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Sagot :
To express the comparative income statements in common-size percents, we convert each item in the statements into a percentage of the total sales for each year. This allows for an easier comparison between years.
### Current Year Common-Size Percentages
1. Sales:
[tex]\[ \text{Sales \% (Current Year)} = \left(\frac{\$740,000}{\$740,000}\right) \times 100 = 100.0\% \][/tex]
2. Cost of Goods Sold (COGS):
[tex]\[ \text{COGS \% (Current Year)} = \left(\frac{\$560,300}{\$740,000}\right) \times 100 = 75.7\% \][/tex]
3. Gross Profit:
[tex]\[ \text{Gross Profit \% (Current Year)} = \left(\frac{\$179,700}{\$740,000}\right) \times 100 = 24.3\% \][/tex]
4. Operating Expenses:
[tex]\[ \text{Operating Expenses \% (Current Year)} = \left(\frac{\$128,200}{\$740,000}\right) \times 100 = 17.3\% \][/tex]
5. Net Income:
[tex]\[ \text{Net Income \% (Current Year)} = \left(\frac{\$51,500}{\$740,000}\right) \times 100 = 7.0\% \][/tex]
### Prior Year Common-Size Percentages
1. Sales:
[tex]\[ \text{Sales \% (Prior Year)} = \left(\frac{\$625,000}{\$625,000}\right) \times 100 = 100.0\% \][/tex]
2. Cost of Goods Sold (COGS):
[tex]\[ \text{COGS \% (Prior Year)} = \left(\frac{\$290,800}{\$625,000}\right) \times 100 = 46.5\% \][/tex]
3. Gross Profit:
[tex]\[ \text{Gross Profit \% (Prior Year)} = \left(\frac{\$334,200}{\$625,000}\right) \times 100 = 53.5\% \][/tex]
4. Operating Expenses:
[tex]\[ \text{Operating Expenses \% (Prior Year)} = \left(\frac{\$218,500}{\$625,000}\right) \times 100 = 35.0\% \][/tex]
5. Net Income:
[tex]\[ \text{Net Income \% (Prior Year)} = \left(\frac{\$115,700}{\$625,000}\right) \times 100 = 18.5\% \][/tex]
### Comparative Income Statements in Common-Size Percents
\begin{tabular}{|l|r|r|}
\hline
\multicolumn{1}{|c|}{\textbf{}} & \multicolumn{1}{c|}{\textbf{Current Year \[tex]$}} & \multicolumn{1}{c|}{\textbf{Prior Year \$[/tex]}} \\
\hline
Sales & 100.0\% & 100.0\% \\
\hline
Cost of Goods Sold (COGS) & 75.7\% & 46.5\% \\
\hline
Gross Profit & 24.3\% & 53.5\% \\
\hline
Operating Expenses & 17.3\% & 35.0\% \\
\hline
Net Income & 7.0\% & 18.5\% \\
\hline
\end{tabular}
### Reason for Decline in Net Income
To determine which item is most responsible for the decline in net income, we compare the common-size percentages of each item from the current year to the prior year:
1. Sales: 100.0\% (Current Year) - 100.0\% (Prior Year) = 0.0\%
2. COGS: 75.7\% (Current Year) - 46.5\% (Prior Year) = 29.2\%
3. Gross Profit: 24.3\% (Current Year) - 53.5\% (Prior Year) = -29.2\%
4. Operating Expenses: 17.3\% (Current Year) - 35.0\% (Prior Year) = -17.6\%
5. Net Income: 7.0\% (Current Year) - 18.5\% (Prior Year) = -11.6\%
The most significant changes are observed in the "Cost of Goods Sold" (COGS) and "Gross Profit" categories.
- The Cost of Goods Sold increased by 29.2 percentage points.
- The Gross Profit decreased by 29.2 percentage points.
Therefore, the item most responsible for the decline in net income is the increase in the Cost of Goods Sold (COGS).
### Current Year Common-Size Percentages
1. Sales:
[tex]\[ \text{Sales \% (Current Year)} = \left(\frac{\$740,000}{\$740,000}\right) \times 100 = 100.0\% \][/tex]
2. Cost of Goods Sold (COGS):
[tex]\[ \text{COGS \% (Current Year)} = \left(\frac{\$560,300}{\$740,000}\right) \times 100 = 75.7\% \][/tex]
3. Gross Profit:
[tex]\[ \text{Gross Profit \% (Current Year)} = \left(\frac{\$179,700}{\$740,000}\right) \times 100 = 24.3\% \][/tex]
4. Operating Expenses:
[tex]\[ \text{Operating Expenses \% (Current Year)} = \left(\frac{\$128,200}{\$740,000}\right) \times 100 = 17.3\% \][/tex]
5. Net Income:
[tex]\[ \text{Net Income \% (Current Year)} = \left(\frac{\$51,500}{\$740,000}\right) \times 100 = 7.0\% \][/tex]
### Prior Year Common-Size Percentages
1. Sales:
[tex]\[ \text{Sales \% (Prior Year)} = \left(\frac{\$625,000}{\$625,000}\right) \times 100 = 100.0\% \][/tex]
2. Cost of Goods Sold (COGS):
[tex]\[ \text{COGS \% (Prior Year)} = \left(\frac{\$290,800}{\$625,000}\right) \times 100 = 46.5\% \][/tex]
3. Gross Profit:
[tex]\[ \text{Gross Profit \% (Prior Year)} = \left(\frac{\$334,200}{\$625,000}\right) \times 100 = 53.5\% \][/tex]
4. Operating Expenses:
[tex]\[ \text{Operating Expenses \% (Prior Year)} = \left(\frac{\$218,500}{\$625,000}\right) \times 100 = 35.0\% \][/tex]
5. Net Income:
[tex]\[ \text{Net Income \% (Prior Year)} = \left(\frac{\$115,700}{\$625,000}\right) \times 100 = 18.5\% \][/tex]
### Comparative Income Statements in Common-Size Percents
\begin{tabular}{|l|r|r|}
\hline
\multicolumn{1}{|c|}{\textbf{}} & \multicolumn{1}{c|}{\textbf{Current Year \[tex]$}} & \multicolumn{1}{c|}{\textbf{Prior Year \$[/tex]}} \\
\hline
Sales & 100.0\% & 100.0\% \\
\hline
Cost of Goods Sold (COGS) & 75.7\% & 46.5\% \\
\hline
Gross Profit & 24.3\% & 53.5\% \\
\hline
Operating Expenses & 17.3\% & 35.0\% \\
\hline
Net Income & 7.0\% & 18.5\% \\
\hline
\end{tabular}
### Reason for Decline in Net Income
To determine which item is most responsible for the decline in net income, we compare the common-size percentages of each item from the current year to the prior year:
1. Sales: 100.0\% (Current Year) - 100.0\% (Prior Year) = 0.0\%
2. COGS: 75.7\% (Current Year) - 46.5\% (Prior Year) = 29.2\%
3. Gross Profit: 24.3\% (Current Year) - 53.5\% (Prior Year) = -29.2\%
4. Operating Expenses: 17.3\% (Current Year) - 35.0\% (Prior Year) = -17.6\%
5. Net Income: 7.0\% (Current Year) - 18.5\% (Prior Year) = -11.6\%
The most significant changes are observed in the "Cost of Goods Sold" (COGS) and "Gross Profit" categories.
- The Cost of Goods Sold increased by 29.2 percentage points.
- The Gross Profit decreased by 29.2 percentage points.
Therefore, the item most responsible for the decline in net income is the increase in the Cost of Goods Sold (COGS).
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