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Compiled by: Jane Chebet
Work-out commercial mathematics is essential for procurement professionals to accurately calculate prices, discounts, and costs in various purchasing scenarios. Mastery of discount calculations enables procurement officers to evaluate supplier offers, negotiate better deals, and ensure value for money in public and private sector procurement. This chapter focuses on three main types of discounts, cash discount, trade discount, and quantity discount, each with distinct calculation methods vital for effective procurement management in Kenya.
Procurement professionals must understand the different discount types to correctly compute final purchase prices and manage budgets. Discounts impact cash flow and supplier relationships, so precise calculations prevent costly errors. This section covers cash discount mathematics, trade discount, and quantity discount calculations, each explained with practical examples.
Cash discounts are incentives offered by suppliers to buyers for early payment within a specified period. This discount encourages prompt payment, improving supplier cash flow and reducing credit risk. The cash discount is usually expressed as a percentage and applies to the invoice amount if payment is made within the discount period.
The formula for calculating the cash discount amount is:
$$ \text{Cash Discount} = \text{Invoice Amount} \times \frac{\text{Discount \%}}{100} $$
The amount payable after cash discount is:
$$ \text{Amount Payable} = \text{Invoice Amount} - \text{Cash Discount} $$
Example 1: A county government office receives an invoice of Ksh 150,000 with a 2% cash discount if paid within 10 days. Calculate the cash discount and amount payable if payment is made within the discount period.
Given: Invoice Amount = Ksh 150,000, Discount = 2%
$$ \text{Cash Discount} = 150,000 \times \frac{2}{100} $$$$ = 150,000 \times 0.02 $$$$ = 3,000 $$
$$ \text{Amount Payable} = 150,000 - 3,000 = 147,000 $$
Answer: Cash Discount = Ksh 3,000, Amount Payable = Ksh 147,000
Example 2: A retail business has an invoice of Ksh 250,000 with terms 3/10, net 30 (3% discount if paid within 10 days). Calculate the amount payable if payment is made on day 8.
Given: Invoice Amount = Ksh 250,000, Discount = 3%
$$ \text{Cash Discount} = 250,000 \times \frac{3}{100} $$$$ = 7,500 $$
$$ \text{Amount Payable} = 250,000 - 7,500 = 242,500 $$
Answer: Cash Discount = Ksh 7,500, Amount Payable = Ksh 242,500
Example 3: A cooperative receives an invoice of Ksh 180,000 with 1.5% cash discount if paid within 15 days. If payment is delayed beyond 15 days, no discount applies. Calculate the amount payable if payment is made on day 20.
Given: Invoice Amount = Ksh 180,000, Discount = 1.5%
Since payment is late, no discount applies.
Answer: Amount Payable = Ksh 180,000
Example 4: A hospital buys medical supplies worth Ksh 320,000 with a 2.5% cash discount for payment within 7 days. Calculate the amount payable if payment is made within discount period and also if payment is made after 7 days.
Given: Invoice Amount = Ksh 320,000, Discount = 2.5%
If paid within 7 days:
$$ \text{Cash Discount} = 320,000 \times \frac{2.5}{100} = 8,000 $$
$$ \text{Amount Payable} = 320,000 - 8,000 = 312,000 $$
If paid after 7 days, no discount applies.
Answer: Within 7 days: Ksh 312,000; After 7 days: Ksh 320,000
Example 5: A SACCO purchases office equipment worth Ksh 90,000 with terms 4/15, net 45. Calculate the amount payable if payment is made on day 10 and on day 20.
Given: Invoice Amount = Ksh 90,000, Discount = 4%
Payment on day 10 (within discount period):
$$ \text{Cash Discount} = 90,000 \times \frac{4}{100} = 3,600 $$
$$ \text{Amount Payable} = 90,000 - 3,600 = 86,400 $$
Payment on day 20 (after discount period):
No discount applies.
Answer: Day 10 payment: Ksh 86,400; Day 20 payment: Ksh 90,000
Example 6: A farmer was allowed a cash discount of Ksh 175 on farm implements worth Ksh 3,500. What was the percentage discount?
Given: Cash Discount = Ksh 175, Invoice Amount = Ksh 3,500
Formula:$$ \text{Discount \%} = \frac{\text{Cash Discount}}{\text{Invoice Amount}} \times 100 $$
Substitute:$$ \text{Discount \%} = \frac{175}{3,500} \times 100 = 0.05 \times 100 = 5\% $$
Answer: Percentage discount = 5%
Example 7: Jane paid Ksh 12,000 for a TV set after she was allowed a discount of 16%. What was the marked price of the TV?
Given: Paid Price = Ksh 12,000, Discount = 16%
Let Marked Price = \( M \)
Formula:$$ \text{Paid Price} = M \times (1 - \frac{\text{Discount \%}}{100}) $$
Substitute:$$ 12,000 = M \times (1 - 0.16) = M \times 0.84 $$
Solve for \( M \):$$ M = \frac{12,000}{0.84} = 14,285.71 $$
Answer: Marked price = Ksh 14,285.71
Trade discounts are reductions in the listed price granted by suppliers to buyers, typically based on the type of customer or the nature of the trade. Unlike cash discounts, trade discounts are not conditional on payment time but are deducted before sales tax or VAT calculations. The trade discount is usually expressed as a percentage of the list price.
The formula to calculate the net price after trade discount is:
$$ \text{Net Price} = \text{List Price} \times (1 - \frac{\text{Trade Discount \%}}{100}) $$
When multiple trade discounts are given sequentially, the net price is calculated by applying each discount in turn.
Example 1: A school orders stationery with a list price of Ksh 50,000 and is offered a 10% trade discount. Calculate the net price.
Given: List Price = Ksh 50,000, Trade Discount = 10%
$$ \text{Net Price} = 50,000 \times (1 - \frac{10}{100}) = 50,000 \times 0.9 = 45,000 $$
Answer: Net Price = Ksh 45,000
Example 2: A university procures books with a list price of Ksh 120,000 and receives two trade discounts of 15% and 5% sequentially. Calculate the net price.
Given: List Price = Ksh 120,000, Trade Discounts = 15%, 5%
Apply first discount:
$$ 120,000 \times (1 - \frac{15}{100}) = 120,000 \times 0.85 = 102,000 $$
Apply second discount:
$$ 102,000 \times (1 - \frac{5}{100}) = 102,000 \times 0.95 = 96,900 $$
Answer: Net Price = Ksh 96,900
Example 3: A retail business buys electronics with a list price of Ksh 200,000 and gets a trade discount of 12%. Calculate the net price.
Given: List Price = Ksh 200,000, Trade Discount = 12%
$$ \text{Net Price} = 200,000 \times 0.88 = 176,000 $$
Answer: Net Price = Ksh 176,000
Example 4: A county government office orders office furniture with a list price of Ksh 350,000 and receives three trade discounts of 10%, 5%, and 3%. Calculate the net price.
Given: List Price = Ksh 350,000, Discounts = 10%, 5%, 3%
Step 1:
$$ 350,000 \times (1 - \frac{10}{100}) = 350,000 \times 0.9 = 315,000 $$
Step 2:
$$ 315,000 \times (1 - \frac{5}{100}) = 315,000 \times 0.95 = 299,250 $$
Step 3:
$$ 299,250 \times (1 - \frac{3}{100}) = 299,250 \times 0.97 = 290,272.50 $$
Answer: Net Price = Ksh 290,272.50
Example 5: A cooperative purchases farm equipment with a list price of Ksh 500,000 and receives a single trade discount of 8%. Calculate the net price.
Given: List Price = Ksh 500,000, Trade Discount = 8%
$$ \text{Net Price} = 500,000 \times 0.92 = 460,000 $$
Answer: Net Price = Ksh 460,000
Example 6: A school orders textbooks with a list price of Ksh 150,000 and receives three trade discounts of 10%, 5%, and 2%. Calculate the net price.
Given: List Price = Ksh 150,000, Trade Discounts = 10%, 5%, 2%
Step 1: Apply first discount:$$ 150,000 \times (1 - \frac{10}{100}) = 150,000 \times 0.9 = 135,000 $$
Step 2: Apply second discount:$$ 135,000 \times (1 - \frac{5}{100}) = 135,000 \times 0.95 = 128,250 $$
Step 3: Apply third discount:$$ 128,250 \times (1 - \frac{2}{100}) = 128,250 \times 0.98 = 125,685 $$
Answer: Net Price = Ksh 125,685
Quantity discounts are price reductions offered by suppliers based on the volume or quantity of goods purchased. These discounts encourage bulk buying, reducing per-unit cost. Quantity discounts may be fixed amounts or percentages and are applied to the total order value or per unit price depending on supplier policies.
The formula for quantity discount percentage is:
$$ \text{Quantity Discount} = \text{Total Price} \times \frac{\text{Discount \%}}{100} $$
Amount payable after quantity discount:
$$ \text{Amount Payable} = \text{Total Price} - \text{Quantity Discount} $$
Example 1: A retail business orders 500 units of a product priced at Ksh 200 per unit. Supplier offers 5% discount for orders above 400 units. Calculate total price and amount payable after discount.
Given: Unit price = Ksh 200, Quantity = 500, Discount = 5%
Total price:
$$ 200 \times 500 = 100,000 $$
Discount:
$$ 100,000 \times \frac{5}{100} = 5,000 $$
Amount payable:
$$ 100,000 - 5,000 = 95,000 $$
Answer: Amount Payable = Ksh 95,000
Example 2: A county government orders 1,200 liters of fuel at Ksh 150 per liter with a 7% quantity discount for orders above 1,000 liters. Calculate amount payable after discount.
Given: Unit price = Ksh 150, Quantity = 1,200, Discount = 7%
Total price:
$$ 150 \times 1,200 = 180,000 $$
Discount:
$$ 180,000 \times \frac{7}{100} = 12,600 $$
Amount payable:
$$ 180,000 - 12,600 = 167,400 $$
Answer: Amount Payable = Ksh 167,400
Example 3: A hospital orders 250 boxes of gloves at Ksh 1,200 each with a 3% quantity discount for orders over 200 boxes. Calculate amount payable after discount.
Given: Unit price = Ksh 1,200, Quantity = 250, Discount = 3%
Total price:
$$ 1,200 \times 250 = 300,000 $$
Discount:
$$ 300,000 \times \frac{3}{100} = 9,000 $$
Amount payable:
$$ 300,000 - 9,000 = 291,000 $$
Answer: Amount Payable = Ksh 291,000
Example 4: A SACCO buys 150 office chairs at Ksh 8,000 each with no discount for less than 200 units. Calculate amount payable.
Given: Unit price = Ksh 8,000, Quantity = 150, Discount = 0%
Total price:
$$ 8,000 \times 150 = 1,200,000 $$
No discount applies.
Answer: Amount Payable = Ksh 1,200,000
Example 5: A retail store orders 2,000 units of a product at Ksh 50 each with a 10% quantity discount for orders above 1,500 units. Calculate amount payable.
Given: Unit price = Ksh 50, Quantity = 2,000, Discount = 10%
Total price:
$$ 50 \times 2,000 = 100,000 $$
Discount:
$$ 100,000 \times \frac{10}{100} = 10,000 $$
Amount payable:
$$ 100,000 - 10,000 = 90,000 $$
Answer: Amount Payable = Ksh 90,000
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Create a free accountThis chapter covers essential commercial mathematics skills starting with different types of discounts, including cash, trade, and quantity discounts, explaining how each reduces the selling price under various conditions. It then explores commissions, detailing how they are calculated as a percentage of sales or transactions. Various methods of calculating wages are examined, focusing on piece rate and hourly rate systems, followed by practical approaches to computing total wages and salaries. The concepts of simple and compound interest are introduced, illustrating their application in financial calculations. The chapter also clarifies the difference between profit margin and mark-ups in pricing decisions. It proceeds to explain how to calculate gross pay and net pay, accounting for deductions. Finally, it addresses the depreciation and appreciation of assets, methods for determining hire purchase prices, and the basics of foreign exchange transactions, ensuring a comprehensive understanding of commercial mathematics in practical business contexts.
A supplier offers a cash discount of 5% on an invoice of Ksh 120,000 if payment is made within 10 days. Calculate the amount payable if the buyer pays within the discount period. (3 marks)
A procurement officer receives a trade discount of 12% and a further 8% on a bulk order priced at Ksh 250,000. Calculate the net price after applying both trade discounts. (4 marks)
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