Question

Describe each of the following situations in the language of options:

a. Drilling rights to undeveloped heavy crude oil in Northern Alberta. Development

and production of the oil is a negative-NPV endeavor. (The break-even oil price is

C$32 per barrel, versus a spot price of C$20.) However, the decision to develop can

be put off for up to five years. Development costs are expected to increase by 5

percent per year.

b. A restaurant is producing net cash flows, after all out-of-pocket expenses, of

$700,000 per year. There is no upward or downward trend in the cash flows, but

they fluctuate, with an annual standard deviation of 15 percent. The real estate

occupied by the restaurant is owned, not leased, and could be sold for $5 million.

Ignore taxes.

c. A variation on part (b): Assume the restaurant faces known fixed costs of $300,000

per year, incurred as long as the restaurant is operating. Thus

The annual standard deviation of the forecast error of revenue less variable costs is

10.5 percent. The interest rate is 10 percent. Ignore taxes.

d. A paper mill can be shut down in periods of low demand and restarted if demand

improves sufficiently. The costs of closing and reopening the mill are fixed.

e. A real-estate developer uses a parcel of urban land as a parking lot, although

construction of either a hotel or an apartment building on the land would be a

positive-NPV investment.

f. Air France negotiates a purchase option for the first 10 Sonic Cruisers produced by

Boeing. Air France must confirm its order in 2005. Otherwise, Boeing will be free to

sell the aircraft to other airlines.

Answer 1

Part (a)

An American call option on oil with following features:

• FIve years maturity
• The initial exercise price is $ 32 per barrel increasing by 5% every year.

Part (b)

An American put option to abandon the restaurant with following features:

• Exercise price = 5 million.
• The restaurant’s current value = $700,000
• The annual standard deviation of the changes in the value of the restaurant = 15%

Part (c)

An American put option to abandon the restaurant with following features:

• Underlying asset is PV(revenue – variable cost)
• Exercise price $ 5 million + PV (future fixed costs avoided by closing down the restaurant) = $5,000,000 + PV of $300,000 as perpetuity = $5,000,000 + 300,00/0.10 = $8,000,000
• The restaurant’s current value = $700,000
• The annual standard deviation = 10.5%

Part (d)

A complex option with following features

• Enables the company to abandon temporarily (an American put) and
• if abandoned i.e if the put is exercised, it enables the firm to subsequently restart (an American call)

Part (e)

An American option

• to choose between two assets:
  • Defer exercise and then determine whether it is more profitable to build a hotel or an apartment building.
  • Wait: however, the developer loses the cash flows from immediate development.
• In the money option

Part (f)

A call option

• Enables Air France to fix the delivery date and price