Among the three largest U.S. airlines, Delta Air Lines (DAL 0.17%) has the lowest debt burden. However, it has large unfunded pension liabilities on its balance sheet. Delta's pension underfunding is dramatically greater than that of United Continental (UAL -1.19%), and also significantly worse than that of American Airlines (AAL 0.99%).

Despite Delta's underfunded pension status, the company hasn't been reporting especially large pension costs in its earnings: less than $250 million in each of the last two years. That's because Delta is projecting a high rate of return on its pension fund assets -- perhaps unrealistically high. If so, it means that Delta's true earnings power is a little lower than it seems.

Delta's pension liability tops $10 billion
At the end of 2015, Delta's total pension liability for its defined benefit plans totaled $20.6 billion. Meanwhile, its pension fund held assets worth $9.4 billion, leaving a shortfall of about $11.2 billion.

Delta's pension plan is underfunded by more than $10 billion. Photo: The Motley Fool

American Airlines also has some catching up to do for its pension fund, but it is in better shape than Delta. At the end of 2015, it had a gross pension obligation of $16.4 billion and $9.7 billion of pension fund assets, leaving it with a $6.7 billion deficit.

By contrast, United Continental dumped most of its pension liabilities in the bankruptcy process many years ago. As a result, it finished 2015 with a comparatively modest $4.5 billion pension obligation and $3.0 billion in its pension fund, leaving it only $1.5 billion underfunded.

Expecting strong investment returns
To calculate the annual cost of its pension program, a company must estimate both the growth of its pension liabilities and the expected growth of its pension assets (among other things). The higher the expected rate of return on a company's pension assets, the lower its reported pension costs.

For the past few years, Delta has been assuming an 8.94% long-term rate of return on its pension assets.

This seems unrealistically high. Many investors would be thrilled to get a 9% annual return after fees from investing in the stock market. Moreover, Delta only invests 40%-50% of its pension fund in "growth-seeking assets", with the remainder split between "income-generating assets" and "risk-diversifying assets". Those latter categories are likely to produce lower returns on average.

Of course, this doesn't mean that it's impossible to earn returns of this magnitude in any given year. In 2012 and 2013, when the stock market was booming, Delta's pension plan returned 10% and 11%, respectively. However, the plan gained just 6.2% in 2014, before posting a -1.4% return last year.

American Airlines and United Continental both use lower expected returns to calculate their pension costs. American Airlines currently has an 8.00% long-term expected return. The comparable figure for United is 7.40%.

Why it matters
In its recent annual report, Delta stated that a 0.50% change in the expected long-term return on its pension assets would impact its net income by $50 million. Using United's more conservative 7.40% expected return figure would reduce net income by a much greater amount: likely about $150 million.

Delta earned an adjusted pre-tax profit of $5.9 billion last year. A $150 million reduction in its pre-tax income certainly wouldn't be a game changer for investors, but it's not peanuts, either.

While the expected return on pension assets determines how much pension expense Delta reports, the actual investment returns determine how much money it has to put into its pension fund. In 2015, Delta contributed $1.2 billion to its pension plan, which barely offset the fund's investment losses and payments to retirees. In the first two months of 2016, Delta has already contributed another $1.2 billion to its pensions.

In effect, below-target investment gains have forced Delta to make extra contributions in 2015 and 2016 beyond the $1 billion in annual pension funding it has touted to investors. To avoid further unwelcome surprises like this, Delta needs to adopt more realistic investment goals for its pension fund.