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.

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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).

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2. Formula

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3. How to Execute the Calculation

Steps:

1. Identify Cash Flows for each year.
2. Determine Discount Rate (given in problem, e.g., 10%).
3. Find PV Factors from the table or calculate as 1/(1+k)^t.
4. Multiply Cash Flow × PV Factor = Present Value.
5. Sum all Present Values.
6. Subtract Initial Investment.

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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.

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5. Merits vs Demerits

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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:

1. Year 1 PV: 60,000 × 0.909 = 54,540
2. Year 2 PV: 60,000 × 0.826 = 49,560
3. Total PV: 54,540 + 49,560 = 1,04,100
4. 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:

1. Wealth Goal: It aligns perfectly with the Wealth Maximization objective. A positive NPV literally means "Wealth added".
2. Sound Theory: It respects the Time Value of Money principle, acknowledging that early cash flows are worth more.
3. Cash Based: It relies on objective cash flows rather than subjective accounting profits.

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Summary

• Logic: Is the Present Value of returns > Cost?
• Rule: Positive = Good; Negative = Bad.
• Significance: The most theoretical sound method in finance.

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Quiz Time! 🎯

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