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Lecture 1

# COMM 122 Lecture 1: formulacheat-sheet

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Queen's University

Commerce

COMM 122

Evan Dudley

Spring

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lOMoARcPSD
Formula/cheat sheet
Finance II (Queen's University)
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30.8 – EPS, PE, Mergers If the price of silver in Japan is ¥700/ounce. Describe an arbitrage opportunity for a trader who has The intrinsic value = current stock price – exercise price = $70 - $60 = $10
Flannery (Target): P/E = 5.25, Shares = 90,000, Earnings = 450,000 $500 available. 23.3 – Payoffs
Stultz (Acquirer): P/E = 21, Shares = 180,000, Earnings = 675,000 The trader can exchange $500 for [$500 x (¥150/$1)] = ¥ 75,000. With ¥75,000, the trader can then Stock current price is $114, Strike Price is $110
*We get 1 Stultz share, for every 3 Flannery shares purchase (75,000/700)=107.1429 ounces of silver in Japan. He can sell the silver for ($5 x Suppose you buy 10 contracts of the Feb call option, how much will you pay?
Q: Find EPS and P/E Ratio 107.1429)=$535.71, for an arbitrage profit of $35.71. Take the ‘Last’ price of 7.60 for February Calls to get the cost
EPS = ($450,000 + 675,000)/[180,000 + (1/3)(90,000)] = $5.357 26.14 – Puts, Calls and Forward Contracts 7.60 x 10 contracts x 100 shares per contract = 7600
P = 21($675,000)/180,000 = $78.75 Suppose there were call options, forward contracts, but no put options. How could someone If the stock price at expiration is $140, calculate options investment worth, if terminal stock price is
P/E = $78.75/$5.357 = 14.70 synthesize a put option? What’s the relationship between the three? $125, calculate investment worth
What is the value of the synergy between firms if NPV is 0? The payoffs for the combined position are exactly the same as those of owning a put. This means Payoff for $140 price = 10(100)($140 – 110) = $30,000
V = $450,000(5.25) = $2,362,500 that, in general, the relationship between puts, calls, and forwards, all being of the same maturity, Payoff for $125 price = 10(100)($125 – 110) = $15,000
The cost = the number of shares offered x acquirer share price must be such that the cost of the two strategies will be the same, or an arbitrage opportunity exists. You buy 10 contracts of the Aug 110 put option, what is the max gain? On expiration, Macrosoft is
Cost = (1/3)(90,000)($78.75) = $2,362,500 In general, given any two of the instruments, the third can be synthesized. selling for $104/share, how much is your options investment worth? What is your net gain?
NPV = 0 = V + Synergy – Cost = $2,362,500 + Synergy – 2,362,500 Tutorial Question Cost = 10(100)($4.70) = $4,700 Aug Put Last found on table
Synergy = $0 You are short 25 gasoline futures contracts, established at an initial settle price of $1.41 per litreThe maximum gain on the put option would occur if the stock price goes to $0. We also need to
30.14 – Merger NPV where each contract is composed of $42,000 litres. Over the subsequent 4 trading days, gasoline’s subtract the initial cost, so:
Synergy value = after tax cash flow/discount rate = $500,000 / 0.08 = $6,250,000 settlement price on each day is: $1.37, $1.42, $1.45 and $1.51. Calculate the cash-flows at the end Maximum gain = 10(100)($110) – $4,700
The value of target to acquirer = synergy + MV of target of each trading day, and calculate your total profitor loss at the end of the trading period. Maximum gain = $105,300
Value = $6,250,000 + 10,000,000 = $16,250,000 Day 0 Cash outflow = $1,480,500, Day 1 cash flow = $42,000, Day 2 cash flow = –$52,500, Day 3 cash If the stock price at expiration is $104, the position will have a profit of:
Acquirer is offering 30% of its stocks, find stock acquisition value flow = –$31,500, Day 4 cash flow = –$63,000, Profit = –$105,000 Profit = 10(100)($110 – 104) – $4,700 = $1,300
Stock acquisition value = percentage x (MV of target + synergy + MV of acquirer) 24.1 – Managers Preference on Cash Vs. Options Suppose you sell 10 of the Aug 110 put contracts. What is your net gain or loss if Macrosoft is
= 0.30($16,250,000 + 26,000,000) = $12,675,000 cost of stock offer If he is risk-averse (doesn’t like risk), he may or may not prefer the stock option package to the selling for $103 at expiration? For $132? What is the break-even price – that is the terminal stock
NPV = value of the acquisition – cost immediate bonus. Even though the stock option has a higher NPV, he may not prefer it because it is price that results in a 0 profit?
NPV of cash offer = $16,250,000 – 13,000,000 = $3,250,000 undiversified. The fact that he cannot sell his options prematurely makes it much more risky than the At a stock price of $103 the put is in the money. As the writer, you will make:
NPV of stock offer = $16,250,000 – 12,675,000 = $3,575,000 immediate bonus. Therefore, we cannot say which alternative he would prefer. Net loss = $4,700 – 10(100)($110 – 103) = –$2,300
30.17 – Calculating NPV w/ Dividends Managers may prefer cash because: At a stock price of $132 the put is out of the money, so
Find the value of the target firm – It has better diversification characteristics Net gain = $4,700
1.EPSTarget $640,000 earnings/500,000 shares = $1.28 per share – They cannot generally capture the time value component of the options before maturity At the breakeven, you would recover the initial cost of $4,700, so:
Price Per ShareTarget P/E ratio x EPS = 10($1.28) = $12.80 – It does not lose value if they shirk $4,700 = 10(100)($110 – S T
2.DPS Target $380,000 dividends/500,000 shares = $0.76 – Options cannot be turned into cash before the vesting period is over ST= $105.30
3. RR = ([DPS x (1 + premerger growth rate)]/PPS) + premerger growth rate Managers may prefer options because: For terminal stock prices above $105.30, the writer of the put option makes a net profit
=[$0.76(1.04)/$12.80] + 0.04 = 0.1018 – Cash is taxed immediately, options are not taxed until and unless they are exercised 23.4 – Call Option Pricing
4. Price per share w/ new g = [DPS x (1 + merger growth rate)]/(RR – merger growth rate) Firms may prefer options because: Price of stock will be either $65 or $85 at the end of the year. Call options are available with one
= $0.76(1.06)/(0.1018 – 0.06) = $19.30 – It aligns the manager’s incentives with those of the firm year to expiration. T-bills currently yield 6%. Suppose the current price of stock is $70. What is the
5. V = SharesTargetPrice per share w/ new g = 500,000($19.30) = $9,647,904.19 – It does not cost anything upfront value of the call option if the exercise price is $60/share?
What is the gain from this acquisition? Firms may prefer cash because: The value of the call = stock price - the present value of the exercise price because the call option is
Gain = $9,647,904.19 – 500,000($12.80) = $3,247,904.19 – Especially for small firms, options can dilute the holdings of other shareholders sure to be exercised so: 0 = $70 – 60/1.06 = $13.40
Find the NPV if acquirer offers $13 per share 21.9 – Equity in Disguise Suppose the exercise price is $80 in a), what is the value of the call option now?
NPV = Value of target – shares of target x offer price per share A 100–year bond looks like a share of preferred stock. In particular, it is a loan with a life that alUsing the equation presented in the text to prevent arbitrage, we find the value of the call is:
$9,647,904.19 – 500,000($13) = $3,147,904.19 certainly exceeds the life of the lender, assuming that the lender is an individual. With a junk bond,C0= [70(0.25)] + $16.25/1.06 = $12. 78
Maximum bid price = $13 + ($3,147,904.19/500,000) = $19.30 the credit risk can be so high that the borrower is almost certain to default, meaning that the Note that delta = 0.25 and that the amount that must be borrowed equals $16./1.06 or $15.09.
Acquirer offers 150,000 shares in exchange for target stocks, what would NPV be? creditors are very likely to end up as part owners of the business. In both cases, the “equity in 23.10 Black-Scholes
Price/share = (MV of acquirer + MV of target)/(acquirer shares + shares offered) disguise” has a significant tax advantage Stock price=46. Exercise price=50. Risk-free rate=6%/yr compounded continuously.
= ($40,600,000 + 9,647,904.19)/(1,000,000 + 150,000) = $43.69 21.10 – Bond Using Risk Neutral Approach Maturity=8months. Standard deviation=54%/yr. Find price of call option and price of put option
NPV = $9,647,904.19 – 150,000($43.69) = $3,093,829.73 Bonds are callable at $1150, interest rate is 9%, 55% probability the rate will increase to 11%, 45% d = [ln($46/$50) + (.06 + .54 /2) x (3/12)] / (.54 x 3/12 ) = –.1183
1
probability that interest rate will decrease to 7%, assume interest rates will fall bonds will be calld2= –.1183 – (.54 x 3/12 ) = –.3883
32.1 – Cross Rates find the coupon rate.
How many Mexican pesos can you get for one Euro? 𝑉 = 𝐶 + 𝐶 , 𝑉 = $1,150+ 𝐶, then use risk neutral formula: N(d 1 = .4529, N(d2) = .3489
12.4194 𝑃𝑒𝑠𝑜𝑠 11% .11 7% –.06(.25)
1 𝑈𝑆 (𝐶 + 𝐶 )× .55 + $1,150+ 𝐶 ) C = $46(.4529) – ($50e )(.3489) = $3.65
𝑀𝑒𝑥𝑖𝑐𝑎𝑛 𝑃𝑒𝑠𝑜𝑠 0.7980 𝐸𝑢𝑟𝑜𝑠 𝑉 = 𝑉11% × 𝑃11% + 𝑉 7% × 𝑃7% = .11 To find price of put option, use the put-call parity:
𝐸𝑢𝑟𝑜𝑠 = 1 𝑈𝑆 0 1.09 1.09
*Originally we’re given indirect quote of 1.2531 US/1 Euro so we had to change that to Euros/US by Solving for C gives us a coupon of $95.42, or a coupon rate of 9.542% –.06(.25)
21.13 – Basis Points (Canada Plus Call) Put = $50e + 3.65 – 46 = $6.90
taking the reciprocal to give us 0.7980 Put-Call Parity Replication Application
32.13 – Expected Spot Rates In 2009, Whitby bought 5M in bonds, bonds yield 80 basis points above Government of Canada Stock=$30. Strike price=$35. Put option costs $3. Rf=8%. 1 year maturity. What does it cost?
Spot exchange rate is HUF 209, inflation in Canada is 3.5%, inflation in Hungary is 5.7%, what is the bonds yielding 7.35%, company agreed to compensate investors on a yield of Canada plus 80 basis t
points if they were ever called, by 2012 rates fell to 5.5% and Whitby could issue new debt at 6.4%, C0= S 0 E/(1 + r) + p0 C 0 $30 - $35/1.08 + $3 = $0.59 Therefore, the portfolio with the same
exchange rate in one year? 1 calculate the annual interest penalty Whitby would have to pay to call the debt. **80 basis points payoff as the call costs $0.59 to set up, so that is what you should pay for the call.
F1= 209 [1 + (0.057 – 0.035)] = HUF 213.60 *****LEAVEROOM FOR DIAGRAMS. **Triangular arbitr
32.14 – Capital Budgeting = 0.8 % **draw different graphs with their values (protective put strategy, lecture 8tutorial, straddle strategy,
Project costs €18M, Cash flow year 1 = €3.6M, year 2 = €4.1M, year 3 = €5.1M, spot exchange rate = NPV of their debt obligations if they do not refinance is:
callable vs noncallable bonds lecture 9,
$1.22/€, Canada risk free rate = 4.8%, Europe risk free rate = 4.1%, Canadian cost of capital = 13%, $5,000,000× .0815
subsidiary can be sold for €12.2M 𝑁𝑃𝑉 𝑛𝑜 𝑟𝑒𝑓𝑖𝑛𝑎𝑛𝑐𝑒= = $6,367,188
1. Find the future spot rates for each year: .064
E(S1) = (1.0480 / 1.0410) $1.22/€ = $1.2282/€ If they do refinance, the NPV of their debt obligations, including the call penalty (which is the second
2 term) is:
E(S2) = (1.0480 / 1.0410) $1.22/€ = $1.2365/€ $5,000,000× .064 $5,000,000× (𝑜𝑙𝑑 𝑟𝑎𝑡𝑒 − 𝐺𝐶 + .008 ) )
E(S3) = (1.0480 / 1.0410) $1.22/€ = $1.2448/€ 𝑁𝑃𝑉 𝑟𝑒𝑓𝑖𝑛𝑎𝑛𝑐𝑒= +
2. Find the cash flow converting the euros into dollars with the spot rates .064 .064
Year 0 cash flow = –€$18,000,000($1.22/€) = –$21,960,000.00 $5,000,000 × .064 $5,000,000× (.0815 − .055+ .008 ) )
= +
Year 1 cash flow = €$3,600,000($1.2282/€) = $4,421,533.14 $5,000,000 × .0825 .064
Year 2 cash flow = €$4,100,000($1.2365/€) = $5,069,496.10 = = $6,445,313
Year 3 cash flow = (€5,100,000 + 12,200,000)($1.2448/€) = $21,534,638.87 .064
The NPV of their debt obligations is higher if they refinance, so they should not refinance.
3. Find NPV discounting back each year with the Canadian rate of 13% 2 3 Callable Bonds example: Perpetual bond w/ face value of $1000. 12% annual coupon. $350 call
NPV = –$21,960,000 + $4,421,533.14/1.13 + $5,069,496.10/1.13 + $21,534,638.87/1.13 premium. What rate will they need to be able to borrow at to make refinancing worthwhile?
NPV = $847,605.21
Tutorial Question – Arbitrage A: will exercise when the PV of calling the bond is at least equal to the PV of not calling.
$1350 = (12% x $1000)/ r r = 0.89. Refinance when u can borrow at 8.9% or lower.
If an ounce of silver costs $5 in Canada. The exchange rate with Japan is ¥150 = $1. Silver in Japan 23.1 – Call Option Hundo Being Exercised
costs ¥800 per ounce.
Does this constitute an equilibrium situation? No T-bills yield 5.5%, Stock is selling currently for $70/share, there is no possibility that the stock w￼ll
If a trader has $500 available at her disposal, can this trader earn arbitrage profit? Yes, $33.33 be worth less than $65 per share in one year, find the value of a call option with a $60 exercise price
and what is the intrinsic value?
If the price of silver in Canada and Japan does not change, what exchange rate will prevail such Because the option will be exercised with certainty, the value of the call = the stock price – the
that the absolute purchasing power parity is satisfied? ¥800/$5 = ¥160/$1
present value of the exercise price
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Chapter 23/24: Options and Corporate Finance Retractable/Put: allows holder to force issuer to buy bond back at stated price Merger absorption of one firm by another; 2/3 of share votes required for approval
Long position = buying, short position = selling 𝑓𝑖𝑟𝑠𝑡 𝑦𝑒𝑎𝑟 𝑐𝑜𝑢𝑝𝑜𝑛 + 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑝𝑟𝑖𝑐𝑒 𝑎𝑡 𝑒𝑛𝑑 𝑜𝑓 𝑦𝑒𝑎𝑟 Consolidation entirely new firm is created; both terminate legal existence, costs more
Strike/exercise Price: K 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑛𝑜𝑛 − 𝑐𝑎𝑙𝑙 𝑏𝑜𝑛𝑑 = 1 + 𝑟 Acquisition of stock
European options can be exercised only at expiry, American be exercised any time up to expiry FV + call premium = call price Tender offer public offer to buy shares made by 1 firm directly to the sh. holders of another; if
Covered Call = long call + bond (FV=K) -if called, call price + coupon shareholders accept, they tender their shares by exch. for cash/securities
Protective Put = long put + long underlying asset (S) -if not, coupon + 𝑐𝑜𝑢𝑝𝑜𝑛 Circular bid mailed directly to target shareholders, stock exchange bid through TSX
𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒
^^this strategy g

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