Obtaining book value (purchase cost) of assets from fair value accounts


It is possible to find the book value (purchase cost) of an investment firm’s assets if the firm uses historical cost accounting as follows:

bookValue = historicalNetAssetValue - accumulatedDepreciation

I am wondering if there is a formula to retrieve the purchase cost of a firm’s assets if the firm uses fair value accounting? I was initially thinking along the following lines:

bookValue = fairNetAssetValue - acccumulatedUnrealizedGainsLosses

where acccumulatedUnrealizedGainsLosses is the running sum of unrealized gains and losses reported in the firm’s income statement over a period of time.

Does this make sense? Can the formula be improved?

Thanks for any pointers.

If it’s carried at fair value, then the book value is the fair value.

Thanks for the reply but the fair value is the mark-to-market value not the historical cost value.

I guess what I am asking is, given a fair value of net assets, is it possible to back out the historical cost value of net assets by adjusting the fair value in some way?

BTW there is a typo in the original post:
bookValue = netHistoricalAssetValue - accumulatedDepreciation
should be
bookValue = netHistoricalAssetValue + accumulatedDepreciation

That’s true.

Book value also is not the historical cost value.

Book value is the net carrying value today.

There was no typo in your original equation. This is correct:

Book value is the current, net value. Historical value is the price originally paid.

Thanks again for the reply and for your patience.

I am reading an article “What is Book Value vs Fair Value?” on the CorporateFinanceInstitute which states:
“Book value (also known as carrying value or net asset value is the value of an asset that is recognized on the balance sheet. It is determined as the cost paid for acquiring an asset minus any depreciation, amortization, or impairment costs applicable to the asset. The concept of book value arises from the practice of recording the assets on the balance sheet at its historical cost.”

I want to find the cost paid for acquring the asset if the firm uses fair value accounting. Is there a way to do that?

Ah . . . now we’re getting somewhere!

Yes, you can get from book value to original cost. You need to add back all of the unrealized gains/losses for that asset. In practice, a company might have a balance sheet account that accumulates those, much like an Accumulated Depreciation account.

Great, so after some further research on GAAP fair value accounting, I have this formula for determining original cost of assets of an investmet company:

originalCost = bookValue-unrealizedGainLossLess12Month-otherComprehensiveIncome

where bookValue is the fair value of assets reported on the balance sheet, unrealizedGainLossLess12Month are unrealized gains and losses are for tradeable debt and equity (securities you plan to sell within 12 months) reported on the income statement. OtherComprehensiveIncome includes unrealized gains and losses on securities available for sale, which is accumulated on a separate line of the balance sheet.

Does this look right?