Risk-Return.
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Measures
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Valuation
& Returns.
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Online
Sources.
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Home
Practice.
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FINA 4610: Entrepreneurial Finance & Private Equity.
Lecture 7 & 8: Ownership & Returns (PART B).
Milivoje Davidovic.
D’Amore-McKim School of Business
Northeastern University
Spring 2023.
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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Ownership & Returns (PART B).
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Valuation
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Home
Practice.
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Outline.
1 Risk & Return.
2 Three Measures of Returns.
3 The Determinants of Valuation & Returns.
4 Home Practice.
5 Online Sources.
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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D’Amore-McKim School of Business
Ownership & Returns (PART B).
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Home
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Notation (REMINDER).
v Notation.
Table 1: Notation for Ownership and Investor Returns.
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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Measures
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Valuation
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Online
Sources.
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Home
Practice.
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1 Risk-Return.
2 Measures of Return.
3 Valuation & Returns.
4 Online Sources.
5 Home Practice.
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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D’Amore-McKim School of Business
Ownership & Returns (PART B).
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Measures
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Valuation
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Online
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Home
Practice.
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Risk & Return.
• Investors provide money with the goal of earning a profit; so, they base their investment decisions on the
returns they expect to earn from the investment.
• Underlying Finance Principle: higher return can be only achieved by taking on more risk (A free lunch in
investing cannot exist because of the constant trade-off investors make between risk and reward).
• If two projects have the same risk, the one with a higher return would be in higher demand, it would
become more expensive, and its return would become lower.
• Risk-Aversion: the tendency to avoid risk and have a low risk tolerance; risk-averse investors prioritize the
safety of principal over the possibility of a higher return on their money.
• Consider two investment alternatives, both with the same level of risk; then, the investors would prefer the
safer project to riskier one.
• Distribution of Risk: diversifiable risk (venture-specific risk), and non-diversifiable risk (systemic part of risk).
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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D’Amore-McKim School of Business
Ownership & Returns (PART B).
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Measures
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Valuation
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Online
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Home
Practice.
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Risk & Return.
⋆ Example 1: Expected Return.
v Consider two venture investments, Investment A and Investment B. Investment A: there is 50%
chance to earn 10%, and 50% chance to earn 5%. Investment B: there is 20% chance to earn 20%,
and 80% chance to earn 5%. What is the expected return on Investment A and Investment B?
⋆ Practice 2: Scenario Analysis.
v Assume that you want to invest in a venture that is exposed to the U.S. economy. The venture
would give certain returns given the general economic trend within the the economy: (1) 5% in
recession; (2) 8% in stable period (normal times); and (3) 12% in expansion (economic boom).
The probabilities of each economic scenarios are given as follows: (a) recession 30%; (b) normal
times 40%, and (c) expansion 30%. Calculate the expected return and risk (proxied by the standard
deviation) of this venture investment.
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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Ownership & Returns (PART B).
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Valuation
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Online
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Home
Practice.
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Risk & Return.
• The risk of financing entrepreneurial ventures: (Q1) whether one has to be ”risk-lover” to invest in
entrepreneurial venture? (Q2) what is different about the returns to venture investing, compared to other
risky investments (e.g., stock market)?
• First Question: venture investors are not necessary ”risk-lovers”; they are rather risk-tolerant investors
who work toward reducing risks.
• Second Question: (a) the risk of investing in entrepreneurial ventures can be extreme (”skewness”,
specifically ”right skew” or ”long right tail”); (b) liquidity risk (it is easier to sell stocks than shares in
private companies).
• Risk-Aversion: is related to the shape of the utility function, and risk-averse investors are assumed to have
concave utility function.
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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Ownership & Returns (PART B).
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Valuation
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Home
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Risk & Return (APPENDIX).
• Normal distribution have the following features.
1
symmetric bell shape; mean and median are equal; both located at the center of the distribution
2
3
4
≈ 68% of the data falls within 1 standard deviation of the mean
≈ 95% of the data falls within 2 standard deviation of the mean
≈ 99.7% of the data falls within 3 standard deviation of the mean
Figure 1: Normal Distribution. .
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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D’Amore-McKim School of Business
Ownership & Returns (PART B).
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Home
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Risk & Return (APPENDIX).
• The Moments: (1) the expected value, (2) the variance, (3) the skewness, (4) the kurtosis.
Figure 2: Skewness and Kurtosis.
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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Ownership & Returns (PART B).
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Measures
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Valuation
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Home
Practice.
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Risk & Return (APPENDIX).
•
Concave Utility and Risk Aversion: A function U defined on an interval [a, b] of real numbers is said to
be concave if for any α with 0 ≤ α ≤ 1 and any x and y in [a, b] there holds
U[αx + (1 − α)y] ≥ αU(x) + (1 − α)U(y) .
A utility function U is said to be risk averse on [a, b] if it is concave on [a, b]. If U is concave everywhere,
it is said to be risk averse.
•
Arrow-Pratt Absolute Risk Aversion Coefficient: the degree of risk aversion is formally defined by:
U′′ (x)
a(x) = − ′
,
U (x)
. where U′ (x) normalizes the coefficient; a(x) shows how risk aversion changes with the wealth level.
•
Certainty Equivalent: the certainty equivalent of a random variable x is the amount of a certain (risk-free)
wealth that has a utility level equal to the expected utility of x:
U(C) = E[U(x)] .
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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Ownership & Returns (PART B).
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Valuation
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Home
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Risk & Return (APPENDIX).
• Concavity: the straight line drawn between the two points on the function must lie below (or on) the
function itself.
• The expected utility of the first alternative (the
50-50 chance) is equal to the value of the straight
line at the point x∗ = 1
x+ 1
y.
2
2
• The expected utility of the second option (the riskless one) is equal to the value of the function at
the point x∗ = 1
x+ 1
y.
2
2
• This value is greater than that of the first alternative when the utility function is concave.
• According to the assumption from the utility theory, more is preferred to less; thus, the sure wealth
of 1
x+ 1
y is preferred to 50 − 50 chance of x
2
2
and y.
Figure 3: Concavity and Risk Aversion.
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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Ownership & Returns (PART B).
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Measures
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Valuation
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Online
Sources.
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Home
Practice.
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1 Risk-Return.
2 Measures of Return.
3 Valuation & Returns.
4 Online Sources.
5 Home Practice.
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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D’Amore-McKim School of Business
Ownership & Returns (PART B).
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Valuation
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Home
Practice.
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Three Measures of Return.
• When venture capitalists are asked what financial metrics hey used for analyzing investments, 63% of the
respondents reported use of cash-on-cash-multiples (CCR), 42% internal rate of return (IRR), and 22% of
them use net present value (NPV).
• In start-ups, returns are entirely driven by the value of the company at exit, which we denote X; in case
of an acquisition, X is the acquisition price, net of any payments to existing debt holders.
• At the time of exit, investors receive an amount of money equal to their ownership share of the company
times the exit value:.
XINV = FINV × X .
• Correspondingly, the entrepreneur‘s share of the exit value is given by XENT = FENT × X ; the time
between the investment and exit (investment duration) is denoted by T; the discount rate is denoted by
d.
• The standard criterion for financial investment decision is the net present value (NPV); it is based on
discounting back to the present all future cash flows.
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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Home
Practice.
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Three Measures of Return.
• The Time Value of Money: the concept that a sum of money is worth more now than the same sum will
be at a future date due to its earnings potential.
• Suppose that investing a sum I over one year earns interest rate d; then, the future value of I, which we
denote FV(I), is given by:
FV(I) = I + d × I ⇒ FV(I) = I(1 + d) ,
where this equation expresses the value of I today as what it will be worth in one year.
• If we define X as the forward value of I, that is, X = FV(I) = I(1 + d); then, we denote the present
value of a future return X by PV(X) (in this case, [PV(X) = I]); then:
PV(X) = X/(1 + d) .
• If an investment lasts more than one yer, we simply consider that each year the value of the investment
is reinvested at the same interest rate; in T years, the investment I becomes:
FV(I) = I(1 + d)T ⇒ PV(X) = X/(1 + d)T .
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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Ownership & Returns (PART B).
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Valuation
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Home
Practice.
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Three Measures of Return.
• The NPV of an investment is derived by the present value by subtracting the cost of investment (I), and
using the investor‘s share of the exit value:
NPV = XINV /(1 + d)T − I .
• Cash-on-Cash-Multiple (CCM): it measures how many times the amount originally invested is returned
to the investor at exit.
CCM = XINV /I .
CCM Drawbacks: (a) fails to account for the timing of cash flows; (b) disregards the amount of risk.
• The Internal rate of Returns (IRR): the discount rate corresponding to an investment‘s zero NPV; if we
set NPV = 0, then we have:
I × (1 + IRR)T = XINV .
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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Ownership & Returns (PART B).
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Valuation
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Home
Practice.
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Three Measures of Return (WorkHorse Example).
• Our investor Michael Archie was excited about WorkHorse, and mentioned it as a co-investment opportunity to the Ang brothers; the brothers had different opinions about the timing of the exit.
• Quentin Ang (Quick Quentin), hoped WorkHorse would sell after two years, assuming $10M as the exit value
of the company; Simon Ang (Slow Simon) thought about exit after four years, with assumed exit value of
$12.5M.
• Their respective values at exit are as follows:
XQuick
= FQuick × XQuick ⇒ XQuick
= 0.10 × $10M = $1M .
Ang
Ang
QSlow
XSlow
= 0.10 × $12.5M = $1.25M .
Ang = FSlow × XSlow ⇒ XAng
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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D’Amore-McKim School of Business
Ownership & Returns (PART B).
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Valuation
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Online
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Home
Practice.
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Three Measures of Return (WorkHorse Example).
• If we assume 10% discount rate, we can calculate NPVs for the two Ang investors:
NPVQuick
= XQuick
/(1 + 0.1)2 − I ⇒ NPVQuick
= $1M/(1 + 0.1)2 − $0.25M = $576K .
Ang
Ang
Ang
Slow
4
Slow
4
NPVSlow
Ang = XAng /(1 + 0.1) − I ⇒ NPVAng = $1.25M/(1 + 0.1) − $0.25M = $604K .
• Now, we can calculate their respective cash-on-cash multiple (CCM):
CCMQuick
= XQuick
/IQuick ⇒ CCMQuick
= $1M/$0.25M = 4 .
Ang
Ang
Ang
Slow
Slow
CCMSlow
Ang = XAng /ISlow ⇒ CCMAng = $1.25M/$0.25M = 5 .
• Finally, we can calculate the IRR setting NPV = 0 for both investors; also, we can follow the same
approach to calculate the company-level and founders-level returns.
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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Ownership & Returns (PART B).
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Measures
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Valuation
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Online
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Home
Practice.
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Three Measures of Return (WorkHorse Example).
• We can calculate the financial gains to entrepreneurs, including both founders (they hold 64%) and the
other parties (they own 16%):
• Accordingly, the founders‘ financial gains at exit would be:
XQuick
= 0.64 × $10M = $6.4M .
ENT
XSlow
ENT = 0.64 × $12.5M = $8M .
• The financial gains to other parties (stock options pool, JP Porto, and U of M) would be:
XQuick
= 0.16 × $10M = $1.6M .
OTHER
XSlow
OTHER = 0.16 × $12.5M = $2M .
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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Ownership & Returns (PART B).
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Measures
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Valuation
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Home
Practice.
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Three Measures of Return (WorkHorse Example).
• Reminder: an investor‘s ownership stake from round i, after round r, is denoted by Fi (r) then,
Fi (EXIT) = Fi (R)
and the value of the investor‘s ownership stake at the time of exit is given by:
Xi = Fi (R) × X .
• Michael Angie though that the Ang brothers were unrealistic; he agreed that the company would need
$2M in the second round (after one year, so R = 2); also, he thought that $12.5M was a realistic exit
value goal.
• Using the above assumptions, we can calculate the investors‘ ownership stake, value at exit, and investment.
Table 1: The Deal Structure.
Ownership
Value at Exit
Investment
Round 1
Round 2
F1 (2) = 0.15
X1 = $1.875M
I(1) = $0.5M
F2 (2) = 0.25
X1 = $3.125M
I(2) = $2M
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© Milivoje Davidovic.
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Ownership & Returns (PART B).
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Measures
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Valuation
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Home
Practice.
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Three Measures of Return (WorkHorse Example).
• Based on the information in Table 1, we can calculate corresponding measures of financial gains/returns;
then, the round Cash-on-Cash Multiples (CCMs) and IRRs are given by:
= 3.75
CCM1 = $1.875M
$0.5M
0=
$1.875M
(1+IRR1 )4
− $0.5M
and
and
CCM2 = $3.125M
= 1.56 .
$2M
0 = $3.125M4 −
(1+IRR)
$2M
(1+IRR2 )1
.
• Using information from Table 1, we can also calculate the net presents values for each round (assuming
d = 10%):
NPV1 = $1.875M4 − $0.5M = $0.71M
(1+0.1)
and
NPV2 = $3.125M4 −
(1+0.1)
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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D’Amore-McKim School of Business
Ownership & Returns (PART B).
$2M
(1+0.1)1
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= $0.29M .
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Measures
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Valuation
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Online
Sources.
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Home
Practice.
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1 Risk-Return.
2 Measures of Return.
3 Valuation & Returns.
4 Online Sources.
5 Home Practice.
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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D’Amore-McKim School of Business
Ownership & Returns (PART B).
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Northeastern University
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Risk-Return.
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Measures
of Return.
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Valuation
& Returns.
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Online
Sources.
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Home
Practice.
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The Determinants of Valuation and Returns.
• The Cash-on-Cash-Multiple (CCM): it is equal the exit value (X) divided by the company‘s post-money
valuation CCM = V X
.
POST
1
For a given post-money valuation (VPOST ), a higher exit value (X) leads to a higher realized investor
return (CCM).
2
For a given exit value (X), a higher post-money valuation (VPOST ) leads to a lower realized investor
return (CCM).
• Entrepreneurial Gain:
(
XENT =
1− V I
POST
)
×X .
1
For a given post-money valuation (VPOST ), a higher exit value (X) leads to a higher entrepreneurial
gain (XENT ).
2
For a given exit value (X), a higher post-money valuation (VPOST ), leads to a higher entrepreneurial
gain (XENT ).
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
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.
D’Amore-McKim School of Business
Ownership & Returns (PART B).
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Northeastern University
22 / 32
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Risk-Return.
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Measures
of Return.
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Valuation
& Returns.
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Online
Sources.
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Home
Practice.
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The Determinants of Valuation and Returns.
• We can use these insights to derive a formula for what the post-money valuation ”should” be, by using
a forward-looking perspective (we consider expected returns, not realized returns).
• By ”expected” we mean the investor‘s required return, that is, the return the investor expects to achieve
in order to commit his or her money.
e
X
VPOST = CCM
e .
1
For a given expected return (CCMe ), a higher expected exit value (Xe ) leads to a higher post-money
valuation (VPOST ).
2
For a given expected exit value (Xe ), a higher expected return (CCMe ) leads to a loer post-money
valuation (VPOST ).
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© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
.
.
.
.
.
D’Amore-McKim School of Business
Ownership & Returns (PART B).
. . . .
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Northeastern University
23 / 32
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Risk-Return.
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Measures
of Return.
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Valuation
& Returns.
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Online
Sources.
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Home
Practice.
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The Determinants of Valuation and Returns.
• Economic Determinants of Valuation:
1
Opportunity Itself: better opportunities promise a higher return, higher exit value, which justifies a
higher valuation.
2
Market Context: a rising stock market has a similar effect; higher stock market values suggest
that start-ups can expect higher exit value, either when they go public themselves or when they get
acquired by a listed company.
3
Deal Competition: valuations for start-ups are determined through a bargaining process; a company
in a very competitive environment may fetch a higher valuation than another company in a less
competitive environment.
4
Investor Quality: the entrepreneurs know that the high-quality investor will add more value to the
venture; if the high-quality investor offered the same valuation as the lower quality investor, the
entrepreneur would always pick the high-quality investor.
.
© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
.
.
.
.
.
D’Amore-McKim School of Business
Ownership & Returns (PART B).
. . . .
. . . .
. . . .
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Northeastern University
24 / 32
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Risk-Return.
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Measures
of Return.
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Valuation
& Returns.
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Online
Sources.
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Home
Practice.
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The Determinants of Valuation and Returns.
• Founder Agreements: determine the allocation of share ownership within the founders‘ team, and defines
the legal rights and commitments of the various founding parties (development of the venture, term sheet,
etc.).
• Founder agreements address five main issues:
1
Team Members: typically current and future roles of the team members; this creates a shared
understanding of internal responsibilities.
2
Salaries: start-ups typically pay low salaries, though there are exceptions.
3
Financial Obligations: the agreement defines any financial obligations of the company toward individual founders (for example, a founder may need to get repaid for a loan or for transferring IP to
the company).
4
Ownership Allocation: allocating common shares among the founders, which shapes voting rights,
as well as the distribution of the eventual financial gains.
5
Contingencies: this means that certain awards (shares or bonuses) depend on certain milestones;
the vesting founder shares: the company withholds a portion of founder shares and releases them
over time, contingent on the founder still remaining within the company (also, SOP).
.
© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
.
.
.
.
.
D’Amore-McKim School of Business
Ownership & Returns (PART B).
. . . .
. . . .
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Northeastern University
25 / 32
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Risk-Return.
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Measures
of Return.
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Valuation
& Returns.
. .. .. .. .. .. .. .
Online
Sources.
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Home
Practice.
. .. .. .
The Determinants of Valuation and Returns.
• Internal Allocation: Q: On what basis should teams allocate founder shares? there is no objective formula;
it creates financial consequences, but may also impact the morale and motivation of the entire team.
• Equal Split (Egalitarian Approach): empirical studies of ownership within start-up teams suggest that
approximately half of all founder‘s teams opt for equal split solution.
• Hi-Tech Start-Ups: choosing an equal split is associated with younger teams (founders have few years of
experience), and more homogenous teams (founders have similar years of prior work experience).
• Principles of Internal Allocation:
1
Backward-Looking Arguments: shares are given on the basis of what founders have already contributed, including financial contributions; certain founders deserve more shares because they had
the ”original idea”.
2
Forward-Looking Arguments: allocating shares are largely based on providing the right incentives
for success (full-time vs. part-time founders); the division of founder equity also has to be sensitive
to bargaining power (a founder prefers to work for the venture over all other ventures).
.
© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
.
.
.
.
.
D’Amore-McKim School of Business
Ownership & Returns (PART B).
. . . .
. . . .
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Northeastern University
26 / 32
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Risk-Return.
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Measures
of Return.
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Valuation
& Returns.
. .. .. .. .. .. .. .
Online
Sources.
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Home
Practice.
. .. .. .
The Determinants of Valuation and Returns.
• The FAST Tool: the Founder Allocation Start Tool (FAST); it helps founder teams to structure their founder
agreements; the main output: a recommendation on how to split founder equity, along with suggestions about
vesting and milestone contingencies.
• The FAST is based on the following six-step procedure (some of them are closely related to five key
elements of a founder agreement):
1
2
3
4
5
6
Define Team Members and Roles.
Define Time Period and Weights.
Allocate Points to Individual Founder Contributions.
Identify Net Transfers.
Make Recommendations for Ownership Stakes.
Make Recommendations for Contingencies.
• Nobel Prize Insight: Holmström and Hart received the 2016 Nobel Price in Economics for their contribution
to contract theory. Please Check: Managing Employee Incentives and Pay For Performance and Beyond .
.
© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
.
.
.
.
.
D’Amore-McKim School of Business
Ownership & Returns (PART B).
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
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.
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.
Northeastern University
27 / 32
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Risk-Return.
. .. .. .. .. .. .. .. .
Measures
of Return.
. .. .. .. .. .. .. .. .. .
Valuation
& Returns.
. .. .. .. .. .. .. .
Online
Sources.
. .. .
Home
Practice.
. .. .. .
1 Risk-Return.
2 Measures of Return.
3 Valuation & Returns.
4 Online Sources.
5 Home Practice.
.
© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
.
.
.
.
.
D’Amore-McKim School of Business
Ownership & Returns (PART B).
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
.
.
.
.
.
.
.
.
.
Northeastern University
28 / 32
.
Risk-Return.
. .. .. .. .. .. .. .. .
Measures
of Return.
. .. .. .. .. .. .. .. .. .
Valuation
& Returns.
. .. .. .. .. .. .. .
Online
Sources.
. .. .
Home
Practice.
. .. .. .
Online Sources.
•
Video 1: Prize lecture: Bengt Holmström.
v Link: Prize lecture (Bengt Holmström).
•
Video 2: Prize Lecture: Oliver Hart.
v Link: Prize Lecture (Oliver Hart).
•
Video 3: Utility and Risk Preferences.
v Link: Utility Function.
.
© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
.
.
.
.
.
D’Amore-McKim School of Business
Ownership & Returns (PART B).
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
.
.
.
.
.
.
.
.
.
Northeastern University
29 / 32
.
Risk-Return.
. .. .. .. .. .. .. .. .
Measures
of Return.
. .. .. .. .. .. .. .. .. .
Valuation
& Returns.
. .. .. .. .. .. .. .
Online
Sources.
. .. .
Home
Practice.
. .. .. .
1 Risk-Return.
2 Measures of Return.
3 Valuation & Returns.
4 Online Sources.
5 Home Practice.
.
© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
.
.
.
.
.
D’Amore-McKim School of Business
Ownership & Returns (PART B).
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
.
.
.
.
.
.
.
.
.
Northeastern University
30 / 32
.
Risk-Return.
. .. .. .. .. .. .. .. .
Measures
of Return.
. .. .. .. .. .. .. .. .. .
Valuation
& Returns.
. .. .. .. .. .. .. .
Online
Sources.
. .. .
Home
Practice.
. .. .. .
Home Practice.
⋆ Practice 1: Ownership Structure & Price of Shares (Seed Investment (Round 1).
v Replicate the WorkHorse example with exactly the same initial investment, funding structure,
and ownership distribution. Calculate the three measures of return for the company, founders,
investors, and other parties.
⋆ Practice 2: Ownership Structure & Price of Shares (Scenario Analysis.
v Replicate the WorkHorse example with different initial founders‘ investments, with five founders
that hold different stakes, and slightly different external funding amounts. Also, build up the
capitalization table for each round, and calculate the ownership stake, and price per share. Finally,
calculate the three measures of return for the company, founders, investors, and other parties.
.
© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
.
.
.
.
.
D’Amore-McKim School of Business
Ownership & Returns (PART B).
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
.
.
.
.
.
.
.
.
.
Northeastern University
31 / 32
.
Risk-Return.
. .. .. .. .. .. .. .. .
Measures
of Return.
. .. .. .. .. .. .. .. .. .
•
Valuation
& Returns.
. .. .. .. .. .. .. .
Online
Sources.
. .. .
Home
Practice.
. .. .. .
Thank You.
.
© Milivoje Davidovic.
FINA 4610: Entrepreneurial Finance & Private Equity.
.
.
.
.
.
D’Amore-McKim School of Business
Ownership & Returns (PART B).
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
.
.
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.
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.
.
Northeastern University
32 / 32
.