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FedEx and DHL are horribly expensive.  I've ordered things via regular mail from North America and had a variety of experiences.  Sometimes things needed customs clearance - forms, money and a long drive to accomplish.  Sometimes they just show up at my door.
Mail delivery (or lack thereof) is not what you'd be used to - better to send to your work where there will probably be someone who knows what to do and how to get it to you, rather than try to send to your apartment where the building cleaner or maintenance person will probably receive it for you and try to get it to you at some point.

I think there are some companies that can deal with that problem cheaper than Fedex and DHL. As I remember,: bidmongol.com is not bad but it is only from the US. You can find out the information from the website about the prices and other things that you need to know.

First, there are no mail deliveries in Mongolia. All mail is sent to a post office. You have to include the recipient's phone number because the Mongolian post office will phone the recipient to advise he/she has mail...and they will charge a small fee when the mail is picked up.
FedEx and UPS do not ship to post office addresses. I think FedEx provides some service to Mongolia via another airline. Not sure where the connection is. And, the shipment will go only to the capital, Ulaanbataar.
I ship frequently to Mongolia. My daughter lives there. I send the shipments to BidMongol Express in California. They forward shipments onward either via air or ocean. You have to tell them which you want. Air, of course, is much more expensive. You do not pay BidMongol. The recipient in Mongolia pays the transportation fee. Shipments go to Ulaanbataar, but they will forward to final destnation, usually by taxi. Thus far we have sent many shipments with 100% reliability. If you want more info about them, contact their manager, Ogi Erdenebat. Email ogi@bidmongol.com.