Project Economics & Decision-Making: NPV, ROI, Cost-Benefit, Break-Even

TAKEAWAYS:

• NPV (Net Present Value) compares present worth of costs vs. benefits using discount rates to select profitable projects.
• ROI (Return on Investment) measures profitability as (Net Profit/Investment)×100% over a timeline.
• Cost-Benefit Analysis quantifies tangible/intangible costs vs. benefits to justify project viability.
• Break-Even Analysis determines when cumulative revenue equals costs, using formulas like $\text{Break-Even Point}=\frac{\text{Fixed Costs}}{\text{Price per Unit}-\text{Variable Cost per Unit}}$.
• Decision Trees model probabilistic outcomes (e.g., project success/failure) to optimize choices.
• Sunk Costs are irrelevant to future decisions; focus on incremental costs/benefits.

Core Concepts: Financial Metrics for Project Selection

1. Net Present Value (NPV)

NPV adjusts future cash flows to present value using a discount rate (often the company’s cost of capital). A positive NPV indicates a project is financially viable.

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

• $C{F}_t$ = Cash flow at time $t$
• $r$ = Discount rate (e.g., 10% for riskier projects)
• $n$ = Project lifespan

Worked Example: Ncell’s 5G Expansion Ncell invests Rs. 20 million in 5G infrastructure. Projected annual cash flows (after costs) for 5 years are:

Discount rate (r): 12% Calculation: $$NPV=\frac{50}{1.12}+\frac{60}{1.12^2}+\frac{70}{1.12^3}+\frac{40}{1.12^4}+\frac{30}{1.12^5}-20$$ $$NPV=44.64+47.62+48.23+26.20+17.85-20=164.54\text{ lakhs (Positive → Approve)}$$

2. Return on Investment (ROI)

Measures profitability as a percentage of the initial investment. Higher ROI = better return.

Formula: $$ROI=\left(\frac{\text{Net Profit}}{\text{Initial Investment}}\right)\times 100\%$$

Worked Example: Daraz’s Warehouse Automation

• Initial Investment: Rs. 50 lakhs
• Projected Benefit (5 years): Rs. 100 lakhs
• Net Profit: Rs. 50 lakhs $$ROI=\left(\frac{50}{50}\right)\times 100\%=100\%\text{ over 5 years}$$ Breakdown by Year:

  Year	Cumulative Benefit (Rs. lakhs)	Cumulative Cost (Rs. lakhs)	Net Profit (Rs. lakhs)
  1	15	15	0
  2	30	15	15
  3	50	15	35
  4	80	15	65
  5	100	15	85

3. Cost-Benefit Analysis (CBA)

Compares tangible (e.g., revenue, savings) and intangible (e.g., brand reputation, employee morale) costs vs. benefits.

Steps:

1. Identify Costs/Benefits: Direct (e.g., hardware), indirect (e.g., training), and opportunity costs.
2. Monetize Intangibles: Assign dollar values (e.g., "faster response time = Rs. X/month in customer retention").
3. Discount Future Values: Use NPV to compare.
4. Calculate BCR (Benefit-Cost Ratio): $$BCR=\frac{\text{Present Value of Benefits}}{\text{Present Value of Costs}}$$
   • BCR > 1: Accept the project.

Example: eSewa’s Mobile Payment Upgrade

Decision-Making Tools

1. Break-Even Analysis

Determines when total revenue = total costs. Critical for startups (e.g., Pathao drivers, Daraz sellers).

Formula: $$\text{Break-Even Point (Units)}=\frac{\text{Fixed Costs}}{\text{Selling Price per Unit}-\text{Variable Cost per Unit}}$$

Example: Kathmandu Traffic Light Optimization

• Fixed Costs (Installation): Rs. 50 lakhs
• Variable Cost (Maintenance/year): Rs. 5 lakhs
• Annual Revenue from Reduced Congestion: Rs. 20 lakhs/year
• Selling Price per Unit (Revenue): Rs. 20 lakhs/year
• Variable Cost per Unit: Rs. 5 lakhs/year $$\text{Break-Even Year}=\frac{50}{20-5}=3.33\text{ years}$$ Visual:

graph TD
    A["Year 0"] -->|"Rs. 50L"| B["Fixed Costs"]
    C["Year 1"] -->|"Rs. 5L"| B
    D["Year 1"] -->|"Rs. 20L"| E["Revenue"]
    F["Year 3.33"] -->|"Cumulative Revenue = Cumulative Costs"| G["Break-Even"]

2. Decision Trees

Model probabilistic outcomes (e.g., project success/failure rates). Used by banks for loan approvals and NEPSE for stock investments.

Example: NTC’s Fiber Expansion

• Initial Cost: Rs. 100 lakhs
• Success Probability: 70% (Revenue: Rs. 200 lakhs)
• Failure Probability: 30% (Loss: Rs. 50 lakhs)
• Discount Rate: 10%

Decision Tree:

sequenceDiagram
    participant Investor as NTC
    participant Success as 70% Chance
    participant Failure as 30% Chance
    Investor->>Success: Rs. 200L (PV = 200/1.1 = 181.82L)
    Investor->>Failure: Rs. -50L (PV = -50/1.1 = -45.45L)
    Note right of Investor: Expected NPV = (0.7×181.82) + (0.3×-45.45) - 100 = 25.64L\n→ Approve

3. Sunk Costs vs. Incremental Analysis

• Sunk Costs: Already incurred (e.g., past R&D). Ignore in future decisions.
• Incremental Costs/Benefits: Only consider additional costs/benefits of a new project.

Example: Bank’s Loan Decision

• Sunk Cost: Rs. 2 lakhs spent on market research (irrelevant).
• Incremental Cost: Rs. 5 lakhs for new software.
• Incremental Benefit: Rs. 8 lakhs/year for 3 years. Decision: Approve (incremental NPV > 0).

Comparative Analysis of Methods

In the Real World

1. eSewa’s Mobile Payment System

   • NPV/BCR Used: eSewa evaluates every feature update (e.g., QR payments) using NPV to justify Rs. 50M+ annual tech spending. Example: Adding UPI integration cost Rs. 10M but generated Rs. 50M/year in transaction fees (BCR = 5).

2. Pathao’s Driver Incentives

   • Break-Even Analysis: Pathao uses break-even to decide driver bonuses. If a Rs. 2000/month bonus increases rides by 15% (revenue Rs. 5000/month), break-even is 4 months (Rs. 8000 cost vs. Rs. 5000 benefit).

3. Ncell’s 4G to 5G Migration

   • ROI Calculation: Ncell’s 5G rollout had a 120% ROI over 5 years due to:
     • Tangible: 30% higher ARPU (Average Revenue Per User).
     • Intangible: Reduced churn (customers switching to competitors).

4. Daraz’s Warehouse Automation

   • Cost-Benefit: Daraz’s Rs. 30M robotics investment saved Rs. 15M/year in labor (BCR = 2.33). Intangible benefits: 20% faster order fulfillment → higher customer retention.

5. NTC’s Fiber Optic Expansion

   • Decision Trees: NTC modeled fiber expansion in Pokhara with:
     • 70% chance: Rs. 80M revenue (NPV = +Rs. 30M).
     • 30% chance: Rs. -20M loss (NPV = -Rs. 10M).
     • Expected NPV: (0.7×30) + (0.3×-10) = Rs. 17M → Approved.

Exam Tip

1. NPV/ROI Calculations:

   • Always show step-by-step discounting (examiners check intermediate steps).
   • Use realistic discount rates (e.g., 10–15% for Nepali tech projects).
   • Example Pitfall: Forgetting to subtract the initial investment in NPV.

2. Break-Even Questions:

   • Draw a cumulative cost/revenue graph (even if not asked).
   • Label axes clearly (e.g., "Years" vs. "Rs. lakhs").

3. Decision Trees:

   • Must include:
     • Probabilities (e.g., 60% success).
     • Discounted cash flows.
     • Expected value calculation.
   • Common Mistake: Ignoring the discount rate.

4. Cost-Benefit Analysis:

   • Separate tangible/intangible in tables.
   • Justify monetization of intangibles (e.g., "faster load time = Rs. X/month in ad revenue").

5. Short Notes (2–3 marks):

   • NPV: "Compares present value of cash inflows/outflows using a discount rate."
   • ROI: "Measures profitability as (Net Profit/Investment)×100%."
   • Break-Even: "Point where total revenue equals total costs."

Nepal’s banks (e.g., NMB) use NPV to evaluate Rs. 100M+ IT infrastructure upgrades like core banking systems. (Image: Federal Bureau of Investigation, Public domain, via Wikimedia Commons)