I just received the loan agreement for a convertible.

Highlights: $200k loan, 5% interest, 3-year term, 15% discount and $2.5m cap.

Then article 4.1 says: “Upon closing of a Qualified Financing, the Loan plus accrued interest (“Conversion Amount”) will be converted into that number of Conversion Shares equal to the quotient obtained by dividing the Conversion Amount by the lower of (A) the price paid per Share in the Qualified Financing minus the Discount, and (B) the Valuation Cap divided by the Fully Diluted Capitalization immediately prior to the closing of the Qualified Financing.”

Oh boy. I have to read this twice to still not understand it.

Spreadsheet time!

**Lawyer Math**

Given my cash-flow planning, I expect that I also need to raise a Series A. Assume $1m at $2m pre-money. That means a price of $2m / 1,000 = $2,000 per share.

The Series A investor gets $1m / $2,000 = 500 shares.

Because of this Series A, the Series Seed investor converts $200k * (1 + 5%) ^ 1 = $210k loan and accrued interest into shares.

The Series Seed investor pays either (A) $2,000 * (1 – 15%) = $1,700 per share or (B) $2,5m / 1,000 = $2,500 per share – whatever is lowest.

So the Series Seed investor gets $210k / $1,700 = 124 shares.

After the Series A is raised I own 1,000 / 1,624 = 62% of the shares.

But wait.

The Series A investor wants to invest $1m at $2m pre-money. That means he wants $1m / $3m = 33% of the shares. He only receives 500 / 1,624 = 31% of the shares.

Something goes wrong because of the Series Seed investor’s convertible.

**Lawyer Math – Revisited**

Let’s take 1 step back.

The Series Seed investor can choose between:

- 15% discount. That is the same as getting 1 / (1 – 15%) = 1.18x as many shares as the Series A investor.
- $2.5m valuation cap. At a $2m pre-money valuation for the Series A, that is the same as getting $2m / $2.5m = 0.80x as many shares as the Series A investor.

Obviously he will choose option A because that gives him the most shares.

That in turn means the Series Seed investor will effectively convert $200k * (1 + 5%) ^ 1 * 1.18 = $247k into shares.

At the same time the Series A investor wants $1m / $3m = 33% of the shares – which he doesn’t get because of the Seed investor’s conversion if they follow the lawyer’s math.

This can be solved by using a single share price for both investors.

How?

The effective pre-money valuation is $2m – $247k = $1.8m.

That means an effective price of $1.8m / 1,000 = $1,753 per share.

The Series Seed investor gets $247k / $1,753 = 141 shares.

The Series A investor gets $1m / $1,743 = 570 shares.

After the Series A is raised the Series A investor owns his required 570 / 1,711 = 33% of the shares.

I own 1,000 / 1,711 = 58% of the shares.

Do your checks and you will see that everything fits!

OK, __now__ I get how a convertible works.

Thanks to Hans Westerhof and Chretien Herben.

*Joachim Blazer is author of The #1 Guide to Startup Valuation. How to value a startup in 6 easy steps. For founders and investors. For seed rounds and Series A.*