$24 for Manhattan a Good Deal? The Finance Perspective

You may have read in history books about how native Americans 'sold' the island of Manhattan for $24 dollars worth of trinkets and how that was a lousy deal. Some writers have tried to rationalize (with deductive reasoning) how this was a good deal.

Here is the finance perspective (with facts taken at face value):

Current estimated* value of Manhattan: $8 Trillion
Initial investment: $24
Investment year: 1626
Current year: 2009
Compounding periods: 383 periods (years)
Compounding rate: Between 4% (considered risk-free - proxy for this is US T-Bill) to 8% (year over year average equity market return)

Considering that financial theory assumes that these principals should hold especially in the long run, if they don't hold for this example (predating the existence and origin of the country itself - 1776) it won't hold for anything!

To calculate the Net Present Value of $24 in 1626 in today's dollars using the two different rates, the formula is:

NPV = Initial Investment * (1 + Compounding rate) ^ Compounding periods

at 4% (RFR, beta = 0) we get
NPV = $24 * (1.04) ^ 383
= $80,164,150
= $80 Billion (bad deal)

at 8% (equity market rate, beta = 1) we get
NPV = $24 * (1.08) ^ 383
= $1.51883E+14
= $151 Trillion (GREAT deal)

So obviously, the implied IRR for this project is between the RFR and the equity market expected rate of return. I think the native Americans would have needed a diversified portfolio with at least some asset allocation in equity.

If only there was a good stock market that they had access to in 1626. They could have bought back the island and then some! This just goes to show, for all the money and advice in the world, the one thing you can't buy is time... and compounding.

* There is a more detailed description of some of the assumptions used here. While this calculation is quite good (especially the cost estimate of Manhattan which I use), I would criticize the use of monthly compounding as I think that unfairly inflates the rate of growth.