CFA CFA Level 2 Private Equity Financing Calculation (with 2 rounds of financing)

# Private Equity Financing Calculation (with 2 rounds of financing)

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• vincentt
Participant
• CFA Level 3
5

I realised there are some differences in terms of calculation when it comes to second round financing, both methods do not have the same answer.

Example:

A company can sell for \$40m in 5 years and the owner currently hold 1m shares. There are two rounds of financing, first being \$3m and second round \$2m (3 years later).
Use discount rate of 40% for the first three years and 30% for the last two years.

My question:
I understand that the 2 rounds of financing amount and time are known. However, the 2 different calculations are:

POST = exit value / (1 + r )^ n

Schweser (Book 4 p97)
1. POST (2nd round) = \$40m / (1.30)^2 = \$23,668,639
PRE (2nd round) = \$23,668,639 – \$2m = \$21,668,639
POST (1st round) = \$21,668,639 / (1.40)^3 = \$7,896,734

and that would be the figure (\$7,896,734) they use to calculate f and all that.

e.g. fractional ownership of investor (1st round) = \$3m / \$7,896,734 = 37.99%

Exam Prep
2. POST (1st round) = \$40m / (1.30)^2 = \$23,668,639 / (1.40)^3 = \$8,625,597

and that would be the figure (\$8,625,597) to calculate everything else.

e.g. fractional ownership of investor (1st round) = \$3m / \$8,625,597 = 34.78%

The question now is why would you take the second financing into account to obtained your present value when clearly the funds are not invested yet (not favouring company owner).
Just imagine, if an investor were to tell company A that they would be funding them in 2 stages, the second one would be \$10m which means that would bring down the company’s present value to \$4,981,282 (\$13,668,639 / (1.40)^3) [\$13,668,639 is from \$23,668,639 – \$10m] refer to #1 above

and the investor would gain more % of the company in the first round but there’s no guarantee that the investor would fund them the second round.

So logically, from what I can see the 2nd method would be correct as it calculates one stage at a time. Can anyone confirm this please?

• 5

np @vincentt – happy to walk through more but it always helps to have the full question to work with ðŸ™‚

• vincentt
Participant
• CFA Level 3
4

Updated the question.

• 4

what is this exam prep line @vincentt? Is that your calculation?

POST (1st round) = \$40m / (1.30)^2 = 23,668,639 / (1.40)^3 = 8,625,597

I think I get what you’re trying to show, but mathematically they don’t add up of course

• 3

@vincentt, because to get to future exit value of \$40m in 5 years time, you need to take into account all the investment made in between. It wouldn’t have got to \$40m otherwise in year 5.

• vincentt
Participant
• CFA Level 3
3

@sophie i thought the \$40m is an estimate of what the company would have worth 5 years down the line? I understand that these companies would have needed the finances to grow, but would it be right to say that the \$40m figure is not “linked” to how much money that is invested into the company (unlike the DCF method where the value is down to the cash flow generated) instead to do with the company’s projected potential?

However in another example: an entrepreneur obtains \$1m funding today, of which he gives 30% of his shares to the financier. 3 years from now, the company needs more cash and he decides to further raise cash by selling equity. In that case, there will be further dilution of shares, and therefore your calculations will need to take those into account (i.e. your Schweser method).

@christine
correct me if i’m wrong, the second funding (in 3 years) would not be known to the entrepreneur so why and how are we able to take that into account? Using the schweser method requires the second funding to be deducted to get the PV of the company’s value.

The question from 7city is something along the line of “first funding is x and 2 years later it requires extra funding of y.”

Whereas the one in schweser states that “instead of paying \$5m they are splitting it into 2 stages, \$3m then \$2m three years after.”

I have not done any mock yet so wouldn’t be able to tell, but would the actual exam go to this extend to trick the candidates?
E.g. if you don’t get the right PV (which is the very first step), you will not get anything else after that correct.

Reference to the schweser question:

• 3

Your calculations seem correct. I don’t see how this can translate to the method you describe here:

Exam Prep
2. POST (1st round) = \$40m / (1.30)^2 = \$23,668,639 / (1.40)^3 = \$8,625,597

and that would be the figure (\$8,625,597) to calculate everything else.

e.g. fractional ownership of investor (1st round) = \$3m / \$8,625,597 = 34.78%

• vincentt
Participant
• CFA Level 3
3

@christine the example by 7city is obviously different (with one discount rate), but in the original post I was using 7city’s approach to calculate a question in schweser (the one with two different discount rates) to see if it’s the same.
7City’s approach which is to discount exit value (\$25m in this example or \$40m in the original example) to obtain it’s present value of the company without taking the second funding into account (\$2m – first example; \$1m second example).

As you can see in the 7city’s method, the \$2m (first example) or \$1m (second example) were not deducted from the PV calculation.

I guess the only difference, like what you mentioned above is to do with whether there’s a known second stage funding.

• vincentt
Participant
• CFA Level 3
3

noted and thanks @christine & @sophie for explaining ! I haven’t got the chance to check the examples in CFAI textbook but I’m glad to know both possible methods.

• Reena
Participant
• CFA Charterholder
2

@vincentt, I must admit I’ve lost you from “exam prep” onwards… care to clarify?

• vincentt
Participant
• CFA Level 3
2

@reena my point is the different methods used to get the POST (PV of exit value), the rest (e.g. fraction, PRE, equity %, price per shares) are the same. Just that with a different (incorrect) POST value, everything else will be incorrect.

• vincentt
Participant
• CFA Level 3
2

@sophie sorry for the confusion, the exam prep is actually from 7city. I’m just applying the calculation method they used onto one of the examples in schweser. One (schweser) includes future funding into the calculation, and the other would dilute it’s share as it goes.

@christine
but logically, even with confirmed future funding, why would the future funding (\$2m in 3 years time) gets deducted to conclude today PV of exit value? For example, current price per share shouldn’t take into account possible future dilution (issuing of more shares due to extra funding).

How should I handle such questions and what are the key things to note?

• vincentt
Participant
• CFA Level 3
2

The example from 7City:

A company wants to raise \$2m of capital. The entrepreneur wants to sell in five years time for \$25m. VC investor will apply a 35% discount rate to reflect the risk they will bear. The entrepreneur want to retain 1.75m shares.

Calculate the following:
1. POST
2. PRE
3. Ownership Fraction
4. Number of shares required by VC investors
5. Share price.

Part 2:
Two years later, Elise Inc needs another \$1m.
Calculate the following:
1. POST
2. PRE
3. Ownership Fraction
4. Number of shares required by VC investors
5. Share price.

The walk through by the tutor for part 2, is actually based on the calculation obtained from part 1.

I don’t have the notes with me, so I might make some mistakes (hopefully not):

Part 1:
POST = \$25m / (1.35)^5 = 5,575,338
VC ownership = \$2m / 5,575,338 = 35.87%
Number of shares (VC) = 1.75m * (0.3587) / (1-0.3587) = 978,832
Share price = \$2m / 978,832 = \$2.04

Part 2:
POST = \$25m / (1.35)^3 = \$10,161,052
VC ownership = \$1m / \$10,161,052 = 9.84%
Number of shares (VC) = (1.75m + 978,832) * (0.0984/(1-0.0984)) = 297,823
Share price = \$1m / 297,823 = \$3.36

• Reena
Participant
• CFA Charterholder
1

I don’t have the Schweser reference notes either…

• 1

I think, as with many CFA questions, the specific question sentence has to be considered carefully here. Both methods you mention can be ‘right’, but they calculate different things.

For your ‘exam prep’ method, the implicit assumption is indeed that the \$2m funding is confirmed and incoming, therefore if you calculate present value you’ll have to also calculate the present value of the future \$2m funding.

The Schweser method can also be correct, depending on how the question is framed (i.e. if the implication is that the \$2m funding is not known, and only confirmed in year 3).

• 1

However in another example: an entrepreneur obtains \$1m funding today, of which he gives 30% of his shares to the financier. 3 years from now, the company needs more cash and he decides to further raise cash by selling equity. In that case, there will be further dilution of shares, and therefore your calculations will need to take those into account (i.e. your Schweser method).

@christine
correct me if i’m wrong, the second funding (in 3 years) would not be known to the entrepreneur so why and how are we able to take that into account? Using the schweser method requires the second funding to be deducted to get the PV of the company’s value.

What I was trying to illustrate was that the 2 rounds of financing are separate and independent (i.e. shares issued for funding separately both times). In which case your Schweser method applies.

This is also the case for the example you posted – in each round of financing, shares are issued, and therefore you have to take out \$2m at year 3.

The 7city calculation you illustrated in your original post (i.e. “fractional ownership of investor (1st round) = \$3m / \$8,625,597 = 34.78%”) will only apply if there are no further share dilutions from the first round, i.e. the \$2m was simply a delayed payment. Would you be able to share a 7city example that requires such a calculation?

From my experience, most questions are like Schweser’s (i.e. they require you to work out share dilution each time). I wouldn’t put it past them at all to twist the question in the actual exam though.

• 1

I didn’t do much! Kudos to @christine! =D>

• 0

@vincentt I would assume that for the ‘exam prep’ calculation, there are no further dilutions of shares.

Going through an example: say there is a company today, of which 700,000 shares are owned by an individual, and 300,000 are owned by a VC firm. The VC has funded the company with \$1m today, and \$2m in 3 years. The \$2m doesn’t necessarily imply further dilution of shares, but can be part of the arranged funding for the original 300,000 shares it obtained. In which case, the 7city method should be used.

However in another example: an entrepreneur obtains \$1m funding today, of which he gives 30% of his shares to the financier. 3 years from now, the company needs more cash and he decides to further raise cash by selling equity. In that case, there will be further dilution of shares, and therefore your calculations will need to take those into account (i.e. your Schweser method).

These calculations are usually nothing more than phased TVM calculations. The issue that you’re seeing is the flexibility of the forms it can be tested, so it’s best understood conceptually. The questions you’re asking shows that you’re on the right track – you just have to look for the right clues in the questions.

If you share specific questions here I’m happy to work them through with you.

• 0

As you say, in the first part of the 7city example, there is no mention of the second financing round, so you have to calculate the valuation without any influence of the second round.

In the Schweser example, the phrase is “instead of a single round of financing of \$5 million, the company will need \$3 million in the first round, and \$2 million (three years later) to finance company expansion to the size expected at exit

The two bolded sentences suggest that this is a planned financing round, and the company should be valued with this round included.

Note that both examples are equally likely to appear in the exam. There is no easy way or rule of thumb I can think of that will be able to tell you how to approach the question except to check that at the time of valuation, all known rounds of financing/share dilutions must be taken into account.