Capital Budgeting: Techniques, Projects & Decision Rules

Core Concepts

What is Capital Budgeting?

Capital budgeting is the process by which a firm evaluates and selects long-term investment projects (capital expenditures) that maximize shareholder value. These decisions are critical because they involve large sums of money and have long-term implications for the firm’s operations and growth.

Why is it important?

• Long-term decisions (e.g., buying machinery, expanding a factory, launching a new product line).
• Irreversible or hard-to-reverse commitments.
• Directly impacts a firm’s profitability, risk, and competitive position.

Key Techniques for Capital Budgeting

1. Net Present Value (NPV)

NPV is the most widely used capital budgeting technique. It calculates the present value of all cash inflows and outflows associated with a project, discounted at the firm’s cost of capital. If NPV > 0, the project is acceptable.

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 (cost of capital),
• $I_0$ = Initial investment,
• $n$ = Project life.

Worked Example: Kathmandu Electronics

Kathmandu Electronics is considering investing in a new production line that costs Rs 5,000,000. The project is expected to generate the following cash flows over 5 years, with a discount rate of 12%:

Step-by-Step Calculation:

1. Calculate the present value (PV) of each cash flow:

   • Year 1: $\frac{1,500,000}{(1.12{)}^1}=1,339,286$
   • Year 2: $\frac{1,800,000}{(1.12{)}^2}=1,385,403$
   • Year 3: $\frac{2,000,000}{(1.12{)}^3}=1,409,285$
   • Year 4: $\frac{1,200,000}{(1.12{)}^4}=752,688$
   • Year 5: $\frac{800,000}{(1.12{)}^5}=463,193$

2. Sum the PVs and subtract the initial investment: $$NPV=1,339,286+1,385,403+1,409,285+752,688+463,193-5,000,000=349,855$$

Decision: Since NPV (Rs 349,855) > 0, the project is acceptable.

2. Internal Rate of Return (IRR)

IRR is the discount rate that makes the NPV of a project zero. It represents the project’s expected return. If IRR > cost of capital, the project is acceptable.

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

Worked Example: Daraz Logistics Expansion

Daraz is evaluating a warehouse expansion costing Rs 10,000,000 with the following cash flows:

Using a financial calculator or Excel’s IRR function, we find: $$IRR\approx 18.5\%$$

Decision: If Daraz’s cost of capital is 12%, the project’s IRR (18.5%) > 12%, so it is acceptable.

3. Profitability Index (PI)

PI (or Benefit-Cost Ratio) measures the ratio of the present value of cash inflows to the initial investment. A PI > 1 indicates a profitable project.

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

Worked Example: Ncell Tower Upgrade

Ncell is considering upgrading a cell tower for Rs 8,000,000. The expected cash flows (discounted at 10%) are:

$$PI=\frac{2,272,727+2,479,339+1,502,625}{8,000,000}=1.06$$

Decision: Since PI (1.06) > 1, the project is profitable.

4. Payback Period (PP)

PP measures how long it takes to recover the initial investment from project cash flows. Shorter PP is generally preferred, but it ignores the time value of money.

Formula: $$PP=\text{Year before full recovery}+\frac{\text{Remaining investment}}{\text{Cash flow in the year of recovery}}$$

Worked Example: Kathmandu Biscuit Factory

The factory is evaluating a new oven costing Rs 4,000,000 with the following cash flows:

Calculation:

• Year 1: Rs 1,200,000 (Remaining: Rs 2,800,000)
• Year 2: Rs 1,500,000 (Remaining: Rs 1,300,000)
• Year 3: Rs 1,800,000 (Recovered in Year 3)

$$PP=2+\frac{1,300,000}{1,800,000}=2.72\text{ years}$$

Decision: If the firm’s target PP is 3 years, this project is acceptable.

5. Discounted Payback Period (DPP)

DPP adjusts PP for the time value of money by discounting cash flows. It is more rigorous than PP.

Formula: Same as PP, but cash flows are discounted.

Worked Example: NTC Fiber Expansion

NTC is investing Rs 6,000,000 in fiber expansion with a 10% discount rate. Cash flows:

Calculation:

• Year 1: Rs 1,818,182 (Remaining: Rs 4,181,818)
• Year 2: Rs 2,066,116 (Remaining: Rs 2,115,702)
• Year 3: Rs 1,502,625 (Recovered in Year 3)

$$DPP=2+\frac{2,115,702}{1,502,625}=3.41\text{ years}$$

Decision: If NTC’s target DPP is 4 years, this project is acceptable.

Comparing Capital Budgeting Techniques

Real-World Applications in Nepal

1. eSewa: Digital Payment Infrastructure

• Idea Used: Capital budgeting for IT infrastructure upgrades.
• How? eSewa invests in servers, cybersecurity, and mobile app development. They use NPV and IRR to evaluate whether the long-term benefits (e.g., reduced fraud, higher transaction volumes) justify the initial costs (e.g., Rs 50 million server upgrade in 2022).
• Example: eSewa’s decision to expand its API for third-party integrations (e.g., Daraz, Pathao) was likely evaluated using PI to ensure the project’s efficiency given limited IT budget.

2. Ncell: 5G Network Rollout

• Idea Used: Capital budgeting for telecom infrastructure.
• How? Ncell spent Rs 20 billion on 5G infrastructure in 2023. They used:
  • NPV to compare the present value of future 5G revenue (e.g., higher data usage, premium services) against the initial investment.
  • IRR to ensure the project’s return exceeded their cost of capital (~15%).
• Real Constraint: Long payback period (5–7 years) due to high upfront costs, but justified by Nepal’s growing mobile internet adoption.

3. Kathmandu Metropolitan City (KMC): Smart Traffic Management

• Idea Used: Public sector capital budgeting for urban projects.
• How? KMC’s Rs 1.2 billion smart traffic light project (2024) was evaluated using:
  • NPV to assess reduced congestion costs (e.g., saved fuel, time) vs. hardware costs.
  • PP to ensure quick recovery from traffic fines and reduced accidents.
• Visual:

  flowchart TD
    A["KMC Traffic Project"] --> B["Initial Investment: Rs 1.2B"]
    B --> C["Cash Flows: Rs 300M/year"]
    C --> D["NPV Calculation: Discount @8%"]
    D --> E["PP: 4.5 years"]
    E --> F["Decision: Approve"]

4. Nepal Electricity Authority (NEA): Hydropower Projects

• Idea Used: Large-scale infrastructure capital budgeting.
• How? NEA’s West Seti Hydropower Project (Rs 18 billion) was evaluated using:
  • IRR > 12% (NEA’s hurdle rate) to justify the investment.
  • PI > 1.2 to ensure efficiency given budget constraints.
• Real Constraint: Long gestation period (5–10 years) and political risks, but critical for Nepal’s energy security.

Step-by-Step: The Capital Budgeting Process

flowchart TD
  A["Identify Investment Opportunities"] --> B["Estimate Cash Flows"]
  B --> C["Determine Discount Rate (Cost of Capital)"]
  C --> D["Select Evaluation Technique (NPV/IRR/PI/PP)"]
  D --> E["Assess Risk and Uncertainty"]
  E --> F["Make Decision: Accept/Reject"]
  F --> G["Implement and Monitor"]
  G --> H["Post-Audit: Compare Actual vs. Projected"]

Risk and Uncertainty in Capital Budgeting

Common Risks:

1. Market Risk: Changes in demand (e.g., Daraz’s e-commerce growth vs. brick-and-mortar retail).
2. Operational Risk: Technology obsolescence (e.g., Ncell’s 5G vs. 4G).
3. Financial Risk: Interest rate fluctuations (e.g., NTC’s debt financing for fiber expansion).
4. Political/Legal Risk: Regulatory changes (e.g., Nepal’s new electricity tariff policies).

Mitigation Strategies:

• Sensitivity Analysis: How does NPV change if sales are 10% lower?
• Scenario Analysis: Best-case, worst-case, and most-likely scenarios.
• Simulation (Monte Carlo): Probabilistic modeling of cash flows.

Example: Kathmandu Manufacturing Company (KMC)

KMC is evaluating a new production line costing Rs 15,000,000 with expected cash flows of Rs 5,000,000/year for 5 years. The discount rate is 14%.

Base Case NPV: $$NPV=-15,000,000+\frac{5,000,000}{1.14}+\frac{5,000,000}{(1.14{)}^2}+\cdots +\frac{5,000,000}{(1.14{)}^5}=1,250,000$$

Sensitivity Analysis:

Decision: The project is risky if sales drop, so KMC might require a higher IRR threshold (e.g., 18%) or seek hedging.

Capital Rationing and Project Selection

When a firm has limited funds, it must prioritize projects. Techniques include:

1. NPV per Rupee Invested: Maximizes value creation.
2. PI Ranking: Selects projects with the highest efficiency.
3. Modified IRR: Adjusts for different project lives.

Example: NEPSE-Listed Company (e.g., Nabil Bank)

Nabil Bank has Rs 500 million to invest in two projects:

• Project A: NPV = Rs 80 million, Investment = Rs 300 million
• Project B: NPV = Rs 60 million, Investment = Rs 200 million

NPV per Rupee:

• Project A: $\frac{80}{300}=0.267$
• Project B: $\frac{60}{200}=0.300$

Decision: Choose Project B first (higher NPV per rupee), then allocate remaining funds to Project A.

Exam Tip: How to Score Full Marks

1. Definitions:

   • Always define key terms (e.g., "NPV is the difference between the present value of cash inflows and outflows...").
   • Example: "Capital budgeting is the process of evaluating long-term investment proposals to maximize shareholder wealth."

2. Formulas:

   • Write the formula clearly and label variables (e.g., $r=\text{cost of capital}$).
   • Example: $$NPV=\sum _{t=0}^n\frac{C{F}_t}{(1+r{)}^t}-I_0$$

3. Worked Examples:

   • Use real Nepali businesses (e.g., Ncell, Daraz, KMC) for context.
   • Show step-by-step calculations with tables for cash flows and NPV/IRR.
   • Example table for NPV:

     | Year | Cash Flow (Rs) | PV Factor (12%) | PV (Rs) |
     |------|----------------|-----------------|---------|
     | 0    | -5,000,000     | 1.00            | -5,000,000|
     | 1    | 1,500,000      | 0.8929          | 1,339,286|
     | 2    | 1,800,000      | 0.7972          | 1,434,960|
     

4. Comparisons:

   • Use tables to compare techniques (e.g., NPV vs. IRR).
   • Highlight when to use each (e.g., "Use NPV for mutually exclusive projects").

5. Real-World Links:

   • Connect theory to Nepali companies (e.g., "Ncell uses IRR to evaluate 5G projects").
   • Mention constraints (e.g., "NTC’s fiber expansion faces long PP due to high upfront costs").

6. Risk Analysis:

   • Always discuss uncertainty (e.g., "Sensitivity analysis shows NPV drops to negative if sales fall 15%").
   • Use scenario analysis in your answer.

7. Decision Rules:

   • State clear accept/reject criteria (e.g., "Accept if NPV > 0 and IRR > cost of capital").
   • Example: "Since the project’s IRR (18.5%) > Ncell’s cost of capital (12%), it should be accepted."

8. Diagrams:

   • Draw the capital budgeting process (use Mermaid flowchart).
   • Show NPV profiles for IRR calculations (graph of NPV vs. discount rate).

Common Mistakes to Avoid

1. Ignoring the Time Value of Money:

   • Never use undiscounted cash flows for NPV or IRR. Always discount!

2. Miscounting Cash Flows:

   • Include all cash flows, including:
     • Initial investment (Year 0).
     • Operating cash flows (Years 1–n).
     • Terminal cash flow (salvage value, if any).

3. Assuming Reinvestment at IRR:

   • IRR assumes cash flows are reinvested at the project’s IRR, which may not be realistic.

4. Overlooking Risk:

   • Always discuss uncertainty (e.g., "The project’s NPV is sensitive to changes in interest rates").

5. Mixing Techniques:

   • Don’t compare NPV and IRR directly without context. NPV is theoretically superior for mutually exclusive projects.

Practice Questions (Based on Past Exams)

1. NPV and Profitability Index: A firm has a project with an initial investment of Rs 10 million and expected cash flows of Rs 3 million/year for 5 years. The discount rate is 10%.

   • Calculate NPV.
   • Calculate PI. Is the project profitable?

2. IRR and Decision Rule: A company is evaluating two projects:

   • Project X: Initial investment = Rs 5 million, IRR = 15%
   • Project Y: Initial investment = Rs 7 million, IRR = 12% The firm’s cost of capital is 10%.
   • Which project(s) should be accepted? Why?

3. Payback Period: A firm invests Rs 8 million in a project with the following cash flows:

   Year	Cash Flow (Rs)
   1	2,000,000
   2	3,000,000
   3	4,000,000
   Calculate the payback period. If the firm’s target PP is 2.5 years, should the project be accepted?

4. Sensitivity Analysis: A project has an NPV of Rs 2 million at base case. If sales drop by 10%, NPV becomes Rs 500,000. If sales increase by 10%, NPV becomes Rs 3.5 million.

   • What does this tell you about the project’s risk?
   • How would you advise the financial manager?

Summary Table: Key Takeaways

Final Checklist for Exam Answers

1. Define the concept clearly.
2. Show calculations step-by-step (use tables for cash flows).
3. Link to a real Nepali business (e.g., Ncell, Daraz, KMC).
4. Discuss risk and uncertainty (sensitivity analysis).
5. State the decision rule (e.g., "Accept if NPV > 0").
6. Use visuals (Mermaid flowchart, NPV table, or sensitivity graph).