Capital Budgeting: NPV, IRR, Payback, PI, and Decision Rules

Key Concepts and Techniques

Capital budgeting is the process of evaluating and selecting long-term investment projects that align with a company’s strategic goals. The primary techniques include:

1. Net Present Value (NPV)

• Measures the difference between the present value of cash inflows and outflows.
• If NPV > 0, the project is acceptable; if NPV < 0, it is reject.
• Formula: $$NPV=\sum _{t=0}^n\frac{C{F}_t}{(1+r{)}^t}-I_0$$ where $C{F}_t$ = cash flow at time $t$, $r$ = discount rate, $I_0$ = initial investment.

2. Internal Rate of Return (IRR)

• The discount rate that makes NPV = 0.
• If IRR > required rate of return, accept; otherwise, reject.
• IRR assumes reinvestment at the IRR rate (may not be realistic).

3. Payback Period

• The time it takes to recover the initial investment from cash inflows.
• Shorter payback = less risk (but ignores time value of money).

4. Profitability Index (PI)

• Ratio of present value of future cash flows to initial investment.
• PI > 1 = accept; PI < 1 = reject.

5. Comparison of Techniques

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How Capital Budgeting Works: The Decision-Making Process

Companies use these techniques to evaluate projects like:

• Expanding a Daraz warehouse (investment in logistics).
• Ncell upgrading its 5G network (capital expenditure).
• A bank issuing a new loan product (long-term commitment).

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Worked Example: Kathmandu Retail Shop’s Solar Panel Investment

Scenario: A retail shop in Kathmandu is considering installing solar panels to reduce electricity costs. The initial cost is NPR 500,000, and the expected annual savings are NPR 80,000 for 10 years. The discount rate is 10%.

Step 1: Calculate NPV

Total PV of Cash Flows = NPR 450,000 NPV = 450,000 - 500,000 = -50,000 → Reject (NPV < 0)

But wait! The shop owner realizes the government offers a 20% subsidy on solar panels. The new initial cost is NPR 400,000.

Total PV of Cash Flows = NPR 450,000 NPV = 450,000 - 400,000 = 50,000 → Accept (NPV > 0)

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In the Real World

1. Daraz (Nepal)

   • Uses NPV and IRR to decide whether to expand warehouses in new cities (e.g., Biratnagar). A project with a 15% IRR (above Daraz’s cost of capital) gets approved.

2. Ncell (Nepal)

   • Evaluates 5G network upgrades using payback period (e.g., recovering costs in 3–4 years) and NPV to ensure profitability over 10 years.

3. Nepal Rastra Bank (NRB)

   • Assesses loan disbursement to businesses using PI (e.g., a loan with PI > 1.2 is prioritized for approval).

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Comparing NPV and IRR: Why They Sometimes Conflict

• NPV is theoretically superior because it uses the company’s cost of capital as the discount rate.
• IRR assumes reinvestment at the IRR rate, which may not match the company’s actual reinvestment opportunities.
• Example: A project with NPV = +50,000 but IRR = 8% may be rejected if the company’s cost of capital is 12%, even though NPV suggests acceptance.

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Payback Period: Simplicity vs. Limitations

• Advantage: Easy to understand, focuses on liquidity.
• Disadvantage: Ignores the time value of money and cash flows after payback.
• Example: A project with NPR 100,000 initial cost and cash flows of NPR 30,000/year has a payback period of 3.33 years. But if the discount rate is 15%, the NPV might still be negative.

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Profitability Index (PI): Ranking Projects

• PI = PV of Future Cash Flows / Initial Investment
• Example: Two projects with the same initial cost (NPR 100,000):
  • Project X: PV of cash flows = NPR 120,000 → PI = 1.2
  • Project Y: PV of cash flows = NPR 110,000 → PI = 1.1
  • Choose X (higher PI).

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Exam Tip

1. Always calculate NPV first—it’s the most reliable method.
2. IRR conflicts? If NPV and IRR give different signals, trust NPV.
3. Payback period is often used in quick screening, but NPV/IRR are preferred for final decisions.
4. Memorize formulas:
   • $NPV=\sum \frac{C{F}_t}{(1+r{)}^t}-I_0$
   • $PI=\frac{PV\text{ of Future CFs}}{I_0}$
5. Real-world twist: In exams, government subsidies or tax benefits may change NPV—always recalculate if new data is given.
6. Mutually exclusive projects? Use NPV to rank (PI may mislead if initial investments differ).

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Final Note: Capital budgeting is not just about numbers—it’s about strategic decision-making. Companies like Daraz, Ncell, and banks use these techniques daily to grow sustainably. Master them, and you’ll be ready for both exams and real-world finance roles!