The breakup at ConocoPhillips on Apr. 30 will be a happy occasion for shareholders.

The impending divorce at one of the world’s largest integrated energy companies may be bittersweet to some insiders, but to shareholders, the breakup will be a happy opportunity to receive a gift from the terms of the “settlement.”

They get two stocks for the price of one from a tax-free spinoff, for starters, plus a chance to quickly bag precious “found-money” should if the spinoff entity is sold off entirely. Shares of parent ConocoPhillips are bound to become a more focused long-term investment value as the second largest U.S. oil company, the world’s fourth-largest publicly traded oil company and the sixth-largest natural gas producer.

Part of what ConocoPhillips is spinning off is its vast refining operations, the third largest U.S. refinery. ConocoPhillips operates in some 40 countries, with the U.S. accounting for 66% of sales. The rest comes from sales all over the world, led by Europe, Asia Pacific and the Middle East. The company’s large chemical operations are done through an equally owned joint venture with Chevron (NYSE:CVX).

As part of ConocoPhillips’ spinoff to shareholders on record as of April 16, 2012, of the company’s refining and marketing operations on April 30, each ConocoPhillips shareholder will receive one share of the downstream business, called Phillips 66. The stock already started trading on Apr. 12 on the New York Stock Exchange on a “when-issued” basis,  with the ticker symbol PSXWI, at $33.25 a share. It’s currently at $34.

Shares of the stub of parent ConocoPhillips began trading on an “ex-distribution” basis on the Big Board under the ticker symbol COPWI at $58. Shares of the integrated ConocoPhillips are trading at $73 a share as of Apr. 13, 2012.

Here’s the deal on how to play the spinoff, as some analysts see it. Sell shares of Phillips 66 (PSXWI) and buy the COP stub (COPWI). Part of the reason is that might take time for the spinoff stock to move up as fast as some analysts expect the stock of COPWI to move.

“We value Phillips 66 (PSX) at $25.74 a share, or $16.38 billion, using 3.3 times fiscal year 2012 EBITDA, which is in line with its peer group’s median multiple,” says Joseph Cornell, president of Spinoff Advisors. The valuation represents a downside of 24% from the current price, notes Cornell, who says Spinoff Advisors’ analysts are initiating coverage of the spinoff with a “sell” recommendation.

He’s upbeat about the COP stub, on the other hand, which he values at $78.70 a share, or $100.20 billion, using a 4.3 times 2012 estimated EBITDA which, he says, is roughly in line with the peer group’s median multiple. That valuation is about 37% higher than the stock’s current market price. So Spinoff Advisors rates the stock a buy.

With regard to the integrated ConocoPhillips’ current stock, Cornell remains bullish and maintains a buy rating on the shares, which SpinOff Advisors figures is worth $91.75 a share, or $116.58 billion. ConocoPhillips pays an attractive dividend yield of 3.6%.

In a recent conference call with analysts, ConocoPhillips assured that both the parent and the spinoff will continue the  generous dividend policy, also promising to continue raising the payout as often as possible.

“Based on the market price of the shares of COP and PSX in the “when-issued” basis, the market offers an opportunity for current investors in COP to exit their stake in the more challenging downstream [refining business] while retaining stake in the upstream [oil and gas exploration and production] business,” says Cornell.

While shares of COP in the “regular-way market are undervalued based on our sum-of-the-parts valuation, we believe investors can also look at exiting their positions in the ‘regular-way’ market and buy shares of COP in the when-issued market, which has a higher upside potential, based on our valuation,” argues Cornell.

ConocoPhillips had been “reshaping its portfolio through a multiyear strategic repositioning to focus on higher growth and profit upstream assets in an attempt to boost returns and cut debt,” notes Michael Kay, analyst at S&P Capital IQ, who  rates the stock of the integrated ConocoPhillips a buy, with a price target of $90 a share. The stock is currently at $73. The asset repositioning “should help ConocoPhillips’ ability to improve future returns,” says Kay. With oil prices strong, he sees the company earning $8.40 a share in 2012, which includes downstream forecasts, off from 2011’s $8.97.

With Big Oil still in a quandary as to what will happen geopolitically, especially with Iran, oil-patch stocks have been unusually quiet, with little excitement among the energy stocks. ConocoPhillips’ stock is one of the few that represents offers the potential of upside momentum right now.