Land Prices, function of rents?

[Malachi]

Ok, the price of all capital goods, not just land, is a derivative of the amount of money you can make by renting it out. Can someone put this in a formula for me?

Mises Daily | Mises Institute

Suppose that sharecroppers calculate that an additional acre of Farmer Smith’s land would allow them to increase their annual earnings by $250. If we have open competition (i.e., no government restrictions), then in equilibrium we would expect that the sharecroppers would pay rent of (nearly) $250 per acre per year for the use of Farmer Smith’s land.

Now suppose that instead of renting out his land, Farmer Smith wants to sell it outright. How much could he expect to get for it?

In the baseline case of certainty about the future, the answer is that Smith would capitalize the present discounted value of all future rental payments accruing to the farmland. For example, suppose the farmland is expected to yield a perpetual annual flow of $250 rental payments. At a constant rate of interest of 5 percent, the market price of an acre of Smith’s land would therefore be $5,000. That’s how much Smith can ask for, and should receive, for selling off his land, at least in a world where everyone is certain about the land’s future earning power and the constant interest rate.

seriously? Multiply the rent by the interest rate?

Mises Daily | Mises Institute

peter schiff:

And I remember one time I went and there was a house for rent. I looked at it and the realtor was there. And, apparently, the person who was renting it out was an investor who just bought the place.

And I asked them what was the rent. I forget what it was. Maybe it was $4,000 a month, whatever it was for this place. And I knew, I said, “Well, what’d the guy pay for this? What’d he pay?” I said, “Well, how could he make any money renting it out to me? Isn’t this going to lose money? Doesn’t he have negative cash flow?”

He said, “Well, yeah, he loses a couple thousand dollars a month.” And I said to him, “But you recommended this as an investment?” He said, “Yeah.”

so at 1.5% interest rate that place was worth 600k? Am I missing something?

[Minarchist]

The idea is that the rent payments out in the future are less valuable than the rent paments nearer to the present, because of time-preference. To get the sale price, you add up all these rent payments. Eventually, at a certain point in the future, the rent payments have no value. Otherwise, the selling price of the capital good would be infinite. What you’re doing is discounting the rents out into the future progressively until they reach 0, and then adding them all up. The easy way to do this mathematically is to divide the rent by the interest rate. The time period of the rent has to match that of the interest rate. So, for example, annual rent and annual interest rate.

So given a pure interest rate of 5%, and a rent of $200, the sale price would be $4000.

You can see why this works by doing it mechnically. I’ll use much higher interest rate because otherwise it’ll take forever.

90% annual interest rate, annual rent of $100.

Year 1: $100

2: $10

3: $1

4: $.10

5: $.01

= $111.11~

100/.9=111.11~

[Smiling_Dave]

You’re missing that you don’t watch enough television.

That which is seen: http://www.tv.com/shows/this-old-house/

That which is not seen: http://www.tv.com/shows/this-old-farm/

[Zlatko]

This is what in finance is known as a perpetuity.

The concept is that the value of something is worth its future cash flows, each discounted by the interest rate. For an infinite cash flow, the value is deceptively easily calculated by the mentioned formula. The mathematical proof of the formula is more complex.

PV = CF / r

where
PV: Present Value
CF: Cash flow
r: discount rate

The value of the apartment in the second example would be 4000 / 0,015 = 266.666

Note that using the formula on capital goods is not strictly correct since no capital good lasts forever.

[abirkmanis]

then in equilibrium we would expect that the sharecroppers would pay rent of (nearly) $250 per acre per year for the use of Farmer Smith’s land.

Only if by “equilibrium” one means an economy without profit. Otherwise, rational sharecroppers will pay nearly $250 x (1-going profit rate). Opportunity costs ftw.

The main question was answered by Zlatko. You do not multiply by the interest rate, you divide by it.

[Malachi]

Well can I add in a part that accounts for capital depreciation? Would an increase in the discount rate account for this? Even if only theoretically?

also, can I apply this to “interest rates” that are derived from futures contracts? Will I get some goofy numbers or what?