Like similar questions I've answered previously (How much does a website cost? or How much does an ecommerce website cost?), the answer to how much you'll spend developing a mobile app comes with a huge level of variance. There are a number of determining factors to think about, and I'll try to touch on as many as I can here to give you a good starting point when shopping for mobile app development services.
The first question is how feature-rich does your mobile application need to be? A simple, stand-alone app (these pretty much don't exist anymore - it's rarely worth building an application without some level of connectivity these days) that only needs to run on one operating system (usually either iPhone or Android) will obviously cost you far less than an app that needs to run on iOS and Android (and potentially others like Windows Phone), sync data to and from a server, and offer other advanced functionality like digital advertising, integration with the phone's native features (camera, calendar, contacts, etc.), or payment processing.
The second question is whether or not a so-called "budget" approach to app development will work for you. There are ways to build cross-platform apps these days that aren't as costly as full-blown native apps, but they come with their fair share of disadvantages, namely in performance and scalability.
A simple way to think about it is this: If you wanted to buy a car and realized you had the option to spend $35,000 or $5,000, your choice would depend on your intended usage. The $5,000 car might not be reliable enough to take on a long road trip but if you just want something to get you back and forth to the train station and you have a backup in the event it breaks down on you, it might be a great way for you to save some money and get only the functionality you need. Software is no different. Quality, reliability, and additionaly features come at a cost, but that cost is not always 100% necessary.
Also similar to buying a car, all mobile app development projects come with a minimum you're going to need to spend to get something that functions at all. You can't even buy a Fiat for less than $15,000, so you know when you go shopping for a new ride, that's your starting price range. Unlike buying a car, an app isn't a tangible good. You can't hold it and feel it and drive it around, so sometimes it's difficult for a lot of people to understand why app development and software engineering costs as much as it does.
To that end, that $15,000 number isn't a bad reference point for an absolute minimum viable product in the mobile app development world (this is a bit on the low side but you could likely get a small cross-platform app done at that price). A more realistic number for a small app with a small feature set that needs to perform well on both Android and iPhone devices would be closer to the $35,000 - $50,000 range for your first release. If you're building the next Twitter or Instagram, your costs will (and absolutely should) exceed the $250,000 mark, and more likely would be in the $500,000 - $750,000 range to get your first release out the door.
If you'd like a better understanding of where those numbers come from, think about it this way. The average salary across the US for a software engineer with 4-6 year's experience is about $100,000 / year. Add in benefits, rent, utilities, hardware, software, etc. and the cost of that employee to be able to build anything is at least $150,000. Assuming that person works 47 weeks out of the year (conservative with the benefits needed to secure quality engineers these days), they cost about $3200 / week. A small, well-built, native mobile app for both iPhone and Android (with a server component) should take 2 or 3 of these guys (or girls!) anywhere from 1 - 2 months to deliver. That means the raw costs of development would be somewhere between $25,000 and $76,800.
From there, it's important to remember your ongoing costs can be significant as well. Most apps require maintenance on iOS and Android, as well as the server component (which itself requires power, storage, bandwidth, CPU cycles, etc.). These costs will increase as your app scales. The more people that download and use your app, the greater the load on your server(s), the more devices and users you need to provide with support ...
Don't forget one of your largest costs either: Customer acquisition. This isn't Field of Dreams; that whole "If you build it, they will come" thing only works in the movies. Here it's more like, "if you build it, you better spend at least twice as much time and/or money trying to get people to use it." If you're an existing business with a good line of communication to your customers and your app is an extension of that current business, you at least have a leg up in this area, but you'll still need to spend time and money getting your customers to use it.
Unlike most firms, we actually do consider equity positions in new business ventures, but even in those rare circumstances that we believe in the idea enough to go that route, there's still a fairly substantial financial component that's unavoidable. (As a side note, feel free to contact me if you think you want to go that route, I'm always willing to listen to a pitch!).