Private Equity Flashcards
PE and VC (179 cards)
1
Q
Give 3 sources of value for Private Equity
A
- Re-engineer Portfolio Company to operate more efficiently
- Obtain more favourable debt finance
- Control mechanisms to align interests of management with Private equity owners
2
Q
Explain how private equity re-engineers a portfolio company
A
- Many private equity firms have experienced industry CEO’s and CFO’s
- They use expertise in reorganisation and consulting and contacts to improve portfolio company’s prospects
3
Q
Using MM explain how private equity firms get better access to debt markets than public companies?
A
- Using Modigliani-Miller - debt increases firm value (lowers WACC) due to after tax value of tax shield. If ROE > ROA
- Eventually increasing Leverage increases risk premiums and offsets value of interest tax shield.
PE firms reduce risk premiums of Leverage due to:
(A) Direct control over management
(B) Good reputation gained through previous transactions
4
Q
Using Jensens FCF hypothesis explain how private equity firms get better access to debt markets than public companies?
A
- Firms with high FCF and large capital budgets tend to invest in projects that destroy value (negative NPV’s)
- Increased leverage means increased debt service costs
- Increased debt payments keep management on their toes and increases scrutiny of new projects
- Increased debt payments reduce discretionary use of funds
5
Q
Which segments of debt markets help Private Equity obtain better terms for debt.
A
- Syndicated loans
- Debt issuance as CLO.
- High yield bonds risk transfer due to CDO’s
6
Q
Give 8 control mechanisms that better align management with owners.
How do these controls increase value?
A
- Board representation - at least for material events
- Required approvals - decisions of strategic importance
- Compensation of managers
- Non-compete clauses of founders and management
- Tag-along, drag along - new shares or acquirer offers made to all including management
- Earn-outs - ties equity valuation and price paid to future performance
- Priority in claims and distributions e. g. dividends
7
Q
What is a ratchet mechanism?
A
It enables the management to increase its equity allocation depending on the company’s performance.
8
Q
Name 6 techniques to value private equity portfolio companies
A
- DCF Analysis - mature companies
- Relative Value or market approach - mature companies
- Real Option - immature companies with flexible strategies
- Replacement cost - not for mature companies with positive cash flow
- Venture capital method
- Leveraged buyout method
9
Q
Which valuation techniques are suitable for mature private equity portfolio companies?
A
- DCF Analysis - mature companies
- Relative Value or market approach - mature companies
- Leveraged buyout method
10
Q
Which valuation techniques are suitable for early stage private equity portfolio companies?
A
- Real Option - immature companies with flexible strategies
- Replacement cost - not for mature companies with positive cash flow
- Venture capital method
11
Q
Describe DCF Analysis for Private equity
A
1.
12
Q
Describe relative value analysis in private equity
A
1.
13
Q
Describe real option analysis in private equity
A
1.
14
Q
Describe leveraged buyout method in private equity
A
1.
15
Q
Describe replacement cost method in private equity
A
1.
16
Q
Describe venture capital method in private equity
A
1.
17
Q
How does use of debt magnify exit value for stockholders?
A
- ROE = ROA x Leverage (average assets / equity)
18
Q
What are the Cash flow characteristics of Buyout and VC investments?
A
- Buyout - steady and Predictable cash flow, realistic projections
- VC - unpredictable, unrealistic projections
19
Q
What is the market position characteristics of Buyout and VC investments
A
- Buyout - attractive market position, proven niche
2. VC - low market history, new market, unproven niche
20
Q
Compare the asset base of a Buyout investment and a VC investment.
A
Buyout - significant possible collateral
VC - weak, not a collateral asset
21
Q
Compare the management team of a Buyout investment and a VC investment.
A
Buyout - strong and experienced management
VC - newly formed, entrepreneurial
22
Q
Compare the leverage of a Buyout investment and a VC investment.
A
Buyout - extensive use of senior, mezzanine and junior debt
VC - primarily equity, limited debt
23
Q
Compare the risk measurement of a Buyout investment and a VC investment.
A
Buyout - mature, operating history, measurable risk
VC - lack of operating history, new markets, new products, new technology
24
Q
Compare the exit strategy of a Buyout investment and a VC investment.
A
Buyout - Predictable exits: secondary buyout, strategic sale, IPO
VC - Exit difficult to anticipate: IPO, trade sale, secondary venture sale
25
Compare the cost reduction / control of a Buyout investment and a VC investment.
Buyout - potential to restructure etc
VC - significant cash burn rate required to establish business and product in the market
26
Compare the working capital requirement of a Buyout investment and a VC investment.
Buyout - low working capital requirement
VC - increasing need for working capital when entering growth phase
27
Compare the due diligence of a Buyout investment and a VC investment.
Buyout - full blown due diligence before investing (FLECTS)
VC - focuses on technology & commercial. Limited due to lack of operating history.
28
What is the full blown (FLECTS) due diligence in buyout investments
FLECTS
```
Financial
Legal
Environmental
Commercials
Tax
Strategic
```
29
Compare the goal setting and monitoring of a Buyout investment and a VC investment.
Buyout - monitor cash flow, strategy and planning
VC - monitor business plan milestones
30
Compare the returns of a Buyout investment and a VC investment.
Buyout - lower variance, lower bankruptcies
VC - few very high returns and many write-offs
31
Compare the capital markets activity of a Buyout investment firm and a VC investment firm.
Buyout - investors typically have significant capital markets footprint
VC - investors less active in capital markets
32
Characterise transactions of a Buyout investment firm and a VC investment firm
Buyout - auctions, multiple acquirers
VC - proprietary and / or relationship based
33
Compare the growth through subsequent fund raising of a Buyout investment firm and a VC investment firm
Buyout - well performing buyout firms attract large funds
VC - tend to be less scalable, grow less quickly
34
Compare the remuneration of a Buyout investment GP and a VC investment GP
Buyout - carried interest, management fee, monitoring fees
VC - carried interest is main fee, management and monitoring fees are rare
35
Compare the products of a Buyout investment and a VC investment.
Buyout - established products
VC - uncertain, new technologies
36
Which two private equity valuation methods require market data?
1. Relative valuation
| 2. Income approach (DCF)
37
What are the 4 key valuation issues for Buyout vs. Venture capital
1. Use of DCF method
2. Use of Relative Value approach
3. Use of Debt
4. Drivers of Equity returns
38
Are Buyouts of VC investments most suitable for DCF methods?
| Why?
Buyouts are most suitable.
Buyouts are mature companies with Predictable cashflows.
VC investments are less mature and have uncertain cashflows
39
Is the relative value method more suitable for Buyout or VC investment?
Why
It is used in buyout vuations to check DCF method analysis
It is difficult to use for VC Investment because there may not be any comparable companies
40
Which type of investment uses debt capital most, Buyout or VC Investment
Buyout - tend to be mature with developed capital stacks of senior, subordinated and mezz
VC investments tend to be early stage with mostly equity funding
41
What are the key drivers of Equity returns for Buyout investment
"Ged red me"
Growth Earnings
Debt RED
Multiples on Exit
42
What are the key drivers of Equity returns for VC investment
VCs have PREMONitions and VALUE INternal DiLUSIONS
1. Pre-MONEY VALUATION
2. INVESTMENT
3. SUBSEQUENT DILUTION
43
Los 41e - What are the Four exit routes for Private Equity Firms
"I Like S&M"
IPO
Liquidation (asset sale)
Secondary market sale
MBO
44
Los 41e - explain private equity exit by IPO, how does it impact value?
1. Taking a company public.
2. Takes time, costly, lose flexibility
3. Achieves highest value (highest multiple) because:
a. Shares are more liquid
b. Public companies attract better management
45
Los 41e - explain private equity exit by Secondary Market, how does it impact value?
1. Sell the investors position to another investor where investment value is greater than market price or FV assets. Usually a sector specialist that can add value or grow the business.
2. Results in the seconds highest valuation possible after IPO
Not common for VC's
46
Los 41e - explain private equity exit by Liquidation, how does it impact value?
1. A sale of the company's assets
| 2. Lowest value, since there is no value placed on the firm
47
Los 41e - explain private equity exit by MBO, how does it impact value?
1. The management by the firm with a leveraged finance package from investors.
2. May add value in theong term through alignment of management interests. But leverage reduces flexibility. (Jensens theory).
48
What type of market data does DCF (Income) approach use?
Comparable companies
1. Discount rate
2. Growth rate
3. Target Betas
4. Target Leverage ratios
49
What type of market data does Relative Value approach use?
Comparables
1. Adjust ratios for stage in life-cycle of target company vis a vis comparable.
50
What is committed capital
The amount promised by LP' s available to be drawn down for investment
51
What is paid in capital
The amount of funds received for investment in portfolio companies
52
What is the NAV of a PE fund
NAV=
ASSETS (value of fund assets)
- ACCRUED Expenses (unpaid)
53
Name 6 ways to value fund assets
1. COST without adjustments until EXIT
2. COST - adjustments for financing and revaluation
3. Lowest of COST or MARKET
4. Marked to MARKET (comparables) with adjustments for illiquidity
5. Marked to Market with discount for restricted securities
6. Re-value on new financing
54
Describe the 8 Economic Terms of a PE fund
Management fees
Transaction fees
Carried interest
Ratchet
Hurdle rate
Target fund size
Vintage year
Term of fund
55
What is a limited partner
1. Provides fund for investment
2. No management responsibility
3. Limited liability
56
Wha is a general partner
1. Manages the fund
| 2. Jointly liable with other GP's for the funds debts
57
Which two types of documents describe a PE fund terms
1. Prospectus
| 2. Limited partnership agreement
58
What two categories of fund terms are there?
1. Economic Terms
| 2. Corporate Governance Terms
59
What 3 fund values can management fee be based on?
1. Committed capital
2. Paid in capital
3. NAV
60
Explain the importance of EXIT Timing for portfolio company value
1. Flexible - do not sell in weak markets. Consider buying additional companies that can merge with portfolio companies.
2. Long term forecasts of exit price are uncertain.
61
What is the main purpose of PE valuation
1. Provide a reference (benchmark) for negotiation of buy or sell
2. Assess the future potential to generate cash flow and hence value
62
What are the two forms of Private Equity fund structures
1. LLP - Limited liability partnership
| 2. CLS - Company Limited by shares
63
Explain how PE fund structures limit redemptions
Most funds are closed end
(A) Redemption only allowed at specified periods
(B) New investors (LP's) only allowed at:
specified times, or
at managers discretion
64
Who benefits from a company limited by shares
The GP
65
What are the two main activities of a PE fund
1. RAISING FUNDS
| 2. MANAGING FUNDS
66
Name the 5 stages of a PE Fund
MIRE
```
1. Marketing
2 investment
3. Realisations / return of capital and exits
4. Extension
5. Follow on Fund
```
67
What is the usual duration term if a PE fund
10-12 Years
+ 2-3 years extension
68
What are the four components of exit value
Ice Grid in Post Mortem
1. Investment Cost
2. Earnings Growth
3. Reduction in debt
4. Increase in Price Multiple
69
Which components of the exit value can a PE firm improve
GEt RID in afternoon PM
Growth Earnings
Reduction in Debt
- > Increase in Price Multiple
70
How does a PE firm enhance the components of Exit Value
GEt RID in afternoon (PM)
1. Operational improvements
2. Better governance
3. Financing
LEADS TO
- increase Earnings GROWTH
- Reduction In Debt
71
What is forecast IRR for PE investments sensitive to?
Time to Exit
Exit Year
72
Outline the steps to compute payoff and IRR for PE investments
1. Calculate exit value
2. Calculate claimants profits
A. PE provided Debt (less paid down debt)
B. PE preference shares
C. PE & MEP share of Residual profit
73
What two valuation figures are relevant for PE and VC
Pre-MONEY valuation
Post Money valuation
74
Describe post money valuation
Post money valuation = (Pre money valuation) + (new investment)
75
What is the calculation of VC share after its investment
Post money share = Investment / (Post money value)
= (Investment) /(investment + pre money value)
76
How does a VC investor estimate Pre-MONEY valuation?
Estimate or value the following
1. IP - e.g. Patents
2. other Intangibles - e.g. Knowhow
3. Product potential
4. Potential markets
5. Financial assets e.g. capital
6. Replacement cost of other assets
77
Describe LBO model
1. Not a valuation model
2. Incorporates the capital structure in determining expected returns for a PE investor.
3. Gives a reference price for negotiation
78
What are the 3 main inputs of a LBO model
1. Forecast of future cash flows
2. Expected return for each provider of capital
3. Total amount of financing
79
How is the LBO model used
1. Determine the maximum price to pay to acquire the target company
2. Estimate EXIT value at various EXIT YEARS
80
What is EVEBITDA
1. EXIT VALUE obtained from comparables - relative value (Market multiple) approach
2. For various EXIT YEAR scenarios
81
What is a buyout
When a buyer acquires a CONTROLLING Stake in a target company
82
Give 3 examples of private equity buyout types
MBO - management buyouts
LBO - leveraged buyouts
Takeovers
83
Give 4 components of an LBO's finance stack
"Mesh"
Mezzanine
EQUITY
SENIOR debt
HIGH YIELD
84
What is the largest component of a LBO finance stack
Senior debt (amortised over time)
85
What is mezzanine finance
Tailored for each transaction
| Bridge between Equity and debt
86
In LBO's what type of debt is amortized
SENIOR
87
What are the two types of PE Fund waterfall
Deal by deal
Total Return
88
Describe a deal by deal waterfall
1. GP gets carried interest after each deal
| 2. Results in earlier distribution to GP
89
Describe a total return waterfall
1. Carried interest is calculated on the entire portfolio value
2. This results in earlier profit distribution to LP
90
Which type of waterfall favours GP
Deal by deal
91
Which type of waterfall favours LP
Total return
92
What are the two types of total return waterfall called
1. Committed capital
| 2. Invested capital
93
How does a total return committed capital waterfall work
1. GP receives carried interest after committed capital has been returned to LPs
94
How does a total return invested capital waterfall work
The fund must return some threshold above invested capital to LPs before the GP receives carried interest
95
Describe the PE term "Transaction fees"
1. Amount paid to GPs for transactions (deals)
| 2. This cost is in management fees so is split between LPs and GPs
96
What is carried interest? How is it usually calculated
1. GP share of the fund profits
| 2. Typically 20% of net fund profits (after management fees)
97
What is a ratchet. How is it calculated.
A mechanism to allocate equity from the PE fund to the management of the Target Company.
Based on actual future performance of portfolio company and its return to the PE fund
98
Describe the term, Hurdle rate.
| How is it calculated.
1. The IRR that must be achieved before the GP receives carried interest.
2. Aligns GP with LP
3. Usually 7-10% of profit
4. Can be deal by deal (portfolio company) or
5. Total return (entire fund)
99
Describe the term "target fund size". What does it show?
1. The fund size stated in the prospectus or PPM
| 2. The fund size the GP is comfortable in managing
100
How do investors view a failure to raise to full amount of target fund size
Questions the GP abilities
101
What is "Vintage Year"
The Launch year of the fund
102
List 9 key Corporate Governance terms for a PE fund
1. Key man
2. Disclosure & Confidentiality
3. Distribution Waterfall
4. Tag along, drag along
5. No fault divorce
6. Removal for cause
7. Investment restrictions
8. Co-investment
9. Clawback
103
Give two examples of investment restrictions
1. Max Leverage
| 2. Min Diversification
104
What are Co-investment rights
1. LPs have first right to invest in other funds managed by GPs
2. Prohibition of using two funds managed by the same GP in the same portfolio company at different times
105
Give an example where a GP of two fubds is conflicted
1. Investing in the same portfolio company at two different times and later when it's struggling
106
Give 5 reasons why due diligence in PE Funds is important
1. Difference in returns between top performers and poor performers is very high
2. Performance is persistent
3. Historical analysis of performance has information
4. PE is illiquid but
5. Good performance leads to interim exits, returning capital and improving liquidity
107
What is the risk of calculating NAV of a PE fund only when new financing rounds?
If financing is infrequent the NAV will be stale
108
What is the risk for NAV with portfolio company valuations
1. No active market for Private companies
| 2. Portfolio companies cannot be valued with certainty before EXIT
109
What are the issues for committed capital with NAV calculations and performance measurement
1. LP's are obliged to satisfy calls for committed capital - held in liquid low return instruments
2. Committed capital is not included in NAV calcs but is an effective liability for the LPs
3. GIPS methods are based on PIC:
DPI
+RVPI
=TVPI
110
How do different strategies affect PE Fund NAV methods
1. Different strategies have different maturities e.g. Early stage VC vs buyout
2. Early stage are valued at cost
3. Mature companies are valued at relative (market comparables)
111
What valuer does LP prefer
1. Third party
112
What type of portfolio company is most affected by asset price bubbles
Inflate mature companies close to exit
113
Describe two-features of a key man clause
1. Names key executives in the PE Fund management (GP)
| 2. New investments may be prohibited if a key person leaves and is not replaced
114
Describe two disclosure and confidentiality terms
1. Only permitted fund performance information may be disclosed by investors
2. Disclosure by investors of portfolio company information is generally prohibited
115
Describe 3 elements of a claw back provision
1. Maintains the profit share ratio between GP and LP
2. True up, periodically reconciles for lower future performance and over payment of carry
3. GP is required to return fees, expenses and capital contributions so that performance sharing is as initially agreed.
116
When are claw backs usually executed
1. Fund Termination
| 2. Periodic true ups e.g. Annual reconciliations
117
What are Tag-along, drag-along rights
1. Acquisition offers are extended to all shareholders of PE fund
2. Acquisition offers are not limited to only controlling shareholders
118
What is a no-fault divorce clause? What is usually required.
1. The right to remove a GP without cause
| 2. A supermajority vote of 75%
119
What is removal for cause
1. Removal variety of reasons, or
| 2. Termination of fund
120
Give five issues that provide "cause" for termination
1. Gross negligence
2. Key person events
3. Felony
4. Bankruptcy of GP
5. Material breach of fund terms
121
Give two differences between private and public equity funds
1. Drawdown of committed capital
| 2. J - curve returns patterns
122
How is committed capital used differently in private equity than in public equity
1. In public equity committed capital is deployed immediately
2. In private equity committed capital is called and drawn down as it is invested.
123
What is the j-curve pattern of returns
1. For some Private equity and VC
2. Starts off negative but turns positive
3. High risk of loss until loss making period ends
124
Give 5 kinds of risk in private equity
1. General PE risk
2. Strategy risk
3. Industry
4. Geographical
5. Investment vehicle/structure
125
List 10 general private equity risks
1. Agency
2. Capital
3. Competition
4. Diversification
5. Liquidity
6. Market
7. Regulation
8. Tax
9. Unquoted
9. Valuation
126
Describe agency risk in PE
1. Managers of portfolio companies not aligned with the PE fund
2. High in early stage deals or where management has a controlling stake
127
Describe capital risk in PE
1. Investors may withdraw capital in regimes of higher risk
| 2. Subsequent rounds for portfolio companies more difficult than expected.
128
Explain liquidity risk with PE investments
1. PE investments do not have a public market
2. No active secondary market
3. Difficult to liquidate a position
129
Describe diversification risk in PE
1. Single funds may be poorly diversified
| 2. Investors should diversify across stage, strategy and vintage
130
Describe competition risk in PE
Competition for reasonably priced portfolio investments may be high
131
Describe regulatory risk in PE funds
Government regulations may affect the goods and services of portfolio companies
132
Explain tax risk for PE
Fund returns may be taxed differently at some point in the future
133
Explain valuation risk in PE
Valuation of portfolio companies may have significant subjective not independent and objective judgement
134
Explain unquoted risk in PE
Private companies are not quoted on public markets and may be riskier than public companies
135
Explain market risk
Private equity is subject to long term changes in market risks such as interest rates and fx
136
List 7 PE fund costs
"Mat's Pad"
1. Management (and performance)
2. Administrative
3. Transaction
4. Setup
5. Placement
6. Audit
7. Dilution costs
137
Explain PE fund management fee costs
1. Typically higher than other investments
| 2. 2 and 20
138
Explain Administrative cost in PE. How often charged?
1. Custodian
2. Transfer agent
3. Accounting
Charged annually.
139
Explain transaction costs in PE Funds
Purchase costs of Portfolio companies
1. Due diligence
2. Bank financing
3. Legal
Sales costs for exits
140
Explain setup costs of PE funds
1. Legal, regulatory, listing costs
| 2. Amortised over fund life
141
Explain placement fees in PE funds
Placement agents charge
1. Often 2% up front, or
2. Annual trail fees
142
Explain audit costs for PE funds
Fixed costs
| Charged annually
143
Explain Dilution costs in PE funds
1. Where portfolio companies require additional rounds of finance
2. Where additional options are granted
144
What is the GIPS return metric for PE?
IRR calculated gross or net of fees
145
Which IRR measures cash flow between PE Fund and Portfolio companies
GROSS IRR
146
What two things does Gross IRR show
1. Ability of PE fund to generate returns
| 2. Cashflows between fund and portfolio
147
What type of IRR is most relevant to LPs
Net IRR
148
How is Net IRR different to Gross IRR. What does it represent
Net of
1. Management fees
2. Carried interest (performance)
3. Other compensation
Represents cash flow between PE Fund and LPs
149
Explain the use of Multiples to evaluate PE Funds. Give 3 benefits and 1 issue with Multiples for PE fund performance evaluation
The ratio of (total return to investors) / (total amount invested)
Total return to investors is Net of fees, carry etc
Multiples are therefore a net measure of PE fund performance
1. Simple to calculate
2. Easy to use
3. Differentiate for realised and unrealised returns
Does not incorporate time value of money
150
Give two ways of evaluating PE fund performance
1. IRR
| 2. Multiples
151
What is the main issue assumed with IRR of private equity
All interim cashflows are reinvested at the IRR
152
What is PIC in absolute
Cummulative (total capital drawn down)
153
What is PIC%
=(total capital drawn down) / (committed capital)
154
Define DPI. Is it gross or net? What is it net of?
DPI=(all realised distributed returns)/(PIC)
It is net of all fees and carried interest.
It is cash on cash return. COC.
155
What is RVPI? Is it gross or net?
RVPI = residual unrealised (undistributed) returns / (PIC)
It is net of management fees and carried interest
156
What is TVPI? Is it gross or net?
DPI + RVPI
Net
157
What are the line items to calculate NAV after distributions
NAV before distribution
- Carried Interest
- Distributions
= NAV after distributions
158
What is the purpose of scenario analysis for adjusting Terminal Value
1. Place bounds around company valuation
| 2. Aid negotiation and bargaining power
159
Compare Private Equity IRR vs Benchmark index returns
1. PE IRR is cash flow weighted return
| 2. Index returns are time-weighted
160
What 3 criteria are important to compare PE funds
Use
1. Comparable Peer Group
2. Median returns
3. Vintage year (cyclicality and common start)
161
What is POST using NPV
Post money value = PV(exit value)
162
Define Pre Money value (NPV and IRR)
Pre money value=post money value - investment
163
What is f VC using NPV method
f = INV / POST
164
Describe Post in terms of VC ownership
POST = INV / f
165
Describe Post money value for a future exit value (IRR and NPV)
Post = (Exit n) / ( 1+R) ^ n
166
What is VC required wealth using desired IRR
Required wealth = INV x (1+IRR)^n
167
What is f of VC ownership using desired IRR
f = Required wealth / Exit
f = FV (INV) / Exit
f = INV x (1+IRR)^n / Exit
168
What is #shares VC given f
#shares VC = #shares Founder x f / (1-f)
169
Describe the price per new share issued to VC investors
PRICE VC = INV / #shares vc
170
Give 4 line items to calculate NAV before distributions
Beg NAV (last NAV after distributions)
+ capital calls
- fees
+/- Operating Results
171
Give 4 line items for calculating CARRIED Interest payable
NAV before distribution
- hurdle
x CI %
- previous CI paid
= CI payable
172
What is the VC fraction, f. What is the founder % post?
f = INV / POST
Founder Post % = (1-f)
173
What is # new shares to issue to VC given f
#shares VC = #shares Founder x f / (1-f)
174
What is price per share to VC
Price per share VC = INV / (#share VC)
175
Describe r* for VC return
(1+r*) = (1+r) / (1-q)
176
What are the two ways of adjusting for probability of failure
1. ADJUST R upwards => R*
| 2. Reduces Terminal Value
177
Give 3 problems with estimating Terminal Value for VC investors
Usual valuation is based on forecast cash flow and earnings-multiples
1. Cash flow is uncertain, earnings are uncertain
2. Price multipliers are volatile
3. Forecast Terminal value is sensitive to both earnings and multiplier uncertainty
178
What are the first 5 phases for calculating multiple VC rounds
1. Discount rates
2. Calculate POST & Pre for second round
3. Calculate POST & Pre for first round
4. Calc f for second round
5. Calc f for first round
179
What is the number of second round shares given f2
#shares VC_2 = ( #shares VC_1 + #shares Founders) x [ f2 / (1- f2)]
