Download Entrepreneurial Valuation Techniques

FIN 673
Private Equity, Network
Economics, and Start-Up Valuation
Professor Robert B.H. Hauswald
Kogod School of Business, AU
Equity in Private
• From start to end: the valuation challenge
– good project assessment makes for sound investments
– tools: moving beyond DCF techniques to options
• Venture capital (VC) and private equity (PE)
– industry overview and the art of start-up financing
– valuation techniques
– biggest sellers of assets: suppliers of M&A deals
• The brave new world of start-ups: key concepts
– network economics and network valuation
– private equity and optionality
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Would You Have Invested?
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Private Equity:
Synonyms and Definitions
• Private equity encompasses early finance cycles
• From idea to inception: seed money
– the MCI crowd: friends&family
– Angel investors: fairy queens or godfathers?
• From inception to viable business
– Angel investors: private VCs with sidelines
– Venture capital: investing other people’s money
• From survival to success:
– Private equity proper: direct institutional investments
– IPO – going public: the endgame
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Firm and Capital Lifecycle
Sources of Capital
Equity Sources
Debt Sources
Public Equity
Mezzanine Capital
Private Debt
Corporate Capital
Commercial Banks
Venture Capital
Finance / Leasing Companies
Family and
Angel Investors
Seed
Start-Up
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Growth
Expansion / Diversification
Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Defining Venture Capital
• All Types of VC’s & Growth Capital
–
–
–
–
–
–
Incubator, Tech Transfer, Seed
Early Stage, First Round
Late Stage, Mezzanine
LBO
Big, small and everything in-between
Specialists to generalists
• Very gray lines between various types of funds
• Focus today is on early stage capital
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Venture Capital
“The very best job I can think of is a
venture capitalist. Not only does it sound
great at parties, but you are expected to fail
90% of the time. I mean no disrespect to
venture capitalists when I say this, but a
hamster could make those kinds of numbers.
It’s good work if you can get it.”
Scott Adams (Dilbert Creator)
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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VC Investment Objectives
• Per annum compounded rates of returns (holding
returns) significantly in excess of public markets
• Diversification: typically 20 independent holdings
– various gestation and industries
•
•
•
•
Long-term capital gains
Deal flow: 400 opportunities reviewed annually
4-5 investments / year
Investments with liquidity expectations within 5 to
7 years
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Hurdle Rates for Venture Capital
Rates of Return (ROR) Sought by Venture Capital Investors
Stage
Annual ROR%
Typical Expected Holding
Period (Years)
Seed and start-up
First stage
Second stage
Expansion
Bridge and mezzanine
LBOs
Turnarounds
50 - 100% or more
40 - 60%
30 - 40%
20 - 30%
20 - 30%
30 - 50%
50% +
More than 10
5 – 10
4–7
3–5
1-3
3-5
3-5
Jeffrey A. Timmons, New Venture Creation, 4th ed., (Irwin: Chicago) 1994, p. 512.
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Venture Capital Realized RoR
• Based on various studies:
–
–
–
–
–
–
14% - 92 firms in ‘60s and ‘70s
23% - before fees, 100 firms in the ‘60s
16% - public fund stock returns from 1959 to 1985
27% - 11 firms from 1974 to 1979
13.5% - from 1974 to 1989
20.7% - from 1987 to 1996
• How are the hurdle rates reconciled with realized
rates?
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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US Private Equity Performance
Source: Venture Economics’ US Private Equity Performance Index (PEPI) 12/31/2004
Venture Economics’ Private Equity Performance Index is calculated quarterly from Venture Economics’ Private Equity Performance
Database (PEPD). The PEPD tracks the performance of over 1,400 US venture capital and buyout funds formed since 1969 and over
425 European private equity funds formed since 1980.
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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The Magic of Venture Capital
Returns
• US Venture Capital returns in
– 1960-1995 average: 45%
– 1999: 150% (of which 1/3 realized early 2000)
• Returns virtually uncorrelated with stock market
– meaning what? how could this be?
• Interesting question: not “Why so much VC
now?” but “Why so little VC before?”
– what were 19th century’s start-up industries? VCs?
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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VC and the dot.com Boom
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Median Pre-Money Valuations
$25.3
$25
$21.1
$20
$15
$10
$16.7
$16.0
$15.5
$13.0
$12.9
$10.0
$11.1
$10.8
$9.3
$10.0
$5
$0
1994
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1995
1996
1997
1998
1999
2000
2001
2002
2003
2004 YTD05
Source: Dow Jones VentureOne/Ernst &Young
Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Median Pre-Money Valuations by Round
$40
$36
$30
$20
$20
$17
$14
$10
$6
$5
$0
$2
$2
3Q02 4Q02 1Q03 2Q03 3Q03 4Q03 1Q04 2Q04 3Q04 4Q04 1Q05 2Q05 3Q05
Later Stage
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Second Round
First Round
Seed Round
Source: Dow Jones VentureOne/Ernst &Young
Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Value Drivers: Exit Decision
IPO: future target
20-25% of
projects generate
bulk of return
Success
Trade Sale: current target
Sale, Buy-back, disposal
Failure
Write-off
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Exit and Liquidity Events
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
0%
20%
40%
60%
M&As
IPOs
80%
100%
Source: Dow Jones VentureOne/Ernst &Young
Private Equity and Start-up Valuation © Robert B.H. Hauswald
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M&A Transactions in VC
458
$120
402
$98.1
$100
450
407
380
356
338
304
$80
232
$60
300
253
197
162
$43.1
$40
150
$26.0
$20
$10.1
$23.4
$21.8
$12.7 $14.8
$27.3
$10.8 $13.1
$0
0
1995
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1997
1999
Amount Paid ($B)
2001
2003
Number of Transactions
2005
Source: Dow Jones VentureOne/Ernst &Young
Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Valuing Start-Ups
• What is a start-up entrepreneur?
– a twenty-three year old with 12 interactive Java slides?
– a fifty-six year old with 75 black&white slides?
• Valuing start-ups depends on the players
– some VCs can pull it off, others not
– private equity investors implicated: nurture or nature
• The biggest valuation challenge of them all
– little information: ideas, promises and opportunities
– most important decisions occur down the road
– what to fall back on: common sense and intuition?
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Typical 90+ Day VC Funding
Process
Referral
Contact
Review
Business
Plan
Meet CEO
Visit
Company
Start Due Diligence
Term
Sheet
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More Due
Diligence,
Documents
Private Equity and Start-up Valuation © Robert B.H. Hauswald
Closing
20
Pitching Deal
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Valuation - a VC’s perspective
• Not a science for early stage companies
• 51% is not important, covenants are
• 3 or 4 companies out of a portfolio of 20 will
provide 75% plus of returns for a VC
• Need to see a potential for fabulous upside (100%
+ per annum)
• 4 to 5 rounds of capital will be raised prior to exit
• Option pool 15% - 20% and must be considered
• An average of $25MM will be required prior to
exit
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Start-Up Valuation Challenges
• New Technologies may not work
– technological uncertainty
• Markets may not develop
– demand, competition uncertainties
• The entrepreneur may know more about the
idea than anyone else: agency conflicts
– asymmetric information
– conflicts of interest
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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The VC (and PE) Method
•
How to value a project/firm with negative CFs?
–
•
terminal value calculation: directly related to IPO or
trade sale objective
The four steps of private equity valuation
1.
2.
3.
4.
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terminal value (TV) estimation often as multiples (of
network penetration measure):
discount TV back at hefty target ROE:
required final % ownership:
retention ratio: subsequent financing and dilution
Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Venture Math
•
Pre-Money Valuation = $2.5MM, initial investment $1.5MM = post money
value = $4MM, therefore Original Investors (OI) own 38%
•
Round A: done at $8MM pre money and $4MM is raised and OI’s put in
$1MM. OI’s own $3MM based on pre-money value plus $1MM invested, or
$4MM total (33%) of the new $12MM post money value.
•
Round B: now assume $20MM pre money value and $8MM is raised with the
IO’s putting in $1MM. The IO’s now own $6.7MM plus the $1MM invested or
$7.7MM of the $28MM post money value, or 28% of the Company.
•
Round C: now assume $30MM pre money value and $10MM is raised with the
IO’s putting in another $1MM. The IO’s now own $8.4MM plus the $1MM
invested or $9.4MM of the $40MM post money value, or 24% of the Company.
•
Exit: assuming the best, the company is sold for $125MM, of which the OI’s get
$30MM in return for $4.5MM invested over 5 + years. 6.7X cash on cash return
or, depending on the exact exit timing, approximately a 30% IRR.
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Private Equity Valuation: TV as
Multiples
• Usual suspects fail with new product or industry
– DCF techniques (APV and NPV): limited usefulness
– real option techniques: plausibility/reality check
• New techniques based on key ratios and multiples:
meant to measure network effects
– Comparables: similar case used for ballpark valuation;
P/E, market cap/tot rev, market/book
– Multiples: cash flow predicted as a multiple of some
underlying number (HMO and members enrolled)
– problem: two firms are never completely comparable;
how to adjust for dissimilarities?
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Comparable Companies Method
• Group of companies comparable with respect
to size, products,
– Recent trends and future prospects
• Key ratios are calculated for each company
• Key ratios are averaged for group
– Average ratios applied to absolute data for
company of interest
– Indicated market values obtained from each ratio
– Valuation judgments are made
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Financial and High-Tech Comps
• Financial ratios of similar public firms:
– Valuation/Sales, Valuation/profits, P/E
– Market value of equity / book value
• High-tech ratios of similar public firms:
–
–
–
–
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Value / Patent
Value / Customer exposure
Value / employee
Value / Ph.D.
Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Pros and Cons of Multiples
• Advantages: common sense approach
– Used to value a company not publicly traded
– Marketplace transactions are used
– Widely used in legal cases, fairness evaluation, and
opinions
• Limitations: comparability
– hard to find companies that are actually comparable
by key criteria
– Ratios may differ widely for comparable companies
– Different ratios may give widely different results
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Justification for Multiples?
• How to explain quick and dirty multiples
valuation: let’s look at start-ups
• Network effects: start-ups attempt to capture the
pole position in a network
– their value is then a given fraction of the network’s
• Value the network and, by extension, the start-up
with respect to users, suppliers, etc.
– network participants vs. financial ratios
– however, what has to be true about the network for this
approach to work?
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Network Industries
• Network Industry = value of any transaction between two
parties A and B affected by
– size (number of users, lines) and state (“congestion”) of network
– integration of A and B into the network: access, switching costs
– classic examples: transportation, electricity grid
• Transaction between A and B feeds back into state of the
network (market size, congestion)
• Network character of IT-technologies:
–
–
–
–
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compatibility: hardware profiles (e.g. Wintel),
software standards (open and proprietary)
coordination effects, audience, market size (VOIP, email use, Kazaa)
economies of scale, pace of innovation
Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Start-ups as Network Industry
Plays
• Many high-tech and internet developments imply
a technological leadership or monopoly position:
– browsers (Netscape), portals (Yahoo!); ISPs (AOL)
• Plumbing: the infrastructure of the goldrush
– server markets, routers: (Cisco, Sun)
– broadband access (UPC), wireless access (UMTS)
• B2C and B2B: amazon.com, chemx.com
– platforms: auctions (ebay, QXL), travel and matching
services (lastminute.com)
– financial services: online brokerage, payment systems,
data content
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Cost Structure
• Expensive to produce, cheap to reproduce
• High fixed cost (sunk!), low marginal cost
• Particular market structures: monopoly
– cost leadership, product differentiation: versioning
• Lock-in and switching costs
– Stereos and LPs: Costly switch to CDs
• Systems lock-in: durable complements
– Hardware, software, and wetware
– Individual, organizational, and societal
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Network Effects: Metcalfe’s Law
• Value depends on number of users
– a: independent value
– b: benefit from adopting standard
• Positive feedback
– Fax (patented in 1843), Internet (1980s)
• Indirect network effects: software
• Research shows that Metcalfe’s Law
overstates network value
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Competition in Networks
• Entrants’ business plan to capture network
monopoly position, dynamic competition for
– speed: time to market, presence, fill out the segment
– best solution: reach as many participants as possible
• Prize attributed by aggregate consumer decision
– “Winner-takes-all” competition: how long a winner?
• Difference to patent races etc.
– uncertainty about final product, market size, market
structure
– determination of winner(s)
• What about incumbent/entrant advantages?
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Race to the Top…
• Market attaches premium for early entrants
before chances to succeed are sorted out
– not necessarily irrational
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Valuation Challenges:
Art and Science
• Network potential
– potential size and growth potential implies total value
– good proxies for these quantities?
• Business idea/plan within network
– know the competition
– how to attack, defend competitive advantage
• Network fallacy: e-conomy
– competition is NOT like VHS vs. Betamax
– internet is a network of networks: blurry boundary
– pole position hard to gain, easy to lose
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Warren Buffet
“If I were a business school professor in
finance, I would assign the following final
exam: How do you value Internet companies?
And I would fail everyone who did not leave
the answer sheet blank.”
Quoted in Rayport, page 294
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Better Tool: Option Analysis
• VC method: arbitrary discount rate selection
– 30% to 75%: all risk lumped together
– analyze and price the different risks separately
• Private equity and VC are staged investments
– typically 2-4 rounds of VC and PE
– milestones need to be met
• Price the optionalities directly: compound options
– each financing round resolves uncertainty
– follow-on investments: call option on firm’s stock
– option to abandon, scale back, exit
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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The Value of Option to Abandon
• Growth and strategy: “GROW or else…”
– perspective: no alternative to maturing quick (Netscape,
Geocities); so look at the converse to price growth!
• Idea: in each financing round, a company
valuation is performed to fix VC’s equity stake
– ex post, sequence of company valuations allows to back
out implied survival probabilities of project
– estimate Present Value of Option to Abandon:
PV(Abandon Option) = Expanded NPV - Passive NPV
= PVInv (Unconditional) - PVInv (Stage Fin.)
= Expected Savings in Investment
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Hurdle Rates for Venture Capital
Rates of Return (ROR) Sought by Venture Capital Investors
Stage
Annual ROR%
Typical Expected Holding
Period (Years)
Seed and start-up
First stage
Second stage
Expansion
Bridge and mezzanine
LBOs
Turnarounds
50 - 100% or more
40 - 60%
30 - 40%
20 - 30%
20 - 30%
30 - 50%
50% +
More than 10
5 – 10
4–7
3–5
1-3
3-5
3-5
Jeffrey A. Timmons, New Venture Creation, 4th ed., (Irwin: Chicago) 1994, p. 512.
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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The Value of Option to Abandon:
Growth and Survival Simulation
• IP Global Net: now quoted on EASDAQ
– realized by U. Hege, HEC and J. van Rijen, Residentie
Investments
– successful start-up with three financing round, over 20
months in 1999/2000
Seed
First
round
Second
round
IPO
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Est. Firm Value
V 0 = 3.98
Investment
I0 = 1.59
Discount rate
0.5
V 1 = 12.08
I1 = 3.24
0.4
V 2 = 27.43
I2 = 2.0
0.3
V 3 = 114.75
--
--
Private Equity and Start-up Valuation © Robert B.H. Hauswald
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The Value of Option to Abandon
Recursive values: dt matters most
V1 = d2 p2 ( V2 – I2 ), etc.
p2
p1
p3
IPO
I2, V2
1 - p3
I1, V1
1 - p2
I0, V0
V3
1 - p1
Stop
Stop
Stop
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Option to Abandon: Success
• Calculate implied survival probability pi as
Vi-1 = di pi ( Vi – Ii )
di = discount factor: contains all interesting information
• Assume salvage value Li = 0: if recapitalization
fails, often very little value left in early rounds
– for IPO clearly unrealistic
• We get: p1 = 68 %, p2 = 66 %, p3 = 31 %
– ex ante success probability was only p1 ·p2 ·p3 = 13 %
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Per Period Success Probabilities
Recursive values: dt matters most
V1 = d2 p2 ( V2 - I2 ), etc.
66%
68%
V3
31%
IPO
I2, V2
69%
I1, V1
34%
I0, V0
32%
Stop
Stop
Stop
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Success: Survival Probabilities
• Financial valuation (post money) implies ultimate
survival chance (total ex ante success probability)
– t = 0: success probability p1 ·p2 ·p3 = 13 %
– t = 1: success probability p2 ·p3 = 20 %
– t = 2: success probability p3 = 31 %
• Roughly corresponds to PE/VC rules
– increasing success probability p, decreasing r
– the higher post money, the lower p: why?
• Final round: success probability understated
– alternative would have been trade sale, not abandoning
– V2 = d3 (p3 V3 + (1- p3) T3 ): solve for p3
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Option to Abandon: Value
• Risk-neutral pricing: recovery of q from RA r
– discount factor contains risk premium information
– back out p: recall recovery of RNP in real options
• Value of the Option to Abandon RO = Expected
savings in investment costs
RO = d1 ·(1 - p1) ·I1 + d1 ·d2 ·[(1 - p1) + p1 (1 - p2) ] ·I2
= 0.76 + 0.61 = 1.38
Passive NPV = V0 - RO = 3.98 - 1.38 = 2.6
RO / Passive NPV = 1.38 / 2.6 = 53 % (in million EUR)
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Absolute Worst Outcome?
• Hidden information and/or hidden action
– the charm of control
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Agency Conflict and Real Options
• Keeping real options in start-up means
– adding option value to firm value
– but some of those real options are likely to reinforce the
discretion of entrepreneur: agency costs increase
• Trade-off determines optimal degree of optionality
– most visible than in exercise of growth options
• The dynamic agency conflicts can be expressed as
(real) options of entrepreneur
– option to manipulate depth, scope
– option to entrench = force continuation
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Firm Value and Real Options
• Explains a trade-off determining optimal
degree of optionality
Value
Option
Value
Agency Costs
Optionality
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Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Throwing Good Money after Bad
• Stage financing levers optionalities in VC
– commitment to pull the plug
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Summary and Outlook
• PE valuation in the information economy
– network economics drives rule of thumb methods; and
– business plans: raise and spend USD 50m on ads in 4Q
• Return to PE valuation and financial strategy in
the context of growth
– real options in PE or VC setting: to grow, abandon, exit
• Capital structure: from economics to finance
– principles: rooted in the economics of the firm
– equity: the currency of the new economy – why?
– the curious absence of debt – fact or fiction?
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Appendix A
Examples of Network Industries
• Almost by definition, most new industries and
products exhibit network characteristics
– a fortiori in an information intensive economy
• Examples: competition in technical standards
–
–
–
–
–
–
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computers: IBM vs. Control Data, PC vs. Apple
software: languages, compilers, application suites
video: Betamax vs. VHS
mobile phones: technical standards as barrier to entry
network software: Novell, Linux, NT, Netscape
pharmaceuticals: race to the market
Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Two Kinds of Networks
• Physical network: direct connection and
interaction
– Existence of a physical network
• Virtual network
– Community of demanders
– Actions affect each other indirectly
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Networks
• Physical
–
–
–
–
–
–
–
–
–
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• Virtual
Telegraph, telephone, fax
Trains, roads, airlines
Credit cards
ATMs
Cable TV
Broadcasting
Internet
Paging
Utilities: electric, gas
•
•
•
VHS video users
Operating systems
Software users
Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Virtual Networks
• No physical or electronic connection
• Benefits of increase in size appear in
ancillary and supporting markets
–
–
–
–
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Videotape users: Blockbusters
Recorded music: Hardware makers
Software: User base attracts developers
Operating system: Compatibility issue (This
one is complicated.)
Private Equity and Start-up Valuation © Robert B.H. Hauswald
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Network Topologies
Departure Point: A Non-network
Allison
Elizabeth
Julianna
Lesley
No network benefits in this configuration (save for
the trivial one – people like bigger communities).
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Two Way Switching Network
Bill
Star Network with Switching
Allison
Elizabeth
AOL/IM
Julianna
Lesley
Abel to Baker is not the same as Baker to
Abel. This is a two way network.
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Characteristics of Switching
Networks
• True positive network externality in consumption
– Usually large economies of scale in production
• Natural monopoly?
– Tipping
– Critical mass
– Winner take all?
• Two way communication to and from the switch
• Possible negative network externality: Congestion
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Network Economics
• Analytic foundations: networks lead to
– externalities: benefits (more wireless users) and costs
(traffic congestion) for other members
– lock-in effects: it is costly to switch – implies what?
– value of network depends on its state and members
• Metcalfe’s law (as attributed by George Gilder)
– developer of Ethernet and founder of 3Com
– if value of participating in a network is proportional to
number of users n, its total value is proportional to n(n
– 1) and increases in the square of the number or users
• Valuation of networks by multiples of users!
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Appendix B
IP Global Net
• Pricing financial flexibility: the option to
financially abandon a project
• Matching financial strategy with business
strategy: spot the optionalities
– staged development: compound options
– staged financing: why?
• Incentive effects for both parties
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Project Valuation Method 1:
Adjust Discount Rates
• The investment decision:
– Today: Invest $100
– In one year: get $V (normal distribution, mean =$110)
– T-Bill (riskless) rate = 5%
• Method 1: risk-adjust the discount rate (NIRL)
– Risk premium is 5%, so risk-adjusted rate is 10%
– E(V) is the expected value (mean) of V
PV =
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E (V )
r
V
=
110
= 100
1 . 10
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62
Project Valuation Method 2:
Adjust Expected Cash Flows
PV =
CEV
r
=
T − Bill
E * (V )
r
T − Bill
=
105
= 100
1 .05
• CEV = Certainty Equivalent Value
(indifferent between CEV for sure or V)
• E*(V) = Expected value using risk-adjusted
probabilities (p*)
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Finding Risk-Adjusted
Probabilities
• Go back to the case of the investment project
without an option: we know that there are two
ways to get the PV:
PV =
E (V )
r
V
=
110
E * (V ) 105
=
=
= 100
1 . 10
1
.
05
r T − Bill
• So, if we know PV outright, or if we know what
rV is, then we can back out the p*’s (basically, we
have the same distribution as for V, but with a
shift of the mean).
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Options Valuation:
Risk-adjusted Probabilities
• Option means contingency:
– quantify uncertainty: probability theory
– adjust probabilities for riskiness: risk-neutral pricing
• An investment problem with an option:
– today: Invest $100
– in one year: Max ($105, V)
(i.e. can sell facility for $105, or use it)
• Take expected value using risk-adjusted probabilities:
PV =
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E * [ Max(105, V )]
r
T − Bill
Private Equity and Start-up Valuation © Robert B.H. Hauswald
65
Staged Financing and Discount
Rate Selection: Experience?
• Start with risk-adjusted discount rate
– “market determined:” private equity investors
determine appropriate r from experience
• Back out risk-adjusted probabilities
– use post money valuations and risk-adjusted
discount rates to find implied probabilities
• Pricing the option to refuse funding
– same risk-adjusted probabilities to be used
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66
Per Period Success Probabilities
Recursive values: dt matters most
V1 = d2 p2 ( V2 - I2 ), etc.
66%
68%
V3
31%
IPO
I2, V2
69%
I1, V1
34%
I0, V0
32%
Stop
Stop
Stop
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Success: Survival Probabilities
• Financial valuation (post money) implies ultimate
survival chance (total ex ante success probability)
– t = 0: success probability p1 ·p2 ·p3 = 13 %
– t = 1: success probability p2 ·p3 = 20 %
– t = 2: success probability p3 = 31 %
• Roughly corresponds to PE/VC rules
– increasing success probability p, decreasing r
– the higher post money, the lower p: why?
• Final round: success probability understated
– alternative would have been trade sale, not abandoning
– V2 = d3 (p3 V3 + (1- p3) T3 ): solve for p3
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68
Options Valuation:
Risk-adjusted Probabilities
• Options means contingency:
– quantify uncertainty: probability theory
– adjust probabilities for riskiness: risk-neutral pricing
• An investment problem with an option:
– today: Invest $100
– in one year: Max ($105, V)
(i.e. can sell facility for $105, or use it)
• Take expected value using risk-adjusted probabilities:
PV =
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E * [ Max(105, V )]
r
T − Bill
Private Equity and Start-up Valuation © Robert B.H. Hauswald
69
Option to Abandon: Value
• Not risk-neutral pricing but recovery of true p
– discount factor contains risk premium information
– back out p: recall recovery of RNP in real options
• Value of the Option to Abandon RO = Expected
savings in investment costs
RO = d1 ·(1 - p1) ·I1 + d1 ·d2 ·[(1 - p1) + p1 (1 - p2) ] ·I2
= 0.76 + 0.61 = 1.38
Passive NPV = V1 - RO = 3.98 - 1.38 = 2.6
RO / Passive NPV = 1.38 / 2.6 = 53 % (in million EUR)
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Internet Related Start-ups
Red Herring
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Deal Flow by Sector
100%
1%
5%
5%
16%
16%
15%
80%
Other
60%
64%
54%
58%
Products &
Services
IT
40%
Healthcare
20%
24%
26%
26%
0%
4Q02
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2Q03
4Q03
2Q04
4Q04
2Q05
4Q05
Source: Dow Jones VentureOne/Ernst &Young
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72
Equity Investments by Sector
100%
1%
5%
11%
17%
3%
11%
80%
60%
Other
58% 63%
51%
Products &
Services
IT
40%
Healthcare
20%
36%
29%
36%
0%
4Q02
2Q03
4Q03
2Q04
4Q04
2Q05
4Q05
Source: Dow Jones VentureOne/Ernst &Young
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Deal Flow by Round
100%
9%
8%
11%
Restart
80%
39%
39%
37%
Later
60%
33%
40%
Second
20%
20%
First
*54%
20%
*35%
*32%
Seed
0%
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
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Investment by Round
100%
80%
9%
9%
Restart
31%
Later
45%
60%
49%
25%
Second
36%
40%
First
20%
20%
*43%
*42%
Seed
*22%
0%
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
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