ROE/ROA after asset impairments

In the first year, both assets and income fall by the same amount (eg. if you write down a $10,000 asset, then you remove this from assets, and also pass the impairment through the income statement as an expense).

So assume your net income was $20,000, your assets were $110,000, and your equity is $60,000. Pre-write down it would be as follows:
ROA = $20,000 / $110,000 = 18.2%
ROE = $20,000 / $60,000 = 33.3%

Post-write down, net income would be $10,000 (as you pass the $10,000 additional expense), assets would be $100,000 (as you wrote down the asset of $10,000), and equity would be $50,000 (as retained earnings would fall as a result of the drop in net income from $20,000 to $10,000). So now:
ROA = $10,000 / $100,000 = 10.0%
ROE = $10,000 / $50,000 = 20.0%

So in the first year ROA and ROE are both lower.

@mattjuniper, thank you so much for your explanation. The net income would decrease by a little less than 10,000 I think, because wouldn’t we have to add back the tax savings?

@shantala true, but in his question it specifically stated to ignore tax effects 😉

Heee! How could I have missed that! :-S

Correction: of course, ROE>1 is less improbable than ROA>1, but it doesn’t change the point.

Strictly speaking, it is not always true. If your ratio>1 (which is rare, but theoretically possible), then it will go up. e.g. E=300, A=200, ROA=1.5.
If you write down 100 worth of assets, new ROA is 200/100=2.0. Same for equity, although ROE>1 is even more improbable.

For the purposes of the exam, “most likely” these ratios will go down.

Sorry ignore that last sentence, I just realised I was talking bollox. The first part still stands though.

@nsker I’m not quite sure what you mean.

ROA is (net profit)/(assets)
ROE is (net profit)/(equity)

Without the net profit figure you cannot calculate the ratios. However, even in your scenario of E=300 and A=200, if 100 was written off then E=200 and A=100.

Yes, if net profit was higher than equity or assets then it would lead to a higher number, but you would be starting from a negative equity position so you could argue that ROE is infinite as equity cannot be less than 0 for a limited company.