Land as an Asset
for ECON 376 by Prof. Kilkenny
Our textbooks explain that the rent paid for a parcel of land in business or residential use will reflect the productivity of the soil (Ricardo), the proximity of the parcel to the market (vonThunen), and the proximity of the parcel to jobs and shopping, etc (Alonso). Freedom of entry or competition for land at each location drives output prices down, costs up, and land rents up, to the point that there are no more local profits:
Profit = PQ – CQ – tdQ –R = 0
Thus, rent is R = (P-C)Q – tdQ .
Where R is the rent (per unit area), P is the price received per unit output, Q is the output (per unit area), C is the unit cost of production, t is the cost of shipping one unit one unit distance, and d is the distance from the business to the destination point for the product. The equation is the bid rent function . It is a static analysis that summarizes the flow value of parcels at different distances during one period.
In words: land rents are higher where value-added is higher, or higher prices are paid for output, more subsidies are collected, there is higher productivity; lower costs of production, larger input subsidies; and lower transport costs or distance.
The graph below shows where farm land rents are relatively high. Farm land rents are higher in counties closer to the river (Clinton, Scott), in counties that have a lot of food and kindred processing activity (Carroll, Black Hawk, Keokuk) and along the interstates and the major rail routes. The lowest rental rates is where the soil is less productive (south central Iowa). There, yields are the lowest in the state: 117 bu/acre in the best acres in Wayne county compared to 145 bu/acre or more in Sioux, Carroll, or Buchanan counties.
[data source: Iowa State University Extension (2001) “Cash Rental Rates for Iowa.”]
An asset is a storage of value: an asset offers either a stream of flow values over time or a final value at a later date (or both).
If the future sale price (VT) of an asset exceeds the original purchase price (V0), the owner who sells captures a capital gain: where the capital gain rate = (VT-V0)/V0 .
Thus, land is an asset that provides the owner a flow of net revenues, rents, or saves them from having to pay rents to someone else; and it may also offer a capital gain.
If no-one expects the flow value of a parcel to increase (or decrease) over time, then the price someone would be willing to pay for a parcel reflects just the stream of rents over time:
DPV of rents, V = R + R/(1+i) + R/(1+i)2…= ∑t R/(1+i)t.
Because people can choose among various assets (saving accounts, bonds, stocks), and they’ll choose the assets that give them the best expected rates of return, given the riskiness and the liquidity (ease of conversion back into cash) of the alternatives, the expected rate of return “eRoR” on all assets move together over time. Denote that rate of return by the interest rate “i”. Use this interest rate to determine the discounted present value of current plus future rents.
Given the mathematical fact that ∑t 1/(1+i)t = 1/i for t approaching infinity, the equation above simplifies to show that the current value of a parcel that offers an unchanging flow rents over time is simply:
V = R/i
Thus, in this case a parcel’s price, V, is higher for higher rent parcels and lower for lower rent parcels. So, land prices reflect the same things that land rents reflect.
But if people expect the flow value of a parcel to rise later, then the price of the parcel will be expected to raise later too. If the parcel’s future price is expected to rise, then the owner not only expects to earn rents but also capital gains on the parcel. As with all assets, this expected future gain will cause the parcel’s value to rise today. Considering also expected capital gains, the value or sale price of a parcel is:
Vt = (R+eVt+1)/(1+i)
Note that instead of taking the trouble of calculating the exact discounted present value of the stream of changing future rents, which would necessarily entail making many guesses (“guesstimates”) about expected future rents and expected future capital gains, we rely simply on one guess. We assume that the expected future price, eVt+1, reflects all of the expected future changes in flow values. It won’t be exact, because neither buyers nor sellers can have perfect information about the future. But we can’t find better current information than that. The information about what a parcel or asset will really be worth later won’t be revealed to anyone until later.
The formula above makes it clear that the price of land as an asset also reflects expected future rents and opportunity cost of other assets (the target expected rate of return, eRoR, or i), infinitely into the future. The graph below shows how Iowa farmland values varied across counties in 2000 [data source: Iowa State University Extension (2002) 2001 Iowa Land Value Survey.]
By the same token, the current one period expected rate of return (eRoR) to the parcel owner is comprised of the flow value (the rental rate: R/V) plus the capital gain rate:
eRoR = R/Vt + eVt+1/Vt - 1
If that’s what the parcel owner could get directly, that’s what he’ll rent the parcel for too, so:
R = Vt(1+ eRoR) - eVt+1
Taking an economy wide rate of return on assets like the interest rate on CDs as a benchmark, labeled “i”, we set eRoR =i , and see that:
R = Vt(1+i) - eVt+1
which says that the rent a landlord will charge on a parcel today reflects three things: the current parcel value, the expected future value of the parcel (which reflects all expected future rents), and the economy wide rate of return on other assets. It also makes it clear that a landlord will charge a lower rent on parcels that offer newly expected future capital gains.
This provides important insight into the phenomenon of uneven urban land use such as idle land downtown. We often observe very low-rent uses of land right next to very high rent uses. How come? Because of capital gains.
The downtown landlord who rents his real estate, for example, to a used-car lot operator is willing to accept low rent today because of the higher capital gain he expects later. Similarly, people buy stocks that don’t pay dividends today if they believe they can sell the stock later for a capital gain. Capital gains will not materialize, however, on land or stock or any other asset that does not, ultimately, generate revenues in excess of costs. (Which is why the NASDAQ equity index tanked when people finally realized that many IT companies were not profitable and probably never would be.)
The expression for rents (R) above also allows us to deduce landlords and developers future expectations and plans about a place, using information available today:
As long as the future poses no big opportunities or threats, we expect parcel rents to reflect current parcel prices and interest rates. These should be rising over time at the rate of inflation, just like all other prices.
Where and when land owners and developers recognize new opportunities, sale prices of parcels rise (V rises because eV rises). Rent payments may remain the same. But relative to current values, land rental rates (R/V) fall.
Thus, we can deduce that wherever R/V is relatively low—compared to comparably productive or profitable parcels—local land market players anticipate growth.
For example, R/V has been relatively low on farmland in counties with the highest rates of farm land conversion to urban uses. The graph below shows where R/V is relatively LOW—indicating where farm land is under pressure to convert to urban uses or other higher-valued purposes. Note that this phenomenon appears to be most evident to the north of Sioux City, around the Quad Cities, Fort Dodge, near the lakes in Emmet and O’Brien counties, and around Iowa’s universities in Ames and Iowa City. Also, in some counties, farm land is being converted from row crops to hog lots, such as in Hamilton county north west of Story County. This also tends to raise land values (and lower rental rates compared to values.)
