Question

A one-year call option contract on Cheesy Poofs Co. stock sells for $1,330. In one year, the stock will be worth $65 or $86 per share. The exercise price on the call option is $78. What is the current value of the stock if the risk-free rate is 3 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

$98.02

Step-by-step explanation:

Data provided in the question:

Value of contract = $1,330

Maximum value = $86

Minimum value = $65

Exercise price = $78

Risk-free rate = 3%

Now,

Current value of stock =
`(\frac{\text{Maximum value-Minimum value}}{\text{Maximum value-Exercise price}}*\text{Call price})+(\frac{\text{Maximum value }}{\text{1+Risk-free rate}})`

also,

a standard contract has 100 shares

thus,

Call price = Value of contract ÷ 100 shares

or

Call price = $1,330 ÷ 100 = $13.30

Thus,

Current value of stock =
`(\frac{\text{86-65}}{\text{86-78}}*\text{13.30})+(\frac{\text{86}}{\text{1+0.03}})`

or

Current value of stock = ( 2.625 × $13.30 ) + $63.1068

= $98.0193 ≈ $98.02