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Comment by avz | Hacker News Reader

> The Fed has held interest rates at 0 (negative, real terms) which makes all cash flows effectively infinite net present value.

No, it doesn't. Net present value (NPV) of future cashflows is defined [1] as the sum over time periods of the ratio of the cashflow in the k-th period to one plus the discount rate raised to the power of k:

    NPV = sum_k r_k / (1 + i)^k

where i is the discount rate. Note that we are dividing by (1+i)^k, not by i^k. Thus, when i=0 the formula above simplifies to

    NPV = sum_k r_k

and NPV is just the sum of all future cashflows. No infinity enters the picture.

[1]: https://www.investopedia.com/terms/n/npv.asp

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thanks

right, so the net present value of, say, a rental unit (or any ongoing productive investment) is the sum of an infinite number of payments which, if my math is correct here, is infinity (regardless of the recurring payment amount)

of course there is a risk discount as well, which, as I mentioned on a sibling comment, has been removed in many cases by the fed backstopping a lot of investments

there's a reason we don't see actual infinite prices, after all

my general point is that as interest rates get very low, npv gets really whippy and I expect that to be what we see going forward

just a guess and I'm not an economist, although experience suggests that's a point in my favor

No, it still isn't infinite. Under reasonable assumptions the series is actually bounded from above by a geometric series [1] which is famous for having a finite sum when ratio is <1 [2]. In this case, the ratio r=1/(1+i) is indeed <1. More importantly, no asset exists an infinite amount of time, so the sum is actually finite anyway.

Perhaps we should dispose with all the math though as it should be intuitively clear that if we discount future cashflows at zero rate, i.e. if we do not discount future cashflows, then their present value should be equal to the future value. After all, discounting just means that you value future money less than today's money. If you don't discount, you value both the same, so whatever formula for discounting you use it must be true that plugging in zero rate yields NPV equal to the sum of future cashflows.

Agreed about risk discount. Perhaps what you mean by "whippy" is that as the risk-free interest rate goes to zero NPV becomes increasingly sensitive to the risk discount.

[1]: https://en.wikipedia.org/wiki/Geometric_series

[2]: See [1]. Also, as an example, recall that 1+1/2+1/4+1/8+...=2.

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