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Compiled by: Jane Kamau
Procurement professionals in Kenya frequently engage with commercial mathematics to accurately calculate costs, discounts, and pricing strategies essential for effective supplier negotiations and budget management. Mastery of discount calculations ensures procurement officers can identify real savings and make informed purchasing decisions that optimize organizational resources. This chapter builds foundational skills in commercial mathematics focusing on discount types commonly encountered in procurement, equipping learners with practical calculation techniques for cash, trade, and quantity discounts.
Discounts reduce the price paid by a buyer, incentivizing prompt payment, bulk buying, or trade relationships. Understanding how to calculate different discount types is crucial in procurement to evaluate offers and negotiate contracts effectively.
Cash discounts are price reductions offered to buyers who pay their invoices promptly, usually within a specified period. These discounts encourage early payment and improve the seller’s cash flow. The cash discount is calculated on the invoice amount excluding any trade discounts.
The formula for calculating the cash discount amount is:
$$ \text{Cash Discount} = \text{Invoice Amount} \times \frac{\text{Discount Rate}}{100} $$
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 5% cash discount if paid within 10 days. Calculate the amount payable if payment is made within the discount period.
Given: Invoice Amount = Ksh 150,000, Discount Rate = 5%
$$ \text{Cash Discount} = 150,000 \times \frac{5}{100} $$$$ = 150,000 \times 0.05 $$$$ = 7,500 $$$$ \text{Amount Payable} = 150,000 - 7,500 = 142,500 $$
Answer: Ksh 142,500
Example 2: A retail business has an invoice of Ksh 320,000 with a 3% cash discount for payment within 15 days. What is the cash discount and amount payable?
Given: Invoice Amount = Ksh 320,000, Discount Rate = 3%
$$ \text{Cash Discount} = 320,000 \times \frac{3}{100} $$$$ = 320,000 \times 0.03 $$$$ = 9,600 $$$$ \text{Amount Payable} = 320,000 - 9,600 = 310,400 $$
Answer: Ksh 310,400
Example 3: A SACCO receives an invoice of Ksh 480,000 with a 4% cash discount. The payment is delayed, and the discount is forfeited. Calculate how much more the SACCO pays by not taking the discount.
Given: Invoice Amount = Ksh 480,000, Discount Rate = 4%
$$ \text{Cash Discount} = 480,000 \times \frac{4}{100} $$$$ = 480,000 \times 0.04 $$$$ = 19,200 $$
Answer: Ksh 19,200 more is paid without the discount
Example 4: A hotel purchases goods worth Ksh 600,000 with a cash discount of 2.5%. The hotel pays after the discount period. Calculate the percentage increase in the amount paid compared to if the discount was taken.
Given: Invoice Amount = Ksh 600,000, Discount Rate = 2.5%
Cash Discount:
$$ 600,000 \times \frac{2.5}{100} = 15,000 $$
Amount payable with discount:
$$ 600,000 - 15,000 = 585,000 $$
Amount payable without discount:
$$ 600,000 $$
Percentage increase:
$$ \frac{600,000 - 585,000}{585,000} \times 100 = \frac{15,000}{585,000} \times 100 \approx 2.56\% $$
Answer: Approximately 2.56% increase
Example 5: A cooperative buys supplies worth Ksh 250,000 with a 6% cash discount if paid within 7 days. They pay after 9 days. Calculate the lost discount amount and new amount payable.
Given: Invoice Amount = Ksh 250,000, Discount Rate = 6%
Cash Discount:
$$ 250,000 \times \frac{6}{100} = 15,000 $$
Amount payable if discount taken:
$$ 250,000 - 15,000 = 235,000 $$
Amount payable after discount period:
$$ 250,000 $$
Answer: Lost discount Ksh 15,000; amount payable Ksh 250,000
Trade discounts are price reductions offered by suppliers on the catalogue price to intermediaries or bulk buyers. Unlike cash discounts, trade discounts are deducted before calculating taxes or cash discounts. Trade discounts are usually expressed as a percentage of the list price.
The formula for the trade discount amount is:
$$ \text{Trade Discount} = \text{List Price} \times \frac{\text{Trade Discount Rate}}{100} $$
The net price after trade discount is:
$$ \text{Net Price} = \text{List Price} - \text{Trade Discount} $$
Example 1: A procurement officer at a university orders equipment listed at Ksh 120,000 with a trade discount of 10%. Calculate the net price after trade discount.
Given: List Price = Ksh 120,000, Trade Discount Rate = 10%
$$ \text{Trade Discount} = 120,000 \times \frac{10}{100} $$$$ = 120,000 \times 0.10 = 12,000 $$$$ \text{Net Price} = 120,000 - 12,000 = 108,000 $$
Answer: Ksh 108,000
Example 2: A county government office receives a list price of Ksh 300,000 with a trade discount of 15%. Find the net price after trade discount.
Given: List Price = Ksh 300,000, Trade Discount Rate = 15%
$$ \text{Trade Discount} = 300,000 \times \frac{15}{100} = 45,000 $$$$ \text{Net Price} = 300,000 - 45,000 = 255,000 $$
Answer: Ksh 255,000
Example 3: A retail business orders goods with a list price of Ksh 400,000 and receives a trade discount of 12%. Calculate the net price.
Given: List Price = Ksh 400,000, Trade Discount Rate = 12%
$$ \text{Trade Discount} = 400,000 \times \frac{12}{100} = 48,000 $$$$ \text{Net Price} = 400,000 - 48,000 = 352,000 $$
Answer: Ksh 352,000
Example 4: A SACCO buys office supplies with a list price of Ksh 220,000 and a trade discount of 8%. Calculate the trade discount and net price.
Given: List Price = Ksh 220,000, Trade Discount Rate = 8%
$$ \text{Trade Discount} = 220,000 \times \frac{8}{100} = 17,600 $$$$ \text{Net Price} = 220,000 - 17,600 = 202,400 $$
Answer: Trade discount Ksh 17,600; Net price Ksh 202,400
Example 5: A cooperative purchases goods with a list price of Ksh 500,000 and a 20% trade discount. Calculate the amount saved and net price payable.
Given: List Price = Ksh 500,000, Trade Discount Rate = 20%
$$ \text{Trade Discount} = 500,000 \times \frac{20}{100} = 100,000 $$$$ \text{Net Price} = 500,000 - 100,000 = 400,000 $$
Answer: Amount saved Ksh 100,000; Net price Ksh 400,000
Example 6: A school bought textbooks worth Ksh 27,027 from Text Book Centre. The bookseller allowed a trade discount of 10% and a cash discount of 5% if payment was made within 7 days. Calculate the final amount payable if the school paid within the discount period.
Given: List Price = Ksh 27,027, Trade Discount = 10%, Cash Discount = 5%
First, calculate the trade discount:$$ \text{Trade Discount} = 27,027 \times \frac{10}{100} = 2,702.70 $$ Net price after trade discount:$$ 27,027 - 2,702.70 = 24,324.30 $$ Now, calculate the cash discount:$$ \text{Cash Discount} = 24,324.30 \times \frac{5}{100} = 1,216.22 $$ Amount payable after both discounts:$$ 24,324.30 - 1,216.22 = 23,108.08 $$ Answer: Ksh 23,108.08
Example 7: A procurement officer receives an order worth Ksh 200,000 with a trade discount of 15% followed by a second trade discount of 10%. Calculate the net amount payable after both discounts.
Given: List Price = Ksh 200,000, Trade Discounts = 15% and 10%
First, apply the first trade discount:$$ \text{First Discount} = 200,000 \times \frac{15}{100} = 30,000 $$ Amount after first discount:$$ 200,000 - 30,000 = 170,000 $$ Apply the second trade discount:$$ \text{Second Discount} = 170,000 \times \frac{10}{100} = 17,000 $$ Net amount payable:$$ 170,000 - 17,000 = 153,000 $$ Answer: Ksh 153,000
Quantity discounts are reductions in price granted for bulk purchases to encourage higher volume buying. These discounts are calculated based on the total quantity or value of goods purchased and can be applied as a percentage or fixed amount.
The quantity discount amount formula is:
$$ \text{Quantity Discount} = \text{Total Purchase Value} \times \frac{\text{Quantity Discount Rate}}{100} $$
The amount payable after quantity discount is:
$$ \text{Amount Payable} = \text{Total Purchase Value} - \text{Quantity Discount} $$
Example 1: A hotel orders stationery worth Ksh 180,000 and receives a 5% quantity discount. Calculate the discount and amount payable.
Given: Total Purchase Value = Ksh 180,000, Quantity Discount Rate = 5%
$$ \text{Quantity Discount} = 180,000 \times \frac{5}{100} = 9,000 $$$$ \text{Amount Payable} = 180,000 - 9,000 = 171,000 $$
Answer: Ksh 171,000
Example 2: A hospital buys medical supplies valued at Ksh 450,000 and is offered a 7% quantity discount. Calculate the amount saved and payable.
Given: Total Purchase Value = Ksh 450,000, Quantity Discount Rate = 7%
$$ \text{Quantity Discount} = 450,000 \times \frac{7}{100} = 31,500 $$$$ \text{Amount Payable} = 450,000 - 31,500 = 418,500 $$
Answer: Amount saved Ksh 31,500; amount payable Ksh 418,500
Example 3: A retail shop orders goods worth Ksh 600,000 and is given a 10% quantity discount for purchasing above a threshold. Calculate the discount and net amount.
Given: Total Purchase Value = Ksh 600,000, Quantity Discount Rate = 10%
$$ \text{Quantity Discount} = 600,000 \times \frac{10}{100} = 60,000 $$$$ \text{Amount Payable} = 600,000 - 60,000 = 540,000 $$
Answer: Ksh 540,000
Example 4: A county government office buys office furniture worth Ksh 750,000 and receives an 8% quantity discount. Calculate the discount and total payable.
Given: Total Purchase Value = Ksh 750,000, Quantity Discount Rate = 8%
$$ \text{Quantity Discount} = 750,000 \times \frac{8}{100} = 60,000 $$$$ \text{Amount Payable} = 750,000 - 60,000 = 690,000 $$
Answer: Ksh 690,000
Example 5: A cooperative purchases farm inputs worth Ksh 1,200,000 and is offered a 12% quantity discount. Calculate the discount amount and payable amount.
Given: Total Purchase Value = Ksh 1,200,000, Quantity Discount Rate = 12%
$$ \text{Quantity Discount} = 1,200,000 \times \frac{12}{100} = 144,000 $$$$ \text{Amount Payable} = 1,200,000 - 144,000 = 1,056,000 $$
Answer: Discount Ksh 144,000; amount payable Ksh 1,056,000
An invoice amount is Ksh 250,000 with a 4% cash discount. Calculate the amount payable if the discount is taken. (4 marks)
A supplier offers a 15% trade discount on goods listed at Ksh 500,000. Calculate the net price after discount. (4 marks)
A hotel orders goods worth Ksh 350,000 with a 6% quantity discount. Find the discount and amount payable. (5 marks)
A SACCO receives goods priced at Ksh 120,000 with a 3% cash discount and a 10% trade discount. Calculate the final amount payable after both discounts. (6 marks)
A county government office receives an invoice of Ksh 400,000 with a 5% cash discount but pays after the discount period. Calculate the extra amount paid compared to paying within the discount period. (5 marks)
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Create a free accountThis chapter covered various types of discounts including cash, trade, and quantity discounts, explaining how each affects pricing in commercial transactions. It examined commissions as a form of payment based on sales performance, followed by methods of calculating wages through piece rate and hourly rate systems. The computation of wages and salaries was detailed to ensure accurate remuneration. The chapter then explored simple and compound interest calculations, essential for understanding financial growth and loan costs. Profit margin and mark-ups were discussed to clarify how businesses determine selling prices and profitability. It also addressed the calculation of gross pay and net pay to highlight deductions and take-home earnings. Finally, the chapter explained depreciation and appreciation of assets, determining hire purchase prices, and managing foreign exchange transactions, equipping learners with comprehensive commercial mathematics skills.
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 payment is made within the discount period. (3 marks)
A procurement officer receives a trade discount of 15% followed by 10% on an order worth Ksh 200,000. Find the net amount payable after applying the trade discounts. (4 marks)
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