Introduction to Corporate Finance (Centre College ECO 353)

8/14/2019 Introduction to Corporate Finance (Centre College ECO 353)

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Corporate Finance Notes

4-3-08

Options, Futures, and Derivatives

Derivative Something that obtains its value from something else Financially engineered commodities Stripped down combinations of anything you can think of

Options, futures, forwards oldest forms of derivativesIts difficult to regulate new derivatives

Very risky

Options A contract that allows you to buy or sell a specified financial asset at a specified

strike price at a specified time and placeo Price = option premiumo Normally sold in 100 share lots

Come in 2 formso Call option to call in or demand the asset at a specific price over a

specified time periodTypically a bullish actionOnly want to act on an option when the share price is above thestrike price listed on the option

o Put option to sell shares at a specified price over a specified timeBearish on the pricesOnly sell when the market price is lower than the strike price listedon the put

Basic option properties:1. The buyer of the call/put always has the flexibility2. The buyers maximum exposure is equal to the premium price of the option, while

the sellers exposure is significant and depends on the markets fluctuation3. Options are a zero sum game no total gains. Every gain is a loss for someone

else.4. A necessary condition for the transaction of an option to take place is that the

buyers and sellers expectations about the future price of the underlying assetmust differ pro quo, the zero sum game


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5. Hence, institutional differences between buyers and sellers usually arise, sellershave more information and more experience they are the ones taking on thehigher risk and thus would have to be fairly well informed to continue operations

Ps = strike priceq = option premiumP t = price of underlying asset at time t T = terminal time for the option

Calls

t = P t P s q 0Profit is the price of the stock at time P less the strike price and the option cost

q = sunk cost, need not be considered when deciding when to exercise the option

Also, at issuance, t = P 0 P s q 0 0

Thus,P0 P s + q 0

Since profit is current price minus strike price minus the cost of the option, the price atthe issuance of the option, P 0, cannot be greater than the strike price plus the option priceor there would be the profit opportunity for infinite arbitrage

Payoff map for calls

Buyers of Calls Sellers of Calls

Max Profit q0Max Loss -q0 -


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A buyer of a call or an option needs to monitor the stock price daily in order to know if its a good time to cash in the option.Sellers do not. They have no further decisions to make.

Its very important at initial investment to: Set a maximum price at which you will sell no matter what the prospects look like Set a minimum price at which you will ditch and sell the option You could be right and have a great increase in the price of the stock but then lose

your gains because you greedily wait too long for a greater increase

Sellers have two real choices when issuing options They can cover their position by going long in the stock and buy more of the

stock at issuance of the options Or, they can go naked and hold no shares of the optioned stock

Ex-post value of callsV = ex post value

Price

No opportunity

Path of stock price

Ps + q 0

P0 = Ps

t


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Puts

t = P s P t q 0Profit for the buyer of a put is the strike price less the price of the stock at time t less the

price of the option

Also, t = P s P 0 q 0 0

Thus,P0 P s + q

Again, similar to the case with calls, the market price of the stock at issuance of theoption must be lower than the strike price of the option plus the cost of the option or elsethere would be a perfect arbitrage opportunity for infinite profit

Ps

V - buyer

V - seller

V

P

45

Buyers of puts Sellers of puts

Max Profit Ps q 0 q0Max Loss -q0 - P s + q 0


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Payoff map for calls

Ex post value of putsV = ex-post value of puts

Price

No opportunityPath A

Path B

P

V - buyer

V - seller

Ps

Ps - q 0

P0 = P s

t

V


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Expected profit functions for buyers/sellers of callsPh = high price outcomeP l = low price outcome

buyer: h = (P h P s) q 0 h = -q 0

a = buyers probability that P h will prevail = (a)( h) + (1-a)( l)

= a(P h P s) q 0The likely profit for the buyer of a call would be the probability of the high priceoutcome times the difference between that outcome and the strike price, less the price of the option

seller: h = q 0 + (P s P h) h = q 0

b = sellers probability that P h will prevail = (b)( h) + (1-b)( l) = (b)(q 0 + P s P h) + (1-b)(q 0)

= q 0 + (b)(P s P h)The probable profit for the seller is equal to the price of the option plus the probability of the high outcome times the difference between the strike price and the high price.

Requirements for buyer and seller: Buyer: = (a)(P h P s) q 0 > 0 Seller: = q 0 + (b)(P s P h) > 0

Must-be case for the seller: 0 > (b)(P h P s) q 0 This makes sense because it shows that the sellers expected probability that the

high price will prevail, b, times the difference in the high price and the strike price, an amount that erodes their profits (they agreed to sell the stock at the strike


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price so any difference between that and the market price is something they haveto pay), less their payoff, the selling price of the option, must stay below zero or they will never offer the option.

Must-be case for the buyer:

(a)(P h P s) q 0 > 0 This is simply the profit formula for the buyer, so, of course they expect that it

will be greater than 0.

Together these show that: (a)(P h P s) q 0 > 0 > (b)(P h P s) q 0 Or simply, (a)(P h P s) q 0 > (b)(P h P s) q 0 This relationship shows the necessary difference in expectations between the

buyer and seller of an option in order for the transaction to take place. The buyer must expect a greater probability that the high price will prevail. This alsohighlights the zero-sum game nature of options. Adding the two sides of this

equation together comes to zero, a complete wash. This equality can even be taken down to a more condensed level by simplifying

to: a > b. This most clearly states the necessary relationship between the buyersand sellers expectations in order for the transaction to take place that the buyer must expect a higher price more than the seller.

4-8-08

Techniques for using options other than trading them: Hedging Insurance

Protective put: Used if youre long in an asset holding it for a long-term profit Wise if youre substantially invested in the asset


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(PV = portfolio value, P = price of stock)

To insure against possibly losses you buy a put at the same price as your current asset forms a protective floor on your losses such that they can only be equal to the price of theoptions instead of an unspecified decline in the stock price.

The Straddle: Used when you expect significant volatility

PP0 = P s

No opportunity

P0

P0 + q

PV


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Buy calls and puts for both ends of the volatility Cost = q c + q v Not holding the asset Straddle compresses the volatility of the assets its being operated on: people

exploit the option and reduce the volatility by arbitrageo Hard to find patterns that are exploitable

Pyramid: Expect little volatility

o Short term Choose a lower bound and an upper bound for P such that P 0 P L = P H P 0

o P0 is between P L and P Ho 2P 0 = P L + P H

qc + q v No opportunity

P0 = P s

Call pay-off function

PP

LP

H

PV


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Cost = q L + q H 2q 0

Payoff functions

Price State Buy Call(P s = P L)

Sell 2 Calls(P s = P 0)

Buy Call(P s = P H)

Pay-off

P t P L 0 0 0 0

PL < P t P 0 (P t P L) 0 0 (P t P L)

P0 < P t < P H (P t P L) -2(P t P 0) 0 (P t P L) -2(P t P 0)

P t P H (P t P L) -2(P t P 0) (P t P H) (P t P L) -2(P t P 0) +(P t P H)

Profit is equal to whatever the payoff is because the cost is 0

PL

P0

PH P

buy a call #1

buy a call #2

PV

sell 2 calls


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This maneuver would have the effect of increasing the volatility of the stock because itexploits a steady stock price. Thus, increased use of this strategy would push up thevolatility of the stock.

4-10-08Options and Option Pricing

Extremely difficult and complicated Always have a terminal value of 0 if not exercised if it is exercised the value of

the option falls on the value function of the option

Call option prices: q t A function of various factors: q t = q(P t , P s, T, r, )

o Pt ~ price of the options base asset at time t : a higher P t increases valueo Ps ~ strike price of the option: higher P s decreases valueo T ~ terminal expiration date of option: higher T increases valueo r ~ rate of interest: higher r increases valueo ~ variance in P t : higher increases value

= P t P s q 0 (P t > P s)

= -q 0 (P t < P s)

PL

P0

PH P

buy a call #1

buy a call #2

C

No opportunity No opportunity

PV

sell 2 calls


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q0 is a sunk cost and thus irrelevant to option pricing

How each factor influences option pricing:

Pt quite simply, the higher the value of the underlying asset the higher the valueof the option Ps The higher the strike price then the less value there is to the option because a

higher rise in the stock price is necessary than if the strike price were lower T The longer the time allowed for the price of the asset to rise/fluctuate the

more likely it is that the strike price will be reached, hence increasing the value of the option

r Interest rates influence on option pricing is a little more complicatedo Options are essentially an installment plan purchase with uncertainty

added in. The uncertainty doesnt play a role in our analysis of interestrates effects on option prices so well disregard the uncertainty in options.

You have a beginning down payment, q 0, the price of the option, and thena final payment to cash it in of the strike price (remember, no uncertainty,so the strike price will be reached). The present value of that final

payment (a payment you will have to pay to cash in your option) would beequal to the present value of the strike price, which depends on r: PV =Ps(1 + r) -T. As we can see, then, the higher r is, the lower the PV of thatfinal payment would be. Thus, as the PV of that cost decreases due toincreases in r, the value of the option increases.

As the variance of the underlying stock price increases the likelihood that thestock price will reach the strike price at some point increases as well, thus raisingthe value of the option.

Trading range for q t : q L q t q H Lower bound:

o qL = 0 (P t P s)o qL = Value function (P t > P s)

Upper bound:o Set P s/q0 = 0 (absolute highest possible value for the option no strike

price to be paid)o Thus, q H = q = P t


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q t *( P t *) = P t * - P s(1 + r) -T

Question: Is the curve above a representation of the equation q t *( P t * ) = P t * - P s(1 + r) -T ? If so, what causes the difference between the two lines to approach zero?

Black Shoals Option Pricing Model

Pricing the option: Find a strategy equivalent to the option strategy that goes long in the asset, with

some leverage, that will yield the same payoff. We assume a high-bound and low-bound and analyze their pay-offs/costs that

equivocate the options pay-offs/costs Then, we solve in order to equivocate the costs between the two such that their

yields are the same

PayoffsStrategy CF 0 PL PH

A Purchase x shares of option o

-xq 0 x(P H P s)

B two parts

1.) Purchase s shares of stock

2.) Borrow PV of P L payoff

1.) -sP 0

2.) + sP L(1 + r) -T

1.) sP L2.) -sP L

1.) sP H2.) -sP L

q

Pt

Upper bound of V

Lower bound of V (Pt - P

s)

Path of V

Ps

Price whereyou exercisethe option

Pt *


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Net payoffs/CFs (B) s(P L(1 + r) -T P 0) 0 s(P H P L)

Set the two payoffs equal [s(P H P L) = x(P H P s)] in order to find the number of sharesyou would have to buy to make the payoffs equal.

s = x(P H P s)/(P H P L): this gives the number of shares that you would have to a.) borrowthe PV of the low outcome and b.) purchase in order to equal x options.

Then, we can see the beginning costs: -xq for the options s(P L(1 + r) -T P 0) for the shares

Since the number of shares that you would have to buy, s, is equal to x(P H P L)/(P H P L),we can see that [x(P H P s)/(P H P L)]*[(P L(1 + r) -T P 0)] would equal the total cost of

purchasing the shares. Now, since we want to make the profits between these two ventures completely equal, weneed to equivocate there costs. In order to do so we can set the cost of the options, withunknown option price q, equal to the costs solved above in order to be in terms of the # of option shares.

-xq = x(P H P s)/(P H P L)]*[(P L(1 + r) -T P 0)

Then, we can solve for q finding,q = (P 0 P L(1 + r) -T)(P H P s)/(P H P L)

This gives us the price of the options. This functions because weve set the payoffs andthe costs of these two strategies equal. We know for sure the costs and payoffs of buyingthe shares and borrowing the PV of the P L outcome, so we can solve for the number of shares in terms of the number of options by setting the two equal. Then, since we knowthe number of shares necessary in terms of the number of options, we can set the

beginning costs equal so that the cost of the options will equal the cost of the shares.This gives us a viable option price.


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4-14-08Firms are exposed to two types of risk:

Macro riskso Can be dealt with/anticipated: such as industry risk

Firm specific risk o Can be diversified away by shareholders

Essentially, the question is why do firms engage in risk management activities whenshareholders could just as easily do so themselves? Firms have no reason to buyinsurance in perfectly efficient markets where shareholders know all the info about everyfirms risk and opportunity. They can then just simply diversify and insure themselves.The question is then, why do firms spend time diversifying risk that they arent paid tocover? The reason comes from the fact that we dont have perfectly efficient capitalmarkets and large stakeholders in firms is a necessity to help control the principal agent

problem. Thus, these large holders have not diversified themselves, but they haventdone so because they are helping to control the efficiency lessening principal agent problem.

Firms, then, must examine the risks that theyre being paid to bear and shed those thatthey are not being paid to carry.

5-step procedure to analyze risk position:1.) Identify where the risk exposure is and what is the worst that could happen.2.) Is the company being paid to carry this risk particular risk?3.) Due diligence: can we lower this risk with our own actions? Explore in house

options to reduce risk. Then, when you go to purchase outside insurance it will cost less because you have minimized your exposure as best you can in house.4.) Can the company purchase insurance to cover losses? Important to then take intoaccount moral hazard. Risk pooling is what makes insurance function. Also shows whysome things arent insured because there isnt a large enough group of people seekinginsurance for it.5.) If there are not enough people to pool together such that insurance would be offeredfor your particular exposure is there some other option that you could explore to cover your position? Lower risk lowers your beta and increases the value to stock holders.

Options : Purchase a call to insure the price of an input. Purchase a put to protect revenue

If a firm is able to remove these risks it can concentrate on those it is supposed to bear.

Futures openly exchanged and traded, all identical contracts, trade like a commodityForwards specifically tailored contracts for a certain party


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Futures : Futures prices can convey information depending on what the future is for Are contracts with specific dates/outcomes

Mechanics of futures trading: Highly standardized Price is fixed today but payment does not come until termination Must put up some margin money when the contract is first signed Sold with marked to market

o Every day between now and the closing date the future will be adjusted for any changes in market value. You will either openly and physicallyreceive a payment for the gain of your future or have to front more moneyon the loss.

The underlying commodity of a future does have a spot price.o As the terminal time of the contract approaches the contract price

converges on the spot price

4-17-08Futures can be used to hedge against risk in interest changes, exchange rate risk, andrevenue risks

Swaps (interest rate/currency)

Cost is the concern ~ a firm could have issued variable bonds and be worriedabout the possible fluctuations in interest payments and want to solidify this risk that its not being paid to bear

o The risk is a variable string of paymentso The objective is to convert the variable stream into a fixed stream without

incurring the massive transactions cost associated with converting the debtinto some other form of financing

o The strategy purchase a variable stream of interest payments whileissuing a fixed income stream as an obligation to pay for the just

purchased variable stream. This leaves you with the obligation to pay asteady stream and gives you a variable income to match the other variablecost. Otherwise known as the notional principle.

Revenue is the concern ~ a portfolio manager could be holding a portfolio of long-term fixed coupon bonds that would have significant capital gains losses if the interest rate rises

o Risk varying portfolio valueo Objective minimize capital gains risk


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o Strategy enter a swap in which you buy a variable stream on the basis of the notional principal while simultaneously selling a fixed income streamof payments. Buy the stream such that any increases in the interest ratethat decreases the portfolio value will provide an insurance income of equal amount.

Currency swap ~ company with overseas operations may be able to raise capitalfor expansion in another country at home giving the firm the responsibility torepay the financing with the home currency even though ops will be in the foreigncurrency.

o Risk currency exchange rate could fluctuate and erode an otherwise profitable venture abroad

o Objective remove exchange rate risk by swapping dollars for foreignexchange without being subject to exchange rate risk

o Strategy borrow domestically, buy foreign currency to make overseasinvestment: enter swaps such that you agree to make a series of foreignexchange payments for a fixed stream of dollar payments in exchange.

Mergers and Acquisitions

#1 question: Are we doing something for the shareholders that they cant do for themselves?

Hard to overcome Stockholders can make whatever mix of stocks that they like

WA ~ current wealth generated by the acquiring companyWT ~ current wealth generated by the target companyW * ~ wealth generated by the combined firmsWMT ~ maximum current wealth possible of target firm

Necessary condition to justify the merger of two firms,W * > W A + W T

To decide the value of a potential merger or acquisition we would need to determinewhat, if anything, could contribute to/influence the W * (opposed to simply the W A and theWT) such that PVGO * > PVGO A + PVGO T?

Classic motives for M&A:

1.) Negative wealth at the target firm: W T < 0a. W T = B M + E M - A M

b. W * = W A + A M B M - E M


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i. A M B M E M > 0 when wealth is negativeii. W * > W A + W T

c. Good acquisition opportunity2.) Replace existing management because maximum potential wealth of the target

firm (W MT) is greater than current wealth (W T).

a. W*

= WA

+ WMT

> WT

+ WA

b. Difficult to determine W MT especially if youre unfamiliar with theindustry. Its hard to analyze the maximum possible wealth without being

personally familiar with the business.i. Analytical errors are common

ii. Even more common are egotistical errors in which managementscoffs another companys management and claims that they would

be able to run things better c. However, shareholders can do neither of the preceding analysis for

themselves.3.) Economies of Scale

a. Long run b. Cost decreases with greater quantityc. Horizontal in nature

i. Horizontal two firms in the same industryii. Vertical a firm in your chain of operation either above or below

youiii. Conglomerate different industries entirely

d. New levels of profitability for both firms:i. W * = W *A + W *T > W A + WT

4.) Mergers of vertical integrationa. More ambiguous than horizontal mergers horizontal mergers have to

prove themselves to be worth going before the FTC but vertical dont b. Firms are more integrated nowadays so that the collusion and connection

between firms in an operation chain it greater. Thus it is harder to findand exploit wealth opportunities that would come through making thesefirms one.

5.) Economies of scopea. Complimentary products/assets

b. One of the most potentially profitable merger reasonsc. More likely to find W * = W *A + W *T > W A + WT

6.) Mergers to use surplus cash (BAD)a. IF a firm has a cash surplus with all positive NPV projects already funded

it has no reason to purchase another firm simply to use cash b. Principle agent problem really manifests itself here management desires

to grow the firm and thus their salaries, and also, having cash on the balance sheet makes the firm look like a good takeover target, threateningthe job security of management.

7.) Diversification (BAD)


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a. There is no reason whatsoever for a firm to try to invest in M&A for the purpose of diversifying itself. This violates the cardinal rule of whether its something shareholders can do for themselves or not.

8.) Bootstrapping: Ponzi schemea. The general principle behind bootstrapping is that (P/E) A > (P/E) T: what

the acquiring firm will do is show its massively impressive P/E ratio andthen issue shares to pay for acquiring the new firm. The Ponzi schemethen follows with the newly acquired firms earnings to its P/E ratio andthen uses the newly boosted (but yet to be tested) P/E ratio to issue its nowmore highly valued shares to purchase another firm. The original firmwill continue this process to continue boosting its P/E ratio etcetera,etcetera. This scheme is unsustainable and will collapse the minute theoriginal firm ceases its acquiring run.

Methods for gaining control of other firms

1.) Proxy contesta. Rare because it rarely succeeds b. Have to solicit shareholders votes to gain control

i. Green mail a group will gather a great enough percentage of control to harass management until management pays them off

c. Regulations make a proxy contest difficult because FTC rules require ashareholder to register at 5%.

i. Because of this someone gathering momentum for a proxy contestor green mail will usually purchase 4.99% of a firm and then buyoptions for another 15-20% of the firm.

2.) Mergers and Acquisitions : two firms come together to make a single firm

usually similar sizea. Sometimes reverses when minnows swallow whales, usually with junk bonds

b. Mergersi. Usually friendly

ii. Usually organized by/originated from investment bankers theysee the opportunities for economies of scale

c. Acquisitions when a larger firm buys a smaller i. Sometimes reverses when small firms use junk bonds to purchase

larger firmsii. Two types of acquisitions

1. Tender offer go for the shares of the target firm: could beeither friendly or hostilea. Friendly tender: Acquiring firm approaches

management and makes a friendly offer for thetarget firm.

i. In this case a friendly conclusion could bereached and the current management would


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support the acquisition to theshareholders/board.

b. Hostile tender i. Acquiring firm secretly buys the other firms

shares whether the target firm likes it or not.

1. Often arrive with winners curse end up paying too much for thetarget.

2. Greater risk in hostile takeovers2. Buying targets assets

a. This method benefits from the fact that if you buythe firm legally through shares you also incur thefirms liabilities

b. However, if you buy only the assets you leave theliabilities with the still legally intact firm.

c. Whats left of the firm and its liabilities will be

distributed to the stockholders3.) Leveraged buyout buying a publicly held firm and taking it privatea. Target firm is paid for in cash

b. LBO leveraged buyouti. Junk bonds issued to finance buyout

c. MBO management buyouti. Usually a bad sign that the stock is undervalued and that there is

more value in the firm than management has been letting on4.) Divestitures subsidiaries that firms decide to spin off

a. Spin-off must be losing money to be worthy of dropping b. Acquiring firm must have significant and tangible advantage over target

firm in using the subsidiary

Defensive Strategies

Poison Pillo Something in the charter of a firm that gives the right of the target firm to

issue shares to stockholders at an attractive low price thus complicatingthe merger

White knighto Savior firm with whom a possible target has a previous arrangement with

a friendly firm that can come in and purchase the target instead of thehostile firm

Shark repellanto In the event that someone proposes a merger it is in the charter that it

would need more than a super majority to pass the merger

Merger Valuation Techniques


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We examine the possibility as if it would be financed with either all cash or all equity.Debt functions like cash, a seller wouldnt distinguish between the two.

100% Cash purchase:

Two questions: What is the source of the EVA offered by this merger/acquisition the economic

gain must be specifically enumerated? Do the terms of this action make sense for our shareholders?

1.) Economic gain present value of the change in free cash flows (PVFCF) frommerger

a. Examine economies of scale, scope, and vertical gains for the source of these EGs

b. Specifically identify the source/amount of the gains

2.) Cost of cash merger a. C = cash - E MT: this is incremental cost and shows a premium on the3.) NPV from the merger = EG cash + E MT = W * - W A W T > 0

a. Can use this EG to set a reservation price at which you will stop bidding

100% Equity purchase

1.) Economic gain (EVA):a. EG = PVFCF

2.) Cost:

a. The biggest difference in the equity option vs the cash option is the cost.With the equity option the cost is dependent on the exchange rate betweenthe two companies and the price of the issuing companys shares.

b. Number of issued shares = the number of target shares over the exchangerate

c. C = P A (price of acquirers shares) * Shares - E MT

3.) NPV = EG C = W * - W A W T > 0

The only significant difference between these two methods is the in the cost side.

Sellers prefer the cash option so they can take it and run.

Buyers prefer the equity option for two reasons:1.) It gives the seller an incentive to see that the merger is successful2.) If the merger fails, the price falls because the value of the shares fall

If sellers will accept nothing other than cash that could signify a significant contingentliability that they havent disclosed.


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Divide the new NPV by the # of shares to give you the incremental change in share price.

Social implications of M&A activity: Wealth transfers

o Junk bondso Tax shieldso Bondholders/price changes

Efficiency gainso Reallocation of resourceso More efficient use of FCFs

Larges costs associated with mergers are dead weight loss

Social imp. Beneficials

o Reallocation of resourceso Better use of FCFso Forces management to pay attention

Badso Impact on laid-off employees without retraining programs

Introduction to Corporate Finance (Centre College ECO 353)

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