Blue Apron (NYSE:APRN) has had a tumultuous couple of years since making its public market debut. It's now on CEO No. 3, Linda Kozlowski, who is tasked with righting the ship and turning things around.

Kozlowski joined the company after the first quarter concluded, but it looks like former CEO Brad Dickerson's plans were starting to show at least some positive results. Kozlowski may be able to take what he left and execute on the company's new strategy of focusing its marketing and customer base to maximize profitability.

Here are five things going right at Blue Apron.

Cheese, produce, and pasta laid out on a wood table

Image source: Blue Apron

Positive free cash flow

Blue Apron generated $3 million in free cash flow in the first quarter. That's a major milestone for a company that burned through $93 million in cash last year.

The biggest contributor to Blue Apron's positive cash flow was its minimal capital expenditures. The company spent just $1.7 million on capital expenditures during the quarter, and it's committed to keeping that figure low throughout the year.

It already spent hundreds of millions in getting its Linden facility up and running, and it's finally starting to bear fruit. Blue Apron's customer base is much smaller than the company had anticipated when it was building out its operations there, so it has plenty of capacity to fulfill orders.

It's not clear Blue Apron will be able to maintain positive free cash flow throughout the full year, however, as the first quarter is seasonally strong, and the company seems to have cut costs as much as possible at this point.

Healthy gross margins

Blue Apron's cost of goods sold totaled just 58.3% of revenue in the first quarter, a record low. CFO Tim Bensley pointed out that's a 20 percentage point improvement from six quarters ago when the company was struggling to fulfill orders on time and with the proper ingredients.

"This is the result of continued improvements in all three of our fulfillment centers and further efficiency gains in labor, food, shipping, and packaging costs from enhanced planning and process-driven strategies," Bensley said during the company's first quarter earnings call.

Blue Apron has room to improve its gross margin even more by expanding its product and distribution channels. In fact, Bensley announced plans to offer same-day on-demand service in the Bay Area in California for orders made directly from the Blue Apron website. Bensley said its capacity will enable the new offering to be margin neutral from the start with the potential to be margin accretive in the future.

Increased orders per customer

Blue Apron's 550,000 customers made an average of 4.5 orders each in the first quarter. That's up from 4.4 last year and 4.1 the year before (when it had nearly twice as many customers). That's strong evidence that Blue Apron is executing on its plan to attract only high affinity diners.

Former CEO Brad Dickerson said increasing orders per customer will be one of the early indications the strategy is working. Blue Apron is a weekly service by default, so if every customer maxed out their subscription, Blue apron would see average orders per customer climb to nearly 13 per quarter (although that number is practically impossible to reach considering churn and new customers coming in mid-quarter). As such, there's still a lot of room for Blue Apron to improve the metric.

Increased average order value

Not only are Blue Apron's customers coming back more often, they're spending more when they do. Average order values increased ever so slightly to $57.15. That's a 1% increase over last year and nearly flat compared with two years ago.

Blue Apron can improve order values by offering cooking utensils and kitchen tools. Increased sales of those types of products should be accretive to gross margin since Blue Apron's brand strength allows it to price items like wine, skillets, and spatulas at very high markups. And the marginal shipping expense is practically nothing, since Blue Apron is sending a box to the customer anyway.

An interesting trend in marketing mix

Blue Apron has shifted its marketing spend to more digital advertising channels over the past year -- 78% of the company's marketing spend went to digital ads in the first quarter. That compares to just 46% in the first quarter last year.

That's important, because digital ads are most capable of targeting the audiences Blue Apron finds produce the best customers. The big digital advertising services even offer lookalike targeting, which allows a company to upload a list of emails from its best users and target other users that exhibit similar characteristics.

Previously, Blue Apron spent a lot of money on offline branded ads -- 43% of its budget went to offline advertising in the first quarter last year. That's down to just 9% last quarter. The shift in ad spend suits Blue Apron's goal of trying to serve everyone to only trying to serve customers it expects to keep coming back and using its products.

Still a long way to go

Blue Apron certainly isn't out of the woods yet. It's customer count continues to shrink, and it's expected to do so through the rest of the year. That means revenue will also keep falling, since improvements in order volume per customer and average revenue per order are slow to increase.

Investors should watch for continued improvement in the above metrics in order to determine whether the company is successfully executing its strategy under the new CEO.