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Cheap international air tickets are generally not refundable. You will get some airport taxes back (probably less than 100 USD) minus an administration fee.
Alternatively you might get a voucher that you can use towards a future flight on the same airline. It depends on how you buy the ticket.
As a rule of thumb a fully refundable ticket will be about three times the price of the cheapest ticket you can find.
Some airlines will let you change your ticket to a future date, but only if you tell them before the flight.
Ten days is not last minute. Last minute is when you arrange your flight in the taxi to the airport. Anyway, ten days before I would expect the price of MCI-RIX-MCI to be about 1000 USD (in economy class), providing your stay includes a Saturday night. Such a ticket is considered a deep discount advance purchase fare and remains unrefundable.
In your shoes I would definitely purchase the ticket after I received the visa.