1. Candle goes out
2. Paper used to carry fire from neighboring candle
3. Paper fails to light wick, but falls to side of glass holder and becomes a new wick
4. After 10 minutes, side of glass holder heats unevenly enough to crack

A basket of investments available to a manager, who has $X to invest and wants to maximize NPV. The investments are represented in the form of completely certain cashflows. What is the optimal choice?

Since NPVs add linearly, you want to pick the cashflows with the highest NPVs. What restricts you from picking all the investments?

Well, the restriction is that at no point in time should your total sum in cash be less than zero.

So there, given a set of cash flows, it's a discrete math problem of picking the set of cash flows that form the largest NPV, but do not run the initial investment sum below zero at any time.

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In reality, knowledge of investments doesn't come in the form of well-defined cash flows--but this is some basic theory which should be known by anyone who needs to think with these terms. Know what they mean!

Where is return on assets in all this? The type of decision making that ROA enables invokes the existence of options  as implied by the one cashflow whose ROA is being examined (i.e., the ability to acquire more of the cashflow with the same profile, but starting at later times, or the ability to sell the asset for some fixed linearly-depreciated amount of its purchase price).

Without considering the optionality of cutting off a cash flow or growing similar profile cash flows using lessons learned for the first one, measures like return on assets (and the income statement view of investment) are meaningless. Refer to the previous post for more information.

Analysis by income statements imply a specific structure of optionality, i.e., the ability to add more assets to get more return in a certain ratio. This is why certain line items are marked as one-time expenses / writedowns--they are there to maintain the optionality structure being communicated. When choosing between different  investments, using the NPV view vs. the ROA view depends on how unique of an opportunity the investment entails and what other possibilities the single cashflow implies the existence of.

A business buys assets and using those assets to convert less valuable input into more valuable output.

A business can do one of three things with any given asset:

1. Continue the business as-is and making profit at the usual rate, but allowing assets to run down without replacing them
2. Buying more assets in order to grow / be able to convert more input to output each day, or to maintain the current asset level
3. Selling assets

When you compare options 1 and 2, what you want to understand is how much it would cost you to grow your business or to replace the assets that are degrading away. This is often approximated with the book value of your assets, and that approximation can be improved by adjusting for inflation and otherwise actually thinking about how much you can buy new assets for (the asking price). You compare this to the gross margin you get from utilizing the assets, or the ROA (return on assets), and that is in turn compared to the cost of capital.

If ROA is very low, you then think about selling the asset, and are comparing options 1 and 3. Instead of considering the replacement value of the asset you now consider the sale value (the bid price) of the asset--if the margin divided by the sale value is lower than the cost of capital, you would choose to sell the asset.

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Considering all this, then, what is the difference between an unprofitable company posting a low return on assets compared to posting a write-down? (In the former, you are using a large denominator with a small numerator, while in the latter you are incurring a one-time loss followed by a higher profit level.)

The difference comes in when you consider what use those book values would be put to in the future. The book value's primary function is as a proxy to replacement or sale value, and so if the assets in question can be bought for less they should be written down, and if they can be sold for more money they should be revalued upwards.

For example, a company that finds out it had overpaid 50% for some machinery it bought should write down that machinery, because that then gives the right signal with regard to whether it should expand or not, i.e., it should show off its ability to use cheaper fixed capital input to generate a given level of gross margin.

Writedowns are used to calibrate decision making and there is a definite correct way to do them!