# The Time Value of Money

There is an apocryphal interview question I’ve come across several times:

Would you prefer to have a dollar today or a dollar one year from now?

I do technical interviews for software engineers. Hence, this isn’t a question I would typically ask candidates (even if at times I wish it was – it could be interesting to see how candidates react!). Although it naturally seems like it would fit in a financial context, it seems too easy to be used as a serious question.

Anyway, the answer I’d go for is “today”, because I could take the dollar and put it in the bank to earn interest. In practice, I’d invest the dollar. Furthermore, inflation is more likely to be positive than not, and this eats away at the value of the dollar. The idea that getting the dollar now is better is known as the time value of money. That said, I can also see legitimate cases why one might argue for “one year from now” – mainly centering around the idea that custody of the dollar is taken care of (assuming we allow this to be assumed!).

Conversely, if you asked me a slightly different question:

Would you prefer to have a dollar today or \$100 one year from now?

I would probably go for the hundred dollars, because my investments are very unlikely to increase hundred-fold (unless we have hyperinflation) in a year. As before, there are legitimate cases why one might go against the grain of financial theory – cash flow issues, in particular.

If the amount is reduced a fair bit, such as to \$1.09 (for me at least), then the decision gets more difficult. Using some kind of intermediate value theorem, there should be some value of r for which I’m indifferent to this question:

Would you prefer to have a dollar today or \$(1 + r) of today’s dollars one year from now?

The conventional theory here is that if I got the dollar today, invested it for a year, and then have (1 + r) of today’s dollars, then I should be indifferent. I’m not sure I agree in practice. This is mainly because of the aforementioned cash flow issues. If 6 months on I find that I need the dollar, I can take it out and still keep the partial returns. You would need to give me an illiquidity premium. (Of course, I’ve assumed here that I invest in liquid securities.)

There is also another shortcoming of this question. The size of the capital relative to my net worth would also affect my answer. Rather interestingly, I think I would take the money early for small or large amounts, but consider waiting for medium-sized ones.

For small amounts, I would need to remember that a capital inflow is coming in a year’s time. The cost of tracking this could exceed the “premium” I derive from waiting. Conversely, for massive amounts, we start delving into the realm of diminishing marginal utility – if I could pick between \$1 trillion today and \$1.1 trillion this time next year, I’m pretty sure I’d pick the former.

Up to this point, we’ve also avoided what’s known as counterparty risk. The person offering the money might become insolvent within the year. This would bias people towards taking the money now, and is reminiscent of a well-known proverb (“a bird in the hand is worth two in the bush”).

Nonetheless, this practice of time discounting is useful when trying to assess the value of investments or securities, such as annuities or structured products. It is also frequently used in discounted cash-flow analyses, which are useful for determining if business ventures are likely to be profitable. I have not had to put this skill into practice yet, though (well, apart from the Computational Finance exam I did at Imperial).

In theory, these concepts should be applicable to other resources or assets which (1) appreciate over time, and (2) can accumulate in value without substantial effort. That said, I’ve struggled to think of assets outside of the standard “investment” universe (stocks, bonds, real-estate, commodities, private equity, collectibles?) that satisfy both criteria.

I did think of social capital (i.e. friendships, reputations) and human capital (for me, software development and other skills). They don’t seem to satisfy (2), though it could be argued that (2) is too strict. For example, by going about my daily routine, I already (hopefully) absorb more and better dev practices. Similarly, one needs to (well, should) do one’s homework regarding asset allocation and understanding one’s investments. Also, in practice to maintain one’s asset allocation one needs to rebalance a portfolio.