RossFCF8ce SM Ch25

8/13/2019 RossFCF8ce SM Ch25

1/15

CHAPTER 25

OPTIONS AND CORPORATE SECURITIES

Learning Objectives

LO1 The basics of call and put options and how to calculate their payoffs and profits.LO2 The factors that affect option values and how to price call and put options using

no arbitrage conditions.LO3 The basics of employee stock options and their benefits and disadvantages.LO4 How to value a firms equity as an option on the firms assets and use of option valuation to evaluate capital budgeting projects.LO5 The basics of convertible bonds and warrants and how to value them.

Answers to Concepts Review and Critical Thinking Questions

1 !LO1" A call option confers the right, without the obligation, to buy an asset at a given price on or before agiven date. A put option confers the right, without the obligation, to sell an asset at a given price on or before agiven date. ou would buy a call option if you e!pect the price of the asset to increase. ou would buy a put

option if you e!pect the price of the asset to decrease. A call option has unlimited potential profit, while a putoption has limited potential profit" the underlying assets price cannot be less than #er .

2 !LO1"

a. The buyer of a call option pays money for the right to buy....b. The buyer of a put option pays money for the right to sell....c. The seller of a call option receives money for the obligation to sell....d. The seller of a put option receives money for the obligation to buy....

3 !LO1" The intrinsic value of a call option is $a! %& ' (,)*. +t is the value of the option at e!piration.

4 !LO1" The value of a put option at e!piration is $a!%( ' &,)*. y definition, the intrinsic value of an option isits value at e!piration, so $a!%( ' &,)* is the intrinsic value of a put option.

5 !LO2" The call is selling for less than its intrinsic value" an arbitrage opportunity e!ists. uy the call for -),e!ercise the call by paying -/0 in return for a share of stock, and sell the stock for -0). ouve made a riskless-0 profit.

# !LO2" The prices of both the call and the put option should increase. The higher level of downside risk stillresults in an option price of #ero, but the upside potential is greater since there is a higher probability that theasset will finish in the money.

$ !LO2" 1alse. The value of a call option depends on the total variance of the underlying asset, not just thesystematic variance.

% !LO1" The call option will sell for more since it provides an unlimited profit opportunity, while the potentialprofit from the put is limited 2the stock price cannot fall below #ero3.

& !LO2" The value of a call option will increase, and the value of a put option will decrease.

1' !LO1" The reason they dont show up is that the government uses cash accounting" i.e., only actual cashinflows and outflows are counted, not contingent cash flows. 1rom a political perspective, they would makethe deficit larger, so that is another reason not to count them4 5hether they should be included depends onwhether we feel cash accounting is appropriate or not, but these contingent liabilities should be measured andreported. They currently are not, at least not in a systematic fashion.

607


2/15

(olutions to Questions and )ro*le+s

NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. ue to

space and readability constraints! when these intermediate steps are included in this solutions manual! rounding

may appear to have occurred. "owever! the final answer for each problem is found without rounding during anystep in the problem.

Basic

1 !LO2"

a. The value of the call is the stock price minus the present value of the e!ercise price, so8

9): -;< ' %-=0>.)=/* : -6/.?0

The intrinsic value is the amount by which the stock price e!ceeds the e!ercise price of the call, so theintrinsic value is -66.

b. The value of the call is the stock price minus the present value of the e!ercise price, so8

9): -;< ' %-/0>.)=/* : -//.==

The intrinsic value is the amount by which the stock price e!ceeds the e!ercise price of the call, so theintrinsic value is -/6.

c. The value of the put option is -) since there is no possibility that the put will finish in the money. Theintrinsic value is also -).

2 !LO1"

a. The calls are not in the money. The intrinsic value of the calls is -).

b. The puts are in the money. The intrinsic value of the puts is -?0 ' ?= : .

c. The $ar call is out of the money.

The @ctober put is mispriced because it sells for less than the uly put. To take advantage of this, sell theuly put for -).?0 and buy the @ctober put for -).=0, for a cash inflow of -).=). The e!posure of theshort position is completely covered by the long position in the @ctober put, with a positive cash inflowtoday.

3 !LO1"

a. (ach contract is for )) shares, so the total cost is8

9ost : )2)) shares>contract32-).6/39ost : -6/)

b. +f the stock price at e!piration is -/), the payoff is8

Bayoff : )2))32-/) ' 6?3Bayoff : -6)))

+f the stock price at e!piration is -6C, the payoff is8

Bayoff : )2))32-6C ' 6?3Bayoff : -,)))

c. Demembering that each contract is for )) shares of stock, the cost is8

6076


3/15

9ost : )2))32-6.)39ost : -6,))

The ma!imum gain on the put option would occur if the stock price goes to -). 5e also need to subtractthe initial cost, so8

$a!imum gain : )2))32-6?3 ' -6,))$a!imum gain : -60,C))

+f the stock price at e!piration is -6/, the position will have a profit of8

Brofit : )2))32-6? ' 6/3 ' -6,))Brofit : -6,C))

d. At a stock price of -60 the put is in the money. As the writer you will make8

Eet loss : -6,)) ' )2))32-6? ' 603Eet loss : '-C))

At a stock price of -/ the put is out of the money, so the writer will make the initial cost8

Eet gain : -6,))

At the breakeven, you would recover the initial cost of -6,C)), so8

-6,)) : )2))32-6? ' &T3&T: -60.C)

1or terminal stock prices above -60.C), the writer of the put option makes a net profit 2ignoringtransaction costs and the effects of the time value of money3.

4 !LO2"

a. The value of the call is the stock price minus the present value of the e!ercise price, so8

9): -?0 ' .);9): -=.60

b. Fsing the equation presented in the te!t to prevent arbitrage, we find the value of the call is8

-?0 : %2-C0 ' 0/3>2-C0 ' C)3*9)G -0/>.);9): -=.;)) shares per contract9): -.0)

Fsing the no arbitrage model, we find that the price of the stock is8

&): -.0)%2-;? ' =2-;? ' ;)3* G -=.)/&): -


5/15

Eote that if the lower possible future value was below the face value of debt, for e!ample the twopossible future values were -)) and -6C, then the debt would be risky and the calculated interest ratewould have turned out to be greater than the risk free rate.

c. The value of the equity will increase. The debt then requires a higher return" therefore the present valueof the debt is less while the value of the firm does not change.

% !LO4"

a. Fsing the no arbitrage valuation model, we can use the current market value of the firm as the stockprice, and the par value of the bond as the strike price to value the equity. oing so, we get8

-)C : %2-/? ' C63>2-/? ' ))3*()G %-C6>.);*(): -?./=0

The current value of the debt is the value of the firms assets minus the value of the equity, so8

): -)C ' ?./=0): -C).;0

b. Fsing the no arbitrage model as in part a, we get8

-)C : %2-;) ' ?)3>2-;) ' ))3*()G %-?)>.);*(): 60.=;

The stockholders will prefer the new asset structure because their potential gain increases.

& !LO5" The conversion ratio is the par value divided by the conversion price, so8

9onversion ratio : -))>-6?9onversion ratio : /.0


6/15

b. The option embedded in the bond adds the e!tra value.

11 !LO5"

a. The minimum bond price is the greater of the straight bond value or the conversion value. The straightbond value is8

&traight bond value : -.)C/)

&traight bond value : -?=.0C

The conversion ratio is the par value divided by the conversion price, so8

9onversion ratio : -))>-0.09onversion ratio : ?.?6

The conversion price is the conversion ratio times the stock price, so8

9onversion value : ?.?62-=.639onversion value : -


7/15

ear 8 EBJ: %'-,0)0,))) G -/),)))2BJ+1A=I,C3* > .=EBJ: 6=,?C).0C

ear 68 EBJ6: %'-,=),))) G -/),)))2BJ+1A=I,?3* > .=6

EBJ6: 6,0?.??

ear /8 EBJ/: %'-,/0,))) G -/),)))2BJ+1A=I, .=/

EBJ/: -C,6* G -=)C,0))(!pected value of project at year : -6,=,


8/15

The EBJ is the present value of the e!pected value in one year plus the cost of the equipment, so8

EBJ : '-,;)),))) G 2-6,=,.=EBJ : -00,;).?C

b. +f we couldnt abandon the project, the present value of the future cash flows when the quantity is /,0))will be8

BJ future 91s : -;/2/,0))32BJ+1A=I,C3BJ future 91s : -,)C),;.=EBJ : -,.=@ption value : -,6/),)?=.06)9onversion price : -0

The conversion premium is the percent increase in stock price that results in no profit when the bond isconverted, so8

9onversion premium : 2-0 ' =.03>-=.09onversion premium : . or .I

b. The straight bond value is8

&traight bond value : -/.602BJ+1A=.0I,=)3 G -))>.)=0=)

&traight bond value : -


10/15


11/15

epreciation /,=3ook value : -,60),)))

&o the ta!es on the salvage value will be8

Ta!es : 2-,60),))) ' /,))),)))32./?3Ta!es : '-;;0,)))

This makes the afterta! salvage value8

607


12/15

Afterta! salvage value : -/,))),))) ' ;;0,)))Afterta! salvage value : -6,//0,)))

The EBJ if we abandon the project after one year is8

EBJ : '-0,C)),))) G -?,?.=EBJ : ?)=,=6=.


13/15

Ta!es : 2-.= G -0,0C,)))>.=6

EBJ : -,/)6,)


14/15

Ta!es : 2-/,.;/

EBJ : -6,60/,6?;.;C

5e should abandon the equipment after three years since the EBJ of abandoning the project after three yearshas the highest EBJ.

APPENDIX 25A

A1 Accurate values for the standard normal distribution are used here based on (!cels E@D$&+&T function. +fstandard normal values are taken from Table 60A. instead, the final value for the option will differ slightly.

a. d: '.0C/.6

/>=*2.C


15/15

A2 Fsing & : -/,=)), ( : -6,C0), t : ,$: .)=0, : .6C : ).0/?08

d: .;;0" d6: .)

Documents

RossFCF8ce SM Ch25