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Consulta recursiva com soma no Postgres


Esta é uma versão simplificada do @a_horse's correto resposta (após discussão com OP nos comentários).
Funciona com qualquer número (razoavelmente finito) de níveis na recursão.

Preço total para determinado project_id

WITH RECURSIVE cte AS (
   SELECT project_id AS project_parent, project_value
   FROM   projects
   WHERE  project_id = 1 -- enter id of the base project here !

   UNION  ALL 
   SELECT p.project_id, p.project_value
   FROM   cte
   JOIN   projects p USING (project_parent)
)
SELECT sum(project_value) AS total_value
FROM   cte;

Preço total para todos os projetos

WITH RECURSIVE cte AS (
   SELECT project_id, project_id AS project_parent, project_value
   FROM   projects
   WHERE  project_parent IS NULL  -- all base projects

   UNION  ALL 
   SELECT c.project_id, p.project_id, p.project_value
   FROM   cte c
   JOIN   projects p USING (project_parent)
   )
SELECT project_id, sum(project_value) AS total_value
FROM   cte
GROUP  BY 1
ORDER  BY 1;

db<>fiddle aqui (com o caso de teste correto)
Antigo sqlfiddle