Recursive query compute parent values - sql

Question

I have 2 tables Persons and Sales. In Person there is relation between child and parent, I want to compute 20 percent of parent values with the following condition
Persons
Id | ParentId | Name
1 NULL Tom
2 1 Jake
3 2 Kate
4 3 Neil
Sales
PersonId | Sale
4 500
I want to get result like this
Id | ParentId | Name | Sale
1 Null Tom 100 <-- (500*20)/100 left 400
2 1 Jake 80 <-- (400*20)/100 left 320
3 2 Kate 64 <-- (320*20)/100 left 256
4 3 Neil 256 <-- (320*80)/100
I wrote this query but it does not give appropriate result
;WITH cte_persons
AS
(
SELECT p.Id, p.ParentId, p.Name, s.Price FROM Persons AS p
INNER JOIN Sales AS s ON s.PersonId = p.Id
UNION ALL
SELECT p.Id, p.ParentId, p.Name, CAST((c.Price - (c.Price*80)/100) AS DECIMAL(6, 2)) FROM #Persons AS p
INNER JOIN cte_persons AS c ON c.ParentId = p.Id
)
SELECT * FROM cte_persons

Answer 1

This should be a two steps algorithm. First traverse the hierachy to get max level. Then apply the level in a reverse order.
WITH cte_persons
AS
(
SELECT 1 as level, p.Id, p.ParentId, p.Name, s.Price, p.Id AS base
FROM Persons AS p
INNER JOIN Sales AS s ON s.PersonId = p.Id
UNION ALL
SELECT level + 1, p.Id, p.ParentId, p.Name, c.Price, c.base
FROM Persons AS p
INNER JOIN cte_persons AS c ON c.ParentId = p.Id
)
SELECT Id, ParentId, Name,
CASE level WHEN 1
THEN price - sum(delta) over(partition by base order by level desc) + delta
ELSE delta END sale
FROM (
SELECT *,
(power (0.8000, max(level) over(partition by base) - level) * 0.2) * price delta
FROM cte_persons
) t
ORDER BY id;
db<>fiddle