Re: Calculated "virtual" rows

[Rick James]

SELECT  year_id, location_id, figure_id, value
    FROM  fact_data    -- ###MAGIC###
    WHERE  figure_id IN ("total_costs", "purchase_costs",
                "goods_costs")
      AND  year_id = 2010;

is fine, especially if fact_data has
INDEX(year_id, figure_id)

So, perhaps your example was not complex enough??

We need to see SHOW CREATE TABLE for the tables in question. We especially need to know the PRIMARY KEY of fact_data.

This subquery begs for an artificial
id INT UNSIGNED AUTO_INCREMENT PRIMARY KEY

SELECT  a.year_id, a.location_id, "purchase_costs",
        a.value + b.value * c.value
    FROM  fact_data a
    LEFT JOIN  fact_data b ON a.year_id = b.year_id
      AND  a.location_id = b.location_id
      AND  b.figure_id = "admin_costs_purchase_dist"
    LEFT JOIN  fact_data c ON a.year_id = c.year_id
      AND  a.location_id = c.location_id
      AND  c.figure_id = "admin_costs"
    WHERE  a.figure_id = "goods_costs"

LEFT JOIN is the way to deal with NULLs; no UNION needed (or maybe I do not understand what you are doing).