Her father considered it as an investment or some form of sponsorship that could prove to be beneficial to him in the future so he was quick to agree.
If it would be successful and there would be good results then he would be more likely to provide further support in the future.
All he would be covering would be the travel and expenses for a couple of people so it would be nothing for him.
If he could take advantage of the situation then he could gain something from it whether it would be monetary or something else entirely.
Even being able to let his daughter succeed in the Capital and help her form her reliable group was something that would end up being beneficial to him in the long term.
Her success would end up being his success too since they were tied together by their father-and-daughter relationship.