Suppose as in Example 17.5 that oil will be selling in April for $59.79, $61.79, or  $63.79 per barrel. Consider a firm that plans to buy 100,000 barrels of oil in April. Show that if the firm buys 100 oil contracts, its net expenditures will be hedged and equal to $6,179,000.

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EXAMPLE 17.5 Hedging with Oil Futures (Concluded) To illustrate, continue to use the oil futures listing in Figure 17.1, and suppose that the only three possible prices for oil in April are $59.79, $61.79, and $63.79 per barrel. The revenue from the oil sale will be 100,000 times the price per barrel. The profit on each contract sold will be 1,000 times any decline in the futures price. At maturity, the convergence property ensures that the final futures price will equal the spot price of oil. Therefore, the profit on the 100 con- tracts sold will equal 100,000 × (F-PT), where PT is the oil price on the delivery date, and Fo is the original futures price, $61.79. Now consider the firm's overall position. The total revenue in April can be computed as follows: Revenue from oil sale: 100,000 X PT + Profit on futures: 100,000 X (Fo - PT) Total Proceeds Oil Price in April, PT $61.79 $6,179,000 $6,179,000 $59.79 $5,979,000 200,000 $6,179,000 0 $63.79 $6,379,000 - 200,000 $6,179,000 The revenue from the oil sale plus the proceeds from the contracts equals the current futures price, $61.79 per barrel. The variation in the price of the oil is precisely offset by the profits or losses on the futures position. For example, if oil falls to $59.79 a barrel, the short futures posi- tion generates $200,000 profit, just enough to bring total revenues to $6,179,000. The total is the same as if one were to arrange today to sell the oil in April at the futures price.