Capital Budgeting: NPV, IRR, Payback, and Decision Rules

Capital Budgeting Overview

Capital budgeting is the discipline of planning, evaluating, and selecting long‑term investment projects that will generate cash flows over multiple years. It is the bridge between a firm’s strategic objectives and its financial resources.

The Capital Budgeting Process

flowchart TD
  A["Identify Investment Opportunities"] --> B["Estimate Cash Flows"]
  B --> C["Determine Discount Rate"]
  C --> D["Compute NPV, IRR, Payback, PI"]
  D --> E["Perform Sensitivity & Scenario Analysis"]
  E --> F["Make Decision: Accept or Reject"]
  F --> G["Implement & Monitor"]

Key Concepts and Definitions

Cash Flow Estimation

Cash flows are divided into initial outlay and operating cash flows.

• Initial Outlay: Purchase of assets, installation costs, working capital changes.
• Operating Cash Flows:
  $$\text{Operating CF}=(\text{Sales}-\text{Variable Costs})\times (1-\text{Tax Rate})+\text{Depreciation}$$
• Terminal Cash Flow: Salvage value plus release of working capital at project end.

Example: Kathmandu Retail Shop – New POS System

Assume WACC = 12 % and tax rate = 30 %. Depreciation is straight‑line over 5 years: 240,000 per year.

Net Present Value (NPV)

NPV is calculated as:
$$\text{NPV}=\sum _{t=0}^n\frac{C{F}_t}{(1+r{)}^t}$$ where $r$ is the discount rate.

Calculations:

Since NPV > 0, the POS investment adds value and should be accepted.

Internal Rate of Return (IRR)

IRR is the discount rate that sets NPV to zero. It can be found by trial‑and‑error or using financial calculators.

For the POS example, IRR ≈ 18 %.

• Interpretation: The project yields an 18 % return per year, higher than the 12 % WACC.
• Decision Rule: Accept if IRR ≥ WACC.

Payback Period

Payback Period = time to recover initial investment from cumulative cash inflows.

Payback = 3 years + (150,000/450,000) ≈ 3.33 years.

Discounted Payback Period

Using discounted cash flows:

Discounted Payback ≈ 4.5 years.

Profitability Index (PI)

$$\text{PI}=\frac{\text{Present Value of Future CFs}}{\text{Initial Investment}}$$ PI = 1.34.

Rule: Accept if PI > 1.

Comparison of Decision Rules

Sensitivity and Scenario Analysis

• Sensitivity: Vary one variable (e.g., sales volume) and observe NPV change.
• Scenario: Define best, base, worst cases and compute NPVs for each.

flowchart LR
  A["Base Case NPV"] --> B["Best Case NPV"]
  A --> C["Worst Case NPV"]
  B --> D["Decision"]
  C --> D

Real Options in Capital Budgeting

Projects often contain optionality: the ability to expand, abandon, or delay. Real‑options valuation (e.g., Black‑Scholes) can be applied to capture this value, especially in volatile markets like Nepal’s telecom sector.

In the Real World

1. eSewa – Payment Gateway Upgrade

   • Uses NPV to evaluate the cost of adding new security features.
   • Discount rate set at 10 % (WACC).
   • Projected cash inflows from increased transaction volume yield an NPV of NPR + 2 million, justifying the upgrade.

2. Daraz – New Warehouse Construction

   • Applies IRR to compare multiple warehouse sites.
   • Site A: IRR = 15 % (WACC = 12 %); Site B: IRR = 10 %.
   • Daraz selects Site A despite higher cost because IRR exceeds WACC.

3. Ncell – 5G Rollout

   • Uses Discounted Payback to ensure the investment recovers within 4 years, aligning with regulatory timelines.
   • Payback period of 3.8 years meets the company’s risk appetite.

Worked Example – Kathmandu Retail Shop

Problem: A shop wants to replace its aging cash register with a modern POS system.

• Initial cost: NPR 1,200,000.
• Expected annual savings: NPR 300,000, increasing by NPR 50,000 each year.
• Salvage value after 5 years: NPR 200,000.
• WACC: 12 %.

Solution:

1. Build cash flow table (shown above).
2. Compute NPV (shown above) → NPR + 413,000.
3. Compute IRR → 18 %.
4. Payback → 3.33 years.
5. Discounted Payback → 4.5 years.
6. PI → 1.34.

Decision: Accept the investment (NPV > 0, IRR > WACC, PI > 1).

Exam Tip

• Understand the decision rules: Know when to use NPV, IRR, Payback, PI.
• Practice cash flow tables: Be able to construct and discount cash flows quickly.
• Know the formulas: Memorize NPV, IRR, PI equations and how to set up the NPV equation for IRR.
• Interpret results: Explain why a project is accepted or rejected based on each metric.
• Sensitivity: Be ready to discuss how changes in discount rate or cash flows affect NPV.

POS terminal used in retail shops (Image: VideoPlasty, CC BY-SA 4.0, via Wikimedia Commons) Traditional cash register in a Nepali shop (Image: Subhrajyoti07, CC BY-SA 4.0, via Wikimedia Commons)