Although DryShips (NASDAQ:DRYS) owns a majority equity stake in public company Ocean Rig UDW (NASDAQ:ORIG), the businesses are very much two distinct and separate entities. DryShips' shipping business desperately needs a life raft while Ocean Rig is getting ready to open the dividend floodgates. Are Ocean Rig's cash bales big enough for DryShips debt and cash burn?

DryShips' debt
DryShips reports its financials in consolidation with Ocean Rig. In order to calculate the liquidity situation for the shipping business of DryShips alone, the company forces you to do a little algebra. Subtract out the current liquid assets and liabilities of Ocean Rig from that of DryShips and the remainders are the totals for DryShips the standalone company.

As of the end of last quarter, that resulted in nearly $250 million in liquid assets and nearly $1.75 billion in liabilities. Obviously this is not a pretty situation for DryShips to be in. Some of its debt was given leniency in the form of a waiver that "relax[es] various financial covenants up till the end of 2014." This kept DryShips from being in default... for now anyway.

Continuing losses
Meanwhile, in order to calculate the rate of net loss for DryShips last quarter, use similar algebra as before. Take the net loss that DryShips reported and subtract out the net loss of Ocean Rig, and you should get around $51 million.

That large net loss was at a time when shipping rates were much higher than they currenlyt are. This means DryShips the shipping company has slim liquid assets, crippling debt, and is continuing to tack on sizable net losses.

Absent a massive and sudden rise in rates, it seems DryShips' only realistic source of hope is the value it holds in Ocean Rig. DryShips owns just over 78.3 million shares of the public drilling company. There are two realistic potential ways that DryShips can extract value out of Ocean Rig. First, it can sell shares in the open market or through private transactions, though it would risk giving up control if it gets below 50% ownership, and it's down to 59% already.

Dividend relief?
The other hope is a dividend. During Ocean Rig's Nov. 5 conference call CEO George Economou announced that Ocean Rig plans to pay a quarterly dividend sum of $25 million beginning in May 2014. Although managing director Anthony C. Argyropoulos said that this is a "prudent starting point," when further pressed in the Q&A session he said it is correct that we should expect this dividend level to remain flat until further notice.

Based on all this, there should be three dividend payouts in 2014 -- in May, August, and November -- for a grand total of $75 million, or around $0.57 per share. Based on DryShips' 78.3 million shares outstanding, this comes out to around $44.6 million in dividend receipts for DryShips.

Spit in the ocean
Pardon the metaphor, but $44.6 million is spit in the ocean considering both the level of debt DryShips holds and its ongoing net losses. For instance, in its last reported quarter alone, DryShips had a greater net loss than the entire 2014 expected dividend payout. If analysts have it right, DryShips' shipping biz will lose around $120 million for the year in 2014. The dividends could reduce this to the $70 million-$80 million range, which is an improvement, but it hardly could be classified as life vest.

DryShips appears to be a sinking ship unless things change fundamentally. While the Ocean Rig dividend may plug a leaking hole or two, it is not nearly enough to save DryShips' shareholders. Fools should continue to swim with caution.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.