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How to find average book value?

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    • Avatar of fishandgipsfishandgips
      Participant
        • FRM Part 1
        09 Apr 2021 at 8:48 pm
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        I’m a bit confused with average book value when looking at accounting return on equity.

        It says in the notes that ROE is net income (available to common shares) divided by the total book value of equity (common shares), and that the book value can be the book value at the beginning of the period or the average book value.

        So if a question cites a book value across 4 years:

        • Year 1: USD 50
        • Year 2: USD 35
        • Year 3: USD 20
        • Year 4: USD 15

        The example seems to just take just Year 1 and 4 values, i.e. ( 50 + 15 ) / 2 = USD 32.5. Why don’t we take an average of all years? i.e. ( 50 + 35 + 20 + 15 ) / 4?

        gontata voted up
      • Avatar of Sophie MaconSophie Macon
        Keymaster
          10 Apr 2021 at 5:56 pm
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          The average book value takes the start and end book values because that are the transactional points, i.e. when you invested and when you divested.

          Just like purchasing a stock, your return depends on the value of the stock when you purchase it to when you sell it. What the value is in between these transactions can be interesting, but irrelevant to your return.

          Net profit is totally different – net profit for all years is relevant to your return calculation, because this is the return you get on your investment and available to common shares via e.g. dividends every year.

          Hope that helps!

        • Avatar of fishandgipsfishandgips
          Participant
            • FRM Part 1
            11 Apr 2021 at 1:29 pm
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            Amazing, thanks. That makes perfect sense.

          • Avatar of mikeymikey
            Moderator
              10 Apr 2021 at 7:44 am
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              Average accounting return is average net profit over average book value.

              Average book value is taken by the start and end of the period divided by 2 because it assumes the book value trends from the start value to the end value in a straight line.

              So expanding on your example, say across 4 years, profit and book value are:

              Year Net Profit Book Value
              1 $ 15,000 $ 50,000
              2 $ 25,000 $ 35,000
              3 $ 20,000 $ 20,000
              4 $ 10,000 $ 15,000

              Return on equity:

              equals fraction numerator begin display style left parenthesis 15 comma 000 plus 25 comma 000 plus 20 comma 000 plus 10 comma 000 right parenthesis divided by 4 end style over denominator begin display style left parenthesis 50 comma 000 plus 15 comma 000 right parenthesis divided by 2 end style end fraction equals fraction numerator 17 comma 500 over denominator 32 comma 500 end fraction equals 54 percent sign

            • Avatar of fishandgipsfishandgips
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                • FRM Part 1
                10 Apr 2021 at 1:02 pm
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                Thanks mikey, but this is exactly what I’m confused about. Why do we take the average of net profit across 4 years, but only take the start and end value of the book value?

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