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

TAKEAWAYS:

• NPV (Net Present Value) measures an investment’s profitability in today’s money using a discount rate.
• IRR (Internal Rate of Return) finds the discount rate where NPV = 0; higher IRR > cost of capital = accept.
• Payback Period tells how long it takes to recover initial cash outflow; shorter = less risk.
• Profitability Index (PI) ranks projects by value created per rupee invested (PI > 1 = good).
• Mutually exclusive vs. independent projects changes how you compare them (e.g., choose the higher NPV).
• Inflation and risk adjustments are critical for real-world decisions (e.g., Kathmandu’s monsoon-season equipment).

1. What is Capital Budgeting?

Capital budgeting is the process of planning, evaluating, and selecting long-term investments (e.g., buying new kitchen equipment for a hotel, expanding a restaurant, or upgrading a POS system). These decisions:

• Affect cash flows for years (unlike short-term working capital).
• Require large upfront costs but generate future benefits.
• Determine a hotel’s growth and profitability.

2. Key Capital Budgeting Techniques

The syllabus focuses on four primary methods, each with strengths and weaknesses. Below is a comparison table to help you decide which to use when:

3. How to Calculate NPV (Step-by-Step)

NPV is the most reliable method because it discounts future cash flows to present value (PV) using a required rate of return (discount rate).

Step 1: Estimate Cash Flows

• Initial Investment (Outflow): Cost of the project (e.g., buying a new deep fryer for Rs 500,000).
• Operating Cash Flows (Inflows): Annual savings or revenue generated (e.g., Rs 150,000/year for 5 years).
• Terminal Cash Flow: Salvage value at the end (e.g., Rs 50,000 after 5 years).

Step 2: Choose a Discount Rate

• This is the cost of capital (e.g., 12% for a hotel).
• Why? Money has a time value—Rs 100 today > Rs 100 in 5 years.

Step 3: Calculate PV of Each Cash Flow

Use the formula: $$\text{PV}=\frac{{\text{CF}}_t}{(1+r{)}^t}$$ where:

• ${\text{CF}}_t$ = Cash flow at time $t$,
• $r$ = discount rate,
• $t$ = year.

Step 4: Sum PVs and Subtract Initial Investment

$$\text{NPV}=\text{PV of Future CFs}-\text{Initial Investment}$$

4. Worked Example: Lumbini Hotel’s Equipment Purchase

Scenario: Lumbini Hotel is considering buying a new commercial ice cream machine for Rs 800,000. It will:

• Save Rs 250,000/year in labor and maintenance for 4 years.
• Have a salvage value of Rs 100,000 at the end.
• The hotel’s cost of capital is 10%.

Cash Flow Timeline

gantt
    title Lumbini Hotel: Ice Cream Machine Cash Flows
    dateFormat  YYYY
    section Initial Investment
    Year 0: -800,000, initial
    section Operating Cash Flows
    Year 1: +250,000, CF1
    Year 2: +250,000, CF2
    Year 3: +250,000, CF3
    Year 4: +250,000, CF4
    section Terminal Cash Flow
    Year 4: +100,000, salvage

NPV Calculation

*Year 4 CF = Operating CF + Salvage Value = 250,000 + 100,000

Decision: Since NPV = Rs 150,550 > 0, Lumbini Hotel should buy the machine.

5. Internal Rate of Return (IRR)

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

How to Find IRR

1. Plug cash flows into a financial calculator or Excel (=IRR() function).
2. Compare IRR to the cost of capital:
   • If IRR > cost of capital → Accept.
   • If IRR < cost of capital → Reject.

IRR for Lumbini Hotel’s Machine

Using Excel:

=IRR({-800000, 250000, 250000, 250000, 350000})

Result: IRR = 15.2%

Decision: Since 15.2% > 10% (cost of capital), accept the project.

6. Payback Period (PP)

PP tells you how long it takes to recover the initial investment.

Formula for Equal Cash Flows

$$\text{PP}=\frac{\text{Initial Investment}}{\text{Annual Cash Inflow}}$$

Lumbini Hotel’s PP Calculation

$$\text{PP}=\frac{800,000}{250,000}=3.2\text{ years}$$ Decision Rule: If the hotel’s PP cutoff is ≤ 3 years, reject. If > 3 years, consider other factors.

7. Profitability Index (PI)

PI = PV of Future Cash Flows / Initial Investment.

• PI > 1: Good (creates value).
• PI < 1: Bad (destroys value).

Lumbini Hotel’s PI

$$\text{PI}=\frac{950,550}{800,000}=1.19$$ Decision: Since PI = 1.19 > 1, accept.

8. Comparing Projects: Mutually Exclusive vs. Independent

Why NPV > IRR for Mutually Exclusive? IRR can rank projects incorrectly if they have different scales or timing. NPV accounts for total wealth creation.

9. Real-World Applications in Nepal

1. eSewa & Khalti: Capital Budgeting for App Development

• Idea Used: NPV and IRR to decide whether to invest in new features (e.g., bill splitting, QR payments).
• How?
  • Initial cost: Rs 5 million for development.
  • Annual revenue boost: Rs 20 million/year for 5 years.
  • Discount rate: 15% (cost of capital for fintech).
  • NPV = Rs 42 million > 0 → Proceed with development.

2. Daraz/Nepal’s Retail Stores: Warehouse Expansion

• Idea Used: Payback Period and PI to evaluate warehouse upgrades.
• How?
  • Cost: Rs 20 million.
  • Annual savings: Rs 5 million (lower logistics costs).
  • PP = 4 years.
  • If Daraz’s PP cutoff is ≤ 3 years, they might reject unless PI > 1.2.

3. NTC’s Fiber Optic Network Expansion

• Idea Used: NPV for large infrastructure projects.
• How?
  • Initial cost: Rs 10 billion.
  • Annual revenue from new subscribers: Rs 3 billion/year for 10 years.
  • Discount rate: 8% (government bond rate).
  • NPV = Rs 12 billion > 0 → Justifies expansion.

10. Adjusting for Inflation and Risk

Inflation

• If cash flows are nominal (not adjusted for inflation), use the nominal discount rate.
• If cash flows are real, use the real discount rate: $$\text{Real Rate}=\frac{1+\text{Nominal Rate}}{1+\text{Inflation Rate}}-1$$ Example: Nominal rate = 12%, Inflation = 5% → Real rate = 6.67%.

Risk Adjustment

• Higher risk → Higher discount rate.
• Example: A new restaurant concept (high risk) might use a 18% discount rate, while a POS system upgrade (low risk) uses 10%.

11. Common Mistakes to Avoid

1. Ignoring the Time Value of Money: Always discount cash flows!
2. Using Accounting Profits Instead of Cash Flows: NPV requires actual cash inflows/outflows, not book profits.
3. Assuming All Cash Flows Are Equal: Real projects have uneven cash flows (e.g., higher maintenance in Year 3).
4. Overlooking Opportunity Costs: If you buy a new oven, the old one’s salvage value is a cash outflow.
5. Multiple IRRs: Can happen with non-conventional cash flows (e.g., negative CFs after initial investment).

12. Exam Tip: How to Score Full Marks

1. Always Show Calculations:
   • For NPV, list each year’s PV in a table.
   • For IRR, mention whether it’s > or < cost of capital.
2. Compare Methods:
   • Example: "While Project A has a higher IRR (20%), Project B has a higher NPV (Rs 5M) because it’s larger in scale."
3. Real-World Tie-Ins:
   • Relate to hotels, restaurants, or Nepali businesses (e.g., "Like Lumbini Hotel’s ice cream machine example...").
4. Decision Rules:
   • NPV: Accept if > 0.
   • IRR: Accept if > cost of capital.
   • PP: Accept if ≤ cutoff.
   • PI: Accept if > 1.
5. Watch for Tricks:
   • Questions may ask for both NPV and IRR—compare them!
   • Some projects have uneven cash flows (don’t assume equal inflows).

13. Quick Revision Table

14. Final Worked Example: Kathmandu’s Restaurant Expansion

Scenario: A restaurant in Kathmandu is considering expanding its seating area for Rs 2,000,000. It expects:

• Additional revenue: Rs 600,000/year for 5 years.
• No salvage value.
• Cost of capital: 12%.

NPV Calculation

Decision: Reject (NPV < 0). Why? The expansion doesn’t earn enough to cover the cost at a 12% discount rate.

15. Summary Flowchart: The Capital Budgeting Process

flowchart TD
    A["Identify Investment Opportunities"] --> B["Estimate Cash Flows"]
    B --> C["Determine Discount Rate"]
    C --> D["Calculate NPV/IRR/PP/PI"]
    D --> E{"NPV > 0?"}
    E -->|"Yes"| F["Accept Project"]
    E -->|"No"| G["Reject Project"]
    F --> H["Monitor & Review"]
    G --> H
    D --> I{"Mutually Exclusive?"}
    I -->|"Yes"| J["Choose Higher NPV"]
    I -->|"No"| K["Accept All Good Projects"]

16. Key Terms to Remember

17. Practice Questions (Exam-Style)

1. NPV Calculation: A hotel is considering a Rs 500,000 spa upgrade with cash flows of Rs 150,000/year for 4 years. Cost of capital = 10%. Calculate NPV.

2. IRR Decision: Project X has IRR = 14%, cost of capital = 12%. Project Y has IRR = 16%, but NPV = -Rs 50,000. Which should you choose? Why?

3. Payback Period: A restaurant’s new grill costs Rs 300,000 and saves Rs 100,000/year. What’s the PP? If the cutoff is 3 years, accept or reject?

4. PI Ranking: You have Rs 1M to invest. Project A: NPV = Rs 200K, initial = Rs 500K. Project B: NPV = Rs 150K, initial = Rs 300K. Rank them by PI.

18. Answer to Practice Question 1 (NPV)

Decision: Accept (NPV > 0).