Business Mathematics: Compensation, Commissions, Inflation, Commercial Pricing, and Value-Added Tax

Core Compensation Concepts: Salary, Wage, Allowance, and Commission

  • Salary Definition and Key Attributes:

    • A salary is a fixed amount of payment that an employee receives regularly, typically on a monthly or semi-monthly basis, for performing a specific job role.

    • Payment Schedule: Disbursed on a predetermined, regular schedule (e.g., monthly or bi-monthly).

    • Applicability: Generally designated for managerial, professional, administrative, or office positions.

    • Workload Invariance: The payment amount remains constant regardless of the total hours worked in a pay period, provided the assigned responsibilities and duties are fully satisfied.

  • Wage Definition and Key Attributes:

    • A wage represents monetary compensation paid for labor or services rendered based directly on the number of hours worked, days completed, or units/pieces produced.

    • Basis of Compensation: Calculated strictly according to time (hourly or daily rates) or measurable output (piecework).

    • Variability: Weekly or monthly total compensation fluctuates based on actual hours clocked or production volume achieved.

    • Applicability: Standard across trade, manual labor, manufacturing, assembly, and service industry roles.

  • Allowance Definition and Key Attributes:

    • An allowance is an additional financial provision given to an employee to help shoulder specific personal or work-related expenses incurred while performing duties.

    • Supplementary Nature: Paid on top of the employee's regular wage or basic salary.

    • Coverage Scope: Commonly allocated for transportation, meals, mobile communication, housing, clothing, internet, or relocation.

    • Distinction from Labor Pay: Not classified as direct compensation or remuneration for work done.

  • Commission Definition and Key Attributes:

    • A commission is performance-based compensation disbursed to an employee—primarily sales agents or marketing professionals—calculated as a percentage of the total sales, revenue, or profit generated.

    • Incentive Alignment: Serves as a direct incentive to drive higher sales performance and output.

    • Structure: Provided either as an incentive on top of a basic salary or as sole compensation (straight commission).

Salary Conversion Across Standard Pay Periods

  • Standard Labor Conversion Constants:

    • Standard working weeks per calendar year=52 weeks\text{Standard working weeks per calendar year} = 52\text{ weeks}

    • Standard working hours per full-time week=40 hours\text{Standard working hours per full-time week} = 40\text{ hours}

    • Standard annual working hours=52 weeks×40 hours/week=2080 hours\text{Standard annual working hours} = 52\text{ weeks} \times 40\text{ hours/week} = 2080\text{ hours}

  • Standard Pay Period Conversion Formulas:

    • Monthly Salary=Annual Salary12\text{Monthly Salary} = \frac{\text{Annual Salary}}{12}

    • Bi-Monthly (Semi-Monthly) Salary=Monthly Salary2\text{Bi-Monthly (Semi-Monthly) Salary} = \frac{\text{Monthly Salary}}{2}

    • Weekly Salary=Annual Salary52\text{Weekly Salary} = \frac{\text{Annual Salary}}{52}

    • Hourly Rate=Annual Salary2080\text{Hourly Rate} = \frac{\text{Annual Salary}}{2080}

    • Annual Salary=Hourly Rate×2080\text{Annual Salary} = \text{Hourly Rate} \times 2080

    • Note on Take-Home Pay: These equations calculate gross compensation before mandatory statutory deductions, tax withholdings, and employee benefit contributions.

  • Worked Application 1 — Deconstructing an Annual Salary:

    • Problem Statement: An employee receives an annual gross salary of Php 750,000.00\text{Php } 750{,}000.00. Calculate their (a) hourly rate, (b) weekly salary, (c) monthly salary, and (d) bi-monthly salary.

    • (a) Hourly Rate Calculation:         Hourly Rate=Php 750,000.002080=Php 360.58\text{Hourly Rate} = \frac{\text{Php } 750{,}000.00}{2080} = \text{Php } 360.58

    • (b) Weekly Salary Calculation:         Weekly Salary=Php 750,000.0052=Php 14,423.08\text{Weekly Salary} = \frac{\text{Php } 750{,}000.00}{52} = \text{Php } 14{,}423.08

    • (c) Monthly Salary Calculation:         Monthly Salary=Php 750,000.0012=Php 62,500.00\text{Monthly Salary} = \frac{\text{Php } 750{,}000.00}{12} = \text{Php } 62{,}500.00

    • (d) Bi-Monthly Salary Calculation:         Bi-Monthly Salary=Php 62,500.002=Php 31,250.00\text{Bi-Monthly Salary} = \frac{\text{Php } 62{,}500.00}{2} = \text{Php } 31{,}250.00

  • Worked Application 2 — Reconstructing Annual and Monthly Pay from Hourly Rate:

    • Problem Statement: A worker is compensated at an hourly rate of Php 140.00\text{Php } 140.00. Determine their (a) annual salary and (b) monthly salary.

    • (a) Annual Salary Calculation:         Annual Salary=Hourly Rate×2080=Php 140.00×2080=Php 291,200.00\text{Annual Salary} = \text{Hourly Rate} \times 2080 = \text{Php } 140.00 \times 2080 = \text{Php } 291{,}200.00

    • (b) Monthly Salary Calculation:         Monthly Salary=Php 291,200.0012=Php 24,266.67\text{Monthly Salary} = \frac{\text{Php } 291{,}200.00}{12} = \text{Php } 24{,}266.67

Overtime Pay and Special Working Conditions Under Philippine Labor Standards

  • Statutory Framework and Definitions:

    • Overtime Work: Any work rendered beyond the standard maximum of 8 hours8\text{ hours} per normal workday.

    • Overtime Pay: Additional compensation mandated by law, enterprise policy, or collective bargaining agreement for labor performed in excess of normal working hours.

    • Legal Basis: Labor Code of the Philippines (Rule IX, Book III).

  • Compensation Rates by Day Classification:

    • Ordinary Working Day:

      • First 8 hours8\text{ hours}: 100%×Daily Wage (DW)100\% \times \text{Daily Wage (DW)}

      • Overtime pay rate: 125%×Hourly Rate (HR)×Number of Overtime Hours (NOH)125\% \times \text{Hourly Rate (HR)} \times \text{Number of Overtime Hours (NOH)}

      • Total Pay=DW+[1.25×HR×NOH]\text{Total Pay} = \text{DW} + [1.25 \times \text{HR} \times \text{NOH}]

    • Rest Day or Special Non-Working Holiday:

      • First 8 hours8\text{ hours}: 130%×DW130\% \times \text{DW}

      • Overtime pay rate: Additional 30%30\% premium applied to the rest day hourly rate (130%×130%×HR×NOH=1.69×HR×NOH130\% \times 130\% \times \text{HR} \times \text{NOH} = 1.69 \times \text{HR} \times \text{NOH}

      • Total Pay=[1.30×DW]+[1.30×1.30×HR×NOH]\text{Total Pay} = [1.30 \times \text{DW}] + [1.30 \times 1.30 \times \text{HR} \times \text{NOH}]

    • Regular Holiday:

      • First 8 hours8\text{ hours}: 200%×DW200\% \times \text{DW}

      • Overtime pay rate: 200%×130%×HR×NOH=2.60×HR×NOH200\% \times 130\% \times \text{HR} \times \text{NOH} = 2.60 \times \text{HR} \times \text{NOH}

      • Total Pay=[2.00×DW]+[2.00×1.30×HR×NOH]\text{Total Pay} = [2.00 \times \text{DW}] + [2.00 \times 1.30 \times \text{HR} \times \text{NOH}]

    • Regular Holiday Falling on a Scheduled Rest Day:

      • First 8 hours8\text{ hours}: 260%×DW260\% \times \text{DW}

      • Overtime pay rate: 260%×130%×HR×NOH=3.38×HR×NOH260\% \times 130\% \times \text{HR} \times \text{NOH} = 3.38 \times \text{HR} \times \text{NOH}

      • Total Pay=[2.60×DW]+[2.60×1.30×HR×NOH]\text{Total Pay} = [2.60 \times \text{DW}] + [2.60 \times 1.30 \times \text{HR} \times \text{NOH}]

    • Special Non-Working Holiday Falling on a Scheduled Rest Day:

      • First 8 hours8\text{ hours}: 150%×DW150\% \times \text{DW}

      • Overtime pay rate: 150%×130%×HR×NOH=1.95×HR×NOH150\% \times 130\% \times \text{HR} \times \text{NOH} = 1.95 \times \text{HR} \times \text{NOH}

      • Total Pay=[1.50×DW]+[1.50×1.30×HR×NOH]\text{Total Pay} = [1.50 \times \text{DW}] + [1.50 \times 1.30 \times \text{HR} \times \text{NOH}]

Summary of compensation formulas for rest days and overtime

  • Comprehensive Worked Problems in Overtime and Special Days:

    • Problem 4 — Overtime on a Scheduled Rest Day:

      • Scenario: A worker receives a daily wage of Php 750.00\text{Php } 750.00 (8 hours8\text{ hours}). She renders 12 hours12\text{ hours} of service on her scheduled rest day. Determine her total pay for that day.

      • Step 1: Compute basic hourly rate:             Basic Hourly Rate=Php 750.008=Php 93.75\text{Basic Hourly Rate} = \frac{\text{Php } 750.00}{8} = \text{Php } 93.75

      • Step 2: Compute pay for regular rest day hours (first 8 hours):             Payfirst 8 hrs=1.30×Php 750.00=Php 975.00\text{Pay}_{\text{first } 8\text{ hrs}} = 1.30 \times \text{Php } 750.00 = \text{Php } 975.00

      • Step 3: Compute overtime pay for hours beyond 8:             Overtime Hours=12−8=4 hours\text{Overtime Hours} = 12 - 8 = 4\text{ hours}             Rest Day Hourly Rate=Php 93.75×1.30=Php 121.88\text{Rest Day Hourly Rate} = \text{Php } 93.75 \times 1.30 = \text{Php } 121.88             Additional 30% Premium=0.30×Php 121.88=Php 36.56\text{Additional 30\% Premium} = 0.30 \times \text{Php } 121.88 = \text{Php } 36.56             Overtime Hourly Rate=Php 121.88+Php 36.56=Php 158.44\text{Overtime Hourly Rate} = \text{Php } 121.88 + \text{Php } 36.56 = \text{Php } 158.44             Overtime Pay=Php 158.44×4=Php 633.76\text{Overtime Pay} = \text{Php } 158.44 \times 4 = \text{Php } 633.76

      • Step 4: Compute total daily compensation:             Total Pay=Php 975.00+Php 633.76=Php 1,608.76\text{Total Pay} = \text{Php } 975.00 + \text{Php } 633.76 = \text{Php } 1{,}608.76

    • Problem 5 — Overtime on a Regular Holiday (Independence Day):

      • Scenario: A saleslady earns a monthly salary of Php 16,500.00\text{Php } 16{,}500.00. She works 11 hours11\text{ hours} on June 12 (Independence Day, a regular holiday). Determine her total compensation for that single day.

      • Step 1: Derive baseline rates:             Annual Salary=Php 16,500.00×12=Php 198,000.00\text{Annual Salary} = \text{Php } 16{,}500.00 \times 12 = \text{Php } 198{,}000.00             Hourly Rate=Php 198,000.002080=Php 95.19\text{Hourly Rate} = \frac{\text{Php } 198{,}000.00}{2080} = \text{Php } 95.19             Daily Wage=8×Php 95.19=Php 761.52\text{Daily Wage} = 8 \times \text{Php } 95.19 = \text{Php } 761.52

      • Step 2: Compute holiday wage components:             Overtime Hours=11−8=3 hours\text{Overtime Hours} = 11 - 8 = 3\text{ hours}             Payfirst 8 hrs=2.00×Php 761.52=Php 1,523.04\text{Pay}_{\text{first } 8\text{ hrs}} = 2.00 \times \text{Php } 761.52 = \text{Php } 1{,}523.04             Overtime Pay=2.00×1.30×Php 95.19×3=Php 742.48\text{Overtime Pay} = 2.00 \times 1.30 \times \text{Php } 95.19 \times 3 = \text{Php } 742.48

      • Step 3: Combine total compensation:             Total Pay=Php 1,523.04+Php 742.48=Php 2,265.52\text{Total Pay} = \text{Php } 1{,}523.04 + \text{Php } 742.48 = \text{Php } 2{,}265.52

    • Problem 6 — Overtime on a Regular Holiday Falling on a Rest Day:

      • Scenario: Using the worker profile from Problem 5 (Monthly Salary=Php 16,500.00\text{Monthly Salary} = \text{Php } 16{,}500.00, HR=Php 95.19\text{HR} = \text{Php } 95.19, DW=Php 761.52\text{DW} = \text{Php } 761.52), determine her pay if the 11 hours11\text{ hours} worked on Independence Day coincide with her scheduled rest day.

      • Step 1: Compute first 8 hours at 260%260\%:             Payfirst 8 hrs=2.60×Php 761.52=Php 1,979.95\text{Pay}_{\text{first } 8\text{ hrs}} = 2.60 \times \text{Php } 761.52 = \text{Php } 1{,}979.95

      • *Step 2: Compute 3 hours overtime at 260\% \times 130\%$:*\n            \text{Overtime Pay} = 2.60 \times 1.30 \times \text{Php } 95.19 \times 3 = \text{Php } 965.23\n * *Step 3: Compute total daily earnings:*\n            \text{Total Pay} = \text{Php } 1{,}979.95 + \text{Php } 965.23 = \text{Php } 2{,}945.18\n * *Problem 7 — Overtime on a Special Non-Working Holiday Falling on a Rest Day:*\n * *Scenario:* A skilled laborer with a daily wage of \text{Php } 1{,}200.00worksworks16\text{ hours} on a declared special non-working holiday that falls on his rest day. Compute his total pay.\n * *Step 1: Compute basic hourly rate:*\n            \text{Hourly Rate} = \frac{\text{Php } 1{,}200.00}{8} = \text{Php } 150.00\n * *Step 2: Compute pay for regular 8 hours at 150\%:*\n            \text{Pay}{\text{first } 8\text{ hrs}} = 1.50 \times \text{Php } 1{,}200.00 = \text{Php } 1{,}800.00\n * *Step 3: Compute overtime for 8 hours beyond normal shift:*\n            \text{Overtime Hours} = 16 - 8 = 8\text{ hours}\n            \text{Overtime Multiplier} = 1.50 \times 1.30 = 1.95\n            \text{Overtime Pay} = 1.95 \times \text{Php } 150.00 \times 8 = \text{Php } 2{,}340.00\n * *Step 4: Compute total daily earnings:*\n            \text{Total Pay} = \text{Php } 1{,}800.00 + \text{Php } 2{,}340.00 = \text{Php } 4{,}140.00\n\n# Commission Systems and Computation Models\n\n* **Classification of Commission Structures:**\n * **Straight Commission:** An employee earns an unchanging, fixed percentage across all cumulative sales made, regardless of the overall transaction amount.\n * **Graduated (Tiered) Commission:** The commission rate escalates across different tiers or brackets of sales volume.\n * **Salary Plus Commission:** The employee is guaranteed a baseline monthly fixed salary, complemented by a percentage commission on goods or services sold.\n * **Draw Against Commission:** A salary advance (a "draw") is provided regularly to stabilize income, which is later fully reconciled and deducted against actual commission earnings.\n * **Override Commission:** An additional commission earned by a sales manager or team leader based on the cumulative sales volume generated by their subordinate sales representatives.\n\n* **Mathematical Models and Problem Demonstrations:**\n * *Straight Commission Model:*\n * \text{Commission} = \text{Commission Rate} \times \text{Total Sales}\n * *Example:* A salesperson receives a 5\%straightcommissionandsellsstraight commission and sells\text{Php } 50{,}000.00 in goods.\n            \text{Commission} = 0.05 \times \text{Php } 50{,}000.00 = \text{Php } 2{,}500.00\n\n![Graduated commission computation table](https://assets.knowt.com/pdf-flow-prod/8d119b70-0c34-4efa-8ffd-01c299188a76-figures/8.jpg)\n\n * *Graduated (Tiered) Commission Model:*\n * *Bracket Rules:* Each commission rate applies exclusively to the sales value falling inside that defined interval, not to the entire total.\n * *Example:* A sales plan defines 3\%onthefirston the first\text{Php } 50{,}000.00,,4\%onthenexton the next\text{Php } 50{,}000.00,and, and5\%onamountsexceedingon amounts exceeding\text{Php } 100{,}000.00.Totalsalesamountto. Total sales amount to\text{Php } 160{,}000.00.\n * *Tier 1 (\text{Php } 0toto\text{Php } 50{,}000):* \n            \text{Commission}_1 = \text{Php } 50{,}000.00 \times 0.03 = \text{Php } 1{,}500.00\n * *Tier 2 (\text{Php } 50{,}001toto\text{Php } 100{,}000):* \n            \text{Commission}_2 = \text{Php } 50{,}000.00 \times 0.04 = \text{Php } 2{,}000.00\n * *Tier 3 (\text{Php } 100{,}001toto\text{Php } 160{,}000):* \n            \text{Excess Amount} = \text{Php } 160{,}000.00 - \text{Php } 100{,}000.00 = \text{Php } 60{,}000.00\n            \text{Commission}_3 = \text{Php } 60{,}000.00 \times 0.05 = \text{Php } 3{,}000.00\n * *Total Tiered Commission:* \n            \text{Total Commission} = \text{Php } 1{,}500.00 + \text{Php } 2{,}000.00 + \text{Php } 3{,}000.00 = \text{Php } 6{,}500.00\n * *Salary Plus Commission Model:*\n * \text{Total Earnings} = \text{Basic Salary} + (\text{Commission Rate} \times \text{Total Sales})\n * *Example:* An employee has a monthly salary of \text{Php } 18{,}000.00andreceivesaand receives a6\%commission.Salesreachcommission. Sales reach\text{Php } 150{,}000.00.\n            \text{Commission} = 0.06 \times \text{Php } 150{,}000.00 = \text{Php } 9{,}000.00\n            \text{Total Earnings} = \text{Php } 18{,}000.00 + \text{Php } 9{,}000.00 = \text{Php } 27{,}000.00\n * *Draw Against Commission Model:*\n * \text{Net Payout} = \text{Earned Commission} - \text{Draw Advance}\n * *Deficit Implications:* When the draw exceeds earned commission, the net payout for that pay period is \text{Php } 0.00, and the deficit carries over as a financial liability owed back to the employer.\n * *Example:* An employee takes a monthly advance draw of \text{Php } 20{,}000.00againstaagainst a5\%commissionstructure.Heproducescommission structure. He produces\text{Php } 350{,}000.00 in sales.\n            \text{Earned Commission} = 0.05 \times \text{Php } 350{,}000.00 = \text{Php } 17{,}500.00\n            \text{Net Payout} = \text{Php } 17{,}500.00 - \text{Php } 20{,}000.00 = -\text{Php } 2{,}500.00\n            \text{Conclusion: The employee receives } \text{Php } 0.00 \text{ that month and owes } \text{Php } 2{,}500.00 \text{ to the company.}\n * *Override Commission Model:*\n * \text{Override Commission} = \text{Override Rate} \times \text{Total Team Sales Volume}\n * *Example:* An area sales director receives a 3\%overrideonhisunit′scollectivesales.Hisgroupsellsthreerealestatecondominiumpropertiestotalingoverride on his unit's collective sales. His group sells three real estate condominium properties totaling\text{Php } 4{,}500{,}000.00.\n            \text{Override Commission} = 0.03 \times \text{Php } 4{,}500{,}000.00 = \text{Php } 135{,}000.00\n\n# Inflation, Purchasing Power, and the Consumer Price Index (CPI)\n\n* **Economic Definitions:**\n * **Inflation:** The sustained percentage increase in the general price level of goods and services over time. It leads to the erosion of real currency value.\n * **Purchasing Power:** The quantity of real goods or services that a single monetary unit can purchase at prevailing prices.\n * **Nominal Wage:** The face value of earnings received by a worker, unadjusted for inflation.\n * **Real Wage:** The purchasing-power-adjusted wage reflecting the real volume of consumer goods the income can acquire: nominal wage adjusted for price indices.\n\n* **Mathematical Formulations:**\n * **Consumer Price Index (CPI):**\n        \text{CPI} = \frac{\text{Cost of Market Basket in Current Period}}{\text{Cost of Market Basket in Base Period}} \times 100\n * *Base Period Convention:* The base period CPI is universally assigned an index value of 100.\n * **Annual Inflation Rate:**\n        \text{Inflation Rate} = \frac{\text{Current Period CPI} - \text{Previous Period CPI}}{\text{Previous Period CPI}} \times 100\n * **Percentage Change in Economic Variables:**\n        \text{Percentage Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\n * *Directionality:* A positive result represents a percentage increase; a negative result represents a percentage decrease.\n\n* **Empirical Demonstrations and Practical Cases:**\n * *Case 1 — Market Basket Evaluation and CPI Derivation:*\n * *Data Source:* Price monitoring across a representative consumer basket (base year 2018 vs. evaluation year 2024):\n * Rice (50\text{ kg}):Baseprice=): Base price =\text{Php } 40/\text{kg}((\text{Php } 2{,}000.00);2024price=); 2024 price =\text{Php } 55/\text{kg}((\text{Php } 2{,}750.00)\n * Meat (10\text{ kg}):Baseprice=): Base price =\text{Php } 180/\text{kg}((\text{Php } 1{,}800.00);2024price=); 2024 price =\text{Php } 220/\text{kg}((\text{Php } 2{,}200.00)\n * Vegetables (10\text{ kg}):Baseprice=): Base price =\text{Php } 30/\text{kg}((\text{Php } 300.00);2024price=); 2024 price =\text{Php } 45/\text{kg}((\text{Php } 450.00)\n * White Sugar (5\text{ kg}):Baseprice=): Base price =\text{Php } 50/\text{kg}((\text{Php } 250.00);2024price=); 2024 price =\text{Php } 75/\text{kg}((\text{Php } 375.00)\n * *Total Market Basket Costs:* \n            \text{Cost}{2018} = 2000 + 1800 + 300 + 250 = \text{Php } 4{,}350.00\n            \text{Cost}{2024} = 2750 + 2200 + 450 + 375 = \text{Php } 5{,}775.00\n * *Index Computation:* \n            \text{CPI}{2024} = \frac{\text{Php } 5{,}775.00}{\text{Php } 4{,}350.00} \times 100 = 1.3276 \times 100 = 132.76\n * *Economic Meaning:* The basket cost increased by 32.76\% relative to the 2018 base year.\n * *Case 2 — Year-Over-Year Inflation Rate:*\n * Given \text{CPI}{2024} = 132.76andpreviousyearand previous year\text{CPI}{2023} = 127.3:\n            \text{Inflation Rate}{2023 \rightarrow 2024} = \frac{132.76 - 127.3}{127.3} \times 100 = \frac{5.46}{127.3} \times 100 = 4.29\%\n * *Case 3 — Commodity Price Inflation:*\n * The price of meat increases from \text{Php } 280.00toto\text{Php } 350.00 per kilogram:\n            \text{Percentage Increase} = \frac{350 - 280}{280} \times 100 = \frac{70}{280} \times 100 = 25\%\n * *Case 4 — Wage Adjustment Relative to Inflation:*\n * An hourly wage increases from \text{Php } 105.00toto\text{Php } 120.00,whileheadlinecommodityinflationis, while headline commodity inflation is13.5\%:\n            \text{Wage Increase} = \frac{120 - 105}{105} \times 100 = \frac{15}{105} \times 100 = 14.29\%\n * *Net Economic Effect:* Because the 14.29\%nominalwageincreasemarginallyexceedsthenominal wage increase marginally exceeds the13.5\% inflation rate, the worker's real purchasing power is preserved, yielding a slight real gain.\n * *Case 5 — Real Wage Deterioration:*\n * A worker's monthly salary rises from \text{Php } 22{,}000.00toto\text{Php } 23{,}800.00,buttheinflationraterunsat, but the inflation rate runs at9.0\%:\n            \text{Salary Increase} = \frac{23{,}800 - 22{,}000}{22{,}000} \times 100 = \frac{1{,}800}{22{,}000} \times 100 = 8.18\%\n * *Net Economic Effect:* The nominal pay raise (8.18\%)fallsbelowtheinflationrate() falls below the inflation rate (9.0\%).Inrealeconomicterms,purchasingpowerdeterioratedby). In real economic terms, purchasing power deteriorated by0.82\%.\n\n# Mathematics of Markups and Discounts\n\n* **Fundamental Terminology:**\n * **Cost Price (C):** The original purchase price or expenditure paid to acquire or manufacture a good intended for resale.\n * **Selling Price (S):** The final monetary consideration at which a good or service is offered to consumers.\n * **Markup (M):** The absolute cash margin added to the cost price to generate a gross profit margin.\n * **Markup Rate (M_r):** The percentage added on top of the cost price.\n * **List Price (L):** The stated catalog or original retail tag price prior to applying any promotional deduction.\n * **Discount (D):** The gross deduction subtracted from the list price.\n * **Discount Rate (D_r):** The percentage reduction applied to the list price.\n * **Net Price (N):** The actual net amount payable after subtracting promotional discounts.\n\n![Formulas for Markup, Discount, and Net Price](https://assets.knowt.com/pdf-flow-prod/6cd8d72b-bef2-4716-9e0e-46912f5d6118-figures/8.png)\n\n* **Core Formula Systems:**\n * *Markup Relationships:*\n * M = S - C\n * M_r = \frac{M}{C} \times 100\n * S = C + [C \times M_r] = C(1 + M_r)\n * C = \frac{S}{1 + M_r}\n * *Discount Relationships:*\n * D = L - N\n * D_r = \frac{D}{L} \times 100\n * D = L \times D_r\n * N = L - D = L(1 - D_r)\n * L = \frac{N}{1 - D_r}\n\n* **Practical Calculation Examples:**\n * *Example 6 — Solving for Markup Rate:*\n * A merchant purchases merchandise for \text{Php } 2{,}500.00andsellsitforand sells it for\text{Php } 2{,}990.00.\n            M = \text{Php } 2{,}990.00 - \text{Php } 2{,}500.00 = \text{Php } 490.00\n            M_r = \frac{\text{Php } 490.00}{\text{Php } 2{,}500.00} \times 100 = 0.196 \times 100 = 19.6\%\n * *Example 7 — Setting Selling Price from Markup Rate:*\n * An appliance retailer procures a washing machine for \text{Php } 8{,}500.00andappliesanand applies an8\% markup rate.\n            M = \text{Php } 8{,}500.00 \times 0.08 = \text{Php } 680.00\n            S = \text{Php } 8{,}500.00 + \text{Php } 680.00 = \text{Php } 9{,}180.00\n * *Example 8 — Computing Discount and Net Price:*\n * An electronic unit carrying a list price of \text{Php } 12{,}600.00ismarkeddownbyais marked down by a15\% discount.\n            D = \text{Php } 12{,}600.00 \times 0.15 = \text{Php } 1{,}890.00\n            N = \text{Php } 12{,}600.00 - \text{Php } 1{,}890.00 = \text{Php } 10{,}710.00\n * *Example 9 — Determining Implied Discount Rate:*\n * A computer listed at \text{Php } 38{,}000.00isliquidatedforis liquidated for\text{Php } 34{,}500.00.\n            D = \text{Php } 38{,}000.00 - \text{Php } 34{,}500.00 = \text{Php } 3{,}500.00\n            D_r = \frac{\text{Php } 3{,}500.00}{\text{Php } 38{,}000.00} \times 100 = 0.0921 \times 100 = 9.21\%\n * *Example 10 — Back-Calculating Cost from Known Selling Price and Markup:*\n * A pair of leather shoes sells at retail for \text{Php } 2{,}800.00,includinga, including a12\% markup rate.\n            C = \frac{\text{Php } 2{,}800.00}{1 + 0.12} = \frac{\text{Php } 2{,}800.00}{1.12} = \text{Php } 2{,}500.00\n\n# Value-Added Tax (VAT) in the Philippines\n\n* **Statutory Definition and Legal Structure:**\n * Defined by the Bureau of Internal Revenue (BIR) as an indirect broad-based tax on consumption.\n * Levied on the sale, exchange, barter, or lease of goods, personal properties, real properties, and services within the Philippines, as well as upon importation into the country.\n * **Tax Shifting Mechanism:** Being an indirect levy, the legal incidence rests on the seller, but the economic burden is shifted entirely to the ultimate purchaser or lessee.\n * **Statutory Rate:** Twelve percent (12\%oror0.12).\n * **Registration Threshold:** Required for commercial entities whose gross annual sales or total receipts exceed the statutory threshold of \text{Php } 3{,}000{,}000.00.\n\n* **Mathematical Notation and Relationship Models:**\n * V_e = \text{Amount exclusive of VAT (base price prior to tax)}\n * V_i = \text{Amount inclusive of VAT (gross price collected from consumer)}\n * V = \text{Value-Added Tax cash component}\n * \text{Statutory VAT Rate} = 12\% = 0.12\n\n* **Analytical Transformation Equations:**\n * *When Starting from VAT-Exclusive Amount (V_e):*\n        V = 0.12 \times V_e\n        V_i = V_e + V = V_e(1 + 0.12) = 1.12 \times V_e\n * *When Starting from VAT-Inclusive Amount (V_i):*\n        V_e = \frac{V_i}{1.12}\n        V = V_i - V_e = V_i - \frac{V_i}{1.12} = \frac{0.12}{1.12} \times V_i\n * *Output VAT:* The gross VAT that a VAT-registered business adds to invoices and collects from buyers on sales of goods or services (V = 0.12 \times V_e), which must be reported and remitted to the BIR.\n\n* **Detailed Worked Tax Applications:**\n * *Example 11 — Computing Tax and Inclusive Total from Base Price:*\n * A product is marketed for \text{Php } 30{,}000.00,exclusiveofVAT(, exclusive of VAT (V_e).\n            \text{VAT Amount } (V) = 0.12 \times \text{Php } 30{,}000.00 = \text{Php } 3{,}600.00\n            \text{Gross Inclusive Amount } (V_i) = 1.12 \times \text{Php } 30{,}000.00 = \text{Php } 33{,}600.00\n * *Example 12 — Back-Calculating Base Price and Tax Component from Tag Price:*\n * An invoice for a television lists a gross price of \text{Php } 21{,}580.00,inclusiveofVAT(, inclusive of VAT (V_i).\n            \text{VAT Amount } (V) = \frac{0.12}{1.12} \times \text{Php } 21{,}580.00 = \text{Php } 2{,}312.14\n            \text{Exclusive Amount } (V_e) = \frac{\text{Php } 21{,}580.00}{1.12} = \text{Php } 19{,}267.86\n            \text{Reconciliation Check: } \text{Php } 19{,}267.86 + \text{Php } 2{,}312.14 = \text{Php } 21{,}580.00\n * *Example 13 — Calculating Remittable Output VAT:*\n * A VAT-registered merchant invoices commercial sales of \text{Php } 65{,}000.00, exclusive of VAT.\n            \text{Output VAT} = 0.12 \times \text{Php } 65{,}000.00 = \text{Php } 7{,}800.00\n            \text{Output VAT remittable to the BIR: } \text{Php } 7{,}800.00\n\n# Practical Exercises and Evaluative Problem Sets\n\n* **Exercise Set 1.1 — Direct Compensation & Pay Calculations:**\n * *Item 1 (Conceptual):* Direct monetary payment received by employees on a bi-monthly or monthly schedule in exchange for services rendered is called a **Salary**.\n * *Item 2 (Conceptual):* Direct monetary compensation received by workers based on production units or hours worked, common in blue-collar roles, is called a **Wage**.\n * *Item 3 (Conceptual):* Additional payments provided to cover expenses like transportation, housing, internet, and meals are known as an **Allowance**.\n * *Item 4 (Conceptual):* Compensation paid primarily to sales personnel as a direct incentive for completing transactions is a **Commission**.\n * *Item 5 (Procedural):* To compute an employee's hourly rate from annual compensation, divide the annual salary by **2,080** (52\text{ weeks} \times 40\text{ hours}).\n * *Item 6 (Computation):* If a worker's hourly rate is \text{Php } 100.00, their annual salary is:\n        \text{Annual Salary} = \text{Php } 100.00 \times 2080 = \text{Php } 208{,}000.00\n * *Item 7 (Computation):* Monthly salary for the employee in Item 6:\n        \text{Monthly Salary} = \frac{\text{Php } 208{,}000.00}{12} = \text{Php } 17{,}333.33\n * *Item 8 (Computation):* An employee receives a daily wage of \text{Php } 800.00((\text{hourly rate} = \text{Php } 100.00)andworks) and works12\text{ hours}onanordinaryday(on an ordinary day (4\text{ hours overtime}):\n        \text{Pay} = \text{Php } 800.00 + [1.25 \times \text{Php } 100.00 \times 4] = \text{Php } 800.00 + \text{Php } 500.00 = \text{Php } 1{,}300.00\n * *Item 9 (Computation):* A worker with an hourly rate of \text{Php } 105.00((\text{Daily wage} = 8 \times 105 = \text{Php } 840.00)works) works11\text{ hours} on his rest day. Pay for the first 8 hours:\n        \text{Pay}{\text{first } 8\text{ hrs}} = 1.30 \times \text{Php } 840.00 = \text{Php } 1{,}092.00\n * *Item 10 (Computation):* Total pay for the worker in Item 9 for all 11 hours (3\text{ hours overtime}):\n        \text{Overtime Pay} = 1.30 \times 1.30 \times \text{Php } 105.00 \times 3 = \text{Php } 532.35\n        \text{Total Pay} = \text{Php } 1{,}092.00 + \text{Php } 532.35 = \text{Php } 1{,}624.35\n\n* **Exercise Set 1.2 — Multi-Tier and Special Working Condition Problems:**\n * *Problem II.1:* An employee works 10\text{ hours}onaspecialnon−workingholidayfallingonarestdaywithadailywageofon a special non-working holiday falling on a rest day with a daily wage of\text{Php } 900.00((\text{hourly rate} = \text{Php } 112.50,,2\text{ hours overtime}):\n        \text{Pay}{\text{first } 8\text{ hrs}} = 1.50 \times \text{Php } 900.00 = \text{Php } 1{,}350.00\n        \text{Overtime Pay} = 1.50 \times 1.30 \times \text{Php } 112.50 \times 2 = \text{Php } 438.75\n        \text{Total Daily Pay} = \text{Php } 1{,}350.00 + \text{Php } 438.75 = \text{Php } 1{,}788.75\n * *Problem II.2:* The same employee (\text{DW} = \text{Php } 900.00,,\text{HR} = \text{Php } 112.50)works) works10\text{ hours}onaregularholidayfallingonarestday(on a regular holiday falling on a rest day (2\text{ hours overtime}):\n        \text{Pay}{\text{first } 8\text{ hrs}} = 2.60 \times \text{Php } 900.00 = \text{Php } 2{,}340.00\n        \text{Overtime Pay} = 2.60 \times 1.30 \times \text{Php } 112.50 \times 2 = \text{Php } 760.50\n        \text{Total Daily Pay} = \text{Php } 2{,}340.00 + \text{Php } 760.50 = \text{Php } 3{,}100.50\n * *Problem II.3:* Josie earns a monthly salary of \text{Php } 20{,}000.00plusplus5\%commissiononsales.Hersalestotalcommission on sales. Her sales total\text{Php } 100{,}000.00:\n        \text{Commission} = 0.05 \times \text{Php } 100{,}000.00 = \text{Php } 5{,}000.00\n        \text{Total Earnings} = \text{Php } 20{,}000.00 + \text{Php } 5{,}000.00 = \text{Php } 25{,}000.00\n * *Problem II.4:* Jimmy earns a 7\%commissiononcommission on\text{Php } 320{,}000.00salesandreceivesadrawofsales and receives a draw of\text{Php } 18{,}000.00:\n        \text{Commission} = 0.07 \times \text{Php } 320{,}000.00 = \text{Php } 22{,}400.00\n        \text{Net Take-Home Pay} = \text{Php } 22{,}400.00 - \text{Php } 18{,}000.00 = \text{Php } 4{,}400.00\n\n* **Exercise Set 1.3 — Inflation Rate & Percentage Change Calculations:**\n * *Employee 1:* Previous monthly salary = \text{Php } 24{,}000.00,Newsalary=, New salary =\text{Php } 28{,}000.00,Inflationrate=, Inflation rate =5.0\%.\n        \text{Percentage Change} = \frac{28{,}000 - 24{,}000}{24{,}000} \times 100 = 16.67\%\n        \text{Real Wage Effect: Increased purchasing power } (16.67\% > 5.0\%)\n * *Employee 2:* Previous daily wage = \text{Php } 650.00,Newdailywage=, New daily wage =\text{Php } 730.00,Inflationrate=, Inflation rate =4.0\%.\n        \text{Percentage Change} = \frac{730 - 650}{650} \times 100 = 12.31\%\n        \text{Real Wage Effect: Increased purchasing power } (12.31\% > 4.0\%)\n * *Employee 3:* Previous hourly wage = \text{Php } 120.00,Newhourlywage=, New hourly wage =\text{Php } 145.00,Inflationrate=, Inflation rate =3.5\%.\n        \text{Percentage Change} = \frac{145 - 120}{120} \times 100 = 20.83\%\n        \text{Real Wage Effect: Increased purchasing power } (20.83\% > 3.5\%)\n * *Comparative Basket Problem (2018 base vs. 2024 current):*\n * Chicken meat: 10\text{ kg} \times \text{Php } 180 = \text{Php } 1{,}800.00;;10\text{ kg} \times \text{Php } 195 = \text{Php } 1{,}950.00\n * Jasmine rice: 50\text{ kg} \times \text{Php } 47 = \text{Php } 2{,}350.00;;50\text{ kg} \times \text{Php } 50 = \text{Php } 2{,}500.00\n * Flour: 10\text{ kg} \times \text{Php } 75 = \text{Php } 750.00;;10\text{ kg} \times \text{Php } 65 = \text{Php } 650.00\n * Brown sugar: 10\text{ kg} \times \text{Php } 40 = \text{Php } 400.00;;10\text{ kg} \times \text{Php } 45 = \text{Php } 450.00\n * Total Basket: \text{Cost}{2018} = \text{Php } 5{,}300.00;;\text{Cost}{2024} = \text{Php } 5{,}550.00\n * \text{CPI}_{2024} = \frac{\text{Php } 5{,}550.00}{\text{Php } 5{,}300.00} \times 100 = 104.72\n * \text{Inflation Rate} = 104.72 - 100.00 = 4.72\%\n\n* **Exercise Set 1.4 — Markups, Discounts, and Value-Added Tax:**\n * *Exercise 1.3, Item 1:* Adding a specific amount to product cost to set selling price for profit is **Markup**.\n * *Exercise 1.3, Item 2:* Deducting a sum from original price to incentivize buying is a **Discount**.\n * *Exercise 1.3, Item 3:* The difference between list price and discount is the **Net Price**.\n * *Exercise 1.3, Item 4:* A shoulder bag priced at \text{Php } 1{,}300.00ismarkeddowntois marked down to\text{Php } 1{,}050.00. Find discount rate:\n        D = 1{,}300 - 1{,}050 = \text{Php } 250.00\n        D_r = \frac{250}{1{,}300} \times 100 = 19.23\%\n * *Exercise 1.3, Item 5:* Running shoes sell for \text{Php } 5{,}400.00withawith a15\% markup rate. Find cost price:\n        C = \frac{5{,}400}{1 + 0.15} = \frac{5{,}400}{1.15} = \text{Php } 4{,}695.65\n * *Exercise 1.4, Item 1:* A vehicle sells for \text{Php } 780{,}000.00,exclusiveofVAT(, exclusive of VAT (V_e). Find VAT amount and gross inclusive price:\n        V = 0.12 \times \text{Php } 780{,}000.00 = \text{Php } 93{,}600.00\n        V_i = 1.12 \times \text{Php } 780{,}000.00 = \text{Php } 873{,}600.00\n * *Exercise 1.4, Item 2:* A refrigerator lists at \text{Php } 31{,}000.00,inclusiveofVAT(, inclusive of VAT (V_i). Find VAT amount and exclusive price:\n        V = \frac{0.12}{1.12} \times \text{Php } 31{,}000.00 = \text{Php } 3{,}321.43\n        V_e = \frac{\text{Php } 31{,}000.00}{1.12} = \text{Php } 27{,}678.57$$