Discounted Cash Flow Methods: NPV & Internal Rate of Return (IRR)

Why is ₹1,00,000 received today worth more than ₹1,00,000 received three years from now? Because of the Time Value of Money (TVM)! Money received today can be invested to earn interest, and inflation erodes future purchasing power. Discounted Cash Flow (DCF) techniques evaluate investment proposals by discounting all future cash flows back to their present value.

1. What is Discounting?

Discounting is the mathematical process of finding the Present Value (PV) of a future cash flow using a specified discount rate (the company’s Cost of Capital / WACC):

Present Value (PV) = Future Cash Flow / (1 + r)^t = Future Cash Flow × Present Value Factor (PVF)

Where:

• r: Required rate of return / discount rate
• t: Year in which cash is received

2. Net Present Value (NPV) Method

The Net Present Value (NPV) method is the internationally recognized gold standard of capital budgeting.

NPV is the difference between the Present Value of all future Cash Inflows and the Present Value of the Initial Cash Outlay:

NPV = Present Value of Total Cash Inflows - Initial Cash Outlay

Decision Criteria:

• If NPV > 0 (Positive): Accept the Project! (The project earns more than the cost of capital, increasing shareholder wealth).
• If NPV < 0 (Negative): Reject the Project! (Destroys shareholder wealth).
• If NPV = 0: The project earns exactly the cost of capital (indifferent).
• Mutually Exclusive Projects: Accept the project with the highest positive NPV!

3. Comprehensive Solved Numerical Problem: NPV Calculation

A company is considering purchasing a modern CNC machine costing ₹5,00,000. The expected cash flows after tax (CFAT) and the discount factors at a 10% cost of capital are:

Step-by-Step Solution:

• Total Present Value of Cash Inflows = ₹5,92,950
• Less: Initial Capital Outlay = (₹5,00,000)

NPV = ₹5,92,950 - ₹5,00,000 = +₹92,950

Recommendation: Since the NPV is positive (+₹92,950), the company should definitely accept the project!

4. Profitability Index (PI / Benefit-Cost Ratio)

When two projects have different initial investment sizes (e.g., investing ₹5 lakhs vs ₹50 lakhs), comparing absolute NPV can be misleading. The Profitability Index measures the present value of return earned per rupee invested:

Profitability Index (PI) = Present Value of Cash Inflows / Initial Cash Outlay

Using the above machine data:

PI = ₹5,92,950 / ₹5,00,000 = 1.186

Decision Rule for PI:

• If PI > 1.0: Accept the project.
• If PI < 1.0: Reject the project.
• Project Ranking: Higher PI ranks higher under capital rationing constraints.

5. Internal Rate of Return (IRR) Method

The Internal Rate of Return (IRR) is that exact discount rate which makes the Present Value of Cash Inflows equal to the Initial Cash Outlay (i.e., the discount rate at which NPV = 0).

At IRR: Present Value of Inflows - Initial Outlay = 0 (NPV = 0)

Trial and Error Interpolation Method:

Since IRR cannot be solved with a simple linear formula, we use two trial discount rates (one giving a positive NPV and one giving a negative NPV), then apply the Interpolation Formula:

IRR = L + [NPV_L / (NPV_L - NPV_H)] × (H - L)

Where:

• L: Lower discount rate (yields positive NPV_L)
• H: Higher discount rate (yields negative NPV_H)
• NPV_L: Positive Net Present Value at lower rate
• NPV_H: Negative Net Present Value at higher rate

Practical Solved Problem on IRR:

A project requires an outlay of ₹1,00,000.

• At 14% discount rate, NPV is +₹4,000.
• At 16% discount rate, NPV is -₹2,000.

Applying the Interpolation Formula:

IRR = 14% + [4,000 / {4,000 - (-2,000)}] × (16% - 14%) IRR = 14% + [4,000 / 6,000] × 2% = 14% + 1.33% = 15.33%

Decision Rule for IRR:

• If IRR > Cost of Capital (k): Accept the project!
• If IRR < Cost of Capital (k): Reject the project!

6. NPV vs IRR: The Conflict in Ranking

For independent single projects, NPV and IRR always yield the identical accept/reject decision. However, when evaluating Mutually Exclusive Projects (where accepting one means rejecting the other), NPV and IRR may conflict due to:

1. Disparity in Project Scale (Investment Size): Project A costs ₹10,000 (IRR 30%, NPV ₹2,000); Project B costs ₹1,00,000 (IRR 20%, NPV ₹15,000).
2. Disparity in Cash Flow Timing: Cash flows arriving early vs cash flows heavily back-loaded in final years.
3. Reinvestment Rate Assumption:
   • NPV assumes cash inflows are reinvested at the firm’s realistic Cost of Capital (WACC).
   • IRR assumes cash inflows are reinvested at the project’s own internal IRR rate (which is often unrealistically high, like 35% or 40%).

Resolution of Conflict: When NPV and IRR conflict in mutually exclusive decisions, always choose the project with the HIGHER NPV! NPV directly measures absolute wealth added to shareholders.

7. Comparative Summary of DCF Techniques

8. Summary & Quick Revision Checklist

• NPV: Present Value of Inflows minus Initial Outlay; accept if NPV > 0.
• PI: Present Value of Inflows / Outlay; accept if PI > 1.0.
• IRR: Discount rate where NPV equals zero; accept if IRR > Cost of Capital.
• Conflict Rule: When NPV and IRR disagree on mutually exclusive proposals, trust NPV.