✏️ Practice

✏️ An Angel investor wants to contribute $4M in return for 70% of the company. What is the post money valuation?
✔For this, we say that the Angel thinks that 70% of the company is worth $4M:
70% × Company = $4M
Therefore,
Company = $4M / 70% = $5.714 M

✏️ The Angel wants 70% of the firm. Suppose that there are already .5M shares outstanding. How many shares will need to be issued and given to the Angel?
✔ Equation: #SharesAngel/#SharesTotal = %OwnedByAngel
Equation: #SharesAngel/(#SharesAngel + #SharesPreviously) = %OwnedByAngel
Plug: #SharesAngel/(#SharesAngel + .5M) = 70%
x/(x + .5M) = 70%
Chug:
x = 70% * (x + .5M)
x = 70%x + 70% * .5M
x = 70%x + $.35M
x - 70%x = $.35M
x (1- 70%) = $.35M
x (30%) = $.35M
x = $.35M / 30% = 1.167 M
Think:
What percentage would the Angel Investor own?
1.167 M / (.5M + 1.167 M) = .700005 = 70%

✏️ Through your networking at Harvard Extension School, you met up with an angel investor who invested in the company that you founded. They gave $300,000 in return for a 40% share of the company. After the transaction, you had 300,000 shares and they had 200,000 shares. You have recently approached a second angel after creating a minimal viable product. Your goal is to take that angel investor’s new money to scale up production. The new Angel requests 20% of the company in return for an investment of $400,000.

• How many shares will the new angel receive?
• What will your ownership percentage be after the transaction?
• What will the first angel’s ownership share be after the first transaction?
• What will the post-money valuation of the company be after the transaction?
• What was the post-money valuation of the company before the transaction? How has it grown over time?

✔

How many shares will the new angel receive?

Like with the last problem, we will solve this problem using plug and chug. The two equations that we used are:
Equation: #SharesAngel/#SharesTotal = %OwnedByAngel
Equation: #SharesAngel/(#SharesAngel + #SharesOwnedByOthers) = %OwnedByAngel

Honestly, though, we only used the second one. The first one was just there so that you knew where the second one came from.
#SharesOwnedByOthers = #SharesOwnedByYou + #SharesOwnedByAngel1 = 300K + 200K = 500K
%OwnedByAngel** = 20%
x/(x + 500K) = 20%
x = 20% * (x + 500K)
x = 20% * x + 100K
x (1-20%) = 100K
x = 100K / (1-20%) = 125K
Think: After the transaction, Angel2 will own 125K and other investors will own 500K.
Angel Percentage = 125K / (125K + 500K) = 20%

Sidebar

🙋 How could I make up my own questions?
✔ You could approach the question in reverse. Imagine that you started with two investors, who have, respectively 1M and 2M shares. A third investor will receive 3M shares. What percentage of the firm will they own? They own: 3M/(1M + 2M + 3M) = 50%. Now you can turn this into a word problem as follows: “Imagine that you started with two investors, who have, respectively 1M and 2M shares. Suppose a third investor approached and wanted 50% of the company. How many shares would you have to give them?” Let’s solve this new problem we just made!

✏️Imagine that you started with two investors, who have, respectively 1M and 2M shares. Suppose a third investor approached and wanted 50% of the company. How many shares would you have to give them?
✔ Equation: #SharesAngel/(#SharesAngel + #SharesOwnedByOthers) = %OwnedByAngel
x/(x + (1M + 2M)) = 50%
x/(x + 3M) = 50%
x = 50%(x + 3M)
x = 50%x + 1.5M
x - 50%x = 1.5M
x(1-50%) = 1.5M
x×50% = 1.5M
x = 1.5M/50% = 3M

What will your ownership percentage be after the transaction?

Angel1 gave $300,000 in return for a 40% share of the company (at the time - right after first round of equity). You have 300,000 shares
Angel1 has 200,000 shares
Angel2 has 125,000 shares
Angel 2 has 20% of the company in return for an investment of $400,000.

✏️ What will your ownership percentage be after the transaction? ✔ #SharesYou/(#SharesYou + #SharesOwnedByOthers) = %OwnedByYou
300K/(300K + (200K + 125K)) = 48.0%

It might have been simpler to just add up the total number of shares first to get #SharesTotal = 300K + 200K + 125K = 625K
#SharesYou/#SharesTotal = %OwnedByYou
300K/625K = 48.0%

What will the first angel’s ownership share be after the first transaction?

If the second angel owns 20% and you own 48%, the first angel must own the remaining 32%.

We can also just apply the standard formula:
#SharesAngel1/#SharesTotal = %OwnedByAngel1
200K/625K = 32%

Post money valuation after second round

Angel1 gave $300,000 in return for a 40% share of the company (at the time - right after first round of equity). You have 300,000 shares Angel1 has 200,000 shares Angel2 has 125,000 shares Angel 2 has 20% of the company in return for an investment of $400,000.

✏️What will the post-money valuation of the company be after the second round?
✔ There are two ways to solve this.

In the lecture, Bruce calculated the “per share” price for the stock and then calculated the market cap.
Per-share price when the second Angel purchased:
P = $400,000/125,000 shares = $3.2 per share
Use the above price to calculate the market cap:
Market Cap = P × Q = $3.2 × #SharesTotal = $3.2 × (300K + 200K + 125K)
Post Money Valuation = $3.2 × 625K = $2M \

It might share save some time to do it another way: If 20% of the firm cost Angel1 $400,000, then 100% of the firm would cost $400K×5 = $2M. Fast!
Or, with algebra:
20%×ValueOfFirm = $400,000
ValueOfFirm = $400,000 / 20% = $2M

Post money valuation after first round?

✏️ Angel1 gave $300,000 in return for a 40% share of the company. Angel1 received 200,000 shares and you had 300,000 shares. What was the post-money valuation after the first round of financing?
✔ Bruce’s method:
Per-share price when the first Angel purchased:
P = $300,000/200,000 shares = $1.50
Use the above price to calculate the market cap:
Market Cap = P × Q = $1.5 × #SharesTotal = $1.5 × (200K + 300K) = $750K

40% of the firm cost Angel1 $300K
40% × ValueOfFirm = $300K
ValueOfFirm = $300K / 40% = $750

How has your investment performed?

We saw above that the post-money valuation of the firm rose from $750,000 to $2,000,000 and that the share price rose from $1.5 to $3.2. (The share price roughly doubled and the market cap roughly tripled. The market cap grew more than the share price because new shares were issued.)

Clearly the firm is doing well.

How about your personal paper wealth?

At both time periods, you had 300,000 shares, but because this is a private company and we can’t go to an exchange to find out how much the shares are worth, we have to use the value of the shares of the last transaction to estimate your value. Of course, the value of shares can go up or can go down in the space of a couple of seconds, and they can do so quite dramatically. Therefore, we refer to this only as paper wealth. If you had dollars, dollars don’t change value quite as rapidly, so it’s much safer to have dollars, but dollars don’t grow like these shares are growing, so you’d probably prefer to have these shares.

Anyway, let’s look at your paper wealth between these two rounds of financing.

After the first round of financing, the value of your investment in this firm is:
300K × $1.5 = $450K

After the second round of financing, the value of your investment in this firm is:
300K × $3.2 = $960K

The value of your investment more than doubled from less than half a million to almost a million dollars. It didn’t triple because even though the market cap almost tripled, your shares were diluted, so you own a smaller amount of a more valuable company. Congratulations! The vast majority of early-stage companies like this tend to fail, but you’ve managed to be one of the lucky ones.