
Answer: ₹11,000
4. Practice Problems
Problem 1: Future Value Calculation
Question: Calculate the future value of ₹50,000 invested for 3 years @ 12% per annum compounded annually.
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Step-by-Step Solution:
Given:
PV = ₹50,000
r = 12% = 0.12
n = 3 years
Formula: FV = PV × (1 + r)^n
Step 1: Calculate (1 + r)^n
(1 + 0.12)^3 = (1.12)^3
= 1.12 × 1.12 × 1.12
= 1.404928
Step 2: Multiply by PV
FV = ₹50,000 × 1.404928
FV = ₹70,246.40
Answer: ₹70,246.40
Verification:
Year 0: ₹50,000
Year 1: ₹50,000 × 1.12 = ₹56,000
Year 2: ₹56,000 × 1.12 = ₹62,720
Year 3: ₹62,720 × 1.12 = ₹70,246.40 ✓
Problem 2: Present Value Calculation
Question: You will receive ₹1,00,000 after 5 years. What is its present value if discount rate is 10%?
Given:
FV = ₹1,00,000
r = 10% = 0.10
n = 5 years
Solution:
Formula: PV = FV / (1 + r)^n
Step 1: Calculate (1 + r)^n
(1 + 0.10)^5 = (1.10)^5
= 1.61051
Step 2: Divide FV by this
PV = ₹1,00,000 / 1.61051
PV = ₹62,092.13
Answer: ₹62,092.13
Interpretation: ₹62,092 today is equivalent to ₹1,00,000 after 5 years @ 10%.
Problem 3: Find Interest Rate
Question: If ₹10,000 grows to ₹12,100 in 2 years with annual compounding, what is the interest rate?
Given:
PV = ₹10,000
FV = ₹12,100
n = 2 years
r = ?
Solution:
Formula: FV = PV × (1 + r)^n
Rearranging:
(1 + r)^n = FV / PV
(1 + r)^2 = ₹12,100 / ₹10,000
(1 + r)^2 = 1.21
Taking square root:
1 + r = √1.21
1 + r = 1.10
r = 0.10 = 10%
Answer: 10% per annum
5. Compounding vs Simple Interest
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TVM uses compound interest for accuracy.
6. Applications in Financial Decisions
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Exam Pattern Questions and Answers
Question 1: "Explain the concept of time value of money with example." (6 Marks)
Answer:
Definition (2 marks): Time value of money is the concept that money available today is worth more than the same amount in the future due to its earning capacity, inflation, and certainty. This means ₹100 today has greater value than ₹100 received after one year because today's ₹100 can be invested to earn returns.
Reasons (2 marks): Money has time value for three main reasons. First, earning potential allows current money to be invested and earn interest - ₹10,000 today invested at 10% becomes ₹11,000 after one year. Second, inflation erodes purchasing power over time, making future money worth less in real terms. Third, current money is certain while future receipts involve risk and uncertainty.
Example (2 marks): If you have choice between receiving ₹10,000 today or ₹11,000 after one year with 10% interest rate available, both are equivalent. This is because ₹10,000 invested today at 10% will grow to ₹10,000 × (1.10) = ₹11,000 after one year. Therefore, present value of ₹11,000 receivable after one year is ₹10,000 today.
Question 2: "Calculate the future value of ₹20,000 invested for 4 years at 8% compounded annually." (4 Marks)
Answer:
Given (0.5 marks):
- PV = ₹20,000
- r = 8% = 0.08
- n = 4 years
Formula (0.5 marks):
FV = PV × (1 + r)^n
Calculation (2 marks):
FV = ₹20,000 × (1 + 0.08)^4
FV = ₹20,000 × (1.08)^4
FV = ₹20,000 × 1.36049
FV = ₹27,209.80
Answer (1 mark): The future value is ₹27,209.80
Question 3: "Find the present value of ₹50,000 receivable after 3 years discounted at 12%." (4 Marks)
Answer:
Given (0.5 marks):
- FV = ₹50,000
- r = 12% = 0.12
- n = 3 years
Formula (0.5 marks):
PV = FV / (1 + r)^n
Calculation (2 marks):
PV = ₹50,000 / (1 + 0.12)^3
PV = ₹50,000 / (1.12)^3
PV = ₹50,000 / 1.404928
PV = ₹35,589.28
Answer (1 mark): The present value is ₹35,589.28
Summary
Key Formulas:
Future Value: FV = PV × (1 + r)^n
Present Value: PV = FV / (1 + r)^n
Compound vs Simple:
- Compound: Interest on interest
- Simple: Interest on principal only
Remember: Always use compound interest for TVM calculations!
Key Concepts:
- Money today > Money tomorrow
- Three reasons: Earning capacity, inflation, certainty
- PV = Today's worth of future money
- FV = Future worth of today's money
- Compounding is standard in TVM
For numerical problems: (1) Write "Given" clearly, (2) State formula, (3) Show step-by-step calculation, (4) Write "Answer" with units. This format ensures full marks!
Quiz Time! 🎯
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