Don’t Let the Funky Math of Convertibles Bite You

Convertible notes tend to be a great way to raise money from angels.  They are easy to paper and don’t lock in a valuation or terms.  But they will impact the valuation of the financing that they convert into and in a way that’s a bit funky.

The math of an investment when there is no converting debt is simple.  For the company as a whole it goes: Pre money valuation + total amount raised = post money valuation.  Ownership for each investor is determined as amount invested / post money valuation.  Consider a Series A financing of $3 million total on a $7 million pre.  The post-money is $7 million + $3 million = $10 million and an investor who puts in $2 million owns $2/$10 = 20%.

Now let’s put a $1 million convertible note into the picture.  Let’s assume that it converts at either a 20% discount or a maximum valuation of $4 million pre (this is a “capped” convertible).  Now the math for the $3 million Series A gets considerably funkier.   Let’s again assume a that the pre-money is $7 million.   A 20% discount on that is $1.4 million which gets you down to $5.6 million which is above the $4 million cap for the convertible.  So the convertible will convert at the $4 million cap.

What does that do to the Series A?  Let’s for a moment assume that the company starts out with 4 million shares.  Then the per-share price paid by the note holders will simply be $4 million pre / 4 million shares = $1/share.  On the other hand the Series A will pay $7 million pre / 4 million shares = $1.75/share.  The note  holders will wind up buying 1 million shares and the Series A in total $3 million / $1.75/share = 1,714,285 shares.  So after the financing is done, there will be 4 million + 1 million + 1,714,285 shares = 6,714,285 shares outstanding.  So what does someone who puts in $2 million into the Series A own now?  $2 million buys $2 million / $1.75/share = 1,142,857 shares and thus 1,142,857 shares / 6,714,285 shares = 17%.

So that’s quite a bit less than the 20% without the convertible.  In fact, we can figure out what the effective (or implied) post-money valuation is.  $2 million / x = 17%, so x = $11.76 million.   Compare that to the previous post-money valuation of $10 million and you notice that the deal has gotten 17.6% more expensive for the new investors because of the convertible!

P.S.  I wrote this post on the train this morning not knowing that Fred had posted about how the size of the option pool is tied directly to valuation as well. It is easy for a deal to be effectively much more expensive than “the sticker.”