Tangible book value per share is an adjusted alternative to NAV per share. However, it only adjusts for intangible assets and more extensive adjustments, such as marking asset values to market, may be necessary for some sectors. It is simple to define:
tangible common equity ÷ number of shares in issue
For valuation purposes use:
price ÷ tangible book value per share
The reasons for applying these adjustments is much the same as adjusting profits with measures such as EBITA and EBITDA. It adjusts numbers whose significance is a result of accounting convention and history, or that are uncertain. Intangibles are completely removed (in most cases they would not have arisen if the company has a different history (e.g. mergers) or past performance (deferred tax assets).
Marking to market replaces values based on depreciation and amortisation with market values. This only really makes sense when there is a market in the assets being valued. This is often the case for the sectors for which NAV is used (property, investment trusts etc.).