Finance Lecture12

MBAM 614 Finance International Finance • MBAM614 Class 12 - 1 Summary of Last Class 1. Granting credit leads to accounts receivable which must be financed there is a cost to granting credit. 2. Credit (from suppliers) is free during the discount period. For the balance of the net period, the cost of credit is the forgone discount. 3. Credit terms are expressed as “a/b, net c” 4. The goal of inventory management is to minimize the total cost of inventory which includes carrying costs and shortage costs 5. The optimal order size, which minimizes the total cost of inventory over time, is given by the Economic Order Quantity (EOQ) Q* = • MBAM614 2T × F CC Class 12 - 2 1 Summary of Last Class 1. Only reason for a merger is synergies which can arise from - Revenue enhancement - Cost reduction - Tax gains - Changes in Capital Requirements 2. The actual cost of an acquisition depends on the method of payment 3. Both the bidder and the target frequently (and correctly) win • MBAM614 Class 12 - 3 Agenda 1. 2. 3. 4. 5. Forex Terminology Foreign Exchange Rates Purchasing Power Parity Interest Rate Parity Forward Rates and the International Fisher Effect • MBAM614 Class 12 - 4 2 Terminology of International Finance Eurobonds are bonds issued in many countries but denominated in a single currency A Belgian Dentist is the stereotypical buyer of Eurobonds Eurocurrency is money deposited outside the country whose currency is involved Foreign Bonds are bonds issued in a single country, in that country’s currency, but by a non-domestic firm or government LIBOR (London Inter-Bank Offer Rate) is the rate international banks charge one another for overnight Eurocurrency loans Swaps are agreements to exchange two securities or currencies • MBAM614 Class 12 - 5 Exchange Rates An Exchange Rate is the price of one country’s currency in terms of another country’s currency A little less than “a dime a dozen” ($0.10/12F = $0.00833/F) In practice, almost all currencies are traded with prices quoted in U.S. dollars • MBAM614 Class 12 - 6 3 Exchange Rate Quotations Number of these Implicit exchange rate between two currencies quoted in a third (usually $US) For each 0.1992 • MBAM614 Class 12 - 7 Triangle Arbitrage If the exchange rate (C1 per C2) is less than the implied cross-rate (C1 per $US)/(C2 per $US) there is an opportunity for arbitrage by buying C1 with $US, trading C1 for C2, then selling C2 for $US Go in the opposite direction if the exchange rate is greater than the implied cross-rate. This is called Triangle Arbitrage Eg. Suppose the indirect quote on Japanese Yen is 60.02 and the indirect quote on South Korean Won is 552.79. If the exchange rate is 0.1050 Yen per Won, does an arbitrage opportunity exist? The no-arbitrage rate is (60.02/552.79) = 0.10858 Yen per Won which is greater than 0.1050 so there is an arbitrage opportunity Use $100 US to buy 6002 Yen trade 6002 Yen for 57,161.905 Won sell 57,161.905 Won for $103.406 US • MBAM614 Class 12 - 8 4 FX Transactions If an exchange of currencies takes place at current prices (“on the spot” or Spot Rates), it is called a Spot Transaction An agreed exchange at some point in the future for a fixed rate (the Forward Exchange Rate) is a Forward Trade Trade today at “Spot” Trade in the future: Forward Rates • MBAM614 Class 12 - 9 Purchasing Power Parity Ideally, goods should have the same real price anywhere in the world regardless of the currency used to purchase them This is called Absolute Purchasing Power Parity – S0 is the spot exchange rate for a foreign currency, F, in $US – PF is the price of a good in the foreign currency – PUS is the price in $US PF = S0 × PUS Due to product differences, barriers to trade, transportation costs, Absolute PPP tends not to hold except for traded commodities with low transfer costs • MBAM614 Class 12 - 10 5 Example: Absolute PPP Gold is a commodity that is easily traded by receipt. If gold is selling for £240 in London, and the spot rate between pounds and dollars is 0.6523, what price is gold likely to be selling for in New York? Since PF = S0 × PUS , rearranging gives PUS = PF / S0 = £240/ 0.6523 = $367.93 • MBAM614 Class 12 - 11 Relative PPP The change in exchange rates between two currencies is determined by the difference in the inflation rates between the two countries – – – – S0 = current indirect quoted spot exchange rate E[St] = expected exchange rate in t periods hUS = expected inflation rate in the U.S. hFC = expected inflation in foreign country E[St] = S0 × [1 + (hFC - hUS)]t This is called Relative Purchasing Power Parity (or simply PPP) • MBAM614 Class 12 - 12 6 Covered Interest Arbitrage Since it is possible to buy and sell currencies forward (lock in a future exchange rate today), there are two ways to invest money at interest: – invest $US in the States and earn RUS – convert $US to foreign currency at S0 earn interest at RF over period t convert back to $US at F1 (the forward rate) If both methods don’t result in the same number of $US, there is a Covered Interest Arbitrage opportunity • MBAM614 Class 12 - 13 Interest Rate Parity To prevent covered interest arbitrage, – domestic investment yields: (1 + RUS) – foreign investment yields: S0 × (1 + RFC)/F1 (1 + RUS) = S0 × (1 + RFC)/F1 S0 / F1 = (1 + RUS) / (1 + RFC) This is the Interest Rate Parity (IRP) condition • MBAM614 Class 12 - 14 7 Approximate IRP IRP can be approximated with (F1 - S0) / S0 = RFC - RUS Ft = S0 × [1 + (RFC - RUS)]t Loosely, IRP says that the difference in interest rates between two countries is exactly offset by the change in the relative value of the currencies • MBAM614 Class 12 - 15 Example: IRP Suppose the French Franc spot rate is 3.5436. If RF = 6% and RUS = 7%, what forward rate, F1, will prevent covered interest arbitrage? Using Approximate IRP: F1 = S0 × [1 + (RFC - RUS)]1 F1 = 3.5436 × [1 + (0.06 - 0.07)] = FF 3.5082 (per $US) • MBAM614 Class 12 - 16 8 Putting it all Together Unbiased Forward Rates (UFR) states that the best estimate of expected future spot rates, E[St], is the forward rate, Ft UFR: PPP: IRP: UFR & IRP: E[St] = Ft E[St] = S0 × [1 + (hFC - hUS)]t Ft = S0 × [1 + (RFC - RUS)]t E[St] = S0 × [1 + (RFC - RUS)]t This is Uncovered Interest Rate Parity (UIP) • MBAM614 Class 12 - 17 Example: UIP & PPP The current French Franc spot rate is 3.6510. If inflation over the next 5 years in the U.S. is expected to be 3% per year and it’s expected to be 5% per year in France, what should the 5 year interest rate be in France if it is 7.25% in the States? From PPP E[S5] = S0 × [1 + (hFC - hUS)]5 = 3.6510 × [1 + (0.05 - 0.03)]5 = 4.0310 (the FF is expected to depreciate against the $US) From UIP E[S5] = S0 × [1 + (RFC - RUS)]5 = 3.6510 × [1 + (RFC - 0.0725)]5 = 4.0310 [1 + (RFC - 0.0725)] = 0.02 or RFC = 0.0925 = 9.25% • MBAM614 Class 12 - 18 9 International Fisher Effect When the UIP and PPP are combined S0 × [1 + (RFC - RUS)]t = E[St] = S0 × [1 + (hFC - hUS)]t or and (RFC - RUS) = (hFC - hUS) (RFC - hFC) = (RUS - hUS) This is the International Fisher Effect which says that real rates must be the same everywhere Eg. Looking at the last example for FF, we have IFE: (RFC - hFC) = (RUS - hUS) or (RFC - 0.05) = (0.0725 - 0.03) RFC = (0.0425) + 0.05 = 0.0925 or 9.25% as before • MBAM614 Class 12 - 19 Key Points Interest rates, inflation rates, and exchange rates are inter-related by UFR: PPP: IRP: UIP: IFE: E[St] = Ft E[St] = S0 × [1 + (hFC - hUS)]t Ft = S0 × [1 + (RFC - RUS)]t E[St] = S0 × [1 + (RFC - RUS)]t (RFC - hFC) = (RUS - hUS) • MBAM614 Class 12 - 20 10 MBAM 614 Finance Options • MBAM614 Class 12 - 21 Agenda 1. 2. 3. 4. Options & Option Terminology Fundamentals of Option Valuation Valuing a Call Option Equity as a Call Option on the Firm • MBAM614 Class 12 - 22 11 Option Terminology An Option is the right, but not the obligation, to buy (or sell) an asset at a fixed price on or before a given date – using an option contract to buy (or sell) the underlying asset is called Exercising the Option – Options specify the price you will pay (or receive) for the asset if you decide to exercise the option. This price is the Exercise or Strike Price – Options have fixed lives. The last day upon which the option may be exercised is called the Expiration Date – There are many kinds of options but most common are American Options may be exercised any time before expiry European Options may only be exercised on expiration date • MBAM614 Class 12 - 23 Example: Car Option You’ve just been looking over a very nice 1979 MG ragtop that someone in town is selling for $6900. You’re interested but undecided. While you were looking at the car, several other people also arrived to look at it so you quickly offered the owner $50 if he would agree to sell you the car at any time on or before next Friday for $6900. You have purchased an American Call option on the car the option’s expiration date is next Friday (March 31) the Strike Price is $6900 (what you will pay for the car) Note: you may pay less for the car or not purchase the car at all in which case, the option expires worthless. If the others start a bidding war however, you know you can get the car for $6900 • MBAM614 Class 12 - 24 12 Types of Options Call Option gives the owner the right, but not the obligation, to buy an asset at a fixed price at some point during the option’s life Put Options give the owner the right, but not the obligation, to sell an asset at a fixed price at some point during the option’s life Option contracts have two parties: – Buyer, who owns the option and has a choice of actions – Seller, or Writer, who must do what the option owner decides Eg. Seller of a put must buy the asset if the option is exercised. • MBAM614 Class 12 - 25 Stock Option Quotoations Option contracts are always for 100 shares Stock Name Expiry Date (always the 3rd Friday of given month) Yesterday’s Closing Stock Price Total volume and offers to trade Specific Option Contract Strike Price Put Options • MBAM614 Globe and Mail, Tuesday, July 30, 1996 Range and last price per share during the day Class 12 - 26 13 Option Payoffs What is the value of an option at expiry? For a call option – if the stock price, S, is greater than the exercise price, E, you can buy the stock for E and sell it for S making a tidy profit of S-E. Value must be S-E – if the stock price is less than E, then, again, you can buy the stock for E (by exercising the option) and sell it for S (which is less than E) but why would you want to? Value must be 0 Value of Call Option = Max(0, S-E) – When the stock price is greater than the exercise price, a call option is said to be “in the money.” – The opposite is true for a put (it would be “out of the money”) • MBAM614 Class 12 - 27 Call Option Payoff at Expiry Since E is fixed, the value of the option increases by $1 for every $1 increase in S Cheaper just to buy stock. Option is worthless Intrinsic Value is the value of an option when exercised. This is the same as the value at expiry. Option Value Use the option, buy stock for E, sell it for S. Make S-E ! Stock Price, S E Option Intrinsic Value • MBAM614 Class 12 - 28 14 Put Option Payoff at Expiry Buy stock for S, use the option to sell it for E. Make E-S ! Option Value E Would you ever sell an option for less than its intrinsic value? Since E is fixed, the value of the option falls by $1 for every $1 increase in S Get a better price for stock by just selling. Option is worthless Stock Price, S Option Intrinsic Value • MBAM614 E Class 12 - 29 Option Payoffs For a Put option at expiry – if the stock price, S, is greater than the exercise price, E, you get less by exercising the option than simply selling. Value must be 0 – if the stock price is less than E, then exercising the option gets you a better price. Value must be E-S Value of Put Option = Max(0, E-S) – When the stock price is less than the exercise price, a put option is “in the money.” Note that options are a zero-sum game: if the option holder gains, the writer loses. • MBAM614 Class 12 - 30 15 Valuing In-the-Money Options Suppose a stock currently sells for $62 and there are two possible outcomes at the end of one period: either the stock will be worth $70 or it will be worth $90. If there is a call option on this stock available with a strike price of $65 and the one period risk-free interest rate is 10%, what is the value of the call option? First, form two portfolios: one with one share and the other with one call option and an investment in the risk-free asset of $65/(1+Rf). What would each portfolio be worth in each state? Stock Value $70 $90 Call Value S-E = $5 S-E = $25 Rf Invest. $65 $65 Total $70 $90 • MBAM614 Class 12 - 31 Valuing In-the-Money Options Since payoffs are identical regardless of state, initial cost must be the same – otherwise we could buy the cheaper one and sell the more expensive one and make a risk-free profit – this is called Arbitrage Cost of stock is S0 = $62 and cost of second portfolio is cost of call, C0, plus the risk-free investment, $65/(1+Rf) S0 = C0 + $65/(1+Rf) or $62 = C0 + $65/(1.10) C0 = $62 - $59.09 = $2.91 • MBAM614 Class 12 - 32 16 Option Value Factors More generally, as long as the stock price is anything greater than the strike price after t periods (with certainty), the same process can be repeated Solving for C0 gives: C0 = S0 - E/(1+Rf)t Note: This is ONLY for this special case Option prices are affected by: The higher the current stock price, the greater the option value The higher the exercise price, the lower the option value The longer the time to expiration, the greater the option value The higher the risk-free rate, the greater the option value (the PV of the exercise price, a cash outflow, goes down with Rf) Class 12 - 33 • MBAM614 Option Valuation Continued When the stock price may be below the exercise price at expiration, loan the present value of the lowest stock price at the risk-free rate and buy enough call options to make up the difference between the low stock price and the high one if the high state occurs Eg. Suppose a stock currently selling for $67 is expected to end up at either $80 or $60. There is a call option with a strike price of $70 on the stock and the risk-free rate is 9%. What is the value of the call option? Portfolio 1: a share of stock • MBAM614 Class 12 - 34 17 Example: Option Valuation Portfolio 2: 1) loan the PV of the lower stock price: $60/(1.09) = $55.05 (payoff is $60 regardless of state) 2) since the difference in stock price outcomes is $80-$60 = $20, you need to buy enough call options so that the call options are worth $20 in the high state (they’re worth nothing in the low state). When the stock price is $80, each call option is worth ($80-E) = ($80-$70) = $10. Thus, $20/$10 = 2 call options are required • MBAM614 Class 12 - 35 Example: Option Valuation Stock Value $60 $80 2 Calls Value 2($0) = $0 2(S-E) = $20 Rf Invest. $60 $60 Total $60 $80 S0 = 2C0 + $60/(1+Rf) 2C0 = S0 - $60/(1+Rf) C0 = ($67 - $55.05)/2 = $5.98 • MBAM614 Class 12 - 36 18 Replicating Payoffs To find the value of a call option given two possible final “states” for stock prices, we create two portfolios with equivalent payoffs in each state. One portfolio is a share of stock and the other is: a risk-free loan of the lower possible stock price discounted at the risk-free rate (for the number of periods in question) – some call options. If ∆S is the difference in possible stock prices and ∆C is the difference in the call option value when the two states occur, then the number of calls is ∆S/∆C • MBAM614 Class 12 - 37 Example: Replicating Payoffs Suppose a stock currently selling for $67 is expected to end up at either $80 or $60. There is a call option with a strike price of $70 on the stock and the risk-free rate is 9%. What is the value of the call option? We found that a portfolio with: – $55.05 invested at Rf $55.05 = $60/(1.09) – two call options ∆S = $80-$60 = $20 ∆C = $10 - $0 = $10 ∆S / ∆C = 2 same payoff in either state as the stock and C0 = $5.98 What if the possible outcomes for stock prices were $55 and $85? • MBAM614 Class 12 - 38 19 Example: Replicating Payoffs portfolio 2 is a risk-free investment of lower stock price ($55) discounted at Rf – $55/(1.09) = $50.46 ∆S / ∆C call options – ∆S = $85 - $55 = $30 – ∆C = $15 - $0 = $15 – ∆S / ∆C = $30/$15 = 2 S0 = 2C0 + $55/(1+Rf) C0 = ($67 - $50.46)/2 = $8.27 Fifth factor affecting option value is Stock Return Variance, σ2 - The higher the stock return variance, the greater the option value • MBAM614 Class 12 - 39 Equity as a Call Option When a firm uses debt, equity can be thought of as a call option on the assets of the firm – exercise price is the face value of the debt – if the assets are worth more than the debt, the option is in the money and stockholders “exercise” by paying off the debt when it’s due – if the option is out of the money (assets worth less than the debt), the option expires unexercised default and bankruptcy effectively, the bondholders own the firm’s assets but have written a call against them • MBAM614 Class 12 - 40 20 Example: Debt is Risk-Free Suppose a firm has assets currently worth $1000 and an outstanding pure discount bond with a face value of $1000. If the assets will be worth either $1,200 or $1,400 in one period and the risk-free rate for one period is 11%, what is the value of the firm’s equity? The assets will always be worth more than the strike price ($1000) The option will always finish in the money and be exercised The debt is risk-free (always repaid) Since options always in the money, we have C0 = S0 - E/(1+Rf)t C0 = $1000 - $1000/(1.11) = $1000 - $900.90 = $99.10 Since assets = liabilities + equity, debt is worth $1000 - $99.10 = $900.90 • MBAM614 Class 12 - 41 Example: Risky Debt What if the assets will be worth either $900 or $1,700? What will the equity be worth? The debt? (note that the debt is now risky because, in the $900 state, the option will expire unexercised) Using our option valuation method: the risk-free investment is $900/(1.11) = $810.81 at expiration, the call (equity) will be worth either $0 or $700 so ∆S / ∆C = ($1,700 - $900) / $700 = 8/7 call options S0 = 8/7C0 + $900/(1+Rf) C0 = $165.54 Value of the debt is $1000 - $165.54 = $834.46 implied discount rate on debt is 19.84% ($1000/$834.46) • MBAM614 Class 12 - 42 21 Key Points 1. An option gives the owner the right, not the obligation, to buy or sell an asset at a fixed price before a certain date. 2. Options are zero-sum: if someone wins, someone else loses 3. The intrinsic value of a call option is Max(0, S-E) and the intrinsic value of a put option is Max(0, E-S) 4. If we know the possible outcomes for stock prices, we can form a portfolio with call options and the risk-free asset that exactly duplicates the payoff on the stock and solve for the option value. 5. There are 5 factors that affect option value: stock price; exercise price; time to expiration; risk-free rate; and stock return volatility 6. When a firm uses debt, equity can be viewed as a call option on the assets of the firm. If the option is in the money (assets worth more than the debt), option is exercised by paying the debt. • MBAM614 Class 12 - 43 22