It starts off like a bad joke, but there is truth in the answer: How much equity do you need to give up when you're seeking to raise capital? As much as it takes.

There is a price at which your transaction will clear the market. A price that you pay in equity dilution and the price investors receive for the risk they are accepting.

When you go to market with a private placement, do the math upfront to make sure i) you're providing your investors with an appropriate return, and ii) that you're not giving away too much equity. To do that, there are six basic steps:

1. Determine a base case forecast for the business.
2. Determine the structure and terms (except for the actual warrant position) of the security you are issuing.
3. Determine the expected enterprise value at the end of the investment horizon.
4. Determine the equity value at the end of the investment horizon.
5. Determine the dollar amount required that results in the targeted IRR.
6. Divide the result you get in step 5 above by the result in step 4. That quotient results in the percent of equity you will need to make available for your investors.

Let's walk through an example with real numbers so you can see how this all comes together. But first, some assumptions to frame the example:

• You are acquiring a business for $5 million, or 4x the business's EBITDA of $1.25MM;
• You've arranged bank financing of $3MM;
• You are able to invest $500 thousand of your own money;
• The financing gap is $1.5MM; and,
• Your investors will require a 30% IRR.

First you need to determine what your base case is for the business over the next five years. What will you be able to grow the EBITDA to over the next five years - the investment horizon? Lets assume for this illustration that you will be able to grow your business to $1.8MM in five years. Or approximately 7.6% compounded annual growth rate. We'll also assume that at the end of five years that you'll still have debt outstanding of $1.2MM (you may have borrowed more to grow your business), and cash of $100K.

Second, you'll need to determine the terms and structure of the security you will be issuing to your investors (yes, you are issuing a security). Again for illustration purposes, we'll assume that you will be issuing Preferred stock (the 'why' is beyond the scope of this article) in the amount of $1.95MM.

If you've noticed that the Preferred issuance is $1.95MM, and not $1.5MM, it's not a typo. The reason you are issuing $1.95MM is because you, the Sponsor of the transaction, will be investing $450K of your $500K investment alongside the investors. The remaining $50K of your investment will go in as common.

This Preferred issuance will have a five-year maturity, will pay an 8% dividend in cash each year, and will have warrants for some percentage of the common equity of the business; again, the question is how much of the equity?

So, lets look at the math:

- Year 5 enterprise value (or terminal value) is equal to EBITDA times your exit multiple. Lets assume that there is no multiple expansion, so that the 4x you paid for the business is the same multiple for the terminal value. The terminal value $1.8MM x 4, or $7.2MM.

- Equity value is enterprise value, less debt, less preferred, plus cash (unrestricted cash). Therefore, equity value is equal to $7.2MM less $1.2MM (debt), less $1.95MM (preferred), plus $100K (cash), or $4.15MM.

- The IRR your investors are targeting is 30%. Since the investors are receiving 8% of their return in cash dividends, 22% of their return needs to come from the increase in equity value. The math then is $1.95MM (the face amount of the Preferred), times 1.22^5 (that's 1 plus the 22% in IRR required from the equity build up to the power of 5, which is the maturity of the Preferred). Doing this math results in $1.95 x 2.7027, or $5.27MM.

- From the $5.27MM we subtract the face amount of the Preferred (return the initial investment) of $1.95MM and end up with $3.32MM of equity value that the Preferred investors need to receive in order to receive a 30% IRR (including the Preferred dividend payments of 8%).

- Finally, since we already determined that the expected terminal equity value is $4.15MM, then the Preferred Stock Issuance should end up with 80% of the equity in your transaction in the form of warrants - $3.32MM divided by $4.15MM.

- The remaining 20% of the equity goes to the common equity holder.

So what is the math to you, the Sponsor?

Since $450K of your investment went into the transaction as Preferred, you share in the returns of all the Preferred investors. Your share of the 80% of the equity to the Preferred Shareholders is 23.08% ($450/$1950), or $766K.

Next, since you are the sole common equity holder - the $50K of your total $500K investment - the remaining $830K of equity value ($4.15 - $3.32MM) goes to you for an IRR of approximately 75% (($830/50)^(.2)).

In all, you tripled your money for a blended IRR of 26% - (($766+$830)/$500)^(.2).

There you have it. Private equity pricing on the back of an envelop in six easy steps.