Will - you've asked a few different questions here, so let me try to go through them one by one.
1. Book value
Quite simply, book value is the equity in a business. It is the value of the total assets minus the total liabilities.
If you start a business tomorrow and throw in $500 then the book value is $500.
This figure would be the same if you took a loan of $1,000 as the assets would increase to $1,500 and the liabilities would increase too. The assets minus the liabilities would still be $500
What relevance does book value have?
It effectively signals the value to shareholders if you were to sell of all the assets in the business, pay off the debts and hand the money back to shareholders.
Of course, that is hugely oversimplifying it as, in reality, the accounting of most business is treated as a "going concern" which means trading from the business is expected to carry on for the foreseeable future.
Not all assets are "tangible" and this is accounted for on the asset side of the balance sheet by "intangible assets". Intangible assets can include goodwill (acquisition of a company at a premium to assets), copyrights, or trademarks.
Some investors like to use this metric to help them value companies. This was probably more relevant in the days when companies owned a lot of fixed (tangible) assets such as property, plant, and equipment.
It's not as useful with companies that create a lot of intangible assets such as service companies or technology companies. Many of the companies in these sectors can operate with very little (or no) equity capital.
In the modern age, this metric is probably more useful in sectors such as banking, property or insurance.
For a full definition of book value from a technical perspective, click here.
NAV stands for "Net Asset Value" and is similar to book value in that it is the value of all the assets minus the liabilities.
The NAV is usually used to tell you the value of the underlying value of the securities in a mutual fund or in an ETF. If you divide the NAV by the number of shares outstanding then you will get the Net Asset Value per share.
An open ended fund will always trade at (or extremely close) to the NAV. This is because an open ended fund is not traded between buyers and sellers but shares are issued when an investor purchases the fund or redeemed when he or she withdraws their investment.
If the fund is "a closed end fund" then investors trade shares in the fund between each other in a market. Therefore the value is determined by the level buyers and sellers agree to rather than the NAV directly.
Often this means closed end funds do not trade at their NAV value. If they trade below the NAV then they trade at a "discount" and if they trade above then they trade at a "premium".
NAV isn't just used for funds. It is frequently used for property companies such as REITS (real estate investment trusts). NAV can be used for any normal business.
NAV is effectively the same as book value for a business which (as described above) is the assets - liabilities.
There is a major difference between calculating the NAV for a fund against calculating it for a business in that for a business, assets are on the balance sheet at HISTORICAL cost or AMORTIZED cost where as a fund will usually use mark to market accounting.
3. Dodgy accounting
Let's hope this is rare! Dodgy accounting does happen but thankfully cases of outright fraud are rare. There is little you can do if you are deliberately deceived but if something does look unusual or doesn't add up (like if earnings are never turning into cash) then it is best to avoid that investment.
Unfortunately book value can be reduced in very legal ways by impairments/writedowns/losses etc. These impairments usually come from a deterioration in the earning power of the asset. Losses will also eat away at the equity of the business.
It is always important to remember the value of liabilities can't be written down (if the company is to operate as a going concern) whereas some assets can. An asset such as cash can't be written down because $100 is simply $100. An asset such as goodwill, though, involves a judgement on its value and can indeed be written down which will lower the result of the assets - liabilities calculation.
Importantly, under GAAP and IFRS accounting rules, goodwill (and some other assets) can't be written UP in value. So if the earning power of an asset increases over time then the book value could be understating the true value of the company. This is why so many companies trade well above their a lot higher on the stock market now.
The reality is that book value is only of limited use to the investor. It is far more important to try and understand the earning power of the company you are analyzing and how sustainable that earning power is. To me, earnings, cash flow, and the strength of the balance sheet are far more important in assessing a suitable investment.