Financial Eng

8/8/2019 Financial Eng

1/97

HEDGING & RELATED RISK

MANAGEMENT TECHNIQUES


2/97

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.


4/97

JOHNSON/STEIN APPROACH

Goal was to minimize the variance of profitassociated with the combined cash and futures

position.

This is applied to traditional commodities.


5/97

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.


7/97

ASSUMED BEHAVIOUR &

ACTUAL BEHAVIOUR OF BASIS

Actual

basis

Assumed

basisActual

path

Assumed

path

S(t)

F(t,T)

Time T

Contract

expiry


8/97

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.


9/97

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.


10/97

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


12/97

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.


13/97

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.


15/97

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


21/97

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


24/97

Three ways to visualize Building Blocks

approach

By way of risk and pay off profiles

Boxed cash flow diagrams

Time line cash flow diagrams


25/97

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


40/97

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


51/97

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


52/97

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


54/97

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.


56/97

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.


57/97

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.


58/97

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%


59/97

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


60/97

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.


61/97

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.


62/97

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.


64/97

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.


65/97

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


70/97

Introduction

A financial deal cannot exist without involvingtax issues.

Tax issues influence how a deal is structured.Such deals are tax driven.


71/97

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.


73/97

An engineered solution

Poison pill plans should be adopted whichcreates inchoate rights.


74/97

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


75/97

Danger:

In a recapitalization, a gain derived from thevalue of property ,other than securities, is

considered a realized gain for taxable purpose.


76/97

An Engineered Solution

RUKs common stock is consider a security soits inclusion in the offer will not generate

realized gain.


77/97

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


78/97

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.


79/97

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.


80/97

An Engineered Solution:

Starburst can make a interest rate swaparrangement.


81/97

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


82/97

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


83/97

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


84/97

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


85/97

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.


86/97

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


87/97

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


88/97

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


89/97

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.


90/97

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:


91/97

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..


92/97

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:


93/97

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:


94/97

Cont

Avoiding the transfer and closing

Solution:


95/97

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



Situation:


96/97

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:


97/97

Cont

Truck rent the land to Humbull or lease for peryear and reduce their property tax from

$90000 annual to $10000 annual.

Solution:

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