Bryn's revenue for 20X5 was £331 330, cost of sales was £227 400 and expenses were £50 551.Revenue in 20X5 was 12.5% higher than in 20X4.Gross profit margin and net profit margin in both years were the same.What were Bryn's expenses in 20X4 (to the nearest £ and working to one decimal place in calculations)?

Question

Quizplus · Accepted Answer

To find the expenses in 20X4, we need to use the information given about the revenue increase and the gross profit margin and net profit margin staying the same. If revenue increased by 12.5%, then we can use the following equation to find Bryn's revenue in 20X4:

Revenue 20X4 * 1.125 = Revenue 20X5
Revenue 20X4 = Revenue 20X5 ÷ 1.125
Revenue 20X4 = £331,330 ÷ 1.125 = £294,928

We also know that the gross profit margin and net profit margin were the same in both years, which means that the cost of sales and expenses were a consistent percentage of revenue. Using this, we can set up the following equation:

Revenue 20X4 - Cost of Sales 20X4 - Expenses 20X4 = Net Profit 20X4
Net Profit 20X4 = Gross Profit Margin × Revenue 20X4 - Expenses 20X4
Gross Profit Margin = (Revenue 20X4 - Cost of Sales 20X4) ÷ Revenue 20X4

We can use the information given in the question to solve for the gross profit margin:

Gross Profit Margin = (Revenue 20X5 - Cost of Sales 20X5) ÷ Revenue 20X5
Gross Profit Margin = (£331,330 - £227,400) ÷ £331,330
Gross Profit Margin = 0.314

We can then use the gross profit margin to solve for the net profit margin:

Net Profit Margin = Gross Profit Margin - Expenses ÷ Revenue
Net Profit Margin = 0.314 - £50,551 ÷ £331,330
Net Profit Margin = 0.114

Now we can use the net profit margin to solve for the expenses in 20X4:

Net Profit Margin = Gross Profit Margin - Expenses ÷ Revenue
0.114 = 0.314 - Expenses ÷ £294,928
Expenses = (£294,928 × (0.314 - 0.114)) = £45,061 (rounded to the nearest pound)

Therefore, the answer is B.

Bryn's Revenue for 20X5 Was £331 330, Cost of Sales