Profit vs. patience

Boston Globe article "Profit vs. patience" (February 28th, 2010) writes on the possibility that myopic investors might make long-term biotech investment difficult for farther-sighted individuals. Corrections fails to see this as a first-order concern.

“There’s really a nightmare scenario in which raiders come in and they flip the company to get the stock up,’’ Pisano said. “And you really could ruin a biotechnology company like that. On the other hand, if you have an investor with a long-term horizon like a Warren Buffett, that could help a company by holding the management accountable but giving them cover from some of the short-term market vagaries.’’

On its face, the quote sounds quite reasonable. However, in Correction's view, there are only two factors in this problem: profits, and time. Stock prices reflect the value of a company (more specifically, the marginal value of an additional portion of a firm's discounted revenue stream). Therefore, we take stock prices and future profits to be inextricably tied together. We conjecture this stylized fact as relatively robust.

One might imagine two plans for a company's future. The first is a "myopic" plan that extracts value quickly over a short amount of time. The second is a far-sighted plan that extracts a greater amount of value, but that is delayed over time. We display the revenue, or profits, of the two plans graphically below (click to enlarge). The first myopic plan is represented by the dotted red line. The second, farsighted plan is represented by the solid blue line. Each colored dot is the point at which total (undiscounted) profits are maximized, and when a firm would want to exit the market.



A more appropriate graphic might be to examine cumulative profits over time, rather than profits per period. This is displayed graphically below (click to enlarge). The red and blue dots represent the same concept: the time at which it is most advantageous for a firm to exit the market, assuming no discounting of profits.



With the above setup, Corrections suggests that further analysis of which plan to adopt is quite simple. Let us imagine the project above cost us .35, in terms of the diagram's units. Then in two periods the first plan would net us .5 extra units of currency, and the second plan would earn us about 1.7 units of currency in 6.8 units of time. The only question is what the rate of time preference is for return. This will be set by the market. If a project's rate of return is higher than the interest rate, then the project will be undertaken. If the project's rate of return is lower, then it is better to take money and invest it in something that does return the interest rate. We note the interest rates required to invest in each project below.

• The interest rate that makes us indifferent between saving and investing until the first project's maximum is 30.9% (this is the project's return from time zero until maximum).
• The interest that makes us indifferent between saving and investing until the second project's maximum is 27.0% (this is the project's return from time zero until maximum).
• The interest rate that makes us invest in the first project, and save those profits at the market rate, rather than undergo the second project until its maximum, is 28.8%.

Therefore, the decision that will be made concerning a firm is:

• If the interest rate is below 27%, then we will invest in the second project.
• If the interest rate is between 27% and 30.9%, then we will invest in the first project, then save our profits.
• If the interest rate is above 30.9%, then we will invest in no project.

There are several conclusions to draw from this. The first is that it is possible one should not maximize the profits they get out of a firm. Both options are viable, depending on the interest rate. Just because a firm is not living up to its full potential does not mean that money is not. If other projects earn a higher rate of return, then the profit-maximizing decision is to extract money quickly and then invest in other projects (here represented by the interest rate).

The second is that individual investor impatience should not matter. If one investor has an idiosyncratic shock to his discount rate, then this does not mean he should switch from a far-sighted project to a short-sighted one. The maximizing decision is never compared to an individual discount rate but to the interest rate. If the far-sighted project has a higher return than the interest rate, then anyone who is saving should be willing to invest in it--it has a higher return.

Corrections concludes that it is difficult to imagine a real issue arising because of impatience--the market appears too liquid for that. If one investor is impatient, then another person who is saving will be willing to pursue the profit-maximizing course.

Corrections suggests that what makes more sense is asymmetry in information about a company causing a knowledgeable investor to be unable to acquire the real net present value of his investment. This may in turn cause him to choose a "lesser" (but sooner) path.

Finally, Corrections notes that we have ridden roughshod across a few technicalities, especially as it concerns optimal stopping points if investment at the interest rate post-liquidation is possible. We suggest this does not change our qualitative conclusions, and would sacrifice pellucidity.