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.

1. this math is wrong. 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

should be 1,331,000 unless I’m wrong for some unknown reason.

2. Both of you are correct. My math was off. 1,331,000 is the correct amount. Thank you for pointing it out.

3. I always check and double and triple check one small mistake could break you especialy with the tight margins today.

4. Math doesn’t matter. It is all speculation on what the value will be in the future. How come no one said the answer should be \$669,000 or 1 million less the decline value of today’s market?
It is a nice post and a nice formula, Ted. But the value or preceived value does not continue to climb every year. In my opinion – of course.

5. Greg, you are right. Thanks for pointing that out. Commercial properties can drop in value just like residential property, however, in my opinion, commercial properties like apartment buildings are better suited as investment vehicles then single family homes. The main reason for this is the fact that apartment buildings generate a steady stream of income. Also, the value of an apartment building is partially determined by the amount of income that it brings in. This helps to keep valuations more closely aligned with reality. For example, a lot of people who bought vacation homes in past 5 years were told by their realtor that the vacation home was a great investment, even at an inflated price. Unfortunately, many of these vacation/investment homes are now facing foreclosure because the owners weren’t able to collect enough rent to pay the annual mortgage payments.

6. Gregory Bain on

Ted,
I have never sold an apartment complex – not many in my area and I have only seen one come on the market. That investor got a real steal. Of course, he had to invest in repairs and had to have the money power to do so. I don’t think he will ever be selling that complex at a loss. In fact, he made so much money on the deal he purchased a tract of land and built another high end (for my area) apartment complex.
On the other hand, I have seen a lot of other “commerical” property that may take ten years to come back to the purchase price. And, there are many “projects” either on hold or moving at a snails pace in the commerical market today.
But, you did start this post with the opening sentence of “apartment building investor” and I have no hands on experience to cast doubt on your time value of money. It is out of my league. Good Luck.

7. like a previous posted pointed, it’s important not to confuse precision (e.g. decimal points in your math) with accuracy (how closely does the 5% assumption match reality).
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