This is possible with the Subscription app, without using the Rental app.

Workflow:

On a Sales Order, add the monthly charge on the first line and the leased machine on the second line (with no price charged to the Customer):

You can then generate the first Invoice showing both lines, and all subsequent Invoices are generated based on the Subscription app.

When the Sales Order is confirmed, the following related documents are created:

• a Manufacturing Order for “Machine (Leased)”
• a Purchase Order for “Machine (New)”
• a Subscription for “Leasing Charge (Monthly)”
• a Delivery Order for “Machine (Leased)”

Note: If you already have any new machines in stock, you won’t get the Purchase Order until you need to reorder.

Once you have received the new machine and recorded the Bill, your Balance Sheet will show the value of your Current Asset and the Liability you have to the Vendor:

Once you have completed the Manufacturing Order, your Balance Sheet will show that your Current Asset has been converted into a Fixed Asset:

Your Income Statement shows the income from the monthly charge, with no income due to the delivery of the machine:

The last step is to create the Asset to start depreciating it. Because we are using the Rental Assets account as a clearing account on the Customer Invoice, we only want to do for debits made using the Assets Journal. You would then select the debit and click CREATE ASSET:

You then have the option to select an existing Asset Model to automate the creation of your depreciation schedule. The Asset will be linked to the Delivery Order, which is itself linked to the Sales Order, so you have traceability to each transaction. 

You can look at the Products in the Customers location to see how many leased machines have not been returned.

If you unhide the Unit Price field on the picking, when returning the leased machine, you can enter the remaining book value of the machine, so that it will be converted into a current asset at the correct residual value. 

The full list of GL Activity at the end of the process (apart from the depreciation entries) is:

Depreciation entries would regularly credit the Rental Assets account and debit the Depreciation Expense account at the time you decide to start depreciating (normally the same day the Delivery to the Customer ships) – depending on the schedule.

Configuration:

Create the following Product Categories:

NEW EQUIPMENT

LEASED EQUIPMENT:

LEASING SERVICES:

Create a product “Machine (New)” inside the New Equipment Category and a product “Machine (Leased)” in the Leased Equipment Category.

Create a recurring Service product “Leasing Charge (Monthly)” linked to a monthly subscription template to represent the lease payments. This would be inside the Leasing Services Category.

Create a Bill of Materials that builds the leased machine by consuming a new machine.

Setup replenishment rules that match the on hand stock levels for your new machine (Preferred Route is Buy with a Vendor set) and with 0 on hand quantity for your leased machine (Preferred Route is Manufacture). 

Create Asset Models, but do not link them to the Rental Assets account (so you don’t get any automatically created rental assets and can do this manually).

The accounts on the Leased Equipment services are very important as they dictate the logic that coverts current assets to fixed assets, then rental assets, then back again when the items are returned.

I realise that the available quantities of rental products are updated with each rental move. In that way the rental module is indeed linked to the inventory module. But what I need are picking orders to be created after confirming a rental order, and also even the receipt order to process the return. Those picking, packing, delivery and receipt orders do not exist when processing rental orders. The 'pick-up' & 'returned' knobs in rental orders themselves are not sufficient.

hi Filip, in previous versions it was necessary to configure the nice Rays solution or customize.
Fortunately in version 17, a new feature was introduced:

I guess i come here a little late, but if it helps: in version 17 Odoo has an option in Setting > Rental that you can just check the box to activate inventory for rentals.

"Rental Transfers: Activate to use stock deliveries and receipts for rental orders"

A bit old but it took me quite a bit to figure out, so if anyone will try to solve this in future..

I managed to do that but I will have to be very careful with testing during updates. What you basically need is to understand differences between addons\sale_stock\models\sale_order.py and addons\sale_stock_renting\models\sale_rental.py and perform proper modification on rental side. You can take most of the necessary code from sales file.

Then you will have to generate return straight after delivery is created. It needs a bit of coding too as it is prohibited by default (with understandable logic). Everything works fine afterwards, together with inventory forecast, etc.

Keep on your mind that this is definitely not a supported solution.

You can use Rental module for product rental service and sale for selling.

Rental module is linked with inventory and accounting.