diff --git a/backend/categorisation/processor.py b/backend/categorisation/processor.py
index 5ed75d8f..590d064f 100644
--- a/backend/categorisation/processor.py
+++ b/backend/categorisation/processor.py
@@ -94,11 +94,15 @@ def choose_cheapest_relevant_plan(
         for plan in eligible_plans
     )
 
-    cheapest_plans: List[Plan] = [
-        plan
-        for plan in eligible_plans
-        if (plan.record.cost_of_works or float("inf")) == min_cost
-    ]
+    if all(p.record.cost_of_works == 0 for p in eligible_plans):
+        cheapest_plans = eligible_plans
+
+    else:
+        cheapest_plans: List[Plan] = [
+            plan
+            for plan in eligible_plans
+            if (plan.record.cost_of_works or float("inf")) == min_cost
+        ]
 
     for priority_scenario_id in scenario_priority_order:
         for plan in cheapest_plans: