Business XYZ has the following projected budget and actual budget for a given month:
\begin{tabular}{|l|r|r|}
\hline & Budget & Actual \\
\hline Payroll & $30,000 & $29,000 \\
\hline Inventory & $13,000 & $13,800 \\
\hline Rent & $8,000 & $7,700 \\
\hline Services & $5,000 & $4,750 \\
\hline
\end{tabular}
Calculate the percent change that Payroll is under budget.
$\Delta=[?] %$
Answer as a percent rounded to the nearest tenth.
Answer (1)
Calculate the difference between the actual and budgeted payroll: $29 , 000 − $30 , 000 = − $1 , 000 .
Divide the difference by the budgeted payroll: $30 , 000 − $1 , 000 = − 30 1 .
Multiply by 100 to get the percentage: − 30 1 × 100 = − 3.333 … .
Round to the nearest tenth: The percent change is − 3.3% .
Explanation
Understanding the Problem We are given the budgeted and actual payroll amounts for Business XYZ and asked to calculate the percent change, specifically how much payroll is under budget. The formula for percent change is: %Δ = Budgeted Value Actual Value − Budgeted Value × 100 In this case, the actual value is the actual payroll, and the budgeted value is the budgeted payroll.
Applying the Formula We are given: Budgeted Payroll = $30,000 Actual Payroll = $29,000 Now, we substitute these values into the percent change formula: %Δ = $30 , 000 $29 , 000 − $30 , 000 × 100
Calculating the Percent Change First, calculate the difference between the actual and budgeted payroll: $29 , 000 − $30 , 000 = − $1 , 000 Now, divide this difference by the budgeted payroll: $30 , 000 − $1 , 000 = − 30 1 Multiply the result by 100 to express it as a percentage: − 30 1 × 100 = − 3 10 ≈ − 3.333 … Round the percentage to the nearest tenth: − 3.333 … ≈ − 3.3
Final Answer The percent change that payroll is under budget is approximately -3.3%. The negative sign indicates that the actual payroll was less than the budgeted payroll.
Examples
Understanding percent change is crucial in business for budget analysis and financial forecasting. For instance, if a company budgets $50,000 for marketing but spends only $45,000, the percent change helps assess the efficiency of spending. In this case, the company spent 10% less than budgeted, which could indicate cost savings or a need to re-evaluate marketing strategies. This type of analysis helps businesses make informed decisions and adjust their financial plans accordingly.
