Howard's Supply Co. suffered a fire loss on April 20, 2013. The company's last physical inventory was taken January 30, 2013, at which time the inventory totaled $220,000. Sales from January 30 to April 20 were $600,000 and purchases during that time were $450,000. Howard's consistently reports a 30% gross profit. The estimated inventory loss is:

Question

Quizplus · Accepted Answer

First, we need to calculate the cost of goods sold (COGS) for the period between January 30 and April 20:

COGS = Beginning Inventory + Purchases - Ending Inventory
COGS = $220,000 + $450,000 - Ending Inventory

To find the ending inventory, we need to estimate the percentage of inventory that was lost in the fire. Since we don't have a physical inventory count after January 30, we'll assume that the loss was proportional to the ratio of sales between January 30 and April 20 to total sales for the year.

Sales from January 30 to April 20 = $600,000
Total sales for the year = $600,000 / (3/4) = $800,000

So the ratio of sales between January 30 and April 20 to total sales for the year is:

$600,000 / $800,000 = 0.75

This means that we can estimate ending inventory as:

Ending Inventory = Beginning Inventory + Purchases - COGS
Ending Inventory = $220,000 + $450,000 - ($600,000 / 0.3)
Ending Inventory = $220,000 + $450,000 - $2,000,000
Ending Inventory = $-1,330,000

This makes no sense since ending inventory cannot be negative. Therefore, we know that something went wrong in our calculation.

We need to calculate the gross profit rate to see if it's consistent with previous years' rates.

Gross profit rate = Gross profit / Net sales
0.3 = Gross profit / ($800,000 – $220,000 + $450,000)
0.3 = Gross profit / $1,030,000
Gross profit = $309,000

Now we can calculate the COGS:

COGS = Net sales – Gross profit
COGS = $800,000 – $309,000
COGS = $491,000

Finally, we can estimate the inventory loss:

Estimated inventory loss = Beginning inventory + Purchases – COGS 
Estimated inventory loss = $220,000 + $450,000 – $491,000 
Estimated inventory loss = $179,000

However, we need to factor in the fact that the fire loss happened after January 30. Assuming that all purchases before the fire were sold, we need to subtract those purchases from total purchases ($450,000) before calculating the loss:

Purchases from January 30 to April 20 = $450,000 – ($600,000 – $220,000) = $70,000

Estimated inventory loss = Beginning inventory + Purchases from January 30 to April 20 – COGS 
Estimated inventory loss = $220,000 + $70,000 – $491,000 
Estimated inventory loss = $-201,000

Again, this cannot be negative. To fix the calculation, we need to assume that some of the purchases made after January 30 were not lost in the fire. Let's assume that purchases made in the last month (i.e., April) were not affected by the fire. This means that purchases to be included in COGS are:

Purchases to be included in COGS = Purchases from January 30 to March 31 + Beginning inventory as of April 1 
Purchases to be included in COGS = ($600,000 – $220,000) + $450,000 – Beginning inventory as of April 1
Purchases to be included in COGS = $830,000 - Beginning inventory as of April 1

Now we can estimate the inventory loss:

Estimated inventory loss = Beginning inventory + Purchases to be included in COGS – COGS
Estimated inventory loss = $220,000 + ($830,000 – Beginning inventory as of April 1) – $491,000 
Estimated inventory loss = $559,000 – Beginning inventory as of April 1

We know that ending inventory as of April 20 was $-1,330,000, which includes the inventory lost in the fire. Since we're looking for the estimated loss, we need to subtract the inventory as of April 1 (which was not affected by the fire) from this figure:

Estimated inventory loss = $-1,330,000 – (Ending inventory as of April 1 – Beginning inventory as of April 1)
Estimated inventory loss = $-1,330,000 – ($220,000 – Beginning inventory as of April) 
Estimated inventory loss = $-1,550,000 + Beginning inventory as of April 1

We also know that the gross profit rate is consistent with previous years' rates (30%), so we can estimate the COGS as:

COGS = Net sales x (1 – Gross profit rate) 
COGS = $600,000 x (1 – 0.3)
COGS = $420,000

Finally, we can solve for the estimated inventory loss:

$420,000 = ($830,000 – Beginning inventory as of April 1) x 0.3 
Beginning inventory as of April 1 = $303,333

Estimated inventory loss = $-1,550,000 + $303,333
Estimated inventory loss = $-1,246,667

Since inventory cannot have a negative value, we can assume that the estimated inventory loss is $0 (i.e., all of the inventory was lost in the fire).

Therefore, the best choice is C) $250,000, since this was the closest possible estimate to the actual loss of inventory. However, it's important to note that this estimate was based on several assumptions and is not exact.