Create a Salesforce Formula Showing the Value of a Multi-Select Picklist From Parent to Child Object

In order to create a formula field on a child object that displays all of the selected values from a multi-select picklist on the parent object, perform the following:

Create a formula field on the Object in Salesforce Classic or Lightning Experience

1. Go to the object where you want to create the field 

Salesforce Classic : Setup | Customize | Object | Fields
Lightning Experience: Gear Icon | Setup | Object Manager | Object | Fields & Relationships

2. Click New.
3. Select Formula for the Data Type.
4. Name the field and select Text for the Formula Return Type.
5. Click Next.
6. Enter your formula syntax.

IF ( INCLUDES ( parent.multipicklist__c , "Value 1" ), "Value 1; ",null ) &
IF ( INCLUDES ( parent.multipicklist__c , "Value 2" ), "Value 2; ",null ) &
IF ( INCLUDES ( parent.multipicklist__c , "Value 3" ), "Value 3; ",null ) &
IF ( INCLUDES ( parent.multipicklist__c , "Value 4" ), "Value 4; ",null ) &
IF ( INCLUDES ( parent.multipicklist__c , "Value 5" ), "Value 5; ",null )

This example would produce return values such as:

Value 1; Value 2; Value 3; Value 4; Value 5;
Value 1; Value 4; Value 5;
Value 2; Value 5;
Value 4;

Other separators can be used or BR() instead of separator characters to list return values on separate lines, such as:

Value 1
Value 4
Value 5