No longer are there headlines about the company's predatory activities. Or about its cock-ups on the railways. Gradually the swashbuckling image of an aggressive company driving rivals off the road and attracting the wrath of the Office of Fair Trading is disappearing.
Instead, Stagecoach is now presenting itself as a respectable FTSE-100 company - which it joined last summer - intent on continued acquisition and growth. It may not yet quite be sober-suited because the company's co-founder Brian Souter, who remains a very active executive chairman, still gallivants around the globe in chinos and cowboy shirts in the search for new acquisitions, but Stagecoach is slowly earning the veneer of respectability that eluded it in its early years.
Mr Souter showed the City that he knew it was time for Stagecoach to grow up when he appointed Mr Kinski, who earned widespread plaudits at Scottish Power, to run the day-to-day business, allowing him to keep on travelling the world looking for deals.
While there have been no new blockbusters of the size of the Porterbrook rolling stock leasing company, bought for pounds 826m in August 1996, there has been a steady stream of purchases over the past year: the stake in Virgin Rail and in the Hong Kong-owned Chinese road toll company Road King; Prestwick Airport; Citybus in Hong Kong; and the Yellow Bus company in Auckland, along with Fuller's Ferries in the same city.
There have also been a number of misses, such as Hong Kong's China Motor Bus, which went to the rival FirstGroup and, more recently, the Melbourne local transport network where Stagecoach failed even to make the shortlist.
Mr Souter's timing in appointing Mr Kinski, was, according to analysts, spot-on. The business was growing too big for him to run on his own, and his co-founder, sister Ann Gloag, had decided to take more of a back-seat role and rest on her considerable laurels. Mr Souter spent only a couple of days each week in the Perth HQ, and the rest of the time he was on the road, mostly seeking acquisitions and living out of his trademark plastic bags, which meant the day-to-day management was becoming neglected.
Mark McVicar, a transport analyst with SG Securities, says that Mr Kinski's appointment ensured that Stagecoach avoided the pitfalls that trap many other high-growth companies: "What works when you are small and doubling your turnover every year is not right when your capitalisation is in the billions.
"Mr Souter realised that he had to blend in his entrepreneurial flair with better management of the subsidiaries, and he addressed this issue before the company's financial reputation was affected."
The South West Trains fiasco in the spring of 1997 was a warning to Mr Souter, who is the first to admit that, despite his accountancy background, running companies is not his strong point. Little more than a year after it took over South West Trains, Stagecoach suffered its worst public relations disaster when it was forced to cancel thousands of trains because of a driver shortage that was compounded by poor labour relations.
Not only did this provoke a deluge of complaints from angry commuters, but it also prompted some City angst about Stagecoach's ability to cope with a more diverse portfolio, as the company sought to expand out of the bus market, which had been its original hunting ground.
So Mr Souter turned to Mr Kinski, a fellow self-made man from a working- class background, and allowed him a free rein in restructuring the company. Mr Kinski quickly sorted out the UK bus division, which consists of 19 different companies acquired around the UK between 1986 and 1997.
Mr Kinski explains: "Previously, there was not a clear, accountable management structure. Some reported to Brian Souter, others to Barry Hinkley [executive director] and others to Neil Renilson [former chairman of Stagecoach Scotland]."
Mr Renilson was edged out, along with another executive, Jim Moffat of Fife Scottish, and Mr Kinski reorganised the mess into three regions, each accountable to him.
Then he set about strengthening the centre and filled what had clearly become gaping holes in the management of a major company - no human resources director and no head of communications. Both appointments were made quickly and an IT director was also brought in to sort out problems such as the different payroll systems used by all the bus companies. It was the birth of corporate Stagecoach, even though elements of the family history remain as Brian Souter still retains 12.6 per cent of the shareholding and Mr Gloag holds 10.2 per cent.
One tangible result of the way Stagecoach has focused more on day-to- day management has been the improvement in its performance on the railways. Reliability on South West Trains services has improved and new trains are on the way, with an order for 30 four-car trains in the spring. And Stagecoach's tiny Island Line, which runs old London Underground trains on the Isle of Wight, last month became the only one of the 25 franchises across the network to obtain the coveted "A" grade from the franchising director who monitors train services.
Now, with restructuring costs no longer a factor, rail has also begun to be highly profitable, with profits up last year by 121 per cent to pounds 17.3m, helped by a 7 per cent rise in passenger numbers.
The subsidy profile on South West Trains is incredibly generous, a reward for Brian Souter's readiness to take on the first franchise back in December 1995, but the company faces a much sterner test with its 49 per cent holding in Virgin Rail, bought last June for pounds 158m after Mr Souter approached Richard Branson. The deal allowed Mr Branson to avoid a flotation on the stock market, where he had his fingers burnt previously, but the benefits for Stagecoach seem less immediately tangible since the subsidy paid to Virgin's two franchises, currently running at pounds 171.8m per year, disappears entirely over the next decade to become a premium payment of pounds 238.5m, a very ambitious task even if the current upgrading of the line is successful in attracting new business.
Virgin Trains continued to attract criticism, topping the rail complaints league, and yet Stagecoach's input in the early months of its investment in the company seems to have been minimal. Last month, however, a new chief executive, Chris Green, who formerly ran InterCity, ScotRail and Network SouthEast, was appointed.
While Mr Green is well regarded in the rail industry, the appointment is not risk-free. Mr Green was forced out of the chief executive's job at English Heritage after falling out with the chairman, Lord Stevens, and getting into a wrangle over his expenses. Mr Green has set about his new task with relish. The complex structure of Virgin Trains and Virgin Rail was immediately simplified, and advertisements have been posted for an operations manager for the West Coast main line, the source of most complaints.
Mr Green finds it extraordinary that no one seemed to be running the railway, and while Stagecoach must take some of the responsibility for this, Mr Kinski explains that the focus was on getting the financing in place for the new trains, which was finally achieved in December.
While many City insiders consider Stagecoach's involvement in Virgin to be a prelude to taking over the whole show, Mr Green is convinced that both companies see the partnership as a long-term proposition: "Mr Branson and Mr Souter are blood brothers. The skills of the two companies complement each other with Virgin providing the entrepreneurial flair and Stagecoach the attention to detail."
He says that a number of schemes involving joint use of Virgin trains and Stagecoach buses are to be announced shortly, such as a link between Carlisle and Stranraer, avoiding the circuitous train journey via Glasgow.
Mr Kinski is also addressing another problem acquisition - Swebus, Sweden's biggest bus company, where margins are in single figures. There is a tighter regulatory framework in Sweden and most services are tendered out in a highly competitive environment, but Mr Kinski insists this is not the problem: "When Stagecoach took it over [in August 1996], it failed to apply its usual model it had used in the UK. Swebus was top-heavy with a head office and four regional offices with each one a fiefdom. Also, even light maintenance was out-sourced to companies taking big margins. Now we are taking costs out, bringing maintenance in-house and we will be able to win tenders and obtain higher margins. We will be in double figures within a couple of years."
Created in 1980 by Brian Souter, his sister Ann Gloag and her then husband Robin Gloag (who was soon eased out), Stagecoach is Britain's biggest start-up company of the Thatcherite era, and grew quickly on the back of successive deregulations and privatisations - coaches, buses and trains.
It is now using the competitive advantage of being based in the country that has been foremost in transport deregulation and privatisation by venturing abroad. Indeed, unless Stagecoach was prepared to take the regulatory flak that a bid for one of its major rivals, FirstGroup or Arriva, would engender, most of its growth is likely to be overseas.
But can it keep up the pace? Not many young companies manage the transition from high-growth, high-risk teenagehood to respectable middle age without a major crisis or a complete change in personnel. Yet Stagecoach, which Mr Souter hopes will double in size again in the next four years, seems, so far, to be making the shift with barely a hiccup.
Some problems remain - under-performing Swebus, the vagaries of the UK rail franchising process, Virgin Rail's over-ambitiousness, Road King's poor share price, the flat margins of the UK bus industry - but all these seem trifling when set against the continued growth in profits, the increase in margins in nearly all sectors, and the continued performance of Porterbrook, the company's milch cow, providing half the profits.
There is also the risk that one day Mr Souter will attempt a deal too far, but there is very little in his record to suggest that he would risk the future of the company on a dodgy deal.
Mr Kinski stresses that he, too, plays an important role in the acquisition process, hinting that he would curb any of his boss's excesses: "Brian brings the ideas to me and to Keith Cochrane [the finance director] before presenting them to the board. I look at how we will operate the new subsidiary, and Keith checks out the figures."
Mr Kinski is also adamant that Stagecoach will not venture into dangerous waters: "We pulled out of Kenya soon after I joined because I don't want to operate in crisis areas. That means we will not be going into Africa, nor into Eastern Europe."
Despite its performance, Stagecoach has never quite been the darling of the City, which remains suspicious of a company that keeps its headquarters in unfashionable Perth and eschews consultants and other expensive City services whenever possible. There are, however, noticeably fewer Cassandras predicting doom for this upstart product of the Thatcher years. And if the double act of Mr Kinski and Mr Souter proves as successful over the next few years as it has so far, the Square Mile may at last embrace the company wholeheartedly.
t Christian Wolmar's book, Stagecoach, a classic rags to riches tale at the frontiers of capitalism, is published by Orion Books at pounds 18.99.
inside a bus and train empire
Turnover (year ending 30 April 1998): pounds 1381.5m (half year to October 31 1998 - pounds 722.7m, up 6 per cent)
Operating profit: pounds 219.1m (half year to October 31 1998 - pounds 132.1m up 30 per cent)
Market capitalisation (24 February 1999): pounds 3.394bn
Employees: 33,000 in seven countries
Board: Brian Souter (chairman), Mike Kinski (chief executive), Keith Cochrane (finance director), Ann Gloag, Barry Hinkley, Brian Cox, Derek Scott; non-executive directors: Ewan Brown, Barry Sealey, Robert Speirs
UK bus: 19 companies including operations in London, Manchester, Newcastle, south coast, Glasgow, Fife and many other towns and cities
Overseas bus: includes companies in Sweden, Finland, Portugal, New Zealand and Australia, and in the process of acquiring Citybus in Hong Kong
Rail: South West Trains, Island Line and Sheffield Tram
Porterbrook: rolling stock company
Airport services: Prestwick, Britain's second largest freight airport
Other investments include Virgin Rail (49 per cent) and Road King (29.2 per cent)