If someone is stupid or careless enough to get pregnant when they don't want to they probably don't earn a great deal. So who pays for that child to be raised? The taxpayer. Making abortions or contraception free and freely available will reduce the burden on the welfare system and lead to lower taxes.
I do believe that Planned Parenthood should receive funding from the state, but only for preventative means not abortion-related practices. Preventive assistance like birth control education, condom supply, and other abstinence education can actually help our social and economical culture because people can learn how to prevent teen pregnancy or babies out of wedlock, which typically result in need for other financial assistance from the government, crime and abuse.
Planned Parenthood is an organization the provides many preventative care services, including health screenings and birth control. Many poor women use Planned Parenthood clinics because they don't have access to other healthcare options. Preventative care is always more cost-effective, and therefore a good investment of tax dollars. While many who oppose abortion believe government support is inappropriate, abortion represents a very small percentage of the services offered at Planned Parenthood clinics.
I personally do not think Planned Parenthood should receive funding from the state. Many voters try so hard to prevent abortion in the first place, and consider it murder. Having them pay into a system that forces them to contribute to such a practice is not something necessary or ethical.