## What Do You Do When an Investment seems Tricky?

by Pat Delaney, CCIM

In a recent social media post, we posted this “WeekLee Challenge“:

A buyer wants to make an offer on an off-market deal. He needs a 5.5% cap rate. The gross annual income is \$1,000,000. The expenses (excluding property tax) are \$30,000 annually, and the property tax rate is 1.25%. What amount does the buyer offer to achieve this return?

In this post, we will break down the answer on a step-by-step basis. So before you read any further, we challenge you to please spend a few minutes solving the above and review the following terms: NOI & CAP rate. Go ahead…we’ll wait!

### The Challenge, Accepted

The basic formula to solve this tricky investment is called the Income Capitalization Approach, which is:

(Net Operating Income (NOI))/(Capitalization Rate (CAP) = Value

However, as we are evaluating this “off-market” deal from the buyer’s perspective, we are looking to find the “Purchase Price” (P). (Let P represent Purchase Price for the remaining of this blog.) This can be denoted as the following:

Purchase Price (P)= NOI/CAP

With the information provided, let’s begin to set up the equation by plugging in what we already know: the CAP rate:

P= NOI/.055

Likewise, since the NOI is not provided, the buyer would need to find the NOI, as well. To solve for NOI, use the following equation:

Gross Annual Income-Expenses (not including property tax)-Property Tax=NOI

So let’s plug in the buyer’s gross annual income and his expenses, less property tax, into the equation:

\$1,000,00-\$30,000- (Property Tax) = NOI

Which brings us to another problem: what do we know about this building’s Property Tax? Well, we know that this building’s property tax is 1.25% of P. Now given this new information, we can now fill in the rest of the equation and solve for NOI:

\$1,000,000-\$30,000-.0125 x P = NOI

When we subtract the known expenses (\$30,000) from the gross income (1,000,000), we get:

NOI=\$970,000-.0125P

We are now able to put it all together:

P= (\$970,000-.0125P)/.055

From here on out, we can use old fashion algebra to solve for P.

Multiply both sides of the equation by .055:

.055P = \$970, 000 – (.0125P)

To get P on one side, Add .0125 to both sides:

.0675P = \$970,000

Now divide both sides by.0675 to isolate P:

P= \$970,000/.0675

P = \$14,370,370

Therefore, the buyer would offer \$14,370,370, for this deal, to achieve a 5.5% cap rate.

### Moving forward: A Shortcut

Use this shortcut to find the correct amount to offer:
Take your gross income, subtract all expenses (except for the Property Tax), and then divide by the CAP rate plus the Property Tax Rate.

### Final Thoughts

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