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An Investment Formula

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To help you decide on your investment options, we’ve included a shortcut formula you can use to evaluate an investment.
The purpose of this article is to explain the thinking behind the formula. The formula is something an economist might use to determine the value of an asset. An asset is something that will last for a long time, such as a fruit-bearing tree.
An asset will yield "rents" (the fruit from the tree) and will enjoy price appreciation (You may be able to sell the tree for more than the original price you paid). The formula is,
Profitability = Rental Rate + Appreciation Rate - Interest Cost
By Profitability, we mean the expected annual profit, expressed as a percent of the price of the asset. The asset could be a house, some shares of stock or of a mutual fund, or a fruit tree.
The Rental Rate is the ratio of the first year rent to the purchase price. The first-year rent would be the rent on an equivalent house, the dividends from the stock, or the proceeds from selling the fruit.
The Appreciation Rate is the rate at which the price increases, expressed as an annual percentage rate. Much of this price increase could be due to general inflation. In the late 1970s, inflation in the United States reached 10 percent and over. More recently, inflation has been closer to 2.5 percent.
Some of the price increase may be specific to the particular market. In housing, over long periods of time prices go up at the same rates as rents in an area. Increases in stock prices are called capital gains. Fruit tree prices will tend to be correlated with the price of their fruit.
The Interest Cost is the cost of financing the asset purchase. With housing, most people think of this as the mortgage interest rate. With stocks or mutual funds, many individuals do not borrow. However, they could have put their money in CD's or bonds and earned interest, and it is this foregone interest (or "opportunity cost") that should be used as interest cost. Whether you borrow to buy the tree or finance the tree with your own funds, there is an interest cost to tying up your money in the tree.
Below is a sample spreadsheet to illustrate these concepts. Lets say we buy an asset (fruit tree) at the end of 2005, using funds borrowed at a 6% interest rate. Until we sell the asset, the amount we owe will increase at 6% per year, minus the amount we can pay off from the proceeds of harvesting the fruit. :
Assumptions:
Buy asset at end of 2005 for $100,000
In 2006 fruit from tree worth $7,000
Rental rate .035 ($3,500/100,000)
Interest rate .06 (6 percent annual interest rate, expressed as a decimal)
Appreciation .03 (3 percent annual appreciation, expressed as a decimal)
Approximation Formula:
Annual Profitability  = Rental Rate + Appreciation - Interest Rate
 = .035 + .03 - .06
Annual Profitability  = .005
(The asset will earn 1/2 percent profit per year)
(The calculations below serve to confirm the formula is approximately correct:)
Year Rent Debt Price Net Worth Profitability
2005 $- $100,000 $100,000 $- --
2006 $3,500 $102,500 $103,000 $500 0.53%
2007 $3,605 $105,045 $106,090 $1,045 0.56%
2008 $3,713 $107,635 $109,273 $1,638 0.59%
2009 $3,825 $110,268 $112,551 $2,283 0.62%
2010 $3,939 $112,945 $115,927 $2,983 0.65%
The formulas for the cells are:
Rent in 2007  = Rent in 2006 * (1 + Appreciation)
Debt in 2006  = Debt in 2005 * (1 + Interest rate) - Rent in 2006
Price in 2006  = Price in 2005 * (1 + Appreciation)
Net Worth in 2006  = Rrice in 2006 - Debt in 2006
Profitability in 2007  = (Net Worth in 2007 - Net Worth in 2006)/
Price in 2006
The spreadsheet shows cash flows in complete detail. The point, however, is the simple approximation of taking rental rate plus appreciation minus interest rate gets you to the right answer. It is exactly right for the first year, and only starts to be a little off later on because it misses the effect of the debt pay down.
 
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