past exam questions
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Past exam questions. 723g28 Financial economics 2012. Example : from past exam. - PowerPoint PPT PresentationTRANSCRIPT
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Past exam questions
723g28Financial economics
2012
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Example: from past exam
• The current price of the stock of AstraZeneca is 300 kr. During each twelve-month period it will either rise by 25 % or fall by 20 %. The interest rate is 3 % a year. Assume no dividends during the life of the option.
• Calculate the value of a two-year American put option on AstraZeneca with an exercise price of 250 kr.
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Option valuation
• S=300 u=25% d=-20% rf =3%, no dividend,• Value of a 2 year American put option at strike
price of 250?
300
375
240300
468,75
192
P=23%/45%=51,1111%1-p=48,8889%
Put at strike =250
0
0
58
0
10
27,529
13,066
The value of the call is 13,07$, 27,53> intrinsic value 10, don’t exercise!
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Svar:
p = 51,1 % (1-p) = 48,9% P1 levande = 27,53 P1 död = 10 P1 levande > S1 död P0 = 13,07 kr
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S=300, Strike price=250. rf=0,03, u=25%, d=-20%
375
240300
192
• The value of the share in 3 periods
300
468,75585,93
375
240
153,6
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Obs: American put can not have less than intrinsic value, option should be exercised at t+2!
0
0
10
96,4
0
4,7465
50,72
26,43
2,25313,66
K-S=10K-S=58
tt+1 t+2
• S=300 u=25% d=-20% rf =3%, no dividend,• Value of a 3 year American put option at strike
price of 250?
What about a 3 year american option value? The same method:
t+3
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Value of an American call with 3 period
335,94
0
0
125
226,0315
62,028
0
141,604
103,6197
The last period value S-K, K=250
Use (p*Cu+(1-p)*Cd)/(1+r)=C(t-1)
Note, the american call can’t not be lower than the intrinsic value, otherwise it is an exercise point.
S-K=218,75S-K= 125
S-K=50
31,703
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Exempel 2: en amerikansk säljoption utan utdelning
Du är innehavare av en 1-årig amerikansk säljoption utan utdelning under löptiden. Aktiens marknadsvärde är idag 100 kr och den kan under varje 6-månadersperiod antingen falla med 10 % eller stiga med 11,1 %. Säljoptionens lösenpris är 102 kr och den riskfria 6-månadersräntan är 5 %. Vad är din amerikanska säljoption utan utdelning värd idag?
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Put option at strike price =102• P=(5%+10%)/(11,1%+10%)=71,09%• 1-p=28,91%• Start from last period: K-S• (2*71,09%+21*28,91%)/1,05=7,136• Etc.
100111,1
90100
81
123,43
0
2
21
7,1360
0,55062,3376
K-S=12
American put option can not be lower than the intrinsic value. Option should be exercised!
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Exam questions:Value the following options:
A European call option written on SKF A selling for 145 kr. The exercise price is 140 kr. The stock’s yearly volatility is 30 %. The option matures in 6 months. The risk-free yearly interest rate is 3 %. A European put option written on the same stock at the same time, with the same EX and expiration date. What is the time value of the call option?
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Call option price=?
S=145, K=140, rf=3%, σ=30%T=1/2Get column value=P0/PV(K) Row value= σ* table value= C0/P0
Row value= 30%*=0,212 Column value=145/(140/(1,03)1/2 )=1,05125=1,05 C0/table value=P0 (table value=(10,9+9,88)/2)=10,39% C0=P0/table value= 145*10,39%= 15,07
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• Put option value is:
• P=c+PV(K)-S=15,07+140/(1+0,03)1/2 -145=8,0
• Time value of the call=call premium-(intrinsic value) =15,07-(145-140)=10,07
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Black & Scholes metod
• En ”genväg” för att beräkna en köpoptions värde med hjälp av Black & Scholes metod:– Beräkna radvärde = σ * √ t– Beräkna kolumnvärde = P0 / PV(X)– Se i tabell 6 för att utläsa optionens värde i procent av underliggande
tillgång (tabellvärde)– Köpoptionens värde (C0) = tabellvärde * P0
– Du får ut säjoptionens värde genom Put-Call parity
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Options on Financial Assets
Executive Stock Options
Warrants
Convertible Bonds
Callable Bonds
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Replicating the call
• The price of the SCA A stock is 100 kr. During the next year the price may either rise by 33 % or fall by 25 %. The yearly interest rate is 3 %. You have an European one-year call option on SCA A with an exercise price of 120 kr.
• Use the replicating-portfolio method to value this call option!
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Strike=120, rf=3%• ∆=(13-0)/(58)=22,41%, • B= -∆*Sd/(1+0,03)=-22,44%*75/1,03=-16,34∆*Su+B(1+r)=13 ∆=(13-0)/(133-75)=22,41%
∆*Sd+B(1+r)=0 B=-16,34 C=100*22,41%-16,34=6,07
100
133
75
C=13
0
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NPV of lease agreement
NLT needs a new forklift. It can either buy it for 2 500 000 kr or lease it. The lease terms require NLT to make 3 annual payments of 1 000 000 kr. The lessor can depreciate the forklift for tax purposes over 3 years. NLT can borrow at 6 %. NLT and the lessor pays tax at 30 %. What is the NPV of the lease for NLT? Is it possible to create a financial lease that has a positive value for both the lessor and NLT? Explain!
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The depreciation tax shield is a forgone benefit of leasing, cash outflow.
t0 t1 t2 t3
IKF 2,5 SA (foregone tax benefit of depreciation) -0,25 -0,25 -0,25
SA = 2,5/3 * 0,3 = 0,25
LA (rental) -1 -1 -1
SL (skatte avdrag) 0,3 0,3 0,3 After tax leasing payment: -0,7
Summa 1,8 -0,95 -0,95 -0,25
Värde leasingavtal 1,8 -0,9117 -0,8783 -0,2210 -0,211
Svar: Leasingavtalet är ej finansiellt lönsamt för leasetagaren NLT
Diskonteringsränta = 6 % * 0,7 = 4,2 %
Discounting the after tax lease payment and the lost depreciation tax shield+ the benefit of renting the machine
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Alternatively,Spread the cost of 2,5 million over the three years.
• 2,5=a*(1/r*(1-1/(1+r)^3)• a=2,5/2,765=0,9042 (Max value for the
company)• 0,25 yearly forgone benefit of depreciation, • 0,7294 yearly cost+0,25>0,9042 n• it is a negative NPV lease contract.