Need step by step explaination for soulution: A firm has net income of #2,610 and tax rate of 33%. The revenue is $20,400, cost are 78 percent of sales, and interest expene is $100. what is th edepreciation expense for the years?
To determine the depreciation expense for the year, we need to use the given information: net income, tax rate, revenue, cost percentage, and interest expense. Here is a step-by-step explanation of how to calculate the depreciation expense:
Step 1: Calculate the taxable income
To calculate the taxable income, we need to deduct the interest expense and the depreciation expense from the net income. In this case, we are given that the interest expense is $100, but the depreciation expense is unknown. Therefore, the taxable income can be calculated as follows:
Taxable Income = Net Income - Interest Expense - Depreciation Expense
Step 2: Calculate the income before taxes
To calculate the income before taxes, we need to add the interest expense deducted in the previous step to the net income:
Income Before Taxes = Net Income + Interest Expense
Step 3: Calculate the pre-tax income by dividing the income before taxes by (1 - tax rate)
Since the tax rate is given as 33% or 0.33, the pre-tax income can be calculated as follows:
Pre-tax Income = Income Before Taxes / (1 - Tax Rate)
Step 4: Calculate the total expenses
To calculate the total expenses, we need to find the cost of sales. The cost of sales is given as 78% of revenue or 0.78 times the revenue:
Cost of Sales = Revenue * Cost Percentage
Total Expenses = Cost of Sales + Interest Expense + Depreciation Expense
Step 5: Use the information given to set up an equation
Now, let's set up an equation by equating the pre-tax income to the total expenses:
Pre-tax Income = Total Expenses
Substitute the values we have:
Income Before Taxes / (1 - Tax Rate) = Cost of Sales + Interest Expense + Depreciation Expense
Step 6: Solve for the depreciation expense
Rearrange the equation to solve for the depreciation expense:
Depreciation Expense = (Income Before Taxes / (1 - Tax Rate)) - Cost of Sales - Interest Expense
Substitute the given values into the equation:
Depreciation Expense = (Net Income + Interest Expense) / (1 - Tax Rate) - Cost of Sales - Interest Expense
Step 7: Calculate the depreciation expense
Now you can calculate the depreciation expense using the formula:
Depreciation Expense = (($2,610 + $100) / (1 - 0.33)) - ($20,400 * 0.78) - $100
Simply calculate the values:
Depreciation Expense = ($2,710 / 0.67) - $15,912 - $100
Depreciation Expense = $4,044.78 - $15,912 - $100
Depreciation Expense = $-11,967.22
Therefore, the depreciation expense for the year is -$11,967.22.