The multitude of possible answers is no doubt keeping Pearson's new chief executive, Marjorie Scardino, awake at night. Her company has five main identifiable product areas: books, television, financial information, theme parks, and banking. Each contains assets that other companies would kill for. Penguin is pre-eminent in paperbacks; the Financial Times and The Economist hold the moral high ground in business journalism; Tussauds is consistently among London's most popular tourist attractions; Thames Television has an enviable library of TV classics; Lazards just came top of Europe's merger and acquisitions league table for 1996.
They should be a potent combination. A brand-led media and financial services conglomerate that has a multitude of cross-pollination prospects, has intellectual property coming out of its ears, and is active in growing markets. What more could a chief executive want?
The answer, according to investors and analysts, is a direction. The company began the process of deciding what it wanted to be under former chief executive Frank Barlow, who oversaw the disposal of Westminster Press and, earlier, Royal Doulton, as well as the reduction in Pearson's stake in BSkyB. In Scardino, and soon-to-be-appointed chairman Dennis Stevenson, the company has the opportunity to rewrite the script.
Some overdue editing work may already be going on. A sale of the company's 50 per cent stake in Lazards is predicted, and will unwind an anomalous, if profitable, arrangement that dates back to 1919. There is also the possibility that Pearson TV head Greg Dyke will be given the opportunity to buy his division out from under the corporate umbrella. And there are possibilities when it comes to honing the conglomerate into a leisure and entertainment group or a business information group.
More will be known in eight weeks' time, when Ms Scardino delivers Pearson's 1996 results. A positive trading statement just before Christmas has primed investors for some good news come March. They will be looking for a plan that will improve Pearson's undistinguished 9.4 per cent return on capital in 1995. They will also be looking for upbeat news on Channel 5, due for launch in April, which has had a difficult pre-natal period. And they will hope that Mindscape, the loss-making software division, does not have any more nasty surprises in store.
How will a Scardino shake-up affect investors? They, like her, face a complex decision as to how they perceive the company's future. If, say, Ms Scardino sold the book division and bought the business information company Bloomberg to merge with its FT Extel service, she would be swapping a low-priced, cash-generative asset for a high-priced one that will still need large cash injections to keep up with Reuters. Earnings would take a dive at first, giving any short-term investor the jitters. But in the long term, the company would have exchanged a low-margin, mature business for a high-margin growing one.
Slice the cake a different way: sell the Financial Times, The Economist stake, Extel et al, and buy Carlton to give a first-class distribution vehicle to Pearson's television production interests. Or sell the television interests, and buy more book companies and maybe even dip a toe into software again. The possibilities for chopping and changing the assets are so endless it could almost be a board game.
The problem Ms Scardino faces is that almost any strategy - including that of breaking the company up - is possible, and each has good and bad points. The difficulty with all of the disposal programmes is that Pearson could find itself saddled with a huge capital gains tax liability. And yet were she to disappoint the corporate financiers and keep the company as it is, minus the Lazards stake, and just concentrate on making the businesses work together, rather than separately, that too would be a strategy that rewarded shareholders - but not in a spectacular way.
This opens the door to the threat of a takeover, which will become more apparent if the market does not take to the Scardino initiatives and analysts get their calculators out to find that the company is one of the cheapest buys in media.
Ms Scardino started her tenure at the top of Pearson earlier this month by quoting General Douglas MacArthur: "Have a plan, execute it violently, and do it today." Wags have pointed out that at least MacArthur knew what he was planning for. Investors will be hoping that Ms Scardino not only has a plan to execute violently, but one which does not leave the media conglomerate fighting the wrong war.
Share price 752.5p
Prospective p/e 25*
Gross dividend yield 2.8%
Year to 31 Dec 1993 1994 1995 1996* 1997*
Turnover (pounds bn) 1.87 1.55 1.83 2.18 2.20
Pre-tax profits (pounds m) 208 256 236 254 308
Earnings p/s (p) 27.9 34.1 28.8 29.7 37.0
Dividend p/s (p) 13 15 16.5 18 19.5
*Panmure Gordon forecasts