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Transcript of Financial Eng
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HEDGING & RELATED RISK
MANAGEMENT TECHNIQUES
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Factors affecting hedging
Risk profile associated with cash position.
Type of risk(all risk or downside risk) .
Cost of hedging with different hedginginstruments.
Effectiveness of different hedging instruments.
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Hedge ratio
Hedge ratio is number of units of the hedginginstrument necessary to hedge one unit of cash
position
Naive Approach. Johnson s and Steins methodology.
Johnson/Stein/Ederington (JSE) methodology.
Dollar Value Basis Point (DV01) Model.
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JOHNSON/STEIN APPROACH
Goal was to minimize the variance of profitassociated with the combined cash and futures
position.
This is applied to traditional commodities.
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JSE METHODOLOGY
Regress the change in spot price against change infutures price.
S = a + b * F + u
where S = S(t) - S(t-1)F = F (t,T) F(t-1,T)
u= error.
b= slope, minimum variance hedge ratio.a= intercept term.
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ASSUMPTION
Regression technique assumes that relationshipbetween regression variable (S) and explanatory
variable (F) is stable
Future price converges to spot price where basisvanishes at time of delivery.
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ASSUMED BEHAVIOUR &
ACTUAL BEHAVIOUR OF BASIS
Actual
basis
Assumed
basisActual
path
Assumed
path
S(t)
F(t,T)
Time T
Contract
expiry
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STORABLE COMMODITIES
The basis is explained by Cost of Carrying.
F(t,T) = S(t) * [1+r(t,T) + w(t,T) c(t,T)]
where r(t,T) is interest rate.w(t,T) is storage cost.
c(t,T) is convenience yield.
As time converges t approaches expiry T . The cost of carry converges to zero, so basis must
vanish.
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DV01
Its applicable to hedging of interest rate risk .
HR = DV01C * Y
DV01f
DV01 of cash & futures are continuously changingbut not necessarily at equal rates.
Yield beta should be periodically re-estimated.
It allows the financial institution to convert all it scash position to common bench mark.
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15 year XYZ bond offering semi annual coupon priced to yield
9.875%. The bond trader estimates it should yield only
9.640%. So bond is under valued. The trader buys $10 million
face value of bond. The trader identifies 7 year ABC bondoffering semi annual coupon to yield 8.25% he estimates it to
yield 8.48%. Bond is over valued. The trader sells $10 million
face value of the bond. The bonds are at par the proceeds from
short sale of ABC bond are sufficient to pay for XYZ bond.
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RISK MANAGEMENT REPORT
BOND POSITION MARKET
VALUE
DV01 Y HR BE
XYZ15 year
+10 M +10 M 0.077369 0.54 0.42306 + 4.2306M
ABC
7 year
-10M -10M 0.052366 0.59 0.31285 - 3.1285M
0 0 +1.102M
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Recent improvements in Hedging
Theory
Significant improvements in the works ofHKM.
To understand the improvements:
Calculate the hedge ratio using HKM in direct hedge
HKMs extension to cross hedges
Benefits from diversification by composite approach.
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Direct hedge employs future contract, written on anunderlying asset delivered in the same market, while
cross hedge is done in a different market.
Example: Winter wheat
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Hedge Ratio in direct hedge
Future price converges to spot price as futurescontract approaches expiry.
F(t,T) = S(t).[1+r+w-c] ; r+w-c: cost of carry
State the cost of carry as continuously compoundedrate (FV=PV.e^in)
Take r+w-c = y and
= length of time until contract expiry and stated as afraction of year.
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F(t,T) = S(t).e^y
S(t) = F(t,T).e^(-y)
Take e^(-y) = h (hedge ratio) Thus, h is dependent on .
To prove whether hedge ratio is estimatable.
ln (S(t)/F(t,T)) = -y ln (S(t)/F(t,T)) = z + d + v ; (-y=z+d)
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2. Hedge Ratio in Cross Hedges
Lets take subscript 1 for the underlyingcommodity on which a futures contract is
written and subscript 2 on cash position
commodity
S1 = F1.e^(-y)
S2 = a + b.S1 + u = a + b(F1.e^(-y)) + u
S2 = a + [b.e^(-y)].F1 + u
Hedge Ratio, h = b.e^(-y)
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3. Composite hedging
Simple hedge: contains single hedging instrument
Composite hedging: contains multiple hedginginstruments
Portfolio consisting of a no. of securities is lessrisky.
systematic
unsystematic risk Unsystematic risk can be reduced by
diversification.
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To determine the risk-minimizing hedge ratio,take the optimal hedge ratio, f = b.e^(-y)
The basis, B = S f.F
The effectiveness of the hedge is found fromthe coefficient of determination:
^2
=1
(B
^2
/ p
^2
) Take covariance of the ith and jth bases= i,j
Variance of the composite hedge;
c ^2 = injn wiwj i,j
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How composite hedging benefits?Futures Basis Spot Price Hedge
effectiveness
1 180 1225 85.3%
2 172 1225 86%
3 194 1225 84.2%
Covariance Matrix of the Bases
Futures
Futures 1 2 3
1 180 32 26
2 32 172 44
3 26 44 194
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Variance of the composite hedges basis byusing c ^2 = injn wiwj i,j = 83.3
Thus the hedge effectiveness =1- (83.3/1225)= 93.2%
Cost of hedge3. 1. 2. .Composite hedge
84.2%
85.3% 93.2%
86%
Hedge effectiveness
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Cost of hedging
Speculator are as: Passive risk bearers andactive forecasters.
Cost of hedging = f.(E[F(L,T)] F(t,T))
Effective hedge: degree to which it reducesrisk. The most effective hedge is the best
hedge
Efficient hedge: Hedge, for any given cost,provides the greatest risk reduction.
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BUILDING BLOCK APPROACH TO
HEDGING
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Concepts to be considered
Correct methodology
Size of the hedge
Alternative hedge instrument Possibility of composite hedging
The cost of alternative hedges
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Three ways to visualize Building Blocks
approach
By way of risk and pay off profiles
Boxed cash flow diagrams
Time line cash flow diagrams
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Miscellaneous risk management issues and instruments
In the over counter options market :
Path dependent option
Look back options
Option linked loans
Other forms of risk management:
Diversification
Credit enhancement
Over collateralization
Assignment
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CHAPTER22
CORPORATERESTRUCTURING
AND THE LBO
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Corporate restructuring and the
LBO
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Corporate Restructuring
The term corporate restructuringencompasses three distinct ,but related,
groups of activities Expansion, Contraction,
Ownership and control under its umbrella.
It is the perception of value gains thatmotivates the corporate restructuring and it is
the financial engineering which makes therestructuring possible.
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Expansion includes :-
Mergers- a)Horizontal merger
b)Vertical merger
c)Conglomerate merger
Consolidations
Acquisitions
Joint ventures which result in an enlargementof a firm or its scope of operations
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Strategies employed in corporate
acquisition
Friendly takeover
Hostile takeover
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Defenses against takeovers
Target block repurchase with an
accompanying Standstill agreement. Also
called as Greenmail.
Leveraged Recapitalizations(Recap).
Poison puts.
White knight through a managementled
leverage buyout or Management
buyout(MBO).
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Contraction results in a smaller firm ratherthan a larger one.
Corporate contraction occurs as a result ofdisposition of assets(sell-offs) which include:-
Spin offs- a) split-off
b) split -up
Divestitures
Equity carve-out
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MERGERS
Merger is of three types-:
1) Horizontal Merger- For eg Daimler-Benz and
Chrystler.2) Vertical Merger- For eg Apple with Intel
3) Conglomerate Merger- For eg Bharti Airtel
with Walmart.
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ACQUISITIONS
Acquisitions consist of two strategies namely-:
Friendly Takeover-: for eg diachy- ranbaxy
Hostile Takeover-: for eg take over of acompany called three par by hp.
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Contractions consist of the sell-offs which meansdisposition of assets.
It can be classified into-:
(i) Spin-off-: parent company transfers some of its assetsand liabilities to a new firm created for that purpose.
(ii) Divestiture-: involves an out and out sale of assets forcash.
(iii) Carve-out-:contraction between a spin-off and adivestiture.
.
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Steps of having Ownership and Control are-:
(i) Determining the terms of the members of
the board.
(ii) Issuing voting power to the members.
(iii)Providing the members with sufficient
power.
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The leveraged Buyout
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In 1980, publicly traded firms went private byemploying Leverage buyout or LBO
The acquisition of another company using asignificant amount of borrowed money (bondsor loans) to meet the cost of acquisition
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Leveraged buyout can be successful if-
1.its assets can be disposed of at a profit
2.The acquires company has an healthy cashflow
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Tools for going private
1. Junk bonds
2. Private placements
3. Bridge financing4. Merchant baking
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Junk bonds- high-risk, non-investment-grade bond with a low creditrating, usually BB or lower.
Junk bonds typically offer interest rates 3-4% percentage pointshigher than safer government issues.
Junk bonds have a issue ofRESET PROVISION
Private Placements-The sale of securities to a relatively smallnumber of select investors as a way of raising capital
Investors involved in private placements are usually large banks,mutual funds, insurance companies and pension funds.
Investors receives a higher return as registration costs are avoided
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Merchant Banking-is a new Endeavour for investmentbanks.
The investment bank takes a portion of the target firmsequity on its own books.i.e. the investment bankbecomes a equity partner in the leveraged buyout
Bridge Financing-is a method of financing, used tomaintain liquidity while waiting for an anticipated and
reasonably expected inflow of cash
These funds are usually supplied by the investmentbank underwriting the new issue. As payment, thecompany acquiring the bridge financing will give a
number of stock at a discount of the issue price to theunderwriters
For example-, when selling a house, the owner may notreceive the cash for 90 days, but has already purchaseda new home and must pay for it in 30 days. Bridgefinancing covers the 60 day gap in cash flows.
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Sources of value in a leveraged Buyout
Creates efficiency-decision making efficiency
Tax benefits
Agency problems-ownership and controlbecome one and the same,reduces the agency
costs
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Disadvantages of leveraged buyout
1. Cause layoffs of the firms employees
2. Damage debt markets
3. Force management to focus on short termgoals, by reducing advertising and research
budgets
4. Results in bankruptcies of the firm
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TYPICAL LEVERAGED BUYOUT
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XYZ CORP.BALANCE SHEET 1985
(ALL VALUES IN MILLIONS)
ASSETS Liability & equity
CurrentAssets Current Liabilities
Cash 0.20 accruals 0.25
Marketable Securities 1.55 accounts payables 0.75
Inventory 1.75 notes payable 0.50
Receivables 0.501.50
4.00 Long term debt 2.50
Fixed assets
Depreciable 12.00 Equity
Less cum dep (12.00) Common stock 0.50
Net 0.00 retained earnings 1.50Non depreciable 2.00 2.00
2.00
Total assets 6.00 Total liability & Equity 6.00
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Profit & loss -1985(all values in millions)
Sales 15.00
Cost of goods sold 8.00
Gross profit 7.00
Selling and administrative 5.50
Operating profit before depreciation 1.50 Depreciation 0.00
Operating profit 1.50
Interest expense 0.35
Earnings before taxes 1.15
Taxes (40%) 0.46 Earnings after taxes 0.69
Cash flow= earnings after taxes +depreciation
=$0.69million+ $0.00 million
=$0.69 million
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XYZ CORP.BALANCE SHEET 1985
(ALL VALUES IN MILLIONS)
ASSETS Liability & equity
CurrentAssets Current Liabilities
Cash 0.20 accruals 0.25
Marketable Securities 1.55 accounts payables 0.75
Inventory 1.75 notes payable 0.50
Receivables 0.501.50
4.00 Long term debt 11.50
Fixed assets
Depreciable 10.00 Equity
Less cum dep (10.00) common stock 3.00
Net 10.00 retained earnings 0.00Non depreciable 2.00 3.00
12.00
Total assets 16.00 total liability & equity 16.00
Profit & loss
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1986 1987 1988 19889 1990 1991
Sales 15.00 15.00 15.00 15.00 15.00 15.00
Cost of goods sold 8.00 8.00 8.00 8.00 8.00 8.00
Gross profit 7.00 7.00 7.00 7.00 7.00 7.00
Selling and administrative 4.00 4.00 4.00 4.00 4.00 4.00
Operating profit before dep 3.00 3.00 3.00 3.00 3.00 3.00
Depreciation 2.50 2.50 2.25 2.00 0.75 0.00
Operating profit 0.50 0.50 0.75 1.00 2.25 3.00
Interest expense 1.67 1.35 0.99 0.72 0.46 0.35
Earnings before taxes (1.17) (0.85) (0.24) 0.28 1.79 2.65Taxes (40%) (0.47) (0.34) (0.10) 0.11 0.72 1.06
Earnings after taxes (0.70) (0.51) (0.14) 0.17 1.07 1.59
Dividend 0.00 0.00 0.00 0.00 0.00 1.27
Cash flow: 1.80 1.99 2.10 2.17 1.82 1.59
Debt remaining:
Short term(10%) 0.50 0.50 0.50 0.50 0.50 0.50Long term bank(12%) 7.50 7.50 5.61 3.44 2.50 2.50
Bonds(18%) 2.20 0.21 0.00 0.00 0.00 0.00
Cumulative retained earnings (0.70) (1.21) (1.35) (1.18) 0.64 0.96
*projected
Profit & loss(all values in millions)
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The financial engineer at work
Engineers job : analyze the cash flows andstructuring a deal
Issues: Sensitiveness of the cash flows
Payment of buyout group for the firm
Kind of debt and how much debt
ESOP structure
Cash out
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Arbitrage : From the Ancient to
the ModernArbitrage
It involve simultaneous transaction in two or more
market in order to exploit price discrepancy
between the market
1.Spatial or Geographic Arbitrage
The arbitrage, sometime spelled arbitrager,seeks
to profit from the price between the market
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LAW OF ONE PRICE
Law of one price=
Pi=Pj+Zi,j
OR
Pi=Pj.Ej+Zi,j
2.Temporal Arbitrage or carrying-chargeArbitrage
Fi(t,T)=Pi(T)+Gi(t,T)
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3.Risk and taxe Arbitrage
4.Academic or pure Arbitrage
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Synthetic securities
It is a cash flow stream creation from acombination or a decomposition of cash flowsassociated with asset of instruments
Two of first synthetic instrument
A)synthetic puts
B)synthetic zero
Put call parity theorem
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Synthesizing derivatives
This is a multiperiod option , such as caps andfloor can be synthesized from a strip of a
single period put or single period call option.
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Cash and carry synthetic
A cash and carry transaction involves thepurchase of an instrument and simultaneous
sale of of a future contract against it in order
to create a synthetic short-term instrument.such synthetic short term instrument are
created in order to earn low risk short terms
rates.
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Suppose 20.5 year treasury bond carries acoupon of8.00% and is currently price at 9316/2. Atthis price instrument provides a yield to maturity8.68%this instrument is deliverable against the
six month forward t-bond futures with aconversion factor of1000. that is ,100,000 facevalue of this bond is deliverable per futurescontract .at the time of delivery, the bond it self
have a maturity of20
yearsthe future contract isprice at 932/32 so what is the return who buys thebond and sell it future.
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First The investor will receive a coupon $4 in a 6month.8/2=4
Now the investor is going to sell the instrument=93*32+16/32
=93.0625 Thus the investor have 4+93.0625 the investor will get =97.0625 Current cost is =93*32+2/3
=93.50 Bey=(97.0625/93.50-10)*2 =7.62%
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Cash and carry in arbitrage:- Enhancing
portfolio return
If the m.k.t were always efficient ,synthetic t-bill return the same rate as real t-bill. But it
depends on the mkt
Let us suppose
Strategy repo rate return net-profit
Cash and carry 7.34 7.62 28bps
Buy t-bill 7.42 7.62 20bps
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Synthetic long bonds
In this we would buy a 3 month t-bill togetherwith t-bond futures. This strategy require us to
equate the volatility of the bill/future position
with the voltality of the target bond that is thereal bond we are attempting to sythesize.
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Suppose you have dividend of $0.0765 at thetime the future contract matures and the t-
bond has a dividend of $0.0684. the yield beta
beta is 1000. how many futures having a facevalue of$0.1 million does it take to replicate a
$50 million position in target bond .asuming
the target bond is $47.5625 million.
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Determine the hedge ratio:-
Hedge ratio= 0.0765/0.0684*11.118
Determine the face value of futures position:-
Face value of future=hedge ratio *face value of position tobe replicated
=1.1184*$50milion
=$55.92
Determine the no of future contract needed:=
No of futures= face value of future needed/face value ofone futures
55.92/0.1=559
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SWAP
SYNTHESIZING A DUAL CURRENCYBONDA dual currency bond is a bond is the bond which is sold and
redeemed in one currency with coupon payment is another
currency.
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A fixed-for-fixed currency swap can itself be synthesized by
combining a fixed-for-floating currency swap with a fixed-for-
floating interest rates swap.
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Synthesizing a Foreign-pay ZeroThe investor has to buy the treasury zero and then enter two separate
swaps. The first swap is zero coupon interest rate swap in which the
investor is the zero coupon payer floating-rate receiver. The second
swap is a yen/ dollar zero coupon currency swap in which the investor
is zero coupon yen receiver and floating rate payer.
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The net cash flow after the cancellation the all set of
transaction appears to the end result in synthetic yen-
pay zero coupon bond.
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Synthetic Equity
A derivative instrument with the essential risk/reward
characteristics of a direct investment in a stock, a specific basket
of stocks, or an appropriately weighted basket of stocks
equivalent to a stock index.
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Qualitative differences between
synthetic and real securities
Identifying Qualitative differencesQualitative consideration
Alternative description cost issue time cost may rise
1
2
3
4
Fixed rate
issue(public)
Fixed rate
issue(public)
FRN with swap
CP with rollover
with swap
13.80%
14.00%
13.50%
12.05%
3 months
7days
3 months
7 days
No
No
No
Yes
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Tax Driven Deals
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Introduction
A financial deal cannot exist without involvingtax issues.
Tax issues influence how a deal is structured.Such deals are tax driven.
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Case 1: Preventing a hostile takeover
Situation:
Celene Corporation is fearful of a hostiletakeover by KEFEnterprises.
To discourage this attempt Celene plans todilute its stock ownership.
Celene plans to adopt a poison pill plan.
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Danger
The poison pill rights can be viewed by thetax authorities as a dividend distribution of
stock.
The shareholders would be reluctant to thepoison pill plan.
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An engineered solution
Poison pill plans should be adopted whichcreates inchoate rights.
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Case 2: Recapitalization of the firmSituation:
RUKs Corporation is heavily on debt and wants torecapitalize.
It plans to exchange securities previously issued for senior
notes.
The prospective purchasers will be reluctant to buy themunless RUK enhances the offer in a visible and tangiblemanner.
They want to offer one of the following: Cash rebates Market discount bonds RUK common stock
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Danger:
In a recapitalization, a gain derived from thevalue of property ,other than securities, is
considered a realized gain for taxable purpose.
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An Engineered Solution
RUKs common stock is consider a security soits inclusion in the offer will not generate
realized gain.
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An instrument can be considered a security on
the following rules:
Whether an instrument is equity based or debt
based
The length of the instruments term
Whether an instrument is secured
The likelihood of repayment on or before thematurity date
C 3 N fit T U l t d
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Case 3: Non-profits: Tax on Unrelated
Business Income
Situation:
Starburst Corporation is a nonprofit organization whoowns an extensive portfolio of investments.
It is planned that Starburst employ various riskmanagement techniques to minimize the risks to itsportfolio.
Starburst has asked its financial engineers to look atthe tax effect of using risk management techniques.
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Dangers:
Non profit organizations are taxed on theirunrelated business income.
Investment property within the InternalCodes definition of debt-financed property
generates unrelated business income.
Borrowed funds are considered as debt-financed.
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An Engineered Solution:
Starburst can make a interest rate swaparrangement.
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MEETING THE NEED FOR SHORT-TERM
FINANCING
Slade Enterprises needs to obtain short-termfinancing. Slade wants to avoid offering an
instrument which federal tax authorities might
view as a debt instrument. Slade is in very low
tax bracket.
Situation:
Avoidanceid
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of debt
instrument
Short Term
Preferred-share
Sell out
any
time
46 days holding
period(dividends
paid)
Auction
Success Failure
Penalty
rate
paid
To avoid tax
Tax exemption for
dividends
paid
Equity security
Avoidance of debt
Investor perception
Investor security
SELF LIQUIDATING PREFERRED
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SELF-LIQUIDATING PREFERRED
STOCK
SituationEmerald Enterprises,Inc wants to acquire EarlCorporation. Emerald would like this reorganization to be
tax free event to the extent possible .Danger
IRS
CONTINUITY OF PROPRIETARY INTEREST
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SECURITIES TO SHARE
45%of amount of
cash paid to Earls
share
50%CASH &
50% SHARES
SELF LIQUIDATION
PREFFERED STOCK
CONTINUITY OF PROPRIETARY
INTEREST
STOCK ISSUEDAT $50 WILLBEREEDEMEDAFTER FIVE YEARNOT
LESS THAN $50
Where Is a White Knight When You
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Where Is a White Knight When You
Need One
Situation
Bannor Corporation is fearful of a hostiletakeover by Satiuz Enterprises.Bannor has
good relations with Delea Corporation whichis not interested in or capable of taking overBannor.
Danger
Satiuz has prepared an attractive offer toBannors share holders.
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TAKE OVER
DELEA CONVERTIBLE
PREFERRED STOCK
SATIUZ PROVIDING EXCESSIVE CASH OR
VALUABLE SECURITIES WITH NO CURRENT
TAX GAIN TOBANNORS SHAREHOLDERS
ABOVE MARKET DIVIDENDRATE
& BELOW MARKET
CONVERSION PREMIUM
WHITE MAIL
TAKE OVERINSURANCE
The company sells the shares to third-
party at below-market prices. White mail
may not halt the takeover attempt all
together, but it does make the deal
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BOND SWAPPING
Techniques to lower your taxes and improvethe quality of your portfolio
Swapping can be a very effective investment
tool to:
increase the quality of your portfolio;
increase your total return;
benefit from interest rate changes; and
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BOND SWAP
Telva Corporation plans to issue a bond which will bepublicly traded. Telva might swap the Bond in the future
with a new bond which reduces the interest it must
pay.Telva believes that a bond swap will work.
DANGER If the issue price of Telva first bond for tax purposes will be
high than the issue price of the new bond ,this would
produce a significant tax gain.
The IRS does not require an actual physical change of bondsto find a bond SWAP occurred. The change of material
terms of an existing bond can be de facto.
SOLUTION
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SOLUTION
Adding a clause in the original bonds indenture for
the deduction in interest rate.RESPONSES
The repayment of the principal could be viewed as
the primary focus of a bond ,bond interest might beviewed as a less material aspect of the bond.
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Renegotiating Debt
Roth Corporation has issued $10 million worthof publicly traded bonds. Each Bond has a
$1000 face value. After the economic
difficulties, The trading price of the bonds has
dropped to $700.
Situation:
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The issuance of junk bonds to replace the current bonds.
Response New debt to generate cancellation of indebtedness income to
the extent that the principal amount of the retired debt
exceeds the IRSs new definition of the Issue Price of the
new debt. (As per the New IRS rules.)
Financial engineers would suggest the use of nonpublic tradeddebt whenever possible in this situation.
Solution:
Cont..
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Taxes and Costs on Real Estate Transfers
Volinstaad is unable to manage a wine productionand distribution business over the long term.
V
olinstaad seeks to aquire the real estate needed togrow and store large quantities of grape over the
next two years.
Volinstaad Corporation anticipates that it will have
applied $30 million of resources, of which $20million would be real estate costs, and would be able
to sell the entire business and its assets for $40
million
Situation:
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Taxes and Costs on Real Estate Transfers
Volinstaad buys the $20 million worth of real estate,
implements its plan and sells the real estate.
The transfer of land would generate the special costsand local taxes ($17,42,500) including Title
Insurance, Transfer Tax, Mortgage Recording Tax,
Filling ofDeed, Points to bank and application Fees.
Situation:
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Cont
Avoiding the transfer and closing
Solution:
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Real Property Taxes
y Tuck Corporation wants to buy one hundred acres
of industrial property as part of its expansionn
efforts. According to Tucks real estate
department has located the following properties-
1. 100 acre parcel of land Price - $5 million
2. 250 acre parcel of land Price - $6 million
3. 40 acre parcel of land Price - $3 million
Situation:
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Real Property Taxes
yTuck Corporation go with second property
option which is a farm called Southbridge
(Humbull Farms the owner). Tuck to buy it for
$1.5 million down
yTucks CEO approves the deal and signs thecontract to buy Southbridge.
yAfter that..
Situation:
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Cont
Truck rent the land to Humbull or lease for peryear and reduce their property tax from
$90000 annual to $10000 annual.
Solution: