For the Royal Shakespeare Company's executive director, Vikki Heywood, submitting a funding request to the Arts Council – the body that holds the pursestrings for UK culture – is "like giving in your homework or doing a tax return". Actually, it's more like reapplying for your own job. Faced with a 30% cut itself, the Arts Council has asked all the organisations it funds to rethink their budgets.

It's particularly problematic for the RSC, as it has just completed a £113m (€135m) transformation of its home in Stratford-upon-Avon.

The new building creates revenue streams from restaurants, cafés and even a viewing tower, but costs more to run. “We started this project on the understanding that we wouldn't be facing cuts at this point,” sighs Heywood. “Now the world has turned and the RSC couldn't have hit a worse moment to be opening this more expensive building.”

Since arriving at the RSC in 2003, alongside artistic director Michael Boyd, Heywood has already solved one set of financial problems. The company had a deficit of £2.8m, and the plans to demolish its ramshackle riverside base, the Royal Shakespeare Theatre, and replace it with a crowd- pleasing Shakespearean theme park, had hit opposition.

Heywood and Boyd cut staffing costs and decided to improve the building they had rather than starting from scratch. Not that the project is lacking in radicalism. The main auditorium has been entirely replaced, exchanging a traditional proscenium-arch layout for a trendy 'thrust stage' in which seats surround the actors on three sides.

“The old theatre was designed like an Odeon cinema, so the audience and actors were really in two separate rooms," she says. "The struggle was always how to bring the performance out into the auditorium, to connect the audience and the actors together.”

The two old halves of the building – a partly burnt-down Victorian theatre plus a hulking 1930s Art Deco construction – are wedded together with new circulation spaces, shops and a rooftop restaurant. A 36m-tall tower provides views of the surrounding town, where William Shakespeare was born, went to school and is buried. Free exhibitions about the playwright and the RSC's history are dotted throughout the building, and include an 'insult chair', which spews out authentic Shakespearean taunts such as: “Your bottom is the best thing about you.” It's all family-friendly and turns the theatre into an all-day attraction.

Deprived of the levels of philanthropy and state funding that American and French institutions respectively rely on, British museums, galleries and theatres have become skilled at making their own money – through shops, restaurants and membership schemes. The RSC is consciously following that model and would like a greater share of the tourist cash that flows into Stratford-upon-Avon.

“About 3 million people visit Stratford a year and they don't necessarily visit us," says Heywood. "The RSC is a rightful meeter and greeter of those people. So we hope that over 300,000 a year will come through our doors, which they never did before.”

Ticket sales are already up. The new season, which starts this month, has seen the highest box-office sales in the company's history. It's exactly 50 years since Sir Peter Hall formed the RSC, the first permanent theatre company dedicated to the Bard's work, and the celebrations begin with a production of Macbeth directed by Michael Boyd.

And there is plenty to look forward to. The RSC will be a key player in the cultural events taking place around next year's Olympics, and it is taking its repertoire and a temporary 1,000-seater auditorium to New York at the end of the summer. That might seem a strange priority – the company has cancelled its regular season in Newcastle – but it's no secret that the Americans have always been very generous supporters.

Asked whether she thinks a rise in philanthropy will be enough to make up for the shortfall in public cash, Heywood is matter-of-fact. “Overall, no," she says. "And I don't think sponsors and donors think that that's their role. They are very nervous of the idea that their money might go to core costs and people's jobs depending on it.

"So while you can heighten awareness and bring in tax breaks – and we will see an increase, probably, over the next few years – I don't think there is anyone who has just submitted their budgets to the Arts Council who is saying: 'Don't worry, I can take a 15% cut because I can increase my philanthropic giving by 15%.'”

She is worried but optimistic. “Anyone can close a business down; it's really clever people who keep them open. And we'll keep the RSC open, there's no doubt about that.

“The great thing about running a theatre company is that every time you're feeling a bit down about the figures or you can't quite see your way through a particular problem, you can just go and stand there at 7.20 when the curtain goes up and it reminds you all over again why you do it.”

The RSC's 50th birthday season opens with Macbeth on 16 April. rsc.org.uk