Question

One of Modular Products (MP) customers would like to obtain a 6-month option to purchase 500,000 tables for $119 each. These tables currently sell for $110 each. Assume u equals 1.0994 and d equals .9096. What price should MP charge for this option if the annual risk-free rate is 3.2 percent

Group of answer choices
a. $338,400
b. $421,900
c. $598,100
d. $479,900
e. $533,600

Answer 1

Option E is correct one.

$533,600

Step-by-step explanation:

% increase = u − 1

% increase = 1.0994 − 1

% increase = .0994, or 9.94%\large % increase = u − 1

% decrease = d − 1

% decrease = .9096 − 1

% decrease = −.0904, or −9.04%

Price with increase = $110(1.0994)

Price with increase = $120.934

Price with decrease = $110(.9096)

Price with decrease = $100.056

rf = Probability of rise(Increase percent) + (1 − Probability of rise)(Decrease percent)

.032(6/12) = Probability of rise(.0994) + (1 − Probability of rise)(−.0904)

Probability of rise = .5606, or 56.06%

Probability of fall = 1 − .5606

Probability of fall = .4394, or 43.94%

Payoff if price increases = $120.934 − 119

Payoff if price increases = $1.934

Payoff if price decreases = $0

Expected payoff = .5606($1.934) + .4394($0)

Expected payoff = $1.0842

Option value = $1.0842/[1 + .032(6/12)]

Option value = $1.0671

Contract value= Option to purchase*Option value

Contract value = 500,000($1.0671)

Contract value = $533,600