Sunday, November 24, 2013

Assets in Perpetuity

As you know, our primary focus in the Econ 567 course has been understanding prices .  We know that prices are really just rationing devices.  All goods are "scarce" and therefore we need some allocation mechanism to ration these scarce goods.

In this post, lets look at how we price assets in perpetuity.  Imagine you got in your car and drove out into the country into prime Illinois farmland with the goal of buying an acre of corn ground.  Suppose you stop at a farm and ask the farmer how much profit he made on an acre of land.  He truthfully reveals "$200 is about the average".  Now,  if you ask him if you could buy the land from him for, say, $220, would he sell it?  Of course not.  While that appears to be better than the $200 profit, that profit is just one year's net.  The corn ground will turn a profit year after year.

In fact, the way the farmer would look at this is to compute the discounted present value (DPV) of a stream of profits over time.  We use DPV because we know that $100 today is worth less than $100 a year from now.  Indeed, when we compute Present Value we are simply asking "how much would $100 in, say, 1 year be worth today?"  Well, if you put $98.04 in the bank today, at 2% interest, it would be exactly $100 in 365 days.  We compute this by saying "$100 a year from now is equal to $100/(1+r) where r is the interest rate."  Likewise, the DPV of $100 in two years from now would be computed by dividing $100 by (1+r) for the second year and (1+r) again for the first year;  that is we compute this as ($100/(1+r)^2).  At an interest rate of 2%, this would be $96.12.  Said differently, if you put $96.12 in a bank today, earning 2% interest, it would be worth $100 exactly 2 years from now.

So, our farmer would compute the Present Value of keeping his land by estimating his profits in year 1, 2, 3, ... out to N with each year divided by (1+r)^t  where t is the year number.  This would be his estimate of what the long run stream of profits to this acre would be worth in today's values.

Now consider the problem of pricing shares of stock.  These pieces of paper, certificates of ownership of corporations, trade hands more than a billion times a day.  How are the prices of these shares determined? Watch this video.

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