Capital Budgeting & Investment Decisions: NPV, IRR, Payback, Risk Analysis

TAKEAWAYS:

• Capital budgeting is the process of planning and evaluating long-term investments (e.g., buying new machinery, expanding stores) to maximize shareholder wealth.
• NPV (Net Present Value) and IRR (Internal Rate of Return) are the two primary methods to assess project profitability, with NPV preferred for consistency.
• The payback period is a simple but flawed method that ignores time value of money but is still used for liquidity checks.
• Risk analysis (sensitivity, scenario, Monte Carlo) helps firms adjust for uncertainty in cash flows (e.g., Daraz’s supply chain delays).
• Mutually exclusive projects require comparing NPV profiles and IRR rankings to avoid conflicts (e.g., NTC’s 5G vs. fiber-optic upgrades).
• Real options (e.g., expanding Pathao’s fleet) add flexibility to traditional NPV/IRR models.

1. Introduction to Capital Budgeting

Capital budgeting is the long-term investment decision-making process where firms allocate funds to projects with returns spanning 1+ years. Unlike short-term working capital (e.g., inventory), these decisions are irreversible and impact the company’s future cash flows.

Why it matters:

• Shareholder wealth maximization requires choosing projects that generate positive NPV (present value of cash inflows > initial investment).
• Example: Daraz must decide whether to open a new warehouse in Pokhara or invest in automation for faster deliveries.

2. Key Methods for Evaluating Projects

A. Net Present Value (NPV)

NPV measures the difference between the present value of cash inflows and outflows of a project. A positive NPV means the project adds value.

Formula: $$NPV=\sum _{t=0}^n\frac{C{F}_t}{(1+r{)}^t}-I_0$$

• $C{F}_t$ = Cash flow at time t
• $r$ = Discount rate (WACC)
• $I_0$ = Initial investment

Example: Kathmandu Retail Shop (NPR 1M Investment) A shop owner buys a new POS system costing NPR 1,000,000 with expected cash flows:

Discount rate (WACC) = 10%

gantt
    title NPV Calculation for POS System
    section Year 0
    Initial Investment :a1, -1,000,000
    section Year 1
    CF1 :a2, 300,000
    section Year 2
    CF2 :a3, 400,000
    section Year 3
    CF3 :a4, 500,000

Calculations:

• PV of CF1 = 300,000 / (1.1)^1 = 272,727
• PV of CF2 = 400,000 / (1.1)^2 = 330,579
• PV of CF3 = 500,000 / (1.1)^3 = 365,888
• **NPV = 272,727 + 330,579 + 365,888 - 1,000,000 = 269,254 (Accept!)

Visual:

NPV (NPR)
   ^
   | 500,000
   |       *
   |      /
   |     /
   |____*________> Project A (NPV=+)
   |     \
   |      \
   |_______*________> Project B (NPV=-)
   |
   0
   --------------------> Investment (NPR)

Key Takeaway: NPV is additive—if two projects are independent, sum their NPVs.

B. Internal Rate of Return (IRR)

IRR is the discount rate that makes NPV = 0. It answers: "What return does this project generate?"

Example (Same POS System): Solve for $r$ in: $$-1,000,000+\frac{300,000}{(1+r)}+\frac{400,000}{(1+r{)}^2}+\frac{500,000}{(1+r{)}^3}=0$$ Solution (using Excel/calculator): IRR ≈ 27.5%

Comparison Table:

When to use IRR?

• When comparing mutually exclusive projects (e.g., NTC’s 5G vs. fiber-optic upgrade).
• If projects have unequal lives, use Equivalent Annual Annuity (EAA).

C. Payback Period

The time it takes to recover initial investment from cash inflows.

Formula: $$\text{Payback}=\text{Year before full recovery}+\frac{\text{Unrecovered cost}}{\text{Cash flow in recovery year}}$$

Example (POS System):

• Year 1: 300,000 (Remaining: 700,000)
• Year 2: 400,000 (Remaining: 300,000)
• Payback = 2 + (300,000 / 500,000) = 2.6 years

Visual:

Year 0: -1,000,000
Year 1: 300,000 (Cumulative: -700,000)
Year 2: 400,000 (Cumulative: -300,000)
Year 2.6: Break-even

Why it’s flawed:

• Ignores time value of money.
• Doesn’t consider cash flows after payback.

When to use?

• For liquidity checks (e.g., Pathao’s fleet replacement).
• If projects have high risk of failure (short payback = safer).

3. Comparing Projects

A. Independent vs. Mutually Exclusive Projects

• Independent: Accept if NPV > 0 (e.g., Daraz’s new warehouse + automation).
• Mutually Exclusive: Choose the one with higher NPV (e.g., NTC’s 5G vs. fiber-optic).

Example: NTC’s Network Upgrade

Decision: Choose 5G (higher NPV).

Conflict: If IRR ranks Fiber-Optic higher (12% vs. 15%), but NPV ranks 5G higher, NPV is preferred (consistent with shareholder wealth).

B. Capital Rationing

When firms have limited funds, they must rank projects by:

1. NPV per unit of capital (e.g., NPR 100,000 per NPR 1M investment).
2. Profitability Index (PI) = PV of inflows / Initial cost (PI > 1 = acceptable).

Example: Kathmandu Retail Shop (NPR 2M Budget)

Decision: Accept POS System (higher PI).

4. Risk Analysis in Capital Budgeting

Projects carry uncertainty—risk analysis adjusts for this.

A. Sensitivity Analysis

Tests how NPV changes if key variables (e.g., sales, discount rate) vary.

Example: Daraz’s Warehouse Project

Visual:

NPV (NPR)
   ^
   | 1,200,000
   |       *
   |      /
   |     /
   |____*________> Base Case (5M sales)
   |     \
   |      \
   |_______*________> -10% Sales (4.5M)
   |
   0
   --------------------> Sales (NPR)

Key Insight: If NPV drops to zero at -20% sales, the project is highly sensitive to demand.

B. Scenario Analysis

Evaluates best-case, worst-case, and most-likely scenarios.

Decision Rule: If worst-case NPV > 0, proceed.

C. Monte Carlo Simulation

Uses random sampling to model probability distributions of NPV.

Example Output (Daraz):

• 50% chance NPV > 500,000
• 20% chance NPV < 0

5. Real Options in Capital Budgeting

Traditional NPV/IRR ignore flexibility. Real options account for:

• Option to expand (e.g., Pathao adding new routes).
• Option to abandon (e.g., Daraz exiting a loss-making region).

Example: Pathao’s Fleet Expansion

• NPV without option: -50,000 (lose money)
• NPV with option to expand: +200,000 (flexibility adds value)

6. Working Capital Considerations

Capital budgeting isn’t just about fixed assets—it includes:

• Increased working capital (e.g., inventory for Daraz’s new warehouse).
• Net working capital (NWC) adjustment: $$NP{V}_{\text{adjusted}}=NP{V}_{\text{project}}-\Delta NWC$$

flowchart TD
    A["Initial Investment: NPR 1M POS System"]
    B["Working Capital Needed: NPR 200,000"]
    C["Operating Cash Flows: NPR 300K/yr"]
    D["Terminal Working Capital Release: NPR 200,000"]
    A -->|"+"| B
    C -->|"-"| B
    D -->|"-"| B
    caption "Working capital cycle for Kathmandu Retail Shop’s POS system (ignored in NPV if net zero)."

Example: Daraz’s Warehouse

• Initial NWC increase: NPR 500,000 (extra inventory).
• Adjusted NPV = 800,000 - 500,000 = 300,000

7. Ethical and Strategic Considerations

• Agency problems: Managers may favor short-term IRR over long-term NPV (e.g., NTC’s political pressures).
• Greenwashing: Some projects are approved for social benefits (e.g., NEPSE’s renewable energy) but have low NPV.

In the Real World

1. Daraz’s Supply Chain Expansion

   • Idea: Uses NPV analysis to decide whether to open a new warehouse in Pokhara or invest in automation for faster deliveries.
   • Why it matters: Daraz must balance initial costs (NPR 20M for warehouse) vs. future savings (NPR 5M/year in logistics).

2. NTC’s 5G vs. Fiber-Optic Upgrade

   • Idea: Compares NPV profiles of two mutually exclusive projects.
   • Why it matters: NTC chose 5G (NPV = NPR 1.2B) over fiber-optic (NPV = NPR 800M) despite lower IRR.

3. Pathao’s Fleet Risk Management

   • Idea: Uses Monte Carlo simulation to model fuel price fluctuations and driver availability.
   • Why it matters: Helps Pathao avoid sudden cash flow shortages during peak seasons.

Exam Tip

• NPV is king: Always prefer NPV over IRR unless projects have unequal lives.
• Show calculations: For numerical questions, present a clear table with years, cash flows, and PV columns.
• Compare methods: If asked to evaluate two projects, use a table like the one above.
• Risk analysis is key: Expect sensitivity analysis questions—always test sales, discount rate, and project life.
• Real-world tie-ins: Link answers to Nepali businesses (e.g., "Like Daraz, a Kathmandu shop must use NPV to justify a POS system").

Sample Exam Answer Structure:

1. Define the method (e.g., "NPV is the present value of cash inflows minus outflows").
2. Calculate NPV/IRR (show work).
3. Compare projects (if mutually exclusive).
4. Discuss risk (sensitivity analysis).
5. Recommend decision (e.g., "Accept Project A due to higher NPV").

Final Visual: The Capital Budgeting Decision Tree

graph TD
    A["Start"] --> B{"Independent Projects?"}
    B -->|"Yes"| C["Accept if NPV > 0"]
    B -->|"No"| D{"Mutually Exclusive?"}
    D -->|"Yes"| E["Choose higher NPV"]
    D -->|"No"| F["Compare NPV/IRR"]
    C --> G["Analyze Risk"]
    E --> G
    F --> G
    G --> H["Implement"]