CFA CFA Level 1 How to find average book value?

How to find average book value?

Topic Resolution: Resolved
• Author
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• fishandgips
Participant
• FRM Part 1
9

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?

• 1

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!

• fishandgips
Participant
• FRM Part 1
1

Amazing, thanks. That makes perfect sense.

• 0

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:

$=\frac{\left(15,000+25,000+20,000+10,000\right)/4}{\left(50,000+15,000\right)/2}\phantom{\rule{0ex}{0ex}}=\frac{17,500}{32,500}\phantom{\rule{0ex}{0ex}}=54%$

• fishandgips
Participant
• FRM Part 1
0

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?