SELECT 
  cscart_product_prices.product_id, 
  MIN(
    IF(
      cscart_product_prices.percentage_discount = 0, 
      cscart_product_prices.price, 
      cscart_product_prices.price - (
        cscart_product_prices.price * cscart_product_prices.percentage_discount
      )/ 100
    )
  ) AS price 
FROM 
  cscart_product_prices 
WHERE 
  cscart_product_prices.product_id IN (
    408640, 423654, 437901, 451860, 447040, 
    402866, 419169, 440094, 409667, 433404, 
    420606, 408565
  ) 
  AND cscart_product_prices.lower_limit = 1 
  AND cscart_product_prices.usergroup_id IN (0, 1) 
GROUP BY 
  cscart_product_prices.product_id

Query time 0.00254

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost": 0.050171963,
    "nested_loop": [
      {
        "table": {
          "table_name": "cscart_product_prices",
          "access_type": "range",
          "possible_keys": [
            "usergroup",
            "product_id",
            "lower_limit",
            "usergroup_id"
          ],
          "key": "usergroup",
          "key_length": "9",
          "used_key_parts": ["product_id", "usergroup_id", "lower_limit"],
          "loops": 1,
          "rows": 24,
          "cost": 0.04252208,
          "filtered": 50,
          "attached_condition": "cscart_product_prices.lower_limit = 1 and cscart_product_prices.product_id in (408640,423654,437901,451860,447040,402866,419169,440094,409667,433404,420606,408565) and cscart_product_prices.usergroup_id in (0,1)"
        }
      }
    ]
  }
}

Result

product_id price
402866 1702.13000000
408565 582.03000000
408640 372.23000000
409667 1665.63000000
419169 1874.47000000
420606 341.62000000
423654 1854.97000000
433404 1164.70000000
437901 1460.85000000
440094 505.51000000
447040 284.13000000
451860 1022.69000000