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Sagot :
Sure, let's solve the problem step by step.
First, we should understand each term:
1. Invoice Cost of Merchandise Purchases: The total cost on the invoice before any discounts or returns.
2. Purchase Discounts: Discounts received from suppliers for early payment or bulk purchases.
3. Purchase Returns and Allowances: The returns made by the company to its suppliers.
4. Cost of Transportation-In: The cost associated with transporting the merchandise to the company.
5. Merchandise Inventory (Beginning and End of Period): The value of the inventory at the beginning and end of the accounting period, respectively.
6. Net Cost of Merchandise Purchases: Calculated as the Invoice Cost + Transportation-In - (Purchase Discounts + Purchase Returns and Allowances).
7. Cost of Goods Sold (COGS): Calculated as the sum of the beginning inventory and net purchases minus the ending inventory.
Let's calculate:
1. For Invoice A:
- [tex]\( \text{Invoice Cost} = \$43,600 \)[/tex]
- [tex]\( \text{Purchase Discounts} = \$1,600 \)[/tex]
- [tex]\( \text{Purchase Returns and Allowances} = \$1,300 \)[/tex]
- [tex]\( \text{Net Cost of Merchandise Purchases} = \$44,300 \)[/tex]
- [tex]\( \text{Beginning Inventory} = \$4,100 \)[/tex]
- [tex]\( \text{Ending Inventory} = \$2,000 \)[/tex]
- Unknown: [tex]\( \text{Cost of Transportation-In} \)[/tex]
To find this:
[tex]\[ \text{Net Cost of Merchandise Purchases} = \text{Invoice Cost} - \text{Purchase Discounts} - \text{Purchase Returns and Allowances} + \text{Cost of Transportation-In} \][/tex]
[tex]\[ 44,300 = 43,600 - 1,600 - 1,300 + \text{Transportation-In} \][/tex]
[tex]\[ 44,300 = 40,700 + \text{Transportation-In} \][/tex]
[tex]\[ \text{Transportation-In} = 44,300 - 40,700 = 3,600 \][/tex]
2. For Invoice B:
- [tex]\( \text{Invoice Cost} = \$20,600 \)[/tex]
- [tex]\( \text{Purchase Returns and Allowances} = \$710 \)[/tex]
- [tex]\( \text{Net Cost of Merchandise Purchases} = \$19,550 \)[/tex]
- [tex]\( \text{Cost of Transportation-In} = \$1,550 \)[/tex]
- [tex]\( \text{Ending Inventory} = \$3,550 \)[/tex]
- [tex]\( \text{Cost of Goods Sold} = \$20,400 \)[/tex]
- Unknown: [tex]\( I \)[/tex] and [tex]\( \text{Beginning Inventory} \)[/tex]
To find [tex]\( I \)[/tex]:
[tex]\[ \text{Net Cost of Merchandise Purchases} = \text{Invoice Cost} - I - \text{Purchase Returns and Allowances} + \text{Cost of Transportation-In} \][/tex]
[tex]\[ 19,550 = 20,600 - I - 710 + 1,550 \][/tex]
[tex]\[ 19,550 = 21,440 - I \][/tex]
[tex]\[ I = 21,440 - 19,550 = 1,890 \][/tex]
Now, to find the beginning inventory:
[tex]\[ \text{COGS} = \text{Beginning Inventory} + \text{Net Cost of Merchandise Purchases} - \text{Ending Inventory} \][/tex]
[tex]\[ 20,400 = \text{Beginning Inventory} + 19,550 - 3,550 \][/tex]
[tex]\[ 20,400 = \text{Beginning Inventory} + 16,000 \][/tex]
[tex]\[ \text{Beginning Inventory} = 20,400 - 16,000 = 4,400 \][/tex]
3. For Invoice C:
- [tex]\( \text{Invoice Cost} = \$15,850 \)[/tex]
- [tex]\( \text{Purchase Discounts} = \$305 \)[/tex]
- [tex]\( \text{Purchase Returns and Allowances} = \$510 \)[/tex]
- [tex]\( \text{Cost of Transportation-In} = \$1,600 \)[/tex]
- [tex]\( \text{Beginning Inventory} = \$3,100 \)[/tex]
- [tex]\( \text{Cost of Goods Sold} = \$16,665 \)[/tex]
- Unknown: [tex]\( \text{Net Cost of Merchandise Purchases} \)[/tex] and [tex]\( \text{Ending Inventory} \)[/tex]
To find [tex]\( \text{Net Cost of Merchandise Purchases} \)[/tex]:
[tex]\[ \text{Net Cost of Merchandise Purchases} = \text{Invoice Cost} - \text{Purchase Discounts} - \text{Purchase Returns and Allowances} + \text{Cost of Transportation-In} \][/tex]
[tex]\[ \text{Net Cost of Merchandise Purchases} = 15,850 - 305 - 510 + 1,600 \][/tex]
[tex]\[ \text{Net Cost of Merchandise Purchases} = 16,635 \][/tex]
Now, to find the ending inventory:
[tex]\[ \text{COGS} = \text{Beginning Inventory} + \text{Net Cost of Merchandise Purchases} - \text{Ending Inventory} \][/tex]
[tex]\[ 16,665 = 3,100 + 16,635 - \text{Ending Inventory} \][/tex]
[tex]\[ 16,665 = 19,735 - \text{Ending Inventory} \][/tex]
[tex]\[ \text{Ending Inventory} = 19,735 - 16,665 = 3,070 \][/tex]
Here are the results in the tabular form:
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline & & a & & b & & c \\
\hline Invoice cost of merchandise purchases & \[tex]$ & 43,600 & \$[/tex] & 20,600 & \[tex]$ & 15,850 \\ \hline Purchase discounts & & 1,600 & & 1,890 & & +305 \\ \hline Purchase returns and allowances & & 1,300 & & 710 & & 510 \\ \hline Cost of transportation-in & & 3,600 & & 1,550 & & 1,600 \\ \hline Merchandise inventory (beginning of period) & & 4,100 & & 4,400 & & 3,100 \\ \hline Net cost of merchandise purchases & & 44,300 & & 19,550 & & 16,635 \\ \hline Merchandise inventory (end of period) & & 2,000 & & 3,550 & & 3,070 \\ \hline Cost of goods sold & & & \$[/tex] & 20,400 & \$ & 16,665 \\
\hline
\end{tabular}
First, we should understand each term:
1. Invoice Cost of Merchandise Purchases: The total cost on the invoice before any discounts or returns.
2. Purchase Discounts: Discounts received from suppliers for early payment or bulk purchases.
3. Purchase Returns and Allowances: The returns made by the company to its suppliers.
4. Cost of Transportation-In: The cost associated with transporting the merchandise to the company.
5. Merchandise Inventory (Beginning and End of Period): The value of the inventory at the beginning and end of the accounting period, respectively.
6. Net Cost of Merchandise Purchases: Calculated as the Invoice Cost + Transportation-In - (Purchase Discounts + Purchase Returns and Allowances).
7. Cost of Goods Sold (COGS): Calculated as the sum of the beginning inventory and net purchases minus the ending inventory.
Let's calculate:
1. For Invoice A:
- [tex]\( \text{Invoice Cost} = \$43,600 \)[/tex]
- [tex]\( \text{Purchase Discounts} = \$1,600 \)[/tex]
- [tex]\( \text{Purchase Returns and Allowances} = \$1,300 \)[/tex]
- [tex]\( \text{Net Cost of Merchandise Purchases} = \$44,300 \)[/tex]
- [tex]\( \text{Beginning Inventory} = \$4,100 \)[/tex]
- [tex]\( \text{Ending Inventory} = \$2,000 \)[/tex]
- Unknown: [tex]\( \text{Cost of Transportation-In} \)[/tex]
To find this:
[tex]\[ \text{Net Cost of Merchandise Purchases} = \text{Invoice Cost} - \text{Purchase Discounts} - \text{Purchase Returns and Allowances} + \text{Cost of Transportation-In} \][/tex]
[tex]\[ 44,300 = 43,600 - 1,600 - 1,300 + \text{Transportation-In} \][/tex]
[tex]\[ 44,300 = 40,700 + \text{Transportation-In} \][/tex]
[tex]\[ \text{Transportation-In} = 44,300 - 40,700 = 3,600 \][/tex]
2. For Invoice B:
- [tex]\( \text{Invoice Cost} = \$20,600 \)[/tex]
- [tex]\( \text{Purchase Returns and Allowances} = \$710 \)[/tex]
- [tex]\( \text{Net Cost of Merchandise Purchases} = \$19,550 \)[/tex]
- [tex]\( \text{Cost of Transportation-In} = \$1,550 \)[/tex]
- [tex]\( \text{Ending Inventory} = \$3,550 \)[/tex]
- [tex]\( \text{Cost of Goods Sold} = \$20,400 \)[/tex]
- Unknown: [tex]\( I \)[/tex] and [tex]\( \text{Beginning Inventory} \)[/tex]
To find [tex]\( I \)[/tex]:
[tex]\[ \text{Net Cost of Merchandise Purchases} = \text{Invoice Cost} - I - \text{Purchase Returns and Allowances} + \text{Cost of Transportation-In} \][/tex]
[tex]\[ 19,550 = 20,600 - I - 710 + 1,550 \][/tex]
[tex]\[ 19,550 = 21,440 - I \][/tex]
[tex]\[ I = 21,440 - 19,550 = 1,890 \][/tex]
Now, to find the beginning inventory:
[tex]\[ \text{COGS} = \text{Beginning Inventory} + \text{Net Cost of Merchandise Purchases} - \text{Ending Inventory} \][/tex]
[tex]\[ 20,400 = \text{Beginning Inventory} + 19,550 - 3,550 \][/tex]
[tex]\[ 20,400 = \text{Beginning Inventory} + 16,000 \][/tex]
[tex]\[ \text{Beginning Inventory} = 20,400 - 16,000 = 4,400 \][/tex]
3. For Invoice C:
- [tex]\( \text{Invoice Cost} = \$15,850 \)[/tex]
- [tex]\( \text{Purchase Discounts} = \$305 \)[/tex]
- [tex]\( \text{Purchase Returns and Allowances} = \$510 \)[/tex]
- [tex]\( \text{Cost of Transportation-In} = \$1,600 \)[/tex]
- [tex]\( \text{Beginning Inventory} = \$3,100 \)[/tex]
- [tex]\( \text{Cost of Goods Sold} = \$16,665 \)[/tex]
- Unknown: [tex]\( \text{Net Cost of Merchandise Purchases} \)[/tex] and [tex]\( \text{Ending Inventory} \)[/tex]
To find [tex]\( \text{Net Cost of Merchandise Purchases} \)[/tex]:
[tex]\[ \text{Net Cost of Merchandise Purchases} = \text{Invoice Cost} - \text{Purchase Discounts} - \text{Purchase Returns and Allowances} + \text{Cost of Transportation-In} \][/tex]
[tex]\[ \text{Net Cost of Merchandise Purchases} = 15,850 - 305 - 510 + 1,600 \][/tex]
[tex]\[ \text{Net Cost of Merchandise Purchases} = 16,635 \][/tex]
Now, to find the ending inventory:
[tex]\[ \text{COGS} = \text{Beginning Inventory} + \text{Net Cost of Merchandise Purchases} - \text{Ending Inventory} \][/tex]
[tex]\[ 16,665 = 3,100 + 16,635 - \text{Ending Inventory} \][/tex]
[tex]\[ 16,665 = 19,735 - \text{Ending Inventory} \][/tex]
[tex]\[ \text{Ending Inventory} = 19,735 - 16,665 = 3,070 \][/tex]
Here are the results in the tabular form:
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline & & a & & b & & c \\
\hline Invoice cost of merchandise purchases & \[tex]$ & 43,600 & \$[/tex] & 20,600 & \[tex]$ & 15,850 \\ \hline Purchase discounts & & 1,600 & & 1,890 & & +305 \\ \hline Purchase returns and allowances & & 1,300 & & 710 & & 510 \\ \hline Cost of transportation-in & & 3,600 & & 1,550 & & 1,600 \\ \hline Merchandise inventory (beginning of period) & & 4,100 & & 4,400 & & 3,100 \\ \hline Net cost of merchandise purchases & & 44,300 & & 19,550 & & 16,635 \\ \hline Merchandise inventory (end of period) & & 2,000 & & 3,550 & & 3,070 \\ \hline Cost of goods sold & & & \$[/tex] & 20,400 & \$ & 16,665 \\
\hline
\end{tabular}
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