Example 1: Calculating Total Revenue

Problem: A company sells a product for \$10 per unit. If 200 units are sold, what is the total revenue?

Solution: Use the formula:
\( \text{Total Revenue } (TR) = P \times Q \)
Here, \( P = 10 \) and \( Q = 200 \). Thus,
\( TR = 10 \times 200 = 2000 \).

Total Revenue = \$2,000

Example 2: Calculating Total Revenue

Problem: If a product is sold at \$25 per unit and 150 units are sold, calculate the total revenue.

Solution:
\( TR = P \times Q = 25 \times 150 = 3750 \).

Total Revenue = \$3,750

Example 3: Calculating Productivity

Problem: A factory produces 500 units using 250 units of input. What is the productivity?

Solution: Use the formula:
\( \text{Productivity} = \frac{\text{Output}}{\text{Quantity of Input}} \)
\( = \frac{500}{250} = 2 \).

Productivity = 2 units per unit of input

Example 4: Calculating Labor Productivity

Problem: A business produces 1000 items using 50 employees. What is the labor productivity?

Solution:
\( \text{Labor Productivity} = \frac{\text{Output}}{\text{Number of Employees}} = \frac{1000}{50} = 20 \).

Labor Productivity = 20 items per employee

Example 5: Calculating Working Capital

Problem: A company has current assets of \$50,000 and current liabilities of \$30,000. What is the working capital?

Solution:
\( \text{Working Capital} = \text{Current Assets} - \text{Current Liabilities} = 50000 - 30000 = 20000 \).

Working Capital = \$20,000

Example 6: Calculating Capital Employed

Problem: If a company has total assets of \$150,000 and total liabilities of \$90,000, what is the capital employed?

Solution:
\( \text{Capital Employed} = \text{Total Assets} - \text{Total Liabilities} = 150000 - 90000 = 60000 \).

Capital Employed = \$60,000

Example 7: Calculating Profit

Problem: A company generates revenue of \$8,000 and the cost of sales is \$5,000. What is the profit?

Solution:
\( \text{Profit} = \text{Revenue} - \text{Cost of Sales} = 8000 - 5000 = 3000 \).

Profit = \$3,000

Example 8: Calculating Profit (Break-Even Analysis)

Problem: If a company’s total revenue is \$10,000 and its total costs are \$7,500, what is the profit?

Solution:
\( \text{Profit} = \text{Total Revenue} - \text{Total Costs} = 10000 - 7500 = 2500 \).

Profit = \$2,500

Example 9: Calculating Total Costs

Problem: A business has fixed costs of \$2,000 and variable costs of \$3,500. Calculate the total costs.

Solution:
\( \text{Total Costs} = FC + VC = 2000 + 3500 = 5500 \).

Total Costs = \$5,500

Example 10: Calculating Average Cost

Problem: If total costs are \$10,000 and 500 units are produced, what is the average cost per unit?

Solution:
\( \text{Average Cost} = \frac{\text{Total Costs}}{\text{Total Units Produced}} = \frac{10000}{500} = 20 \).

Average Cost = \$20 per unit

Example 11: Calculating the Break-Even Point (Units)

Problem: A company has fixed costs of \$4,000. The selling price per unit is \$50 and the variable cost per unit is \$30. Determine the break-even point in units.

Solution:
First, compute the contribution per unit:
\( \text{Contribution per Unit} = SP - VC = 50 - 30 = 20 \).
Then, the break-even point is:
\( BE = \frac{FC}{Contribution\ per\ Unit} = \frac{4000}{20} = 200 \) units.

Break-Even Point = 200 units

Example 12: Calculating Contribution per Unit

Problem: If the selling price is \$75 and the variable cost per unit is \$45, what is the contribution per unit?

Solution:
\( Contribution\ per\ Unit = SP - VC = 75 - 45 = 30 \).

Contribution per Unit = \$30

Example 13: Calculating the Margin of Safety

Problem: A company has a maximum production capacity of 1000 units and a break-even output of 600 units. What is the margin of safety?

Solution:
\( Margin\ of\ Safety = Maximum\ Output - Break-even\ Output = 1000 - 600 = 400 \) units.

Margin of Safety = 400 units

Example 14: Calculating Gross Profit

Problem: If a company’s revenue is \$12,000 and its cost of sales is \$7,000, what is the gross profit?

Solution:
\( Gross\ Profit = Revenue - Cost\ of\ Sales = 12000 - 7000 = 5000 \).

Gross Profit = \$5,000

Example 15: Calculating Gross Profit Margin (%)

Problem: With a gross profit of \$5,000 on revenue of \$12,000, what is the gross profit margin percentage?

Solution:
\( Gross\ Profit\ Margin \% = \frac{Gross\ Profit}{Revenue} \times 100 = \frac{5000}{12000} \times 100 \approx 41.67\% \).

Gross Profit Margin ≈ 41.67%

Example 16: Calculating Net Profit

Problem: A company has a gross profit of \$5,000 and fixed expenses of \$1,500. What is the net profit?

Solution:
\( Net\ Profit = Gross\ Profit - Fixed\ Expenses = 5000 - 1500 = 3500 \).

Net Profit = \$3,500

Example 17: Calculating Net Profit Margin (%)

Problem: Given a net profit of \$3,500 and revenue of \$12,000, calculate the net profit margin.

Solution:
\( Net\ Profit\ Margin \% = \frac{Net\ Profit}{Revenue} \times 100 = \frac{3500}{12000} \times 100 \approx 29.17\% \).

Net Profit Margin ≈ 29.17%

Example 18: Calculating Return on Capital Employed (ROCE)

Problem: A business has a net profit of \$3,500 and capital invested of \$35,000. Calculate the ROCE.

Solution:
\( ROCE = \frac{Net\ Profit}{Capital\ Invested} \times 100 = \frac{3500}{35000} \times 100 = 10\% \).

ROCE = 10%

Example 19: Calculating the Current Ratio

Problem: If a company has current assets of \$40,000 and current liabilities of \$20,000, what is the current ratio?

Solution:
\( Current\ Ratio = \frac{Current\ Assets}{Current\ Liabilities} = \frac{40000}{20000} = 2 \).

Current Ratio = 2:1

Example 20: Calculating the Acid Test Ratio

Problem: A company has current assets of \$50,000, inventory of \$10,000, and current liabilities of \$25,000. What is the Acid Test Ratio?

Solution:
\( Quick\ Ratio = \frac{Current\ Assets - Inventory}{Current\ Liabilities} = \frac{50000 - 10000}{25000} = \frac{40000}{25000} = 1.6 \).

Acid Test Ratio = 1.6:1 (a safe ratio is around 1.5:1)

Example 21: Calculating Depreciation Expense

Problem: An asset costs \$20,000, has a residual value of \$2,000, and a useful life of 6 years. Calculate the annual depreciation expense.

Solution:
\( Depreciation = \frac{Cost - Residual\ Value}{Useful\ Life} = \frac{20000 - 2000}{6} = \frac{18000}{6} = 3000 \).

Annual Depreciation Expense = \$3,000

Example 22: Calculating Sales Growth Rate

Problem: Last year, a company had sales of \$80,000, and this year sales increased to \$100,000. What is the sales growth rate?

Solution:
\( Sales\ Growth\ \% = \frac{Current\ Sales - Previous\ Sales}{Previous\ Sales} \times 100 = \frac{100000 - 80000}{80000} \times 100 = \frac{20000}{80000} \times 100 = 25\% \).

Sales Growth Rate = 25%

Example 23: Calculating Market Share

Problem: A company’s sales are \$50,000 in a market where total sales are \$500,000. What is its market share?

Solution:
\( Market\ Share\ \% = \frac{Company's\ Sales}{Total\ Market\ Sales} \times 100 = \frac{50000}{500000} \times 100 = 10\% \).

Market Share = 10%

Example 24: Calculating the Asset Turnover Ratio

Problem: A company has total revenue of \$120,000 and total assets of \$60,000. What is the asset turnover ratio?

Solution:
\( Asset\ Turnover = \frac{Revenue}{Total\ Assets} = \frac{120000}{60000} = 2 \).

Asset Turnover Ratio = 2

Example 25: Calculating the Inventory Turnover Ratio

Problem: A company’s cost of goods sold is \$90,000, and its average inventory is \$15,000. What is its inventory turnover ratio?

Solution:
\( Inventory\ Turnover = \frac{Cost\ of\ Goods\ Sold}{Average\ Inventory} = \frac{90000}{15000} = 6 \).

Inventory Turnover Ratio = 6 times per period

Example 26: Another Revenue Calculation

Problem: A firm sells 350 units of a product at \$18 per unit. Calculate the total revenue.

Solution:
\( TR = 18 \times 350 = 6300 \).

Total Revenue = \$6,300

Example 27: Detailed Break-Even Analysis

Problem: A company has fixed costs of \$5,000. Its selling price per unit is \$40, and the variable cost per unit is \$25. Determine:

1. Contribution per unit
2. Break-even point (units)

Solution:
Contribution per unit:
\( C = SP - VC = 40 - 25 = 15 \)
Break-even point:
\( BE = \frac{FC}{C} = \frac{5000}{15} \approx 333.33 \) units (approximately 334 units when rounded up).

Break-Even Point ≈ 334 units

Example 28: Calculating Markup Percentage

Problem: A product costs \$20 to produce. It is sold for \$30. What is the markup percentage?

Solution:
\( \text{Markup \%} = \frac{SP - C_p}{C_p} \times 100 = \frac{30 - 20}{20} \times 100 = \frac{10}{20} \times 100 = 50\% \).

Markup Percentage = 50%

Example 29: Another Markup Calculation

Problem: If the cost price is \$45 and the selling price is \$60, calculate the markup percentage.

Solution:
\( \text{Markup \%} = \frac{60 - 45}{45} \times 100 = \frac{15}{45} \times 100 \approx 33.33\% \).

Markup Percentage ≈ 33.33%

Example 30: Calculating Profit Margin

Problem: A company has a profit of \$4,500 on revenue of \$15,000. What is the profit margin percentage?

Solution:
\( \text{Profit Margin \%} = \frac{4500}{15000} \times 100 = 30\% \).

Profit Margin = 30%

Example 31: Calculating Net Profit Margin

Problem: If a business has a net profit of \$3,000 and revenue of \$12,000, what is the net profit margin?

Solution:
\( \text{Net Profit Margin \%} = \frac{3000}{12000} \times 100 = 25\% \).

Net Profit Margin = 25%

Example 32: Calculating Return on Capital Employed (ROCE)

Problem: With a net profit of \$2,800 and capital invested of \$28,000, calculate the ROCE.

Solution:
\( ROCE = \frac{2800}{28000} \times 100 = 10\% \).

ROCE = 10%

Example 33: Calculating Working Capital

Problem: A business reports current assets of \$70,000 and current liabilities of \$40,000. What is its working capital?

Solution:
\( Working\ Capital = 70000 - 40000 = 30000 \).

Working Capital = \$30,000

Example 34: Calculating the Current Ratio

Problem: With current assets of \$90,000 and current liabilities of \$45,000, what is the current ratio?

Solution:
\( \text{Current Ratio} = \frac{90000}{45000} = 2 \).

Current Ratio = 2:1

Example 35: Calculating the Acid Test (Quick) Ratio

Problem: A company has current assets of \$80,000, inventory worth \$20,000, and current liabilities of \$40,000. What is its quick ratio?

Solution:
\( Quick\ Ratio = \frac{80000 - 20000}{40000} = \frac{60000}{40000} = 1.5 \).

Quick Ratio = 1.5:1

Example 36: Calculating Labor Productivity

Problem: A firm produces 1,200 units with 60 employees. What is its labor productivity?

Solution:
\( Labor\ Productivity = \frac{1200}{60} = 20 \) units per employee.

Labor Productivity = 20 units per employee

Example 37: Calculating General Productivity

Problem: If a factory uses 400 units of input to produce 800 units of output, what is the productivity?

Solution:
\( Productivity = \frac{800}{400} = 2 \).

Productivity = 2 units per unit of input

Example 38: Calculating Average Cost

Problem: Total costs amount to \$25,000 for producing 1000 units. What is the average cost per unit?

Solution:
\( Average\ Cost = \frac{25000}{1000} = 25 \).

Average Cost = \$25 per unit

Example 39: Calculating Contribution per Unit

Problem: A product sells for \$100, and its variable cost per unit is \$70. What is the contribution per unit?

Solution:
\( Contribution\ per\ Unit = 100 - 70 = 30 \).

Contribution per Unit = \$30

Example 40: Calculating Margin of Safety

Problem: A business’s maximum output is 1200 units, and its break-even output is 800 units. What is its margin of safety?

Solution:
\( Margin\ of\ Safety = 1200 - 800 = 400 \) units.

Margin of Safety = 400 units

Example 41: Calculating Sales Growth

Problem: A company's sales grew from \$70,000 last year to \$84,000 this year. What is the percentage growth?

Solution:
\( Sales\ Growth \% = \frac{84000 - 70000}{70000} \times 100 = \frac{14000}{70000} \times 100 = 20\% \).

Sales Growth = 20%

Example 42: Calculating Market Share

Problem: A company makes \$40,000 in sales in a market where total sales are \$400,000. Calculate its market share.

Solution:
\( Market\ Share \% = \frac{40000}{400000} \times 100 = 10\% \).

Market Share = 10%

Example 43: Depreciation Expense Calculation

Problem: An asset costs \$15,000, has a residual value of \$1,500, and a useful life of 5 years. Calculate the annual depreciation expense.

Solution:
\( Depreciation = \frac{15000 - 1500}{5} = \frac{13500}{5} = 2700 \).

Annual Depreciation Expense = \$2,700

Example 44: Calculating Asset Turnover Ratio

Problem: A business earns \$90,000 in revenue and has total assets of \$45,000. What is the asset turnover ratio?

Solution:
\( Asset\ Turnover = \frac{90000}{45000} = 2 \).

Asset Turnover Ratio = 2

Example 45: Calculating Inventory Turnover Ratio

Problem: A company’s cost of goods sold is \$120,000 and its average inventory is \$30,000. What is its inventory turnover ratio?

Solution:
\( Inventory\ Turnover = \frac{120000}{30000} = 4 \).

Inventory Turnover Ratio = 4

Example 46: Combined Break-Even and Profit Calculation

Problem: A business has fixed costs of \$6,000. Its selling price per unit is \$60, and variable cost per unit is \$40. If the company sells 350 units (above the break-even point), calculate the break-even point and the profit for the extra units.

Solution:
First, calculate the contribution per unit:
\( C = 60 - 40 = 20 \)
Then, the break-even point is:
\( BE = \frac{6000}{20} = 300 \) units.
The extra units sold = 350 - 300 = 50 units.
Extra profit = 50 × 20 = \$1,000.

Break-Even Point = 300 units; Extra Profit = \$1,000

Example 47: Calculating Markup and Profit Margin

Problem: A product costs \$35 and is sold at \$50. Calculate both the markup percentage and the gross profit margin if the cost of sales equals the cost price.

Solution:
Markup Percentage:
\( \text{Markup \%} = \frac{50 - 35}{35} \times 100 \approx 42.86\% \)
Gross Profit = \(50 - 35 = 15\).
Gross Profit Margin:
\( \frac{15}{50} \times 100 = 30\% \).

Markup ≈ 42.86%, Gross Profit Margin = 30%

Example 48: ROCE and Working Capital

Problem: A company has a net profit of \$4,000, total assets of \$50,000, and total liabilities of \$20,000. Calculate the capital employed, ROCE, and working capital.

Solution:
Capital Employed = Total Assets − Total Liabilities = \(50,000 - 20,000 = 30,000\).
ROCE = \( \frac{4000}{30000} \times 100 \approx 13.33\% \).
Suppose current assets = \$25,000 and current liabilities = \$10,000, then Working Capital = \(25,000 - 10,000 = 15,000\).

Capital Employed = \$30,000; ROCE ≈ 13.33%; Working Capital = \$15,000

Example 49: Calculating Liquidity Ratios

Problem: A company has current assets of \$100,000, inventory of \$30,000, and current liabilities of \$50,000. Compute the Current Ratio and Acid Test Ratio.

Solution:
Current Ratio = \( \frac{100000}{50000} = 2 \).
Acid Test Ratio = \( \frac{100000 - 30000}{50000} = \frac{70000}{50000} = 1.4 \).

Current Ratio = 2:1; Acid Test Ratio = 1.4:1

Example 50: Comprehensive Business Scenario

Problem: A company produces gadgets with the following details:

• Selling Price per unit (SP): \$80
• Variable Cost per unit (VC): \$50
• Fixed Costs (FC): \$10,000
• Total Units Produced: 500
• Total Assets: \$60,000; Total Liabilities: \$25,000
• Current Assets: \$20,000; Current Liabilities: \$10,000

Calculate:

1. Total Revenue
2. Total Costs and Profit
3. Break-Even Point (units)
4. Gross Profit Margin (if cost of sales = total variable cost)
5. Net Profit Margin (assume fixed costs are the only other expenses)
6. Working Capital and Current Ratio
7. Capital Employed and ROCE (assume net profit is profit after fixed costs)

Solution:

(1) Total Revenue: Assuming all 500 units are sold,
\( TR = 80 \times 500 = 40000 \).

(2) Total Costs: Variable Costs = \( VC \times \) units = \(50 \times 500 = 25000\).
Total Costs = Fixed Costs + Variable Costs = \(10000 + 25000 = 35000\).
Profit = Revenue − Total Costs = \(40000 - 35000 = 5000\).

(3) Break-Even Point (units):
Contribution per unit = \( SP - VC = 80 - 50 = 30 \).
\( BE = \frac{FC}{SP - VC} = \frac{10000}{30} \approx 333.33 \) units (approximately 334 units).

(4) Gross Profit Margin: Gross Profit = Revenue − Variable Costs = \(40000 - 25000 = 15000\).
\( \text{Gross Profit Margin \%} = \frac{15000}{40000} \times 100 = 37.5\% \).

(5) Net Profit Margin: Net Profit = Profit (assumed after fixed costs) = \$5,000.
\( \text{Net Profit Margin \%} = \frac{5000}{40000} \times 100 = 12.5\% \).

(6) Working Capital: \( WC = Current Assets - Current Liabilities = 20000 - 10000 = 10000 \).
Current Ratio = \( \frac{20000}{10000} = 2 \).

(7) Capital Employed: \( CE = Total Assets - Total Liabilities = 60000 - 25000 = 35000 \).
ROCE = \( \frac{Net Profit}{Capital Employed} \times 100 = \frac{5000}{35000} \times 100 \approx 14.29\% \).

Summary: Revenue = \$40,000; Profit = \$5,000; Break-Even ≈ 334 units; Gross Profit Margin = 37.5%; Net Profit Margin = 12.5%; Working Capital = \$10,000; Current Ratio = 2:1; Capital Employed = \$35,000; ROCE ≈ 14.29%.