Sure, let's solve each part step-by-step.
### 5.1 Cost of Sales
To determine the cost of sales, we need to calculate the net purchases and then adjust for the change in the stock.
Step 1: Calculate Net Purchases
1. Purchases: R342,000
2. Goods returned to creditors: R900 (a reduction in purchases)
3. Carriage on purchases: R12,700
4. Additional carriage on purchases not recorded: R150
5. Customs duty: R5,500
Net Purchases = Purchases - Goods returned to creditors + Carriage on purchases + Additional carriage on purchases + Customs duty
Net Purchases = 342,000 - 900 + 12,700 + 150 + 5,500
Net Purchases = 359,450
Step 2: Calculate Cost of Sales
1. Opening Stock: R56,000
2. Net Purchases: R359,450 (calculated above)
3. Closing Stock: R48,000
Cost of Sales = Opening Stock + Net Purchases - Closing Stock
Cost of Sales = 56,000 + 359,450 - 48,000
Cost of Sales = 367,450
So, the Cost of Sales is R367,450.
### 5.2 Gross Profit
To calculate the gross profit, we need the total sales and then subtract the cost of sales from it.
Step 1: Calculate Total Sales
1. Cash Sales: R280,000
2. Credit Sales: R425,000
Total Sales = Cash Sales + Credit Sales
Total Sales = 280,000 + 425,000
Total Sales = 705,000
Step 2: Calculate Gross Profit
Gross Profit = Total Sales - Cost of Sales
Gross Profit = 705,000 - 367,450
Gross Profit = 337,550
So, the Gross Profit is R337,550.
### 5.3 Actual Mark-Up Percentage Achieved
Finally, to find the actual mark-up percentage achieved, we use the following formula:
[tex]\[ \text{Actual Mark-Up Percentage} = \left( \frac{\text{Gross Profit}}{\text{Cost of Sales}} \right) \times 100 \][/tex]
Actual Mark-Up Percentage = [tex]\(\left(\frac{337,550}{367,450}\right) \times 100\)[/tex]
Actual Mark-Up Percentage ≈ [tex]\(91.86\%\)[/tex]
So, the Actual Mark-Up Percentage Achieved is approximately 91.86%.
