When an investor invests in a start up company, the investor will also ask how do you estimate the company's market value. How do you calculate this value? Does it require some professional accountant to calculate it?
You're really going about it the wrong way. Sure, investors would like to have a set value for your company, but the fact is that, usually, nobody really has a good idea of what the company is worth. So, you put out a value based on what you think the size of the market is and how much of it you think you will capture. The investor will counter that the market is smaller than you think, and you won't capture as much of it as you think. Then, there's discussion back and forth, and you eventually end up with the investor agreeing to invest $X, for Y% of the company on a certain set of terms.
Why does it work like this? Because valuing a startup company is more of an art than a science. The problem is that you get nonsense when you apply traditional metrics like discounting cash flow, valuing patents by looking at comparables, etc... So, getting a good value involves a lot of research and guesswork. The further along you go, the more defined the value is. And, if you have one investor who assigned a value, that's a decent clue to the next investor.
Now, if you actually want a more precise answer, don't go to an accountant -- they don't generally have the skillset to do the analysis. Instead, you want to find somebody who does startup valuations for a living. Luckily, since 2007, there's been a growth in the number of people who do have this skillset, thanks to rules under Section 409A of the tax code, which require startup options to be priced at the fair market value of the underlying stock. (Google "409A valuations" to find people who do this.) Their numbers may not be any better than what you come up with yourself, but at least they have the sheen of being arrived at independently and methodically.
market value is a term generally associated with publicly traded companies. You look the stock price up in the newspaper and multiply it by the number of shares outstanding. As you can well imagine, for an actively traded stock this a reasonably good number.
For a company whose stock has no market, that is nobody is buying or selling any stock, the concept of "market value" really has no meaning since there is no market. In such a case the "market value" is what somebody is willing to pay you for the company (thus establishing the market if you choose to accept the offer). Only a valid offer that is accepted would establish the market value. So for example if someone offers you $10 for your company that is not the market value since you would probably think the value should be much higher. Similarly just because you think your company is wotrth a billion dollars does not make it so until someone is willing to pay you that is cash.