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You own a transportation company that offers long-haul truck driving services to customers. Your company has 500 truck drivers employed as independent contractors. Each truck

You own a transportation company that offers long-haul truck driving services to customers. Your company has 500 truck drivers employed as independent contractors. Each truck driver has the autonomy to choose how many miles they drive each year (details described below). You have promised to provide 50,000,000 total miles of truck driving services to your customers at times t = 0, 1, and 2 and you charge customers $3.25 per mile for this service. These payments are made at the end of the year.

Each of your independent contractors can drive up to 100,000 miles per year. You pay them a trucking fee of $2.50 per mile if fuel prices are below $3.50 per gallon and $2.75 per mile otherwise. This fee policy will stay constant over time. At the beginning of each year, truckers choose how much to drive and what type of truck to rent (since neither you nor they own trucks). Truckers directly pay for fuel and the 1-year rental fee for the truck. For simplicity, assume that all the payments described in this paragraph (the trucking fee, fuel, and rental fee) are charged at the beginning of the year.

In terms of truck rentals, truckers can rent one of two trucks. The first option is a low fuel efficiency truck for $10,000 per year. This truck gets 6 miles per gallon. The second option is a high fuel efficiency truck for $25,000 per year. This truck gets 8 miles per gallon. Of course, as independent contractors, these truckers can also choose not to drive if doing so isnt sufficiently profitable. In making this drive/dont drive decision, assume that truckers must earn at least $30,000 during the year to drive. They make both the rental and drive/dont drive decision at the beginning of each year. If your independent contractors dont supply the 50,000,000 total miles that youve promised to provide to customers, you must hire temporary truck drivers to make up the difference. These drivers charge your company $3.00 per mile regardless of fuel prices.

The current price of fuel is $3 per gallon, the convenience yield on fuel is 0% per year (Remark: Convenience yield on a commodity is like a dividend yield on a financial asset), the volatility of fuel is 35% per year, and the riskless rate is 2% per year.

Question: Why is the assumption that you can hire temporary drivers at $3.00 per mile regardless of fuel prices unrealistic? Would you expect a more realistic valuation of the company to increase or decrease in light of this observation?

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