By the end of this chapter, you will be able to:
Mastering these commercial calculations will help you make smart financial decisions and succeed in the engineering trade.
Commercial calculations are critical for industrial control and installation professionals in Kenya. Accurate pricing and sales evaluation ensure project profitability, competitive bidding, and sustainable business operations. Mastery of these calculations enables technicians to make informed decisions when costing installations, quoting clients, or analysing sales outcomes in both private and public sector projects.
Correctly determining the price of an engineering product or service is essential to cover costs and ensure profit. Product pricing involves calculating the total cost and then adding a profit margin or markup to set a selling price.
The total cost of a product includes all direct and indirect expenses involved in its production or acquisition. The basic formula is:$$ \text{Total Cost} = \text{Cost of Materials} + \text{Labour Cost} + \text{Overheads} $$
Example 1:
A technician installs a control panel for a county government office. The materials cost Ksh 12,000, labour is Ksh 5,500, and overheads are Ksh 2,000. Find the total cost.
Given:
\(\text{Cost of Materials} = 12,000\) Ksh
\(\text{Labour Cost} = 5,500\) Ksh
\(\text{Overheads} = 2,000\) Ksh
$$ \text{Total Cost} = 12,000 + 5,500 + 2,000 $$$$ \text{Total Cost} = 19,500 \text{ Ksh} $$ Answer: 19,500 Ksh
Example 2:
A farm requires installation of an automated irrigation system. Materials cost Ksh 28,000, labour Ksh 8,000, and overheads Ksh 4,500. Calculate the total cost.
Given:
\(\text{Materials} = 28,000\) Ksh
\(\text{Labour} = 8,000\) Ksh
\(\text{Overheads} = 4,500\) Ksh
$$ \text{Total Cost} = 28,000 + 8,000 + 4,500 $$$$ \text{Total Cost} = 40,500 \text{ Ksh} $$ Answer: 40,500 Ksh
Example 3:
A hotel contracts a technician to install smart lighting controls. Material cost is Ksh 17,200, labour is Ksh 6,300, overheads are Ksh 1,800.
Given:
\(\text{Materials} = 17,200\) Ksh
\(\text{Labour} = 6,300\) Ksh
\(\text{Overheads} = 1,800\) Ksh
$$ \text{Total Cost} = 17,200 + 6,300 + 1,800 $$$$ \text{Total Cost} = 25,300 \text{ Ksh} $$ Answer: 25,300 Ksh
Example 4:
A SACCO office requires a digital access control system. Material cost is Ksh 21,000, labour is Ksh 9,500, overheads are Ksh 2,500.
Given:
\(\text{Materials} = 21,000\) Ksh
\(\text{Labour} = 9,500\) Ksh
\(\text{Overheads} = 2,500\) Ksh
$$ \text{Total Cost} = 21,000 + 9,500 + 2,500 $$$$ \text{Total Cost} = 33,000 \text{ Ksh} $$ Answer: 33,000 Ksh
Example 5:
A retail shop wants a temperature monitoring system. Materials: Ksh 11,500, Labour: Ksh 4,400, Overheads: Ksh 1,600.
Given:
\(\text{Materials} = 11,500\) Ksh
\(\text{Labour} = 4,400\) Ksh
\(\text{Overheads} = 1,600\) Ksh
$$ \text{Total Cost} = 11,500 + 4,400 + 1,600 $$$$ \text{Total Cost} = 17,500 \text{ Ksh} $$ Answer: 17,500 Ksh
Profit is the difference between the selling price and the total cost. Markup is the profit expressed as a percentage of the cost price.
Profit formula:$$ \text{Profit} = \text{Selling Price} - \text{Total Cost} $$
Markup percentage formula:$$ \text{Markup (\%)} = ( \frac{\text{Profit}}{\text{Total Cost}} ) \times 100 $$
Example 1:
A technician quotes Ksh 30,000 for an installation. The total cost is Ksh 25,000. Find the profit and markup percentage.
Given:
\(\text{Selling Price} = 30,000\) Ksh
\(\text{Total Cost} = 25,000\) Ksh
Profit:$$ \text{Profit} = 30,000 - 25,000 = 5,000 \text{ Ksh} $$
Markup percentage:$$ \text{Markup (\%)} = ( \frac{5,000}{25,000} ) \times 100 = 20\% $$
Answer: Profit is 5,000 Ksh, Markup is 20%.
Example 2:
A university pays Ksh 45,000 for a lab automation system. The total cost was Ksh 36,000. Calculate profit and markup.
Given:
\(\text{Selling Price} = 45,000\) Ksh
\(\text{Total Cost} = 36,000\) Ksh
Profit:$$ \text{Profit} = 45,000 - 36,000 = 9,000 \text{ Ksh} $$
Markup:$$ \text{Markup (\%)} = ( \frac{9,000}{36,000} ) \times 100 = 25\% $$
Answer: Profit is 9,000 Ksh, Markup is 25%.
Example 3:
A county office is billed Ksh 60,000 for a security system. The total cost is Ksh 50,000.
Given:
\(\text{Selling Price} = 60,000\) Ksh
\(\text{Total Cost} = 50,000\) Ksh
Profit:$$ \text{Profit} = 60,000 - 50,000 = 10,000 \text{ Ksh} $$
Markup:$$ \text{Markup (\%)} = ( \frac{10,000}{50,000} ) \times 100 = 20\% $$
Answer: Profit is 10,000 Ksh, Markup is 20%.
Example 4:
A hospital is invoiced Ksh 72,000 for an access control upgrade. The total cost is Ksh 60,000.
Given:
\(\text{Selling Price} = 72,000\) Ksh
\(\text{Total Cost} = 60,000\) Ksh
Profit:$$ \text{Profit} = 72,000 - 60,000 = 12,000 \text{ Ksh} $$
Markup:$$ \text{Markup (\%)} = ( \frac{12,000}{60,000} ) \times 100 = 20\% $$
Answer: Profit is 12,000 Ksh, Markup is 20%.
Example 5:
A retail outlet is charged Ksh 22,000 for a POS installation. The cost is Ksh 17,600.
Given:
\(\text{Selling Price} = 22,000\) Ksh
\(\text{Total Cost} = 17,600\) Ksh
Profit:$$ \text{Profit} = 22,000 - 17,600 = 4,400 \text{ Ksh} $$
Markup:$$ \text{Markup (\%)} = ( \frac{4,400}{17,600} ) \times 100 = 25\% $$
Answer: Profit is 4,400 Ksh, Markup is 25%.
To set a selling price with a specified markup, the formula is:$$ \text{Selling Price} = \text{Total Cost} + ( \frac{\text{Markup (\%)}}{100} \times \text{Total Cost} ) $$
Example 1:
A technician wants a 15% markup on a project costing Ksh 30,000. Find the selling price.
Given:
\(\text{Total Cost} = 30,000\) Ksh
\(\text{Markup} = 15\%\)
Markup value:$$ \text{Markup Value} = \frac{15}{100} \times 30,000 = 4,500 \text{ Ksh} $$ Selling price:$$ \text{Selling Price} = 30,000 + 4,500 = 34,500 \text{ Ksh} $$
Answer: Selling price is 34,500 Ksh.
Example 2:
A school laboratory needs an installation with a cost of Ksh 22,000. Required markup is 25%. Determine the selling price.
Given:
\(\text{Total Cost} = 22,000\) Ksh
\(\text{Markup} = 25\%\)
Markup value:$$ \text{Markup Value} = \frac{25}{100} \times 22,000 = 5,500 \text{ Ksh} $$ Selling price:$$ \text{Selling Price} = 22,000 + 5,500 = 27,500 \text{ Ksh} $$
Answer: Selling price is 27,500 Ksh.
Example 3:
A hotel project costs Ksh 48,000. Desired markup is 10%. Calculate the selling price.
Given:
\(\text{Total Cost} = 48,000\) Ksh
\(\text{Markup} = 10\%\)
Markup value:$$ \text{Markup Value} = \frac{10}{100} \times 48,000 = 4,800 \text{ Ksh} $$ Selling price:$$ \text{Selling Price} = 48,000 + 4,800 = 52,800 \text{ Ksh} $$
Answer: Selling price is 52,800 Ksh.
Example 4:
A SACCO job costs Ksh 18,500. The technician wants a 20% markup. What selling price should be quoted?
Given:
\(\text{Total Cost} = 18,500\) Ksh
\(\text{Markup} = 20\%\)
Markup value:$$ \text{Markup Value} = \frac{20}{100} \times 18,500 = 3,700 \text{ Ksh} $$ Selling price:$$ \text{Selling Price} = 18,500 + 3,700 = 22,200 \text{ Ksh} $$
Answer: Selling price is 22,200 Ksh.
Example 5:
A retail store installation costs Ksh 13,600. Markup required is 12.5%. Calculate the selling price.
Given:
\(\text{Total Cost} = 13,600\) Ksh
\(\text{Markup} = 12.5\%\)
Markup value:$$ \text{Markup Value} = \frac{12.5}{100} \times 13,600 = 1,700 \text{ Ksh} $$ Selling price:$$ \text{Selling Price} = 13,600 + 1,700 = 15,300 \text{ Ksh} $$
Answer: Selling price is 15,300 Ksh.
Percentage profit or loss is calculated based on the cost price.
Percentage profit formula:$$ \text{Percentage Profit} = \frac{\text{Profit}}{\text{Cost Price}} \times 100 $$
Percentage loss formula:$$ \text{Percentage Loss} = \frac{\text{Loss}}{\text{Cost Price}} \times 100 $$
Example 1:
A technician installs a system at a cost of Ksh 20,000 and sells it for Ksh 22,000.
Given:
\(\text{Cost Price} = 20,000\) Ksh
\(\text{Selling Price} = 22,000\) Ksh
Profit:$$ \text{Profit} = 22,000 - 20,000 = 2,000 \text{ Ksh} $$ Percentage profit:$$ \text{Percentage Profit} = \frac{2,000}{20,000} \times 100 = 10\% $$
Answer: Percentage profit is 10%.
Example 2:
A project costs Ksh 25,000 but is sold at Ksh 24,000 due to negotiation.
Given:
\(\text{Cost Price} = 25,000\) Ksh
\(\text{Selling Price} = 24,000\) Ksh
Loss:$$ \text{Loss} = 25,000 - 24,000 = 1,000 \text{ Ksh} $$ Percentage loss:$$ \text{Percentage Loss} = \frac{1,000}{25,000} \times 100 = 4\% $$
Answer: Percentage loss is 4%.
Example 3:
A university technician installs equipment for Ksh 38,000, selling at Ksh 41,800.
Given:
\(\text{Cost Price} = 38,000\) Ksh
\(\text{Selling Price} = 41,800\) Ksh
Profit:$$ \text{Profit} = 41,800 - 38,000 = 3,800 \text{ Ksh} $$ Percentage profit:$$ \text{Percentage Profit} = \frac{3,800}{38,000} \times 100 = 10\% $$
Answer: Percentage profit is 10%.
Example 4:
A technician spends Ksh 16,500 on materials and sells the product for Ksh 15,675.
Given:
\(\text{Cost Price} = 16,500\) Ksh
\(\text{Selling Price} = 15,675\) Ksh
Loss:$$ \text{Loss} = 16,500 - 15,675 = 825 \text{ Ksh} $$ Percentage loss:$$ \text{Percentage Loss} = \frac{825}{16,500} \times 100 = 5\% $$
Answer: Percentage loss is 5%.
Example 5:
A retail system is bought for Ksh 19,200 and sold for Ksh 20,160.
Given:
\(\text{Cost Price} = 19,200\) Ksh
\(\text{Selling Price} = 20,160\) Ksh
Profit:$$ \text{Profit} = 20,160 - 19,200 = 960 \text{ Ksh} $$ Percentage profit:$$ \text{Percentage Profit} = \frac{960}{19,200} \times 100 = 5\% $$
Answer: Percentage profit is 5%.
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Create a free accountThis chapter explored a range of commercial calculations vital for civil engineering and business operations. It began with methods for determining product pricing, followed by techniques for calculating average sales to analyze revenue trends. Stock turnover was examined to measure inventory efficiency, while various approaches to income calculations were demonstrated. The chapter provided detailed procedures for computing profit and loss, as well as step-by-step calculations for both gross and net salaries. Different wage systems were covered, including time rate, flat rate, overtime, piece rate, commission, percentage, and bonus payments. The conversion of currencies and the calculation of exchange rates were addressed, with attention given to both devaluation and revaluation scenarios. These topics collectively equip students with essential skills for handling commercial mathematics in engineering contexts.
Given:
Selling price \( = 18,000 \) Ksh
Cost price \( = 14,500 \) Ksh
Formula:$$\text{Profit} = \text{Selling price} - \text{Cost price}$$
Substitution:$$\text{Profit} = 18,000 - 14,500$$
Calculation:$$\text{Profit} = 3,500$$
Final Answer:
Profit = 3,500 Ksh
Given:
Sales: \( 265,000 \), \( 310,000 \), \( 280,000 \), \( 295,000 \) Ksh
Formula:$$\text{Average Sales} = \frac{\text{Total Sales}}{\text{Number of Months}}$$
Calculation:$$\text{Total Sales} = 265,000 + 310,000 + 280,000 + 295,000 = 1,150,000$$$$\text{Average Sales} = \frac{1,150,000}{4}$$$$\text{Average Sales} = 287,500$$
Final Answer:
Average monthly sales = 287,500 Ksh
A contractor at a Nairobi industrial site purchases electrical control panels at a unit price of Ksh 18,500. If he needs 12 panels, calculate the total cost, including a 16% VAT. (4 marks)
A technician at a manufacturing firm records monthly sales for three products: Ksh 45,000, Ksh 32,000, and Ksh 53,000. Find the average sales for the month. (4 marks)
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