Ernst Equipment Co. wants to prepare interim financial statements for the first quarter. The company
wishes to avoid making a physical count of inventory. Ernst’s gross profit rate averages 30%. The
following information for the first quarter is available from its records:
January 1 beginning inventory . . . . . . . $ 752,880
Cost of goods purchased . . . . . . . . . . . 2,159,630
Sales . . . . . . . . . . . . . . . . . . . . . . . . . 3,710,250
Sales returns . . . . . . . . . . . . . . . . . . . . 74,200

Required
Use the gross profit method to estimate the company’s first quarter ending inventory.

Check Estim. ending inventory,
$367,275

If someone could please explain in detail how to do this problem I would greatly appreciate it.

Well, we aren't really here to do someone's homework for them, but since you've already been given a check-figure, I see no reason not to show you how this was worked out. This is not that difficult for someone with experience, but is usually fairly difficult to learn cause it just appears like a big jumble of numbers.

First, get net sales since it's not given. i.e. gross sales less the returns gives you net sales of 3,636,050. That's the number you need to work with.

You also need to learn this equation:
Beginning Inventory
+ Purchases
= Cost of Goods Available for Sale

This gives you the total of everything the company had for sale, at their cost. You need to be careful about differentiating between the cost and the sales price when doing this.

Everything the company has must go one of two places: it either got sold, or they still have it. But you must remember that the COST of what was sold is called Cost of Goods Sold. (i.e. Sales and COGS are the same inventory -- it's just that one is at the company's cost and other is at the retail sales price, and I think that concept gets lost.) So the available for sale either becomes COGS or ending inventory. If you subtract one from available for sale, you'll get the other.

So:
Available for Sale
- COGS
= Ending inventory (estimated in this case)

Now, remember that what was sold is the same items as COGS. But COGS is the cost to the company and sales is the retail price. That means the 3,636,050 of sales is the same items as COGS. Except you don't have the cost of those items, but only the sales amount, right? But it says gross profit is 30%. So now you need to recall this:

Sales 100%
- COGS
= Gross Profit 30%

If gross profit is 30% of the sales price, then COGS has to be 70% of it. (100 -30). So COGS is 70% of sales.

Sales is 3,636,050, so 70% of that is 2,545,235. So our cost equivalent of the sales is the COGS of 2,545,235.

So we can now complete this:

752,880 beginning inventory
+ 2,159,630 purchases
= 2,912,510 available for sale
- 2,545,235 estimated COGS (70% of net sales)
= 367,275 estimated ending inventory

I hope you could follow all that. It's much easier to explain in person than in writing!