Apartment Building Investment and the Time Value of Money

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The apartment building investor should always be aware of the amount of money that he or she has invested in an apartment building and more importantly the “time value” of that money. This concept of money’s value over a period of time becomes extremely important when comparing and contrasting different apartment building finance strategies. For example, the investor may want to evaluate an offer to buy his apartment building by another investor who requires that he offer owner financing. When offering the sale of an apartment building with an owner held note, the seller has to figure out what the value of the mortgage payments, over a specified period of time would be equal to in today’s dollar. The investor/owner must make these calculations so that he or she is able to compare the purchase offer to other offers which differ in terms. To figure out how the time value of money will effect investment returns the apartment building investor must determine what the “present value” and the “future value” of the money invested is and will be.

For example, an investor considering the purchase of an apartment building with an asking price of $1,000,000.00. The investor believes that the property should appreciate by about 5% over the next five years and he wants to figure out what the value of the “future value” of the property will be after five years based on this assumption. Even for the beginning apartment building investor it is important to learn how to make some important mathematical calculations when determining the value of different potential apartment acquisitions.

Scenario: The investor is considering the purchase of an apartment building. The owner is asking $1,000,000.00. The investor expects that the apartment building investment will increase in value by 10% annually. Or, each year the value the apartment building will increase at the anticipated 10% on the principal and on any interest previously earned.

To figure out what the future value of the apartment building property will be, the investor must know the following figures:

Present value =                    $1,000,000.00
Future value (unknown) =           unknown
Return rate=                       10%   
Time length=                       3 years

We don’t know the future amount, but we can easily find it.

Let today be time zero, when the apartment building is worth $1,000,000.00

Let’s put this process on a time line to see how the value of the land increases over three years:

0                    1                           
1,000,000  1,000,000(1+.10) 

2                                     3
1,000,000(1+.10)(1+.10)  1,000,000(1+.10)(1+.10)(1+.10)

Thus, the value of the land at the end of year three can be found by:
1,000,000(1+.10)(1+.10)(1+.10) = $1,191,016.00

or, equivalently,

1,000,000(1+.10)³ = $1,191,016.00

This leads us to the formula for the Future Value of a lump sum:
FV = PV(1+i)?

Here, PV = present value or amount, i=interest rate, n = length of time.

Note By BiggerPockets: These are opinions written by the author and do not necessarily represent the opinions of BiggerPockets.