Capital Budgeting & Cash Flow Analysis: Projects, NPV, IRR, Payback

TAKEAWAYS:

• Capital budgeting is the process of planning and evaluating long-term investments (e.g., buying a new factory or launching a new product line).
• Cash flows are the lifeblood of capital budgeting: only incremental cash inflows and outflows matter, not accounting profits.
• NPV (Net Present Value) is the gold standard for project evaluation—if NPV > 0, the project creates value.
• IRR (Internal Rate of Return) is the discount rate that makes NPV = 0; it’s intuitive but can mislead with multiple IRRs or negative cash flows.
• The payback period is simple but ignores time value of money—useful for liquidity-focused firms like Pathao.
• Sensitivity analysis and scenario analysis help managers understand risks (e.g., Daraz’s supply chain disruptions during monsoon).

1. Introduction to Capital Budgeting

Capital budgeting is the process of deciding whether to invest in long-term assets (e.g., machinery, real estate, new product lines). Unlike short-term decisions (e.g., buying inventory), these investments are irreversible and affect the company for years. Firms use cash flow-based methods (not accounting profits) because:

• Cash flows reflect actual money in/out (e.g., Daraz’s warehouse expansion costs Rs 50M upfront but saves Rs 10M/year in logistics).
• Accounting profits ignore timing (e.g., depreciation is a non-cash expense).

Key Question: "Should we spend Rs X today to generate Rs Y in the future?" Answer: Yes, if the present value of future cash flows exceeds the initial cost.

2. Types of Capital Budgeting Decisions

Firms make three main types of capital decisions:

3. Cash Flow Estimation: The Heart of Capital Budgeting

Cash flows are not the same as accounting profits. We focus on incremental cash flows—the difference between the project’s cash flows and what the firm would earn without it.

A. Initial Investment (Outflow)

• Capital expenditure (CapEx): Cost of assets (e.g., Rs 20M for a new Daraz warehouse).
• Working capital: Temporary assets (inventory, accounts receivable) minus liabilities (accounts payable). Must be recovered at project end!
  • Example: If Daraz needs Rs 5M in extra inventory, this is an initial outflow. At project end, it’s a Rs 5M inflow.

B. Operating Cash Flows (Inflows)

These come from the project’s operations. Calculate as: $$\text{Operating Cash Flow}=(\text{Revenue}-\text{Variable Costs}-\text{Depreciation})\times (1-\text{Tax Rate})+\text{Depreciation}$$

• Why? Depreciation is a non-cash expense, so we add it back.
• Taxes: Only operating income (EBIT) is taxed. Interest is already accounted for in WACC (Unit 7).

Example: Kathmandu Café’s Espresso Machine

• Initial Cost: Rs 500,000 (CapEx) + Rs 100,000 (working capital) = Rs 600,000 outflow.
• Annual Revenue: Rs 300,000 (200 cups/day × Rs 150/cup).
• Variable Costs: Rs 120,000 (beans, labor, utilities).
• Depreciation: Rs 100,000/year (5-year life).
• Tax Rate: 25%.
• Operating Cash Flow (Year 1): $$(300,000-120,000-100,000)\times (1-0.25)+100,000=105,000+100,000=\text{Rs 205,000 inflow}$$

C. Terminal Cash Flow (End of Project)

• Recover working capital: Rs 100,000 inflow.
• Salvage value of asset: If the espresso machine is sold for Rs 50,000, add that.
• Total Terminal CF: Rs 150,000.

4. Capital Budgeting Methods

Firms use three main methods to evaluate projects. We compare them in a table below.

A. Payback Period

• Definition: Time to recover initial investment.
• Formula: $$\text{Payback Period}=\frac{\text{Initial Investment}}{\text{Annual Cash Flow}}$$
• Advantages:
  • Simple to understand.
  • Focuses on liquidity (important for Pathao’s daily operations).
• Disadvantages:
  • Ignores time value of money (Rs 100 today ≠ Rs 100 in 5 years).
  • Doesn’t consider cash flows after payback.

Example: Daraz’s Drone Delivery

• Initial Cost: Rs 2M.
• Annual CF: Rs 500,000.
• Payback Period: 2M / 500K = 4 years.
• But: What if the drone fails in Year 3? Payback doesn’t show this.

B. Net Present Value (NPV)

• Definition: Present value of future cash flows minus initial investment.

• Formula: $$\text{NPV}=\sum \frac{{\text{CF}}_t}{(1+r{)}^t}-\text{Initial Investment}$$ Where:

  • $r$ = Discount rate (WACC from Unit 7).
  • ${\text{CF}}_t$ = Cash flow in year $t$.

• Decision Rule:

  • NPV > 0: Accept the project (creates value).
  • NPV < 0: Reject it (destroys value).
  • NPV = 0: Indifferent (breaks even).

Worked Example: Kathmandu Café’s Espresso Machine

• Initial Investment: Rs 600,000.
• Annual CF (Years 1–5): Rs 205,000.
• Terminal CF (Year 5): Rs 150,000.
• Discount Rate (WACC): 12%.
• NPV Calculation:

  flowchart TD
      A["Year 0: -Rs 600,000"] --> B["Year 1: Rs 205,000 / 1.12"]
      B --> C["Year 2: Rs 205,000 / 1.12²"]
      C --> D["Year 3: Rs 205,000 / 1.12³"]
      D --> E["Year 4: Rs 205,000 / 1.12⁴"]
      E --> F["Year 5: (Rs 205,000 + Rs 150,000) / 1.12⁵"]
      F --> G["NPV = Sum of all PV CFs - Rs 600,000"]

  • PV of Annual CFs (Years 1–4): $$205,000\times \left(\frac{1-(1.12{)}^{-4}}{0.12}\right)=205,000\times 3.037=\text{Rs 622,085}$$
  • PV of Year 5 CF: $$(205,000+150,000)/1.12^5=355,000/1.762=\text{Rs 201,450}$$
  • Total PV of CFs: Rs 622,085 + Rs 201,450 = Rs 823,535.
  • NPV: Rs 823,535 - Rs 600,000 = Rs 223,535.
• Decision: Accept! NPV > 0.

C. Internal Rate of Return (IRR)

• Definition: Discount rate that makes NPV = 0.
• Formula: Solve for $r$ in: $$0=\sum \frac{{\text{CF}}_t}{(1+r{)}^t}-\text{Initial Investment}$$
• Decision Rule:
  • IRR > WACC: Accept (project earns more than cost of capital).
  • IRR < WACC: Reject.

Advantages:

• Easy to explain (e.g., "This project earns 18% IRR").
• Useful for comparing projects of different sizes.

Disadvantages:

• Multiple IRRs: If cash flows change signs (e.g., initial outflow, then inflow, then outflow), IRR may give multiple answers.
• Scale Problem: A larger project may have a higher IRR but lower NPV (e.g., buying a Rs 10M factory vs. a Rs 1M machine).

Example: Daraz’s Warehouse Expansion

• Initial Cost: Rs 50M.
• Annual CFs: Rs 12M (Years 1–5), then Rs 8M (Years 6–10).
• IRR: ~15% (calculated via financial calculator or Excel).
• WACC: 12%.
• Decision: Accept (IRR > WACC).

5. Comparing NPV and IRR

Example Conflict:

• Project A: Rs 10M initial, Rs 5M/year forever → IRR = 50%, NPV = Rs 10M.
• Project B: Rs 20M initial, Rs 10M/year forever → IRR = 50%, NPV = Rs 0.
• NPV says: Choose A (NPV > 0).
• IRR says: Both are equal (50%).
• Solution: Always use NPV for final decisions.

6. Risk Analysis in Capital Budgeting

Real-world projects have uncertainty. Firms use:

A. Sensitivity Analysis

• What-if analysis: How does NPV change if assumptions change?
• Example: What if Daraz’s drone delivery reduces costs by only Rs 300K/year instead of Rs 500K?
  • Recalculate NPV with new CFs.

B. Scenario Analysis

• Best-case, worst-case, base-case scenarios.
• Example for Pathao:
  • Best-case: 20% more riders → NPV = Rs 5M.
  • Worst-case: 10% fewer riders → NPV = -Rs 2M.
  • Base-case: 5% growth → NPV = Rs 1M.

C. Monte Carlo Simulation

• Uses probability distributions to model thousands of possible outcomes.
• Example: NTC’s 5G rollout—simulates demand, costs, and regulatory delays.

7. Real-World Applications

In the Real World

1. Daraz’s Expansion to Rural Nepal

   • Idea Used: Capital budgeting with NPV/IRR to decide whether to open warehouses in remote areas.
   • How: Daraz estimates:
     • Initial cost: Rs 15M/warehouse (CapEx + working capital).
     • Annual CF: Rs 4M (higher margins in rural areas due to lower competition).
     • NPV: Positive at WACC = 14% → Accepted.
   • Risk: Monsoon floods disrupt supply chains (mitigated via sensitivity analysis).

2. Pathao’s Electric Scooter Fleet

   • Idea Used: Payback period and IRR to justify fleet purchases.
   • How:
     • Initial cost: Rs 500,000/scooter.
     • Annual savings: Rs 150,000 (lower fuel/maintenance costs).
     • Payback Period: 500,000 / 150,000 = 3.3 years.
     • IRR: ~20% (higher than WACC of 12%) → Accepted.
   • Real Example: Pathao’s 2022 fleet expansion used IRR to prioritize scooters with fastest payback.

3. NEPSE’s Stock Market Listing

   • Idea Used: NPV of future dividends to evaluate whether to list a company.
   • How: Investors calculate:
     • Expected dividends: Rs 5M/year.
     • Discount rate: 15% (risky market).
     • NPV: If PV of dividends > listing costs, the company is listed.

8. Common Mistakes in Capital Budgeting

Students (and even managers!) make these errors:

1. Ignoring Sunk Costs

   • Mistake: Including past expenses (e.g., Rs 1M spent on R&D already).
   • Fix: Only consider incremental cash flows.

2. Forgetting Working Capital

   • Mistake: Not adding back working capital at project end.
   • Fix: Always include recovery of working capital in terminal CF.

3. Using Accounting Profits Instead of Cash Flows

   • Mistake: Assuming profits = cash flows (e.g., ignoring depreciation).
   • Fix: Use operating cash flow formula (as shown above).

4. Overestimating Cash Flows

   • Mistake: Assuming demand will grow forever (e.g., Daraz expecting 50% YoY growth).
   • Fix: Use conservative estimates and sensitivity analysis.

9. Exam Tips

1. Always show calculations for NPV/IRR.

   • Examiners love to see the PV formula or Excel steps (e.g., =NPV(rate, CFs)).
   • For IRR, state: "IRR is the rate that makes NPV = 0."

2. Compare NPV and IRR in your answer.

   • Example:

     "While both methods suggest accepting Project X, NPV is preferred because it explicitly considers the time value of money and avoids the reinvestment rate assumption of IRR."

3. Include a sensitivity analysis in numericals.

   • Example:

     "If the discount rate increases to 15%, the NPV of the project drops from Rs 200,000 to Rs 50,000, indicating higher risk."

4. Label all cash flows clearly.

   • Use a table like this for clarity:

     | Year | Cash Flow (Rs) | PV Factor (12%) | PV (Rs) |
     |------|----------------|-----------------|---------|
     | 0    | -600,000       | 1.000           | -600,000|
     | 1    | 205,000        | 0.893           | 183,015 |
     | 2    | 205,000        | 0.797           | 162,885 |
     | ...  | ...            | ...             | ...     |
     | Total|                |                 | **NPV** |
     

5. For payback period, show the exact year.

   • Example:

     "The cumulative cash flow reaches Rs 600,000 in Year 4 (Rs 820,000 - Rs 600,000 = Rs 220,000 surplus), so the payback period is 3.5 years."

6. Mention real-world limitations.

   • Example:

     "While NPV is theoretically superior, IRR is often used in practice due to its simplicity, especially for small businesses like Kathmandu’s mom-and-pop shops."

10. Fully Worked Example: Nepali Business

Scenario: Sagar’s Spices, a Kathmandu-based spice exporter, is considering buying a new grinding machine to expand production.

Given:

• Initial Investment: Rs 1,200,000 (machine) + Rs 200,000 (working capital) = Rs 1,400,000.
• Annual Revenue: Rs 800,000 (new market demand).
• Variable Costs: Rs 300,000 (ingredients, labor).
• Depreciation: Rs 240,000/year (5-year life).
• Tax Rate: 25%.
• WACC: 10%.
• Salvage Value (Year 5): Rs 200,000.
• Working Capital Recovery (Year 5): Rs 200,000.

Step 1: Calculate Annual Operating Cash Flow

$$\text{Operating Income}=800,000-300,000-240,000=\text{Rs 260,000}$$ $$\text{Tax}=260,000\times 0.25=\text{Rs 65,000}$$ $$\text{Net Income}=260,000-65,000=\text{Rs 195,000}$$ $$\text{Operating Cash Flow}=\text{Net Income}+\text{Depreciation}=195,000+240,000=\text{Rs 435,000/year}$$

Step 2: Terminal Cash Flow

$$\text{Terminal CF}=\text{Salvage Value}+\text{Working Capital Recovery}=200,000+200,000=\text{Rs 400,000}$$

Step 3: NPV Calculation

gantt
    title NPV Calculation for Sagar's Spices
    dateFormat  YYYY
    section Initial Investment
    Year 0 :a1, 1400000, 2023
    section Annual CFs (Years 1-5)
    Year 1 :a2, 435000, 2024
    Year 2 :a3, 435000, 2025
    Year 3 :a4, 435000, 2026
    Year 4 :a5, 435000, 2027
    Year 5 :a6, 835000, 2028
    section PV Calculation
    PV Year 1 :b1, after a2
    PV Year 2 :b2, after a3
    PV Year 3 :b3, after a4
    PV Year 4 :b4, after a5
    PV Year 5 :b5, after a6
    NPV :c1, after b5

• PV of Annual CFs (Years 1–4): $$435,000\times \left(\frac{1-(1.10{)}^{-4}}{0.10}\right)=435,000\times 3.170=\text{Rs 1,378,950}$$
• PV of Year 5 CF: $$835,000/1.10^5=835,000/1.6105=\text{Rs 518,500}$$
• Total PV of CFs: Rs 1,378,950 + Rs 518,500 = Rs 1,897,450.
• NPV: Rs 1,897,450 - Rs 1,400,000 = Rs 497,450.

Step 4: Decision

• NPV > 0 → Accept the project!
• IRR: ~15% (higher than WACC of 10%) → Confirms acceptance.

Step 5: Sensitivity Analysis

Conclusion: The project is robust but sensitive to revenue declines.

11. Summary Table of Key Formulas

12. Final Exam Practice Question

Question: "Nepal Bank Ltd. is considering a project with the following cash flows:

• Initial Investment: Rs 5,000,000
• Annual CFs (Years 1–3): Rs 2,000,000
• Terminal CF (Year 3): Rs 1,500,000
• WACC: 12%

Calculate:

1. NPV of the project.
2. Payback period.
3. IRR. 4. Should Nepal Bank accept the project? Justify your answer."

Answer Structure:

1. NPV Calculation:

   • PV of Annual CFs: $2,000,000\times \left(\frac{1-(1.12{)}^{-3}}{0.12}\right)=2,000,000\times 2.4018=\text{Rs 4,803,600}$
   • PV of Terminal CF: $1,500,000/1.12^3=\text{Rs 1,100,000}$
   • Total PV: Rs 4,803,600 + Rs 1,100,000 = Rs 5,903,600
   • NPV: Rs 5,903,600 - Rs 5,000,000 = Rs 903,600.

2. Payback Period:

   • Cumulative CFs:
     • Year 1: Rs 2,000,000 (Total: -3,000,000)
     • Year 2: Rs 2,000,000 (Total: -1,000,000)
     • Year 3: Rs 3,500,000 (Total: Rs 2,500,000)
   • Payback: Between Year 2 and 3.
   • Exact: $\frac{1,000,000}{3,500,000}=0.286$ years → 2.29 years.

3. IRR:

   • Use financial calculator or Excel (=IRR(-5000000, 2000000, 2000000, 3500000)) → ~18%.

4. Decision:

   • NPV > 0 and IRR > WACC → Accept the project.
   • Note: IRR is higher than WACC, confirming NPV result. Payback is quick (2.29 years), which is good for liquidity.