This post is a question for anyone that can help me answer
it. I no longer have access to
professors, colleagues, staff, teaching assistants etc. so I'm not sure how to
get at this and while I've been asking around I still can't figure it out
myself yet. The money machine metaphor
is a cover for dividend investing in
retirement but since the word dividend can trigger some people I'm hiding that
word for now.
The Machine.
Let's say I buy two money machines for $100 each. The machine itself is basically free but
there is $100 inside each. Each year the
money machine prints a dollar. One machine prints it and stores it inside while the other
machine prints it out and I put it in my pocket.
At the end of N years I get to open each machine and keep whatever I still
have a claim to plus whatever I have in my pocket at which point the machine is
broken and worthless.
Each year, I forgot to mention, it costs me $1 in
electricity to run the machine. At the
beginning of year 1 my two machines are each worth $100. At the end of year 1 each are worth $101 if
you include the dollar in my pocket. If electricity were free, both would be
worth $102 at the end of year 2 but in year 1 through N I have to pay for my
electricity. I pay for machine 2's electricity with the dollar it printed. For machine 1, I sell to my neighbor
a fractional share of the machine worth a dollar and I use that to pay for the
electricity it uses. So far my money
machines, like my children, are loved equally. Both have created a dollar of
value I can use.
The Question.
Where am I going wrong on this? Am I naively mis-modeling? Economic
and finance theory and an awful lot of papers and articles are pretty insistent
that I should be indifferent between the machines where here I clearly love machine 1 less than machine 2 (all else being equal).
My best guess is that the difference in value between the two machines in
any given year other than year 1 is something like
[1]
where S0 is original shares owned at the outset, Sn gets lower due to consumption selling and D0 is the original claim on the dividend (I mean money-machine output) but I might be wrong here. I'm not really a math guy.
Making it More Real?
Also, to properly carry the metaphor I should probably make
machine 1 treat the retained dollar worse than I would, maybe squandering some
of it on something going on inside the machine I can't see or control that has
no value to me. In addition, once the town I live in sees me making dollars
from my machines they will want a piece of that, a little different for each
machine, to help pay for the mayor's pension because he keeps me safe from
marauding neighbors even though the $100 I used to buy each machine used to be $200 before the mayor took
some of that, too.
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Update - 2/12/2017 Link to "Two Responses to My Money Machine Question"
Links
-----------------------------------------
The Dividend Disconnect, Hartzmark and Solomon, UofC and USC.
Episode #28: “There is Literally No Logical Reason for
Anyone to Have a Preference for Dividends” mebfaber.com
notes
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[1] I probably got the notation wrong, too. It's supposed to be the sum of the results at each n along the way after year 1. I'll ask my daughter again to write it for me. Also I haven't figured out how year 1 works into all of this since the Portf values of the two "machines" are equal in year 1. Whatever, the general question still stands...
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