Net Present Value (NPV) Method
Prerequisites
Before studying this chapter, make sure you understand:
- Time Value of Money - CRITICAL: You must know how to discount future cash flows.
- Goals - Wealth Maximization - NPV is the direct measure of wealth addition.
1. Definition
Net Present Value (NPV) is a discounted cash flow technique that calculates the difference between the Present Value of Cash Inflows and the Present Value of Cash Outflows.
It measures the absolute value added to shareholder wealth.
Decision Rule:
- NPV > 0 (Positive): Accept. The project adds value.
- NPV < 0 (Negative): Reject. The project destroys value.
- NPV = 0: Indifferent (Break-even).
2. Formula
NPV = Total PV of Cash Inflows - Total PV of Cash Outflows
Mathematically: NPV = Σ [ CFt / (1 + k)^t ] - Initial Investment
Where:
- CFt: Cash Flow at year t
- k: Risk-adjusted discount rate (Cost of Capital)
- t: Time period
- Initial Investment: Cash Outflow at Year 0
3. How to Execute the Calculation
Steps:
- Identify Cash Flows for each year.
- Determine Discount Rate (given in problem, e.g., 10%).
- Find PV Factors from the table or calculate as
1/(1+k)^t. - Multiply Cash Flow × PV Factor = Present Value.
- Sum all Present Values.
- Subtract Initial Investment.
4. Numerical Problem
Problem: Calculate NPV for a project with the following details:
- Initial Investment: ₹50,000
- Cost of Capital (Discount Rate): 10%
- Annual Cash Inflows:
- Year 1: ₹10,000
- Year 2: ₹20,000
- Year 3: ₹30,000
Solution:
Step 1: Create Analysis Table
| Year | Cash Inflow (₹) (A) | PV Factor @ 10% (B) | Present Value (₹) (A × B) |
|---|---|---|---|
| 1 | 10,000 | 0.909 (1/1.10^1) | 9,090 |
| 2 | 20,000 | 0.826 (1/1.10^2) | 16,520 |
| 3 | 30,000 | 0.751 (1/1.10^3) | 22,530 |
| Total | 48,140 |
Step 2: Apply NPV Formula NPV = Total PV of Inflows - Initial Investment NPV = ₹48,140 - ₹50,000 NPV = -₹1,860 (Negative)
Step 3: Conclusion Since NPV is Negative (-1,860), the project should be REJECTED. It will reduce shareholder wealth by ₹1,860.
5. Merits vs Demerits
Merits (Why it's the Best)
- Time Value: Fully accounts for timing of money.
- Wealth Max: Directly measures value increase.
- Profitability: Considers Total Profitability, not just recovery.
- Additivity: NPVs of different projects can be added.
Demerits (Difficulties)
- Complex: Harder to calculate than Payback.
- Discount Rate: Difficulty in determining accurate Cost of Capital (k).
- Ranking Issue: May give conflicting ranks with IRR for mutually exclusive projects.
Exam Pattern Questions and Answers
Question 1: "Calculate NPV and decide." (6 Marks) Given:
- Investment: ₹1,00,000
- Cash Flows: Year 1: ₹60,000, Year 2: ₹60,000
- Discount Rate: 10%
- PV Factors: Year 1 (0.909), Year 2 (0.826)
Solution:
- Year 1 PV: 60,000 × 0.909 = 54,540
- Year 2 PV: 60,000 × 0.826 = 49,560
- Total PV: 54,540 + 49,560 = 1,04,100
- NPV = 1,04,100 - 1,00,000 = ₹4,100.
Decision: Accept the project (Positive NPV).
Question 2: "Why is NPV considered the best method?" (4 Marks) Answer: NPV is considered the superior method because:
- Wealth Goal: It aligns perfectly with the Wealth Maximization objective. A positive NPV literally means "Wealth added".
- Sound Theory: It respects the Time Value of Money principle, acknowledging that early cash flows are worth more.
- Cash Based: It relies on objective cash flows rather than subjective accounting profits.
Summary
- Logic: Is the Present Value of returns > Cost?
- Rule: Positive = Good; Negative = Bad.
- Significance: The most theoretical sound method in finance.
Always memorize PV factors for 10% for up to 5 years (0.909, 0.826, 0.751, 0.683, 0.621). If the question doesn't provide them, use 1 / (1.10)^n on your calculator.
Quiz Time! 🎯
Test Your Knowledge
Question 1 of 2
1. If NPV is positive, it means the project: