Suppose a risk-neutral power plant needs 10,000 tons of coal for its operations next month. It is uncertain about the future price of coal. Today it sells for $60 a ton but next month it could be $50 or $70 (with equal probability). How much would the power plant be willing to pay today for an option to buy a ton of coal next month at today's price? (Ignore discounting over the short period of a month.)
A)5
B)4
C)3
D)0

Question

Quizplus · Accepted Answer

The power plant would be willing to pay the difference between the potential future prices of $50 and $70, which is $20. Therefore, the maximum price it would be willing to pay today for an option to buy a ton of coal next month at today's price is $20. Since the option to buy at today's price is worth $60 (the current price of coal), the power plant would be willing to pay $60 - $50 = $10. However, since the option only allows the plant to save $10 (the difference between the current price and the lower potential future price), the plant would only be willing to pay half of that amount, or $5, for the option. Therefore, the best choice is A) 5.

Suppose a Risk-Neutral Power Plant Needs 10,000 Tons of Coal