Business Mathematics: Salary, Wage, and Commission

Educational Context and Objectives

Institution: Berea Arts and Sciences High School, located at Ponce St., Phase 7, Vista Verde Executive Village, Antipolo City, Rizal.
Subject: Business Mathematics.
Lesson: Business and Finance: Salary, Wage, and Commission (Lesson 1).
Learning Objectives:
- Differentiate between salary and wage based on payment structures.
- Calculate periodic wages and salaries from annual rates.
- Compute overtime pay under various working day conditions.
- Calculate various types of commissions based on sales volume.
- Solve for piecework earnings.
- Compute gross and net income after taxes and benefits.

Defining Compensation: Salary, Wage, Allowance, and Commission

Salary:
- A salary is a fixed amount of money agreed upon annually or monthly between an employer and an employee.
- It is typically paid at regular intervals (e.g., monthly, semi-monthly).
- Payment is consistent regardless of the specific number of hours worked, provided the established duties are fulfilled.
Wage:
- Compensation based on an hourly or daily rate.
- It varies depending on the actual time worked or the number of pieces produced.
- Wage earners are subject to "no work, no pay" policies.
- Wage earners are entitled to overtime pay for extra hours rendered.
Allowance:
- A sum of money granted to an employee to cover specific expenses related to their work.
- Common Examples:
  - Transportation Allowance.
  - Rice Subsidy.
  - Clothing/Laundry Allowance.
  - Communication Allowance.
Commission:
- A payment based on the amount of sales generated by an employee.
- It serves as an incentive for sales personnel to perform better.
- It can be a fixed amount or a percentage of the total sales value.

Comparative Analysis: Salary vs. Wage

Feature	Salary	Wage
Basis	Fixed Periodic Amount	Hourly, Daily, or Piece Rate
Payment Period	Monthly / Semi-monthly	Weekly / Daily
Overtime Pay	Generally not included	Strictly calculated
Status	Regular / Administrative	Manual / Operational

Key Periodic Salary Calculations

To calculate smaller period payments from an annual rate, the following methods are used:

Monthly Salary:
- Scenario: Annual salary is $\text{₱480,000}$ .
- Calculation: $\frac{\text{₱480,000}}{12} = \text{₱40,000}$ per month.
Weekly Salary:
- Scenario: Annual earnings are $\text{₱312,000}$ .
- Calculation: $\frac{\text{₱312,000}}{52} = \text{₱6,000}$ per week.
Hourly Rate:
- Scenario: Annual earnings are $\text{₱416,000}$ and the employee works 40 hours a week.
- Weekly Earnings: $\frac{\text{₱416,000}}{52} = \text{₱8,000}$ per week.
- Hourly Rate: $\frac{\text{₱8,000}}{40} = \text{₱200}$ per hour.

Overtime (OT) Compensation Fundamentals

Definition: Overtime pay is the additional compensation paid to employees for work rendered beyond the regular 8-hour workday.
Variation: Rate varies based on the type of day the work was performed (Ordinary, Rest, or Holiday).

Ordinary Working Day

Formula: $\text{Regular Hourly Rate} + (\text{25\%} \times \text{Regular Hourly Rate})$ .
Example: Hourly rate is $\text{₱100/hr}$ . Employee worked 3 hours OT.
Solution: $\text{₱100.00} \times 1.25 \times 3 = \text{₱375.00}$ .

Rest Day or Special Holiday

First 8 Hours: $130\%$ of Daily Wage (Multiplier: $1.30$ ).
Beyond 8 Hours (OT): The effective multiplier is $1.69$ .

Regular Holiday

First 8 Hours: $200\%$ of Daily Wage (Double Pay).
Beyond 8 Hours (OT): The effective multiplier is $2.60$ .
Case Study Example: Employee X has an hourly rate of $\text{₱150}$ . Worked 10 hours on a Regular Holiday.
- First 8 Hours: $\text{₱150} \times 2.0 \times 8 = \text{₱2,400.00}$ .
- OT (2 Hours): $\text{₱150} \times 2.0 \times 1.3 \times 2 = \text{₱780.00}$ .
- Total Earnings: $\text{₱2,400} + \text{₱780} = \text{₱3,180}$ .

Regular Holiday on a Rest Day

First 8 Hours: $260\%$ of the basic hourly rate.
Total Pay (1st 8h): $\text{Hourly Rate} \times 2.60 \times 8$ .
OT Pay (Beyond 8h): $\text{Hourly Rate} \times 2.60 \times 1.30 \times \text{OT Hours}$ .

Special Non-Working Holiday on Rest Day

Multiplier for first 8 hours: $1.50$ ( $150\%$ ).
OT Pay: $\text{Hourly Rate} \times 1.50 \times 1.30 \times \text{OT Hours}$ .
Effective OT Multiplier: $1.95$ .

Overtime Multiplier Summary Table

Day Type	First 8 Hours Multiplier	OT (beyond 8) Calculation
Ordinary Day	$1.00$ ( $100\%$ DW)	$\text{(HR)} \times 125\%$
Rest Day or Special Non-Working Day	$1.30$ ( $130\%$ DW)	$\text{(HR)} \times 130\% \times 130\% = \text{(HR)} \times 169\%$
Rest Day AND Special Non-Working Day	$1.50$ ( $150\%$ DW)	$\text{(HR)} \times 150\% \times 130\% = \text{(HR)} \times 195\%$
Regular Holiday	$2.00$ ( $200\%$ DW)	$\text{(HR)} \times 200\% \times 130\% = \text{(HR)} \times 260\%$
Regular Holiday on Rest Day	$2.60$ ( $260\%$ DW)	$\text{(HR)} \times 260\% \times 130\% = \text{(HR)} \times 338\%$

Note: DW stands for Daily Wage; HR stands for Hourly Rate.

Commission Structures and Motivations

Commission structures motivate agents by linking pay directly to performance.

Straight Commission: The agent is paid only a percentage of his/her sales.
- Example: $5\%$ commission on $\text{₱1,000,000}$ sales result in $\text{₱50,000}$ .
Graduated Commission: Rates increase as sales volume reaches specific tiers.
- Tiers Example:
  1. First $\text{₱100,000} \rightarrow 2\%$
  2. Next $\text{₱100,000} \rightarrow 5\%$
  3. Over $\text{₱200,000} \rightarrow 10\%$
- Graduated Calculation Example: Sales of $\text{₱250,000}$ .
  - First $\text{₱100,000} \times 0.02 = \text{₱2,000}$ .
  - Next $\text{₱100,000} \times 0.05 = \text{₱5,000}$ .
  - Excess $\text{₱50,000} \times 0.10 = \text{₱5,000}$ .
  - Total Commission: $\text{₱12,000}$ .
Salary Plus Commission: Guaranteed base pay plus additional earnings from sales.
- Example: $\text{₱15,000}$ base salary + $3\%$ of $\text{₱200,000}$ sales.
- Total Earnings: $\text{₱15,000} + (200,000 \times 0.03) = \text{₱15,000} + \text{₱6,000} = \text{₱21,000}$ .
Draw Against Commission: An advance on expected commissions.
- If commissions earned are less than the draw, the agent may owe the difference or it is carried over.
- Example: Draw amount is $\text{₱10,000}$ . Commission earned is $\text{₱12,000}$ . The agent receives the extra $\text{₱2,000}$ .
Override Commission: A manager earns a percentage of the total sales made by their subordinates.
- Example: Team Sales $\text{₱5,000,000}$ , Override Rate $0.5\%$ . Manager earnings: $\text{₱25,000}$ .

Analysis of Gross and Net Income

Gross Income: The total amount of money earned before any deductions (taxes, insurance, government contributions, or loan payments).
- Formula: $\text{Gross Income} = \text{Salary before deductions}$ .
Net Income: The actual amount received after all deductions have been subtracted from the gross income.
- Formula: $\text{Net Income} = \text{Gross Income} - \text{Total Deductions}$ .

Common Deductions

Withholding Tax: A progressive tax based on income level.
SSS / GSIS: Social security contributions.
PhilHealth: Medical/Health insurance.
Pag-IBIG: Housing fund contributions.

Calculation Example

Gross Monthly Salary: $\text{₱30,000}$ .
Deductions:
- Income Tax: $\text{₱1,500}$ .
- SSS: $\text{₱1,125}$ .
- PhilHealth: $\text{₱600}$ .
- Pag-IBIG: $\text{₱200}$ .
Total Deductions: $\text{₱1,500} + \text{₱1,125} + \text{₱600} + \text{₱200} = \text{₱3,425}$ .
Net Income: $\text{₱30,000} - \text{₱3,425} = \text{₱26,575}$ .

Complex Problem Solving Case

Employee Y:
- Basic Earnings: $\text{₱25,000}$ .
- OT Pay: $\text{₱3,500}$ .
- Commission: $\text{₱2,000}$ .
- Gross Income: $\text{₱25,000} + \text{₱3,500} + \text{₱2,000} = \text{₱30,500}$ .
- Deductions: Tax ( $\text{₱1,200}$ ) + SSS ( $\text{₱1,125}$ ) + Pag-IBIG ( $\text{₱100}$ ) + PhilHealth ( $\text{₱500}$ ) = $\text{₱2,925}$ .
- Net Income: $\text{₱30,500} - \text{₱2,925} = \text{₱27,575}$ .

Exercises for Practice

Monthly Salary: Find the monthly salary of an agent earning $\text{₱576,000}$ annually.
Bi-monthly Salary: An employee earns $\text{₱80,000/month}$ . What is the bi-monthly salary?
OT Pay: Compute OT pay for 5 hours on an ordinary day if hourly rate is $\text{₱160}$ .
Annual Salary: Weekly salary is $\text{₱12,500}$ . Calculate annual salary.
Holiday Earnings: Worked 8 hours on a Regular Holiday with base hourly rate of $\text{₱220}$ . Calculate total earnings.
Straight Commission: Compute $7\%$ straight commission on $\text{₱850,000}$ sales.
Graduated Commission: $5\%$ on 1st 50k, $8\%$ on excess. Total sales: $\text{₱120,000}$ .
Gross Income Calculation: Salary of $\text{₱22,000}$ plus $2\%$ of $\text{₱150,000}$ sales.
Piecework: $\text{₱15.50}$ per unit. Finished 400 units. Find total earnings.
Net Income: Gross Income $\text{₱45,000}$ . Total deductions $\text{₱6,750}$ . Find Net Income.