A new report said the value of the airlines' credit card affiliations has long been dramatically underestimated because it hasn't been broken out by the carriers.

"There is, currently, a clear and significant disconnect in the market between how much the loyalty programs within airlines are worth and how the total airline is being valued," wrote Stifel analyst Joseph DeNardi in the report issued Monday.

"We are confident that this chasm will begin to close as airlines begin to provide improved disclosures as to how valuable the programs are over the next 12 to 24 months," DeNardi said. "We see the upside potential to current stock prices as highly compelling."

While airlines trade around 10 times earnings, the multiple should be far higher due to the unrecognized value of the loyalty programs, DeNardi said.

He dramatically raised target prices.

American (AAL) - Get Report closed Friday at $41.72. DeNardi's target price is $95. Alaska closed Friday at $93.36. DeNardi's target price is $145. Delta (DAL) - Get Report closed Friday at $46.51. DeNardi's target price is $75.

Also, Southwest closed Friday at $53.18. DeNardi's target price is $80. United (UAL) - Get Report closed Friday at $66.79. DeNardi's target price is at $125.

Shares in all five carriers were modestly higher on Monday morning.

Airline loyalty programs link specific credit cards to frequent flier miles and other affinities with individual airlines.

DeNardi's estimated value for the programs considers both their price/earnings ratio and his estimates of the discounted cash flow from the programs.

Probably the most controversial component is that DeNardi applies a 22x multiple to his after-tax estimate of 2018 earnings from the loyalty programs.

"We suspect there will be some degree of disagreement with the use of a 22x multiple," he acknowledged. "However, we view it as rather conservative given the profitability metric and growth potential for the programs. "

DeNardi argued that airlines don't disclose enough information about their loyalty programs.

Yet a few disclosures have occurred.

America has said it expects its agreement with Citibank and Barclays to add $800 million to EBIT between 2015 and 2018. Delta has said it expects its relationship with American Express to add $1.6 billion in revenue between 2015 and 2021. That means revenue of $4 billion, up from $2.4 billion in 2015.

One could conclude from DeNardi's report that airlines could profit by spinning off their frequent flier programs.

However, he said, "Our view that a sum-of-the-parts is the best way to value airlines does not mean we advocate airlines spinning out their loyalty programs. We do not.

"Rather, we would like {each airline} to begin reporting the loyalty program as its own operating segment, similar to what United did from 2002-2005," he said. "We believe this will provide a clearer picture as to how valuable the loyalty program is and result in management focusing on improving the profitability of the core airline rather than relying so much on the credit card partnership."

This article is commentary by an independent contributor. At the time of publication, the author held no positions in the stocks mentioned.