The Hearts owner has been boosted, however, by impressive season ticket sales, with the club selling over 10,000 in just three weeks.
The new stand, which will see the capacity of Tynecastle rise to 20,099, was originally slated to cost £12 million.
Budge is adamant the club have the funds in place to make up the difference and will finish the project on schedule.
Budge, who confirmed that the demolition of Hearts’ existing main stand will be completed by the end of next month, said: “In terms of current progress, the first thing to say is that we remain on schedule, for our first league game next season to be played at Tynecastle, in front of the new stand, on 9 September.
“As I have said repeatedly, every day brings its own challenges on a project of this size and complexity and, not entirely unexpectedly, we have been faced with a number of changes that have resulted in some budget overruns.
“However, these are at a level that are manageable and capable of being met from club funds; and most importantly, will not result in us failing to achieve our very tight timescales. In short, things continue to be managed very tightly and everything is still going to plan.”
In a lengthy statement, Budge assured supporters that the arrivals of Christophe Berra and Cole Stockton are the first of several summer signings and urged fans to sign up to the “One in a Million” fund, which aims to raise cash for the redevelopment of
Tynecastle and has already raked in £300,000. Budge also revealed that Hearts had already sold 10,500 season tickets for next term in the space of 21 days.
“This is quite a remarkable a response considering that our season tickets have only been sale for three weeks,” she added.