ASOS says back on course for $4 bln sales by 2020

* 2013-14 pretax profit 46.9 mln stg, down 14 pct

* Sees flat profit in 2014-15, "small increase" 2015-16

* Shares (Berlin: DI6.BE - news) rise up to 19.3 pct

* Shares had fallen 68 pct this year before Tuesday (Adds detail, CEO, analyst comments, shares)

By James Davey

LONDON, Oct 21 (Reuters) - British online fashion retailer ASOS (Other OTC: ASOMF - news) believes it can reach its target of 2.5 billion pounds ($4 billion) in annual sales by 2020, with price cuts helping to reignite growth after three profit warnings this year.

Shares in ASOS, which had lost two-thirds of their value this year following a procession of bad news, jumped as much as 19 percent on Tuesday on signs the business was stabilising.

Until this year, ASOS had been the great success story of UK retailing and a darling of the stock market, helped by its appeal to internet-savvy twentysomethings and high-profile fans including singer Rita Ora and U.S. First Lady Michelle Obama.

Having floated at 20 pence in 2001, ASOS shares hit a high of 71.95 pounds in February.

But they were then clobbered by a slowdown in growth due in part to the strength of sterling, as well as disruption from investments in warehouses, a fire at its Barnsley, northern England, depot in June, and the launch of its business in China.

ASOS said last month it would cut prices to reverse the slowdown in sales growth in foreign markets.

Chief Executive Nick Robertson said on Tuesday the strategy would take time to deliver, but that 10 percent growth a year in its active customer base for the next five to six years -- "which would be not particularly heady growth" -- would add another billion pounds of sales.

"You could see then ... that 2.5 billion pounds is more than achievable," he told reporters.

ASOS's pretax profit fell 14 percent to 46.9 million pounds($75.9 million) in the year to Aug. 31 2014. That was just above analysts' reduced expectations but down from the 54.7 million pounds made in 2012-13.

Though total retail sales grew 27 percent to 955.3 million pounds, the strength of sterling hit sales growth overseas, particularly in markets such as Australia and Russia.

Robertson, ASOS's founder and 9-percent shareholder, expects flat profits in 2014-15 and "a small increase" in 2015-16.

"Management has now bought itself some time to tackle the issues with its flat FY 15 profit guidance. Key to sentiment this year will be visibility on the extent of, and reaction to, price investment in key markets, and the time needed to move to profit in China," said analysts at N+1 Singer.

At 0845 GMT, ASOS shares were up 16 percent to 22.51 pounds, valuing the firm at 1.9 billion pounds.

"We are in a period of major investment that comes at a short term cost, but the medium-term benefits will be significant," said Robertson.

ASOS also said it had promoted chief financial officer (CFO) Nick Beighton to chief operating officer. It is now looking for a new CFO.

(1 US dollar = 0.6189 British pound) (Editing by Kate Holton and Mark Potter)