Economic Analysis of Business Decisions: Decision-Making, Cost-Benefit, LP & Risk

TAKEAWAYS:

• Decision-making under uncertainty uses payoff tables and criteria (Maximax, Maximin, Minimax Regret) to choose optimal strategies—critical for startups like Pathao facing unpredictable demand.
• Linear programming solves constrained optimization problems (e.g., Daraz’s warehouse allocation) by graphing feasible regions and identifying corner points.
• Cost-benefit analysis compares monetary and non-monetary impacts (e.g., NTC’s fiber-optic expansion vs. traffic congestion trade-offs).
• Risk assessment quantifies uncertainty (e.g., NEPSE stock volatility) using probability distributions and expected value calculations.
• Break-even analysis determines minimum sales volume (e.g., a local bakery’s Rs. 500/day threshold) to cover costs.
• Sensitivity analysis tests how changes in variables (e.g., fuel prices for Ncell’s logistics) affect outcomes.

---

1. Decision-Making Under Uncertainty

Businesses often face decisions where outcomes depend on unpredictable factors (e.g., market trends, competitor actions). Decision theory provides structured methods to evaluate options using payoff tables and decision criteria.

Key Concepts

• States of Nature (S₁, S₂, ...): Possible future scenarios (e.g., "high demand," "low demand").
• Strategies (N₁, N₂, ...): Actions the decision-maker can take (e.g., "increase production," "reduce prices").
• Payoff Matrix: A table showing outcomes (profits/losses) for each strategy-state combination.

Decision Criteria

Worked Example: eSewa’s Marketing Strategy

Payoff Table (in Rs. '000):

| State of Nature | Strategy N₁ (TV Ads) | Strategy N₂ (Social Media) | Strategy N₃ (Influencers) |
|-----------------|----------------------|----------------------------|--------------------------|
| S₁ (High Demand)| 400                  | 200                        | 700                      |
| S₂ (Moderate)   | 100                  | 600                        | 300                      |
| S₃ (Low Demand) | 500                  | 300                        | 100                      |

Solutions:

1. Maximax Approach:

   • Highest payoff in each column: 700 (N₃).
   • Decision: Choose Strategy N₃ (Influencers).

2. Maximin Approach:

   • Minimum payoff in each column: 100 (N₁), 200 (N₂), 100 (N₃).
   • Decision: Choose N₁ or N₃ (both have the same worst-case outcome).

3. Minimax Regret:

   • Step 1: Calculate regret for each outcome (best payoff in the row minus actual payoff).

     | S₁ | N₁ (0) | N₂ (200) | N₃ (0) |
     | S₂ | N₁ (500) | N₂ (0) | N₃ (300) |
     | S₃ | N₁ (0) | N₂ (200) | N₃ (400) |
     

   • Step 2: Find maximum regret for each strategy: N₁ (500), N₂ (200), N₃ (400).
   • Decision: Choose N₂ (Social Media) to minimize maximum regret.

Real-World Application: Pathao’s Driver Incentives

Pathao uses Maximax for high-growth periods (e.g., Dashain) to maximize rider sign-ups, while Minimax Regret guides driver incentives during low-demand seasons to avoid driver attrition.

---

2. Linear Programming (LP)

LP optimizes constrained problems (e.g., maximizing profit or minimizing cost) using linear equations. Key terms:

• Objective Function: What to maximize/minimize (e.g., Z = 4x + 3y).
• Constraints: Limitations (e.g., 2x + y ≤ 10).
• Feasible Region: Area satisfying all constraints.
• Corner Points: Optimal solutions lie here (graphical method).

Graphical Solution Steps

1. Plot constraints as lines (equality) and shade feasible regions.
2. Identify corner points (intersections of constraint lines).
3. Evaluate the objective function at each corner point.

Worked Example: Daraz’s Warehouse Allocation

Problem: Maximize Z = 4x + 3y (profit from products X and Y) Subject to:

• 2x + y ≤ 10 (storage constraint)
• x + y ≤ 6 (labor constraint)
• x ≥ 0, y ≥ 0

Solution:

1. Plot Constraints:
   • 2x + y = 10 → Intercepts: (5,0), (0,10)
   • x + y = 6 → Intercepts: (6,0), (0,6)
2. Feasible Region: Shaded area satisfying all constraints.
3. Corner Points:
   • (0,0), (0,6), (3,0), (4,2)
4. Evaluate Z:
   • Z(0,0) = 0
   • Z(0,6) = 18
   • Z(3,0) = 12
   • Z(4,2) = 22 Optimal Solution: Produce 4 units of X and 2 units of Y for max profit of Rs. 22,000.

Real-World Application: NTC’s Network Expansion

NTC uses LP to allocate budgets for fiber-optic cables in Kathmandu and Pokhara, balancing:

• Constraint 1: Total budget ≤ Rs. 500 million.
• Constraint 2: Coverage must reach ≥ 80% of urban areas.
• Objective: Maximize internet speed (measured in Mbps).

---

3. Cost-Benefit Analysis (CBA)

CBA compares the monetary and non-monetary impacts of a project. Used by:

• Government: NTC’s fiber-optic expansion (benefits: economic growth; costs: traffic congestion).
• Businesses: Daraz’s warehouse relocation (benefits: lower shipping costs; costs: employee relocation).

Steps:

1. Identify Costs and Benefits:
   • Tangible: Measurable in Rs. (e.g., construction costs, revenue).
   • Intangible: Non-monetary (e.g., reduced pollution, improved safety).
2. Discount Future Values: Use PV = FV / (1 + r)^n (where r = discount rate, n = years).
3. Net Present Value (NPV): NPV = Σ(Benefits) - Σ(Costs).
   • If NPV > 0, accept the project.

Worked Example: NEPSE’s Stock Market Expansion

Project: Expand trading hours to 10 AM–6 PM (current: 11 AM–5 PM). Costs:

• Infrastructure upgrade: Rs. 20 million (one-time).
• Annual maintenance: Rs. 5 million. Benefits:
• Increased liquidity: Rs. 10 million/year.
• Reduced volatility: Rs. 5 million/year (intangible, valued at Rs. 3 million/year for analysis).

NPV Calculation (Discount Rate = 10%, 5 Years):

Real-World Application: Kathmandu Traffic Management

Project: Convert Thapathali into a pedestrian zone. Costs:

• Road construction: Rs. 50 million.
• Business relocations: Rs. 20 million. Benefits:
• Reduced congestion: Rs. 30 million/year (savings in fuel/time).
• Health benefits: Rs. 10 million/year (lower pollution-related diseases). NPV (12% discount rate, 10 years): Rs. 120 million → Feasible.

---

4. Break-Even Analysis

Determines the minimum sales volume where Total Revenue (TR) = Total Cost (TC). Formula:

Break-Even Point (Units) = Fixed Costs / (Price per Unit - Variable Cost per Unit)

Graph:

• TR: Linear (P × Q).
• TC: Linear (FC + VC × Q).
• Break-Even Point: Where TR and TC intersect.

Worked Example: Local Bakery

• Fixed Costs (FC): Rs. 5,000/month (rent, salaries).
• Variable Cost per Unit (VC): Rs. 20 (ingredients, labor).
• Selling Price (P): Rs. 50 per cake. Break-Even Calculation:

Break-Even (Units) = 5,000 / (50 - 20) = 166.67 → **167 cakes/month**

Profit at 200 cakes:

TR = 200 × 50 = Rs. 10,000
TC = 5,000 + (200 × 20) = Rs. 9,000
Profit = Rs. 1,000

Real-World Application: Ncell’s SIM Sales

• FC: Rs. 20 million (marketing, infrastructure).
• VC per SIM: Rs. 500 (subsidy, network access).
• Price per SIM: Rs. 1,500. Break-Even:

20,000,000 / (1,500 - 500) = 20,000 SIMs/month

Implication: Ncell must sell >20,000 SIMs/month to avoid losses.

---

5. Risk Assessment and Expected Value

Businesses quantify uncertainty using probability distributions and expected value (EV).

Key Formulas

1. Expected Value (EV):

   EV = Σ (Probability of Outcome × Payoff)
   

2. Variance:

   Variance = Σ [(Outcome - EV)² × Probability]
   

Worked Example: NEPSE Stock Investment

Scenario: Invest Rs. 100,000 in a stock with:

• 30% chance of +20% return.
• 50% chance of +5% return.
• 20% chance of -10% return. EV Calculation:

EV = (0.3 × 120,000) + (0.5 × 105,000) + (0.2 × 90,000)
   = 36,000 + 52,500 + 18,000 = **Rs. 106,500**

Decision: Invest if EV > initial investment (Rs. 100,000).

Real-World Application: Khalti’s Loan Default Risk

Khalti assesses loan risk using:

• EV of Repayment:
  • 70% chance of full repayment (Rs. 50,000).
  • 20% chance of 50% repayment (Rs. 25,000).
  • 10% chance of default (Rs. 0).

  EV = (0.7 × 50,000) + (0.2 × 25,000) + (0.1 × 0) = **Rs. 37,500**
  

• Decision Rule: Lend only if EV > cost of funds (e.g., Rs. 35,000).

---

In the Real World

1. eSewa’s Payment Risk:

   • Uses Minimax Regret to minimize losses from fraud (e.g., if a transaction fails, the regret is the amount lost minus the refund).
   • Example: If eSewa processes a Rs. 10,000 transaction with a 1% fraud risk, the regret for not verifying is Rs. 100. The system is designed to minimize such regrets.

2. Daraz’s Inventory Optimization:

   • Applies Linear Programming to balance stock levels across warehouses in Kathmandu, Pokhara, and Biratnagar, ensuring:
     • Constraint 1: Total storage ≤ 500,000 sq. ft.
     • Constraint 2: Delivery time ≤ 48 hours for 90% of orders.
     • Objective: Minimize holding costs while maximizing order fulfillment.

3. NTC’s Fiber Expansion:

   • Conducts Cost-Benefit Analysis to decide between:
     • Option A: Expand in Kathmandu (high cost, high demand).
     • Option B: Expand in rural areas (lower cost, lower revenue).
   • Intangible Benefit: Option A reduces urban congestion (valued at Rs. 20 million/year).

4. Pathao’s Driver Payouts:

   • Uses Break-Even Analysis to determine minimum rides per driver to cover fuel and vehicle costs.
   • Example: A driver with Rs. 1,000/day fixed costs and Rs. 50/ride variable cost must complete 20 rides/day at Rs. 75/ride to break even.

5. NEPSE’s Index Calculation:

   • Relies on Expected Value to predict market movements. For example, if the NEPSE index has a 60% chance of rising by 2% and a 40% chance of falling by 1%, the EV change is:

     EV = (0.6 × 2%) + (0.4 × -1%) = 0.8% increase
     

   • Investors use this to decide whether to buy/sell.

---

Exam Tip

What Examiners Look For

1. Decision Theory:

   • Always label payoff tables clearly and show all three criteria (Maximax, Maximin, Minimax Regret).
   • Common Mistake: Forgetting to calculate regret for Minimax Regret. Always subtract the best payoff in the row from each payoff.

2. Linear Programming:

   • Graphical Method: Plot constraints accurately and shade the feasible region correctly. Examiners deduct marks for incorrect shading.
   • Corner Points: Solve for intersections algebraically (e.g., solve 2x + y = 10 and x + y = 6 simultaneously).
   • Objective Function: Evaluate only at corner points—never inside the feasible region.

3. Cost-Benefit Analysis:

   • Discounting: Show the formula and calculations for each year. Use a table for clarity.
   • Intangible Benefits: Justify how you monetized them (e.g., "reduced pollution valued at Rs. X based on health studies").

4. Break-Even Analysis:

   • Graph: Label axes, plot both TR and TC lines, and mark the break-even point.
   • Formula: Always show the step-by-step calculation of (FC) / (P - VC).

5. Risk and Probability:

   • Expected Value: Multiply each outcome by its probability and sum correctly.
   • Variance: Show the squared deviations and weighted sum.

High-Scoring Strategies

• Diagrams: Draw all graphs (LP feasible regions, break-even charts) neatly. Label axes, lines, and key points.
• Real-World Links: Relate every example to Nepali businesses (e.g., "Like Daraz’s warehouse problem...").
• Units: Always include Rs. '000 or Rs. '00 in tables/graphs to match exam questions.
• Assumptions: If data is missing (e.g., discount rate), state a reasonable assumption (e.g., "Assume 10% discount rate as per NEPSE guidelines").

Common Pitfalls to Avoid

• Ignoring Constraints: In LP, forgetting x ≥ 0, y ≥ 0 can lead to nonsensical solutions.
• Incorrect Shading: In LP graphs, the feasible region must satisfy all constraints simultaneously.
• Miscounting Regret: In Minimax Regret, ensure you’re calculating opportunity loss, not just differences.
• Forgetting Non-Monetary Factors: In CBA, intangible benefits (e.g., "improved safety") must be quantified to score full marks.

---

In the real world

• Pathao’s Driver Incentives: Uses Maximax during peak seasons (e.g., Dashain) to maximize rider sign-ups by offering higher bonuses, while applying Minimax Regret in low-demand periods to minimize driver attrition by adjusting incentives based on historical demand patterns.
• NTC’s Fiber-Optic Expansion: Applies Linear Programming to allocate budgets between Kathmandu and Pokhara, balancing coverage constraints (80% urban reach) and cost constraints (≤ Rs. 500 million) to maximize internet speed (Mbps).
• Daraz’s Warehouse Allocation: Uses Cost-Benefit Analysis to compare tangible costs (storage, labor) and intangible benefits (faster delivery times) when deciding warehouse locations, ensuring NPV > 0 for expansion projects.