Capital Budgeting Techniques: NPV, IRR, Payback, Profitability Index

TAKEAWAYS:

• Capital budgeting is the process of evaluating long-term investment projects using quantitative techniques like NPV, IRR, Payback Period, and Profitability Index to maximize shareholder value.
• NPV (Net Present Value) is the gold standard for project evaluation, comparing the present value of cash inflows against the initial investment at a firm’s cost of capital.
• IRR (Internal Rate of Return) is the discount rate that makes NPV zero, but can be misleading with non-normal cash flows or multiple IRRs.
• Payback Period is simple but ignores time value of money; Profitability Index adjusts for project scale by comparing PV of inflows to initial cost.
• Sensitivity analysis and scenario testing help assess how changes in variables (e.g., sales volume, interest rates) impact project outcomes.
• Nepalese firms like Daraz (e-commerce expansion) and NTC (fiber-optic rollout) use these techniques to justify multi-million-rupee infrastructure investments.

1. Introduction to Capital Budgeting

Capital budgeting is the long-term decision-making process where firms allocate funds to projects with durable assets (e.g., machinery, buildings, R&D) that generate cash flows over 1+ years. Unlike short-term decisions (e.g., inventory management), these projects are irreversible and require rigorous analysis to avoid costly mistakes.

Why it matters in Nepal?

• Daraz evaluates whether to open a new warehouse in Pokhara using NPV to compare costs vs. future sales.
• NTC assesses fiber-optic network expansion in remote districts using IRR to justify government subsidies.
• Sagarmatha Bank decides whether to invest in a new ATM network based on payback period and profitability.

2. Key Capital Budgeting Techniques

Firms use five primary techniques to evaluate projects. Below is a comparison table:

3. Net Present Value (NPV): The Gold Standard

Definition: NPV measures the present value of future cash flows minus the initial investment. A positive NPV means the project adds value to shareholders.

How it works:

1. Estimate cash flows (operating, salvage, terminal).
2. Discount at WACC (Weighted Average Cost of Capital).
3. Compare to initial cost:
   • If NPV > 0, accept the project.
   • If NPV < 0, reject it.

Example: Kathmandu Bookshop’s New Printer A bookshop in Thamel invests Rs. 500,000 in a new printer. Expected cash flows (WACC = 12%):

NPV = 182,070 – 500,000 = -317,930 Decision: Reject (NPV < 0). But wait—this assumes no salvage value. If the printer sells for Rs. 50,000 in Year 4, add it to Year 4’s CF: $$NPV=-500,000+107,160+119,550+128,160+(127,200+50,000)=-167,930$$ Still negative. Moral: Always include all cash flows!

4. Internal Rate of Return (IRR)

Definition: The discount rate that makes NPV = 0. It answers: "What return does this project offer?"

How to calculate:

1. Plug cash flows into a financial calculator or Excel (=IRR()).
2. Compare IRR to cost of capital (WACC).
   • If IRR > WACC, accept.
   • If IRR < WACC, reject.

Example: Daraz’s Warehouse Expansion Daraz invests Rs. 20M in a new warehouse in Pokhara. Cash flows:

IRR = 18.7% (calculated via Excel). WACC for Daraz = 15%. Decision: Accept (IRR > WACC).

But beware!

• Multiple IRRs: If cash flows change signs more than once, IRR may give multiple answers. Example:

flowchart TD
    A["Year 0: -₹1M"] --> B["Year 1: ₹2M"]
    B --> C["Year 2: -₹1M"]
    C --> D["Year 3: ₹1.5M"]
    E["Multiple IRRs due to sign changes"] --> C

This has two IRRs (100% and 50%). NPV is safer here.

• Reinvestment assumption: IRR assumes cash flows are reinvested at IRR, which may not match WACC.

5. Payback Period

Definition: The time (in years) it takes to recover the initial investment from cash inflows.

How to calculate:

1. List cumulative cash flows year by year.
2. Find the year when cumulative CF ≥ initial cost.

Example: Pathao’s Bike Fleet Pathao buys 5 motorcycles for Rs. 1.5M. Annual cash flows (depreciation + savings):

Payback = 2.5 years (recovered by Year 3).

Strengths:

• Simple to understand.
• Focuses on liquidity (how soon can the firm recover costs?).

Weaknesses:

• Ignores time value of money (Rs. 1M in Year 1 ≠ Rs. 1M in Year 3).
• Arbitrary cutoff: A 3-year payback is "good," but why not 4?

6. Profitability Index (PI)

Definition: The ratio of PV of future cash flows to initial investment. Helps rank projects when capital is limited.

Formula: $$PI=\frac{P{V}_{inflows}}{InitialInvestment}$$

Example: NTC’s Fiber-Optic Project

• Project A: Rs. 10M initial, PV inflows = Rs. 12M → PI = 1.2
• Project B: Rs. 8M initial, PV inflows = Rs. 10M → PI = 1.25

Decision: Choose Project B (higher PI per rupee invested).

When to use PI?

• When capital is scarce (e.g., government budgets).
• To rank projects alongside NPV.

7. Sensitivity Analysis

Definition: Tests how changes in key variables (e.g., sales volume, interest rates) affect project outcomes.

mindmap
  root((Sensitivity Analysis for Lumbini Furniture))
    Initial Investment
      - Base Case: ₹2,000,000
      - +10%: ₹2,200,000
      - -10%: ₹1,800,000
    Sales Growth
      - Base Case: 15%
      - +5%: 20%
      - -5%: 10%
    Discount Rate
      - Base Case: 12%
      - +3%: 15%
      - -3%: 9%
    NPV Impact
      - Base: ₹182,070
      - Worst Case: -₹500,000
      - Best Case: ₹500,000
    Break-even Analysis
      - Sales: 80% of forecast
      - Discount Rate: 14%

Example: Lumbini Hotel’s New Restaurant

• Base case: NPV = Rs. 500,000 (WACC = 12%).
• Scenario 1: Sales drop by 10% → NPV = -Rs. 200,000.
• Scenario 2: Interest rates rise to 15% → NPV = Rs. 200,000.

Visualization:

flowchart TD
    A["Base NPV: ₹500K"] --> B["Sales -10%: NPV = -₹200K"]
    A --> C["Interest +3%: NPV = ₹200K"]
    A --> D["Break-even sales: 80% of forecast"]
    E["Scenario Analysis"] -->|"Worst Case"| B
    E -->|"Best Case"| C

Key takeaway: The restaurant is risky if sales drop. Management might:

• Seek government subsidies.
• Reduce fixed costs (e.g., rent).

8. Real-World Applications in Nepal

In the real world

1. Daraz’s Expansion:

   • Idea: Uses NPV analysis to decide whether to open a new fulfillment center in Biratnagar.
   • How: Discounts projected sales growth (Rs. 50M/year) at Daraz’s WACC (18%) to compare against Rs. 200M initial cost.
   • Worked example: If NPV > 0, they proceed; otherwise, they delay or choose a smaller location.

2. NTC’s Fiber-Optic Rollout:

   • Idea: Applies IRR and Payback Period to justify rural connectivity projects.
   • How: IRR must exceed NTC’s cost of capital (15%), and payback must be <5 years to secure government funding.
   • Worked example: A Rs. 100M project in Doti with IRR = 20% and 4-year payback gets approved.

3. Sagarmatha Bank’s ATM Network:

   • Idea: Uses Profitability Index to prioritize ATM locations.
   • How: Banks with limited funds rank projects by PI to maximize returns per rupee invested.
   • Worked example: An ATM in Kathmandu (PI = 1.3) is preferred over one in Bhojpur (PI = 1.1).

9. Common Pitfalls and Exam Tips

Exam Tip: What Markers Look For

1. Correct technique application:

   • For NPV, show the discounting process (PV table or formula).
   • For IRR, mention assumptions (e.g., "IRR assumes reinvestment at IRR").
   • For payback, explain the cumulative CF method.

2. Comparison of methods:

   • Always compare NPV and IRR in answers (e.g., "NPV is preferred as it aligns with shareholder wealth").
   • For PI, link it to capital scarcity (e.g., "Useful when funds are limited").

3. Sensitivity analysis:

   • Show a table or graph of how NPV changes with variables (e.g., sales volume, interest rates).
   • Example:

     Sales Volume	NPV (NPR)
     80%	-50,000
     90%	100,000
     100%	250,000

4. Real-world context:

   • Tie examples to Nepalese firms (e.g., "Like Daraz evaluating e-commerce expansion").
   • Use NPR and local data (e.g., WACC = 15% for manufacturing).

Common Mistakes to Avoid

• Ignoring time value of money: Always discount cash flows unless using payback.
• Assuming IRR > WACC always means accept: Check for multiple IRRs.
• Forgetting salvage value: Include terminal cash flows (e.g., asset sale).
• Overlooking risk: Always discuss sensitivity analysis in answers.

10. Worked Example: Lumbini Furniture (Pvt) Ltd.

Scenario: Lumbini Furniture evaluates two projects (X and Y) with:

• Initial cost: Rs. 20M each.
• WACC: 15%.
• Cash flows:

Step 1: Calculate NPV

• Project X: $$NP{V}_X=\frac{8M}{1.15}+\frac{10M}{1.15^2}+\frac{5M}{1.15^3}+\frac{3M}{1.15^4}-20M$$ $$NP{V}_X\approx 7M+7.5M+3.2M+1.6M-20M=-1.7M$$

• Project Y: $$NP{V}_Y=\frac{5M}{1.15}+\frac{12M}{1.15^2}+\frac{10M}{1.15^3}+\frac{8M}{1.15^4}-20M$$ $$NP{V}_Y\approx 4.3M+9.2M+6.5M+4.9M-20M=4.9M$$

Step 2: Calculate IRR

• Project X: IRR ≈ 10% (use Excel or financial calculator).
• Project Y: IRR ≈ 20%.

Step 3: Decision

• NPV rule: Choose Project Y (NPV > 0).
• IRR rule: Both IRRs > WACC, but Y is better.
• Payback Period:
  • X: 2.5 years.
  • Y: 2 years.
  • Y is faster, but NPV is more reliable.

Step 4: Sensitivity Analysis Assume sales drop by 20%:

• Project Y’s NPV drops to Rs. 1.5M (still positive).
• Project X’s NPV becomes -Rs. 3.2M (reject).

Final Decision: Project Y is safer and more profitable.

11. Summary Table of Techniques

12. Final Exam Tip

• Always prefer NPV over IRR in answers unless asked otherwise.
• Show calculations (even if approximate) for full marks.
• Link to Nepal: Use NPR, WACC = 15%, and firms like Daraz, NTC, Sagarmatha Bank.
• Discuss risk: Mention sensitivity analysis to show depth.

Example answer structure:

1. Define the technique (1 mark).
2. Show calculation (3 marks).
3. Compare with other methods (2 marks).
4. Discuss real-world application (2 marks).
5. Sensitivity analysis (2 marks).