Adding a foreign key to simplify a query - good or bad modeling?

[Joseph Hesse]

My question involves 3 tables:
"SalesPeople" in a car dealership who invoice clients "Invoices" for one or more cars "CarsSold"

The cardinality relationships are:
"SalesPeople" 1-to-n "Invoices" 1-to-n "CarsSold"

The 3 table definitions are:

CREATE TABLE SalesPeople (
SalesPersonID INT NOT NULL ,
SalesPersonName VARCHAR(45) NULL ,
PRIMARY KEY (SalesPersonID) );

CREATE TABLE Invoices (
InvoiceID INT NOT NULL ,
SalesPersonID INT NOT NULL ,
CompanyName VARCHAR(45) NOT NULL ,
PRIMARY KEY (InvoiceID, SalesPersonID) ,
INDEX fk_Invoices_SalesPeople_idx (SalesPersonID ASC) ,
CONSTRAINT fk_Invoices_SalesPeople
FOREIGN KEY (SalesPersonID )
REFERENCES SalesPeople (SalesPersonID ) );

CREATE TABLE CarsSold (
VinNumber VARCHAR(100) NOT NULL ,
InvoiceID INT NOT NULL ,
CarModelName VARCHAR(45) NOT NULL ,
PRIMARY KEY (VinNumber, InvoiceID) ,
INDEX fk_CarsSold_Invoices1_idx (InvoiceID ASC) ,
CONSTRAINT fk_CarsSold_Invoices1
FOREIGN KEY (InvoiceID )
REFERENCES Invoices (InvoiceID ) );

I want a query that lists all the SalesPersonName and the CarModelName they have sold. The query involves joining 3 tables and looks like:

SELECT SalesPersonName, CarModelName
FROM SalesPeople
JOIN Invoices ON SalesPeople.SalesPersonID=Invoices.SalesPersonID
JOIN CarsSold ON Invoices.InvoiceID=CarsSold.InvoiceID;

If I add another foreign key to the "CarsSold" table that refers to SalesPeople.SalesPersonID then I could do the same query with only 2 table joins. The modified "CarsSold" table and the shorter query are shown below.

CREATE TABLE CarsSold (
VinNumber VARCHAR(100) NOT NULL ,
InvoiceID INT NOT NULL ,
SalesPersonID INT NOT NULL , # <== Add foreign key
CarModelName VARCHAR(45) NOT NULL ,
PRIMARY KEY (VinNumber, InvoiceID, SalesPersonID) ,
INDEX fk_CarsSold_Invoices1_idx (InvoiceID ASC) ,
INDEX fk_CarsSold_SalesPeople1_idx (SalesPersonID ASC) ,
CONSTRAINT fk_CarsSold_Invoices1
FOREIGN KEY (InvoiceID )
REFERENCES Invoices (InvoiceID )
CONSTRAINT fk_CarsSold_SalesPeople1
FOREIGN KEY (SalesPersonID )
REFERENCES SalesPeople (SalesPersonID ));

SELECT SalesPersonName, CarModelName
FROM SalesPeople
JOIN CarsSold ON SalesPeople.SalesPersonID=CarsSold.SalesPersonID;

My question is: I have added a foreign key for the purpose of simplifying a query. Is this good data modeling?

Thank you for reading this lengthy question.
Joe