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1. Financial Options
Edoardo, Max, Tim
20/11/2017
Financial Markets
EBC2006
Option Valuation
Payout Policy

2. The Agenda
p i c t u r e s presentation d i s c u s s i o n entertainment
Data Case Chapter 17
Chapter 20
Chapter 21.1

3. Data Case Payout Policy
Client: 1 million shares
Bought at $13.98 on Feb 28, 2003
Dividend & Capital gain taks rate = 20%
4.95 Billion Shares Outstanding
Share Price at Close Nov 15, 2017 = $34.11
Cash Jul 29, 2017 = $11,708,000,000

4. Data Case Payout Policy
Half of Cash = $5,854,000,000
Share Repurchase
Dividend Per Share
=$5,854,000,000/$34.11
=171,621,225.45
=$5,854,000,000/4.95 Billion
=$1.182626

5. Data Case Payout Policy
Cash received from Dividend
1,000,000 Shares held
20% Dividend Tax
dividend per share $1.182626
payout before taxes $1,182,626.00
taks payment $236,525.20
payout after taxes $946,100.80

6. Data Case Payout Policy
shares held 1,000,000.00
shares repurchased 171,621,225.45
total shares outstanding 4,950,000,000.00
fraction owned by client 0.02%
indirect repurchased 34,670.95
share price $34.11
payout before taxes $1,182,626.26

7. Data Case Payout Policy
initial price $13.98
indirect repurchased 34,670.95
cost $484,699.95
payout before taxes $1,182,626.26
gain on sale $697,926.32
capital gain taks $139,585.26
payout after taxes $1,043,041.00

8. Data Case Payout Policy
adjusted share price $32.93
shares held 1,000,000.00
cost $13,980,000.00
payout before taxes $32,927,374.00
gain on sale $18,947,374.00
capital gain taks $3,789,474.80
payout after taxes $29,137,899.20
dividend $946,100.80
total payout $30,084,000.00
Dividends

9. Data Case Payout Policy
shares held 965,329.05
cost $13,495,300.05
payout before taxes $32,927,373.74
gain on sale $19,432,073.68
capital gain taks $3,886,414.74
payout after taxes $29,040,959.00
repurchase $1,043,041.00
total payout $30,084,000.00
Repurchase

10. adjusted share price $32.93
shares held 1,000,000.00
cost $13,980,000.00
payout before taxes $32,927,374.00
gain on sale $18,947,374.00
capital gain taks $3,789,474.80
payout after taxes $29,137,899.20
dividend $946,100.80
total payout $30,084,000.00
shares held 965,329.05
cost $13,495,300.05
payout before taxes $32,927,373.74
gain on sale $19,432,073.68
capital gain taks $3,886,414.74
payout after taxes $29,040,959.00
repurchase $1,043,041.00
total payout $30,084,000.00
RepurchaseDividends
Q6: Under Which Program would you be better off
before and after taxes?

11. Data Case Payout Policy
Share Prices in 5 and 10 years
Returns are 10%
After dividend share price = $32.93
$32.93*1.10^5=$53.03
$32.93*1.10^10=$85.41
Repurchase share price = $34.11
$34.11*1.10^5=$54.93
$34.11*1.10^10=$88.47

12. Q7c: Calculate the total after taks cash flows at
both points in time if the remaining shares are sold.
5 years 10 years
adjusted share
price $53.03 $85.41
shares held 1,000,000.00 1,000,000.00
cost $13,980,000.00 $13,980,000.00
payout before
taxes $53,034,094.30 $85,411,939.21
gain on sale $39,054,094.30 $71,431,939.21
capital gain taks $7,810,818.86 $14,286,387.84
payout after taxes $45,223,275.44 $71,125,551.37
dividend $946,100.80 $946,100.80
total payout $46,169,376.24 $72,071,652.17
Dividends
5 years 10 years
shares held 965,329.05 965,329.05
cost $13,495,300.05 $13,495,300.05
payout before taxes $53,029,864.68 $85,405,127.36
gain on sale $39,534,564.62 $71,909,827.31
capital gain taks $7,906,912.92 $14,381,965.46
payout after taxes $45,122,951.75 $71,023,161.90
repurchase $1,043,041.00 $1,043,041.00
total payout $46,165,992.75 $72,066,202.90
Repurchase

13. Data Case Payout Policy
Share Prices in 5 and 10 years
Returns are 20%
After dividend share price = $32.93
$32.93*1.20^5=$81.94
$32.93*1.20^10=$203.89
Repurchase share price = $34.11
$34.11*1.20^5=$84.88
$34.11*1.20^10=$211.20

14. Q8: Calculate the total after taks cash flows at both
points in time if the remaining shares are sold.
5 years 10 years
adjusted share
price $81.94 $203.89
shares held 1,000,000.00 1,000,000.00
cost $13,980,000.00 $13,980,000.00
payout before
taxes $81,940,377.60 $203,893,880.39
gain on sale $67,960,377.60 $189,913,880.39
capital gain taks $13,592,075.52 $37,982,776.08
payout after taxes $68,348,302.08 $165,911,104.31
dividend $946,100.80 $946,100.80
total payout $69,294,402.88 $166,857,205.11
Dividends
5 years 10 years
shares held 965,329.05 965,329.05
cost $13,495,300.05 $13,495,300.05
payout before taxes $81,933,842.62 $203,877,619.26
gain on sale $68,438,542.56 $190,382,319.21
capital gain taks $13,687,708.51 $38,076,463.84
payout after taxes $68,246,134.11 $165,801,155.42
repurchase $1,043,041.00 $1,043,041.00
total payout $69,289,175.10 $166,844,196.42
Repurchase

15. Q9: Calculate the NPV under both holding period
assumptions.
Dividend 5 years 10 years
10% $45,223,275.44 $71,125,551.37
20% $68,348,302.08 $165,911,104.31
NPV 10% 10% $28,080,096.02 $27,421,979.04
20% $42,438,918.16 $63,965,912.91
NPV 20% 10% $18,174,220.13 $11,487,173.63
20% $27,467,649.69 $26,795,569.61
dividend $946,100.80 $946,100.80
repurchase 5 years 10 years
10% $45,122,951.75 $71,023,161.90
20% $68,246,134.11 $165,801,155.42
NPV 10% 10% $28,017,802.90 $27,382,503.46
20% $42,375,479.88 $63,923,522.85
NPV 20% 10% $18,133,902.29 $11,470,637.16
20% $27,426,590.67 $26,777,812.25
repurchase $1,043,041.00 $1,043,041.00

16. Chapter 20
Financial Options

17. Basics
A contract gives its owner the right to buy or sell an asset in
the future at a fixed price.
A gives the owner the right to buy the asset.
A gives the owner the right to sell the asset.
If the payoff from exercising an option immediately is positive the option is
said to be
If the payoff from exercising the option immediately is negative the option
is said to be
financial option
call option
put option
in-the-money
out-of-the-money

18. Concept Check
20.1
American option vs European Option
Difference?
Right to exercise American option on
any date
Does the holder of an option have
to exercise it?
No, he has a right but not an
obligation

19. Option Payoffs at Expiration
Call Value at expiration
𝐶 = max 𝑆 − 𝐾, 0
Put Value at expiration
𝑃 = max(𝐾 − 𝑆, 0)
Long Position

20. Option Payoffs at Expiration
Call Value at expiration
𝐶 = −max 𝑆 − 𝐾, 0
Put Value at expiration
𝑃 = −max(𝐾 − 𝑆, 0)
Short Position

21. Net payoffs from Options
Positive payoff only if:
S > max(S-K, 0) + option premium x (1+i) t (call option)
S > max(K-S, 0) + option premium x (1+i)t (put option)

22. Holding an Option to Expiration
The more the options are out-of-the-money, the
higher both risk and return
Call option: positive beta and higher expected
returns
Put option: negative beta and lower expected
returns
Generally held to hedge risk in a portfolio

23. Combinations of Options
3 main investment strategies on options
High volatility:
1)Straddle
2)Strangle

24. Combinations of Options
3 main investment strategies on options
Low volatility:
3)Butterfly spread

25. Portfolio insurance
Protective put (individual stock or
portfolio level)
1)Stock + Put
2)Risk-free bond + Call

26. Put-Call Parity
S + P = PV(K) + C
𝐶 = 𝑃 + 𝑆 − 𝑃𝑉 𝐾 − 𝑃𝑉(𝐷𝑖𝑣)

27. Factors affecting option prices
A price of an option cannot be negative
American option worth more than European
counterpart
Maximum payoffs:
Put options: payoff=strike price
Call options: payoff=stock price
Extreme case: S=0

28. Factors affecting option prices
Intrinsic value: value if the option expired
immediately
American option > Intrinsic value
Time value: current option price – intrinsic
value
Maturity is relevant for American options
Volatility, asymmetry in the option’s payoff

29. Exercising options early
In which case? Non-dividend vs. dividend
Non-dividend paying stocks:
Call options
Exercise option early is not optimal
European option = American option

30. Exercising options early
Non dividend-paying stocks
Put options
European option < American option

31. Exercising options early
Dividend-paying stocks:
Call options
European option < American option

32. Exercising options early
Dividend-paying stocks:
Put options
Opposite effect of the dividends

33. Exercising options early
When to exercise the option early?
1)Non-dividend call  No
2)Non-dividend put  High strike price and
deep in-the-money
3)Dividend call  Yes, if expected drop in
stock’s price
4)Dividend  No

34. Options and corporate finance
3 ways to interpret the capital structure as
options on the firms’ assets
1)Equity as a call option

35. Options and corporate finance
2)Debt as an option portfolio
Risky debt = Risk-free debt – Put option on
firm’s assets
a)Assets – Equity Call option
b)Risk-free bond – Put option (Short position)

36. Options and corporate finance
3)Credit Default Swap
Risk-free debt = Risky debt + Put option on
firm’s assets
Insurance or speculation

37. Agency conflicts
What is the agency conflict between equity
and bond holders?
The higher the risk:
The better off will be the equity holders (call
option)
The worse off will be the bond holders (short
position in a put option)

38. Chapter 21.1
The Binomial Option Pricing Model

39. A Two-State Single-Period Model
∆ = 0.5
B = -18.87
LOOP  option = replicating portfolio
50∆ + B = value portfolio
Replicating Portfolio
60∆ + 1.06B = 10
40∆ + 1.06B = 0
50(0.5) – 18.87 = 6.13

40. The Binomial Pricing Formula

41. A Multiperiod Model
Work Backwards from the last period to the first.
S=50  C=6.13
S=30  C=0

42. The End

43. References
• Corporate Finance 4th Edition, Pearson, DeMarzo & Berk