Question

The price of TSC stock will be either $42 or $46 at the end of the year. Currently, T-bills yield 4.1 percent and TSC sells for $43 a share. What is the per share value of a one-year TSC call option if the exercise price is $45 per share? Multiple Choice $1.03 $.81 $0 $.72 $.66

Answer 1

Let the probability of price UP be "X" so probability of price down is (1-x)

Spot price :[PU*Pu+PD*Pd] /(1+i)

43 = [(46*X)+ 42(1-X)]/(1+.041)

43 *1.041 = 46X +42 -42X

44.763 = 4X +42

44.763 -42 = 4X

X = 2.763/4

          = .69075 or 69.075%

Probability of price UP = 69.075 % so probability of price down = 1-.69075 = 30.925%

After one year :

If price is	payoff	probability	payoff *probability
42	not exercised since exercise price is higher than spot price	30.925%	0
46	46-45 =1	69.075%	1*.69075=.69075
		Total payoff in one year	.69075

Value of option today = .69075/(1+.041)= $ .6635 (rounded to .66)

correct option is "E"