Structured Notes & Acquisitions

1. Structured Notes & Acquisitions

2. Pricing and Designing Structured Notes • A structured note has interest or maturity payments that are not fixed in dollars, but are contingent on something • Structured notes can make payments based on stock prices, interest rates, commodities, currencies, or anything that that derivatives can be written on. • Structured notes often have embedded derivatives • Used to create custom hedging devices

3. Structured Note BasicsWhat is the price of a bond that pays one barrel of oil 1 year from now? We can contract today to buy oil at $20.5 in one year, therefore, the most I’d pay for the bond is 20.5*.9388 = $19.2454 (19.2454 is the pre-paid forward price)

4. Payoff for the bondholder FV of your bond payment Buying this type of commodity linked bond is equivalent to a long forward contract in oil Issuing this type of commodity linked bond is equivalent to taking a short forward position in the commodity

5. Suppose the following… • If the oil company issued the bond, they raise $19.245 per barrel paid through bond (in prior example) • Oil company might want to raise more dollars per bond • Also, bond buyers might want to receive cash during the life of the bond.

6. Extend the example… • What quarterly cash coupon must the firm pay to make the bond worth $24.00? • The promised barrel has a PV of $19.245 • The PV of 4 coupon payments must have a PV of $4.755 = 19.245 • Coupon*(.9852+.9701+.9546+.9388)=4.755 • Coupon*(3.8487)=4.755 • Coupon = $1.235 each quarter

7. New example: embed an option in a bond • Suppose the corporation wants to “buy a put” and offers a bond with payments: • If oil < $18, payment = $24 – ($18-ST), otherwise payment = $24 • Rewrite as payment = $24 – max(0,$18-ST). • There are no coupon payments • What is the price of the bond? • Assume volatility of oil is 35% • 1-year interest rate: 0.9388 = 1e-r(1), therefore r=.0631 • Since F=20.5 = 20.90e(.0631-)1, therefore =0.0824

8. What does the bondholder pay? • Bond price = PV($24) – PV(put) • First, value the put option component • (S=20.9, K=18, r=.0631, =.0824, =.20, t=1) • Bond Price = 24 e-.0631 -1.5 = $21.12

9. Bond buyer’s payoff The bondholder keeps the premium if S>K!

10. Bond issuer’s payoff The commodity-linked bond replicates a put option

11. Last example – embed call option in coupon paying commodity-linked bond • Suppose now that a bond promises a $1.235 quarterly coupon, 1 barrel of oil at the end of the year, and 3*max(0,ST-$20.5), where $20.5 is the 1 year forward price of oil. • What is the value of this bond if the volatility of oil is 35%?

12. Valuing the structured note • Bond price = • PV(quarterly coupon) + prepaid forward + 3*max(0,ST-$20.5), • PV 4 coupon payments = 4.755 • Prepaid forward = 19.245 • Need to value a call option where the underlying asset pays a lease rate • 1-year interest rate: 0.9388 = 1e-r(1), therefore r=.0631 • Since F=20.5 = 20.90e(.0631-)1, therefore =0.0824 • Option price = • Bond value = 4.755+19.245+3*2.67 = $32.01 As before… these two = $24

13. Payoff to the bondholder The issuing firm has the opposite exposure Can adjust the multiple to get required slope..

14. Let’s structure notes for Golddiggers(from the text) • S0=$405/oz, F=420/oz, r=.05, lease rate=.01296 • Cost of producing gold is $380/oz

15. Structure of the note • Since S=405, structure note so that firm receives 405/oz today • (lock-in sell price of $405) • The lease rate is like a dividend payment to the holder of the bond • 405*.01296 = $5.25 • So bond pays $5.25 + 1oz at maturity • PV = (420+5.25)/1.05 = $405

16. Net position FV of $405 So, issuing a commodity-linked bond paying a unit of commodity at maturity is equivalent to selling forward Bondholders absorb price risk of a drop in gold prices – they have a long forward contract

17. Big differences between structured notes and forward contracts • Structure notes will have higher transaction costs • Structure notes may provide financing • Next – examine equity linked bonds

18. Zero-Coupon Equity-Linked Bonds • Suppose an equity-linked bond • pays the bondholder one share of stock at time T • there are no interim payments • What is a fair price for this bond? • The prepaid forward price

19. Zero-Coupon Equity-Linked Bonds (cont’d) • For a nondividend-paying stock, the prepaid forward price is Thus, the prepaid forward price is the stock price • For a stock making discrete dividend payments of Dti, the prepaid forward price is (15.3)

20. Cash Coupon Payments • Notation: represent the price of a bond paying n coupons of c each and a share at maturity as B(0, T, c, n, ST) • The valuation equation for such a note is (15.4) And this is just like we did in the oil example

21. Cash Coupon Payments (cont’d) • If the stock pays dividends, then in order for the bond to sell at par—the current stock price —it must pay coupons with a present value equal to the present value of dividends over the life of the bond • To see this, use equation (15.3) to rewrite equation (15.4) • In general, if we wish to price an equity-linked note at par, the coupon, c, must be set so that (15.5) PV of coupons = price difference

22. Interest In-Kind • An alternative to paying interest in cash is to pay interest in fractional shares • Example, what is the value of a bond paying 1-share of XOM in one year? (first case: with no interest in-kind). • Suppose S0=$63, r=.05, T=1, div=0.32 per quarter. What is the value of a bond paying 1 share of XOM in 1 year? • Since r=.05, then

23. Example continued • = 63 - 0.32(.9875+.9753+.9632+.9512) • = 63-1.24 • = 61.76 • Now, what dollar interest would XOM have to pay in order for the bond to be priced at par? • 63-61.76 = 1.24 • 1.24 = c*Pt = c*3.875, therefore c=$0.32 (no surprise!)

24. Example continued • What amount of shares would XOM have to pay in-kind to price the bond at par ($63)? • In this case 1.24 = PV of share-dividends • c* FPt =1.24 (this is equation 15.6 rearranged) • c = 1.24/248.87 = 0.0049825 shares each quarter • Check: • .0049825*(248.87)+1(61.76) = 1.24+61.76 = $63 Treating each as a zero coupon bond on fractional shares

25. Options in Coupon Bonds • Assume that an equity-linked note has a structure where, at maturity, the holder can receive some fraction of the return on the stock but does not suffer a loss of principal if the stock declines • This protection against loss is accomplished by embedding call options in the note • The value V0 of such a note is (15.11) • where  is the price participation of the note (i.e., the extent to which the note participates in the appreciation of the underlying stock)

26. Options in Equity-Linked Notes • With an equity-linked note, the maturity value is shares rather than a fixed number of dollars • The price of a note at par paying one unit of a share at expiration is (15.13) • If the share pays no dividend, then the equity-linked note can sell at par only if c =  = 0 • If the share pays dividends, it is necessary for the note to offer either coupons or options =S0

27. Valuing an Equity-Linked CD • Consider a CD with a 5.5-year maturity and a return linked to the S&P 500 index, where • the S&P index at issue is S0 and is S5.5 at maturity • the CD pays back S0 at maturity • the CD pays no coupons, i.e., c = 0 • the CD gives the investor 0.7 at-the-money calls, i.e.,  = 0.7 and K = S0

28. Pricing the CD ‘K’ • After 5.5 years the CD pays (15.14) • Using equation (15.11), the value of this payoff at time 0 is (15.15) where • To perform this valuation, we make the following assumptions: • The 5.5-year interest rate is 6% • The S&P index is currently at 1,300 • The 5-year index volatility is 30% • The dividend yield is 1.5%

29. Pricing the CD (cont’d) • We have 2 pieces to value • The zero-coupon bond paying $1,300 is worth $1,300 e–0.06 5.5 = $934.60 • The 0.7 call options are worth 0.7  BSCall($1,300, $1,300, 0.3, 0.06, 5.5, 0.015) = $309.01 • The 2 pieces together would cost $934.60 + $309.01 = $1,243.61 Note that in the book, the CD sells for $1300, the mark-up of 56.39 represents the mark-up paid to the bank (4.3%). The theoretical wholesale price is 1243.61.

30. Payoff to the CD holder Borrower is trading risk-free rate of return for higher equity-linked returns

31. Basic Acquisition Structures

32. The Use of Collars in Acquisitions • When firm A buys firm B, it can pay cash to B’s shareholders or it can pay shares, exchanging A shares for B share • Cash offers have relatively less risk than a share offer. Why? • Once Company B accepts a share offer, the acquisition will take time to complete • Which company bears the risk of a change in the stock price of company A?

33. The Use of Collars in Acquisitions (cont’d) • There are 4 common ways to structure an offer • Fixed stock offer • A offers to pay B a fixed number of A shares per B share. • Floating stock offer • A offers to pay B however many shares have a given dollar value, based on A’s share price just before the merger is completed • Fixed collar offer • There is a fixed range for A’s share price within which the offeris a fixed stock offer • Floating collar offer • There is a fixed range for A’s share price within which the offer is a floating stock offer

34. WorldCom/MCI acquisition • On October 1, 1997, WorldCom Inc. CEO (Bernard Ebbers) sent the following note to the CEO of MCI (Bert Roberts): • “I am writing to inform you that this morning WorldCom is publicly announcing that it will be commencing an offer to acquire all the outstanding shares of MCI for $41.50 of WorldCom common stock per MCI share. The actual number of shares of WorldCom to be exchanged for each MCI share in the exchange offer will be determined by the stock price of WorldCom on the closing day of the offer, but will be no less than 1.0375 shares (if WorldCom’s stock price exceeds $40) or no more than 1.2206 shares (if WorldCom’s stock price is less than $34).

35. Profile of the offer • The payoff is contingent upon price of WCOM: Slope=1.0375 Slope=1.2206 In the flat range the number of shares is altered such that shares*price=41.5

36. Structuring the offer • The offer can be decomposed into three products • A risk-free bond paying 41.5 • 1.2206 short put options with K=34 • 1.0375 long call options with K=40

37. GTE enters the mix • Two weeks later, on October 15th, GTE bid for MCI, offering $40 in cash. • On that day, WCOM stock closed at $35.4375. • Suppose that, if approved on October 15, the WorldCom offer would have taken exactly four months to close (due to regulations), while the GTE offer could have been closed immediately. Finally, assume that on October 15, 1997, the continuously compounded risk free rate of return was 5.5%, the volatility of WCOM was 0.38, and WCOM was not expected to pay any dividends over the life of the offer.

38. Picture of the competitive offers

39. Which offer is greater? • Need to compare PV of WCOM offer to $40 • PV call = 1.695 • PV put = 2.088 • PV bond = 41.5e(-.055*.3333)=40.746 • Sum = 40.746-1.2206*2.088+1.0375*1.695=$39.95 < $40

40. Apache / Amoco acquisitionHBS Case by Peter Tufano • In 1991 Amoco decided to sell marginal oil and gas properties • Created a new organization, MW Petroleum Corporation • 9,500 oil wells • 300 producing fields • Hired Morgan Stanley to market the unit to potential buyers

41. Apache Corporation • An independent oil and gas company was an aggressive acquirer of oil and gas fields • Apache’s strategy • “…is a bit like a pig following a cow through the cornfield. The scraps are pretty good for someone with our particular mission.” • They viewed MW Petroleum as good scraps

42. It all hinges on the price • Amoco argues that oil prices will be great in the future, therefore they ask for a price that assumes high oil prices • Apache (of course) believed oil prices would be stable or lower (following Gulf War I) – resulting in a lower bid • Bid-ask spread was about 10% • Too high to “split the difference”

43. Good news • The deal hinged upon a disagreement about a commodity price in the future • Amoco doesn’t want to have sold too low if oil prices turn out high • Apache doesn’t want to have paid too much if oil prices turn out low • Therefore the deal is structured so that both sides shared the risk of future price movements

44. Proposed deal structure • Amoco could write Apache a “capped price support guarantee”. • If oil prices fall too low over the next 2 years Amoco would make payments of K-ST where $K is the price support level. • Simultaneously, Apache would pay Amoco if oil prices exceeded a designated “price sharing” level over the next 5-8 years • If oil prices rise over K, Apache pays Amoco ST-K.

45. The commodity collar • Apache/Amoco collared the offer on the price of oil • Apache gives up some upside in return for downside protection • Apache wrote a call and bought a put • Note, each party gets the price it had forecast if their forecast was accurate • A ‘win-win’ deal structure

46. Comments on Apache • “It did not take financial engineering skills to recognize that the risks of this deal could be shared” • “Financial engineers, however, could value the collar by using actual data and financial models. Moreover, their pricing exercise was not merely theoretical. After the deal was closed, both sides were approached to sell off their positions.