# STARTUP MATH

## FORMULAS AND VARIABLES THAT AFFECT DEALS AND COMPANY OWNERSHIP

**Table of Contents**

**I. Summary of Startup MathII. What is Startup Math and Why it's ImportantIII. Know the Goals: What the Entrepreneurs Want & What Investors WantIV. Basic Principles: Underlying Ideas that Guide the FInancing Deals**

**A. Investors purchase stock of a company in an equity financingB. Adding new stockholders dilutes previous stockholdersC. Investors purchase shares of the company (equity) from the company in a financing based on valuation and other factorsD. The difference between pre-money valuation and post-money valuation**

**V. Guiding Formula**

**A. How to use this formulaB. How to manipulate itC. Examples**

**VI. Adding Complexity to the Formula: Employee Stock Options**

**A. The employee option pool is used creatively to effectively result in a lower price per shareB. Employee option pool mechanicsC. Example questions**

**VII. Convertible Debt Math**

**A. Basic Principles of Convertible DebtB. Example**

**VIII. Getting Out**

**A. Liquidation Preference**

**IX. Summary Again**

## I. SUMMARY OF STARTUP MATH

A. Investors buy equity of a company based on a formula

B. That formula is: price per share = pre-money valuation / number of fully-diluted shares

C. Investors want to buy shares at a low price. Current stockholders wants the price to be high. The two parties negotiate and manipulate the variables of this formula to achieve their goal.

D. One way to manipulate the formula is to change the pre-money valuation. A lower pre-money valuation results in a lower price. A higher valuation results in a higher price.

E. Another way to manipulate the formula is to adjust the number of employee stock options and to include that number in the denominator of the formula. More employee stock options results in a lower price per share for investors.

F. Convertible debt converts when there is a qualified financing. At that point it will affect the capitalization table and current stockholders will be diluted.

G. Preferred stockholders receive a liquidation preference. This affects how much founders/common stockholders will receive on an exit.

## II. WHAT IS STARTUP MATH AND WHY IT'S IMPORTANT

If you change the width of a race car's tires by a certain amount, then someone who is inexperienced with race cars will simply think that all that's changed is the width of the tire. Someone who is knowledgeable will instantly realize that by changing just the width of the tire, a lot of other elements have also been changed. The gas mileage of the car can change, the balance, the turning radius and many other components. They'll know not just that these variables are affected but HOW they are affected.

In other words, variables such as tire width don't exist in a vacuum. One item affects another item.

Similarly, variables in the mathematics of company ownership don't exist in a vacuum.

If the valuation of a company changes by a certain amount, then that affects the price of the stock, the amount of equity that an investor purchases, etc.

Startup math is about knowing and understanding what kinds of equations, numbers, and variables are used with startups--most frequently in the context of a financing.

**Why do you need to understand this interplay between variables when it comes to company ownership?**

**Because if you have a working knowledge of this interconnectedness you will be able to better think about: deals on the fly, company ownership, and your overall system during a negotiation or when simply managing the company. **

## III. WHAT THE ENTREPRENEURS WANT & WHAT INVESTORS WANT

Knowing the goal helps.

You might not be sure what tire width to put on a race car, but you know the general goal. It's something like you need speed and excellent handling. From there you can work out the details.

Likewise, know the goal when it comes to startup math.

**The investors' goal is to have a low price per share before they invest.** This is for two reasons: (1) investors want to buy assets (stock) of the company for a low price, have the assets increase in price over time, and then sell for a high price; (2) they will have to invest less dollars into the company to buy an otherwise greater percentage of the company.

**Those who are already stockholders want a high price per share.** This is because (1) it may indicate that their shares went up in value; and (2) more dollars will need to be poured into the company by investors in order to buy an otherwise smaller percentage of the company.

## IV. BASIC PRINCIPLES: UNDERLYING IDEAS THAT GUIDE FINANCING DEALS

There are certain guiding principles to understand before getting to the nitty-gritty numbers.

### A. Investors purchase stock of a company in an equity financing

Investors purchase a certain number of shares of stock (equity) of the company in order for the company to raise money. How many shares they purchase will then determine what percent of the company they purchased.

Investors can of course also figure it out the other way and decide they want to purchase a certain percent of the company. This will then determine the specific number of shares of stock.

The investors figure out how much money they want to invest in the company and a whole bunch of other stuff on their end. They then negotiate and buy shares of the company at a certain price eventually translating into the investors owning a certain percent of the company.

The formula they used to determine these numbers is this: price per share = pre-money valuation of the company / number of fully diluted shares. This is explained with more detail later in this article.

### B. Adding new stockholders dilutes previous stockholders

How does an investor buying shares affect other stockholders?

Whenever an investor or anyone acquires equity of the company, existing stockholders get diluted. This means that existing stockholders own less as a percentage of the overall company than they owned before.

If you own 100% of the company by holding 1,000 shares of stock and an investor comes in and buys 250 shares from the company, you will then own 80% [1000 shares / (1000 + 250 shares)] of the company with 1,000 shares and the investor will then own 20% [250 shares / (1000 + 250 shares)] of the company with 250 shares.

What happened? The *percent* of the company you owned went down. This is called dilution. (There are ways to protect against dilution. See the article on dilution.)

[Note that the number of your actual shares, in this case--1,000 did not change. Where did the other 250 shares come from? Those are shares that the company is allowed (authorized) to give out but were previously unissued.]

### C. Investors purchase shares of the company (equity) from the company in a financing based on valuation and other factors

A valuation of the company is how much the company is worth. It's figured out using a host of factors such as historical financials of the company, competition, growth potential, industry outlook, etc. There are many different methods and it is an inexact science.

Investors can and do use the value of the company and other variables to figure out how how much to invest and for what price.

### D. The difference between pre-money valuation and post-money valuation

These are terms that are thrown around in a financing negotiation.

Pre-money valuation is the valuation of the company (i.e. how much the company is worth) before an investment takes place. Post-money is the valuation of the company after the investment takes place. So pre-money + investment amount = post-money.

**Why this is important:** "Pre-" or "post-" terminology can change the deal substantially. For example:

If an investor wants to own 50% of the company at a $5 million "valuation," then:

**If "valuation" means "pre-money valuation"**--the company with the investment will be worth $10 million. Pre-money valuation ($5M) + investment ($X) = post-money valuation ($10M). The investor will have to invest $5M in order to own 50% of the company.

**If “valuation” means "post-money valuation"**-- then the company with the investment will be worth $5 million. Pre-money valuation + investment = post-money valuation. The investor will have to invest half of the post-money valuation if the investor wants to own 50% of the company. The investor will have to invest $2.5M in order to own 50% of the company.

Notice the result. The use of the prefix "pre-" or "post-" resulted in a multi-million dollar difference. Most of the time when individuals say "valuation" they mean "pre-money valuation." But don't assume this.

## V. GUIDING FORMULA

The basic formula that determines how much an investor is going to pay for a part of the company is:

### Price per share = pre-money valuation of the company / number of fully diluted shares

Definitions:

*Price per share:* this means how much the price of each share of stock is going to be.

*Pre-money valuation:* this means the value of the company immediately before the investment, i.e. the valuation of the company without including the investment-to-be dollars.

*Number of fully diluted shares:* this means the number of all of the common stock (including potential common stock (i.e. stock and options, etc. that can convert into common.))

### A. How to use this formula

The parties take the price per share and figure out how many ever amount of shares the investment amount will purchase. This will in turn determine what percent of the company their investment will purchase.

### 1. What each party wants:

As mentioned before--know the goal.

**Investors:** Investors want the price per share to be low. This can be achieved by causing the pre-money valuation of the company to be low and/or to have the number of fully diluted shares be high. Remember that valuation is an inexact science and subject to negotiation.

**Founders:** Founders and existing shareholders want the price per share to be high. This can be achieved by causing the pre-money valuation of the company to be high, and the number of fully diluted shares to be low.

### B. How to manipulate it

### Price per share = pre-money valuation of the company / number of fully diluted shares

The right side of the formula (valuation and number of shares) is played with and negotiated on in order to determine how many shares that investor's investment will purchase.

### 1. Pre-money valuation

In basic math terms, this is the top of the fraction: the larger this number is, the higher the price per share and the better for the founders/company. The lower the number, the better for investors.

The valuation can be difficult to play with if the parties are stubborn. This is true even though valuation is extremely difficult to pinpoint and there's no right or wrong answer.

### 2. Number of fully diluted shares

This is the bottom of the fraction. Founders/company want this to be low. investors will want this to be high.

The number of fully diluted stock includes potential common stock. This means that warrants or convertible securities or options are included in this amount.

Because options are included in this amount the number of options to grant for an option plan is an area that is often negotiated. The lower the number of stock set aside for options translates to less shares and an overall percentage of ownership for investors. The higher the number is, the better for founders and existing shareholders.

### C. Examples

**Stock ** ** % Ownership**

Founder 1: 5,500,000 55%

Founder 2: 3,500,000 35%

Early Employees: 1,000,000 10%*Total:* 10,000,000 100%**What happens when an investor wants to come in and invest $2,000,000?**

Because you've been reading this article you know that a few things will happen. Investing that cash for shares of stock will result in investor owning part of the company. 1. So how much of the company will investor own?

2. How many shares will investor purchase and at what price? ** **

We know that bringing in an investor dilutes previous stockholders. 3. What percent of the company will other stockholders have and what will the resultant cap table look like?

**1. So how much of the company will investor own?*** *

The pre-money valuation of the company is $5,000,000. Where did this $5M come from? It's a number that was determined using various valuation techniques and through negotiation. If the pre-money is $5M, that means that the valuation of the company after the investment (the “post-money” valuation) is $7,000,000. So the investor will be purchasing **28.57% of the company** ($2M/$7M).**2. How many shares will investor purchase and at what price? **

Price per share = pre-money valuation / number of fully diluted shares

x = 5,000,000 / 10,000,000

x = 0.5

The price per share is $0.50

The investor’s $2,000,000 will buy at **$0.50 per share** for a **total of 4,000,000 shares** [$2,000,000 / $0.50].

**3. What percent of the company will other stockholders have and what will the resultant cap table look like? **

So to calculate the percent of ownership of founder I can either take the number of shares he owns divided by the total number of shares (5,500,000 / 14,000,000) or I multiply the percent before, 55%, by the percent indicative of the decrease of ownership (55% x (100%-28.57%)). In other words, the investor is going to purchase 28.57 percent of the company, so that means that the percent Founder 1 owns after the investment is going to be 71.43% of 55%.

Do this for Founder 2 and Early Employees.

**Stock % Ownership**

Founder 1: 5,500,000 39.29% (5,500,000/14,000,000) OR (55% x 71.43%)

Founder 2: 3,500,000 25.00% (3,500,000/14,000,000) OR (35% x 71.43%)

Early Employees 1,000,000 7.14% (1,000,000/14,000,000) OR (10% x 71.43%)

Investor 4,000,000 28.57%*Total: * 14,000,000 100%

Notice that all of the prior shareholders (Founder 1, Founder 2, and Early Employees) were all diluted. For instance, Founder 1 went from 55% ownership to 39.29%

You can quickly figure out the percentage ownership of how much a certain shareholder will get diluted after the next round by multiplying their percentage ownership by percentage ownership of all parties accounting for the dilutive round.

So taking a look at the last example. Let’s say another financing is done and Investor 2 will purchase 20% of the company. Then Founder 1 will own 39.29% x (100% - 20%) = 31.43%; Founder 2: 25% x (100% – 20%) = 20%; Early employees 7.14% x (100% – 20%) = 5.71%; Investor 1: 28.57% x (100% – 20%) = 22.86%.

## VI. ADDING COMPLEXITY TO THE FORMULA: EMPLOYEE STOCK OPTIONS

## A. The employee option pool is used creatively to effectively result in a lower price per share

The employee stock option pool is the amount of stock of the company held for employee option plans. Stock of the company is given as part of a compensation package to employees to motivate them. Usually the amount of stock set aside for such a plan is 10-20% of the stock of the company.

Investors like to negotiate a sizable pool so that a greater allocation of options is not needed down the road. It is beneficial to investors to allocate the option pool before they invest rather than after they invest. Think about how existing stockholders get diluted when more stock is dished out.

In other words, the investors would rather the pre-money valuation take into account the option pool rather than the post-money valuation. This is pretty normal.

## B. Employee option pool mechanics

Go back to the main formula: price per share = pre-money valuation / number of fully diluted shares

You already negotiated with the investor that the pre-money valuation is $X amount. The number of fully diluted shares is Y. So the price per share for the investor to invest will be X/Y. The investor then demands, within reason, that an option pool is created and that the pre-money valuation takes the option pool into account. This means that:

Price per share = pre-money valuation (which includes value of option pool shares) / number of fully diluted shares including option pool shares

So essentially, the pre-money valuation doesn’t change: the value of the company is the value of the company, but the number of fully diluted shares does change. What you get is:

Price per share = X/(Y+Options)

Remember than founders and already existing stockholders want the denominator of the fraction to be low. A low denominator means a higher price per share. Which means that the investor’s investment buys a lower percentage of the company.

So what happens is that the option pool decreased the price per share. The standard option pool size is any where from 10-20%. So the larger the pool, the more price per share will decrease.

## C. Examples

**Facts:** Investor wants to invest $5 million dollars in a company with a pre-money valuation of $15 million dollars. There are currently 10 million shares of the company.

1. What is the price per share?

2. What is the price per share if the option pool is 10%?

3. What is the price per share if the option pool is 20%?

1. What is the price per share?

**Stock % Ownership**

Founders: * * 10,000,000 100% (10,000,000/10,000,000)

*Total:* 10,000,000 100%

Price per share = pre-money valuation / number of fully diluted shares

Price per share = $15,000,000 / 10,000,000

**Price per share = $1.50**

2. If price per share is $1.50, what does the resulting cap table look like?

This means that the investor’s $5,000,000 will buy $5,000,0000 / $1.50 or 3,333,333.33 shares. You can see that this makes sense. When all is said and done, the investor put in $5M and the total value of the company is $20M—so 25%. To put it in pre-money, post-money terminology: the investor invests $5,000,000 on a post money valuation of $20,000,000 (pre-money valuation of $15,000,000 + $5,000,000 investment) so that is 25% of the company. Therefore, the investor is buying 25% of the company with $5M.

The shares he owns will reflect 25% ownership of the company—which this does. 3,333,333.33 shares divided by the total amount of shares (10,000,000 (held by existing shareholders)+ 3,333,333.33 (new shares issued to the investor) = 25%

** Stock % Ownership**

Founders: 10,000,000 75% (10,000,000/13,333,333.33)

Investor 3,333,333.33 25% (3,333,333.33/13,333,333.33)*Total: * 13,333,333.33 100

### 3. What is the price per share if the option pool is 10%?

Note: when an investor demands that the option pool is a certain size, it almost always means that the option pool size is that certain size after the financing is complete. So the RESULTING size of the option pool needs to be 10% after the calculations, not before.

Price per share = pre-money valuation / number of fully diluted shares

Recall that the option pool value is built into the pre-money valuation, so the pre-money valuation number does not change.

The number of fully diluted shares will change however. The number will include the existing shares of 10,000,000 plus an amount that will be 10% of the total number of fully diluted shares after the financing is complete.

So that does NOT mean 10% of 10,000,000 shares equaling 1,000,000. That would be incorrect.

Solving for the number of fully diluted shares:

Know that the final make up of the post-money value of the company will be--

65% founders shares + 10% option pool + 25% investor cash = 100% post-money valuation of the company

We know that founders will be at 65% because the option pool needs to be at 10% and the investors will purchase 25% of the company.

We know that $20M will be the post-money valuation of the company ($15M pre-money + $5M investor cash). This means that the 10% option pool will be 10% of the $20M post-money valuation. Thus, the option pool’s value will be $2M. And we know that the founders 10,000,000 existing shares have a value of $13M (65% of $20M):

65% [$13M] [Founders] + 10% [$2M] [Option Pool] + 25% [$5M] [Investors] = 100% [$20M] [Total]

If 10,000,000 shares have a value of $13,000,000 that means $13,000,000 / 10,000,000 shares will give the price per share--

**This means that each share is $1.30**.

### 4. What does the cap table look like with a 10% option pool?

**Number of shares of stock in option pool: **The $2M option pool at $1.30 per share means the option pool will be the size of $2,000,000 / $1.30 or 1,538,461.54 shares.

**Number of shares of stock for Investor:** There are many ways to find out the amount of shares that the investor would purchase from this point. You can multiply 2.5 by the amount of shares that the option pool will have (because it is 2.5 times bigger) or going back to the original formula:

*Price per share = Pre-money valuation / number of fully diluted shares*

Price per share = $15M / (10,000,000 + 1,538,461.52)

Price per shares = $1.30

Shares that investor purchases with $5M cash = $5,000,000 / $1.30

Shares that investor purchases with $5M cash = 3,846,153.84615

**Stock % Ownership**

Founders: 10,000,000 65% (10,000,000/15,384,615.2)

Option Pool: 1,538,461.52 10%

Investor: 3,846,153.85 25% (3,333,333.33/13,333,333.33)*Total: * 15,384,615.37 100

### 5. What is the price per share if the option pool is 20%?

*Price per share = pre-money valuation / number of fully diluted shares*

Price per share = $15M / (10,000,000 + x)

55% founders + 20% option pool + 25% investor = 100%

$11,000,000 founders [55%] [10,000,000 shares] + $4,000,000 option pool [20%] [x number of shares] + $5,000,000 investors [25%] [y number of shares] = $20M [100%] [10,000,000 + x + y]

10,000,000 shares for founders is $11,000,000 of value. So each share is $11,000,000 / 10,000,000 or** $1.10**

$4,000,000 / $1.10 = x

x = 3,636,363.6363 shares

To use the original formula:

Price per share = $15,000,000 (10,000,000 + 3,636,363.6363)

**Price per share= $1.10**

### 6. What does the cap table look like with a 20% option pool?

**Option Pool: **Already calculated how many shares there would be for the option pool. Again:

$4,000,000 / $1.10 = 3,636,363.6363 shares

**Investors: ** $5,000,000 / $1.10 = 4,545,454.5454 shares

**Stock % Ownership**

*Founders:* 10,000,000 55% (10,000,000/15,384,615.2)*Option Pool:* 3,636,363.6363 20% *Investor:* 4,545,454.5454 25% *Total:* 18,181,818.1818 100%

### 7. What are the takeaways in this example scenario?

(a) When it comes to option pooling, it is the founders/existing shareholders that get the brunt of the dilution. Notice that it is their percentage ownership that goes down in each example and not the investor’s 25%. So the larger the option pool, the more current stockholders get diluted.

(b) The option pool is used creatively to effectively result in a lower price per share. This allows investors to buy a certain amount of the company for a lesser price.

## VII. CONVERTIBLE DEBT MATH

## A. Basic Principles of Convertible Debt

### 1. Conversion

Convertible debt converts into equity at a qualified financing. It converts into the same type of equity as that which is being purchased in the qualified financing round. The convertible debt deal will also call for a discount. Additionally, there may be a valuation cap in play.

### 2. Cap Table

Convertible debt does not affect the cap table/company ownership if and until the debt converts. NOTE: You may see cap tables where all potentially converted stock is also listed.

## B. Example

Here is a very simplified example to show these principles.

### Formation: Founders own 1,000,000 shares representing 100% of the company. What does the cap table look like?

This situation is simple and there is hardly anything to calculate.

*Cap Table after formation:*

**Stock % Ownership**

Founders: 1,000,000 100%*Total: * 1,000,000 100

**1st Investment: Investor CD comes along and invests in the company with a convertible debt deal done: $100,000, 4% interest, qualified financing of $1M, valuation cap of $3M. 20% discount. What does the cap table look like?**

Nothing changes on the cap/ownership table. The convertible debt is debt and there are no shares issued simply because convertible debt was issued.

*Cap Table after 1st Investment*

**Stock % Ownership**

Founders: 1,000,000 100%*Total: * 1,000,000 100

**2nd Investment: Investor Y comes along and invests $200,000 at a valuation of $800,000 (not a convertible debt deal.) What does the cap table look like?**

The convertible debt did not get triggered because the qualified financing of $1M was not reached.

To figure out what the cap table will look like after Investor Y purchases stock of the company, we have to (i) solve for the price per share that Investor Y will invest at. Then using this value (ii) solve for how many shares investor Y's $200k will purchase.

(i) Solving for the price per share that Investor Y will invest at

Price per share = pre-money valuation / number of fully diluted shares

Price per share = 800,000 / 1,000,000

Price per share = $0.80

(ii) Solving for how many shares will be purchased at that price

Shares purchased by investor: $200,000 / $0.80 = 250,000

*Cap Table after 2nd investment: *

**Stock % Ownership**

Founders: 1,000,000 80%

Investor Y: 250,000 20%*Total:* 1,250,000 100

**3rd Investment: Investor Z comes along and invests: $1M at a pre-money valuation of $2M. What happens in that case? **

In this case, the amount in this financing does meet the qualified financing threshold and so the debt will convert.

So then what is the price that investor Z pays?

Price per share = pre-money valuation / number of fully diluted capitalized shares.

Price per share = 2,000,000 / 1,250,000

Price per share = $1.60

Shares purchased: $1,000,000 / $1.60 = 625,000

What is the price that convertible debt Investor CD pays?

That convertible debt will convert into shares at the lesser of (a) 80% of the price per share paid by the purchasers in the qualified financing (remember the 20% discount); or (b) the valuation cap divided by the fully-diluted capitalization immediately prior to the closing.

80% of the $1.60 is $1.28.

So is $1.28 lower or is the price per share lower than the valuation cap price? The valuation cap is $3M.

So the price per share if the valuation is $3M is:

Price per share = 3,000,000 / 1,250,000

Price per share = $2.40

So the price per share will be $1.28 as it is lower.

Number of shares purchased by Investor CD via conversion: $100,000 / $1.28 = 78,125

*Resulting cap table after Investor Z:*

**Stock % Ownership**

Founders: 1,000,000 51.2%

Investor Y: 250,000 12.8%

Investor Z: 625,000 32%

Investor CD: (conversion) 78,125 4%*Total:* 1,953,125 100%

## VIII. GETTING OUT

The above covered how the numbers and cap table work out when an investor purchases shares to get into a company. Now I will cover how the numbers work when investors exit the deal with a liquidation preference. So what happens between "getting in" and "getting out?" That time period mostly has to do with an investor protecting their position within their company with various types of anti-dilution and other types of rights. Check out the article on dilution for more information on that.

## A. Liquidation Preference

A liquidation preference is one of the most important terms in a financing deal. It can make or break the deal. A liquidation preference details what happens to the proceeds when there is a liquidity event (e.g. sale of the company.) It is called a preference because the preferred stockholders receive this amount before the common stockholders receive any proceeds from the liquidity event.

The investment terms in an equity deal should spell out what the liquidation preference is. It is usually described as a multipler (1x, 1.5x, 2x, etc.) of the investment. Recall that preferred stock can convert into common stock. What happens in an event of liquidation is that the preferred stockholders can either:

1. convert into common stock and receive proceeds of the sale on a pro-rata basis with all of the other stockholders; OR

2. they can receive their liquidation preference; OR

3. if their preferred stock is "participating" they can get their liquidation preference *and* then receive proceeds of the sale as if they converted into common (this is called "participation.") Participation can be capped. If the proceed amount is greater than the cap amount, then the participation will not happen and either (1) or (2) above will occur.

If after the preferred receive their liquidation preference from an event of liquidity and there is not enough proceeds for common stockholders, that is tough luck for the common stockholders.

I recommend that founders negotiate with investors for a 1x liquidation preference, non-participating.

## IX. SUMMARY OF STARTUP MATH

A. Investors buy equity of a company based on a formula

B. That formula is: price per share = pre-money valuation / number of fully-diluted shares

C. Investors want to buy shares at a low price. Current stockholders wants the price to be high. The two parties negotiate and manipulate the variables of this formula to achieve their goal.

D. One way to manipulate the formula is to change the pre-money valuation. A lower pre-money valuation results in a lower price. A higher valuation results in a higher price.

E. Another way to manipulate the formula is to adjust the number of employee stock options and to include that number in the denominator of the formula. More employee stock options results in a lower price per share for investors.

F. Convertible debt converts when there is a qualified financing. At that point it will affect the capitalization table and current stockholders will be diluted.

G. Preferred stockholders receive a liquidation preference. This affects how much founders/common stockholders will receive on an exit.