Mathematical Models & Baselines

Methodology & Data Baseline Sources

Every tool and calculation engine on Roznamcha is built upon open, empirical formulas and officially recognized Pakistani economic baselines. This document details the mathematical logic, regulatory sources, and empirical assumptions powering our calculators.

1. Electricity Bill Estimator & Slab Logic

Residential electricity billing in Pakistan is structured under progressive tariff schedules administered by the National Electric Power Regulatory Authority (NEPRA). Our model reflects the exact tiered billing algorithm:

Progressive Slab Calculation Formula:

Base Slab Cost = Σ [ min(Remaining Units, Slab Bracket Size) × Slab Per-Unit Rate ]

Total Payable Bill Formula:

Total Bill = (Base Slab Cost) + (Units × FPA Rate) + Financing Surcharge + Electricity Duty + GST (17%) + Fixed Meter Charges + TV Fee (Rs. 35)

Regulatory Sources: NEPRA Federal Tariff Notifications (SROs) for DISCOs (LESCO, K-Electric, IESCO, FESCO, MEPCO, GEPCO, PESCO, HESCO, SEPCO, QESCO). Our system explicitly distinguishes between Protected Consumers (under 200 kWh/month for 6 consecutive months) and Unprotected Consumers, dynamically simulating the financial cliff that occurs upon crossing unit thresholds.

2. Kitchen Ration & Grocery Price Baselines

Food budgeting requires isolating non-perishable staple carbohydrates and cooking fats from perishable daily items. The Ration Cost Estimator focuses exclusively on core non-perishable kitchen drivers:

CommodityStandard UnitPrimary Baseline SourceReview Cadence
Wheat Flour (Atta)20 kg bag / 10 kg bagPBS Weekly SPI / Wholesale Grain MandiMonthly
Cooking Oil / Ghee1 Litre / 5 Litre pouchWholesale Grain Mandi + Open RetailMonthly
Basmati & IRRI RiceKilogram (kg)Punjab & Sindh Mandi Rate ListsMonthly
Refined White SugarKilogram (kg)Ex-Mill & Retail Benchmark ReportsMonthly
Pulses (Daal Da Chana, Moong, Masoor)Kilogram (kg)Importers Association & Wholesale IndicesMonthly

Why Fresh Produce is Separated: Perishables (tomatoes, onions, fresh milk, beef, and chicken) experience localized volatility of up to 40% in a single week based on fuel freight adjustments and seasonal monsoon cycles. Households should calculate dry staples first to anchor their non-negotiable kitchen baseline, then assign a distinct flexible line item for weekly bazaar shopping.

3. Monthly Household Budgeting & Surplus/Deficit Metrics

Our Monthly Household Budget Calculator categorizes spending across 6 localized expenditure vectors: Rent, Ration, Utilities, Education, Transport, and Miscellaneous/Medical.

Net Surplus / Deficit: Monthly Take-Home Income − Total Categorized Expenses.

Savings Rate Percentage: (Surplus / Monthly Income) × 100.

Healthy Budget Thresholds: In urban Pakistan, a savings rate ≥15% represents strong resilience against unexpected shocks. A savings rate between 5%–14% indicates a compressed budget vulnerable to mid-month emergencies. A rate <0% represents an active deficit that compounds debt.

4. Solar Net Metering ROI & 10-Year Battery TCO

Solar financial modeling operates under NEPRA’s Net Billing framework, distinguishing between daytime self-consumption and exported grid energy:

Avoided Grid Cost: Self-Consumed Solar Units × Avoided Retail Grid Slab Tariff (Rs. 42 to 71+/kWh).

Export Credit Revenue: Exported Units × National Average Buyback Rate (~Rs. 11.00/kWh).

Simple Payback Period (Years): Total Turnkey Installation Cost (CAPEX) / Annualized Total Net Financial Savings.

10-Year Battery TCO Comparison: Tall Tubular lead-acid batteries (50% max Depth of Discharge, 900 cycles, 2.5-year replacement interval) incur 3 full bank replacements over a 10-year span. Lithium Iron Phosphate (LiFePO4) storage (90% usable DoD, 5,000–6,000 cycles, 10+ year lifespan) eliminates mid-term replacements, delivering an effective 35%–40% lower cost per stored kilowatt-hour.

5. School Fees Planner & Annual Amortization

Education budgeting fails when families treat monthly school vouchers as their total cost, ignoring annual admission fees, activity charges, and examination registration deadlines.

Real Monthly Cost Formula: (Children Count × Monthly Tuition) + [(Annual Charges + Exam Fee × Exam Frequency) / 12].

Inflation Planning Margin: Real Monthly Cost × (1 + Inflation Buffer % / 100). Private schools in Pakistan escalate tuition by an average of 10% to 15% each academic cycle.