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.

—

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 optionsÂ 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 differentÂ 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.