Question

A gold mining firm is concerned about short-term volatility in its revenues. Gold currently sells for $1,620 an ounce, but the price is extremely volatile and could fall as low as $1,500 or rise as high as $1,700 in the next month. The company will bring $4,000 ounces to the market next month.
a.	What will total revenues be if the firm remains unhedged for gold prices of $1,500, $1,620, and $1,700 an ounce?
			Gold price
			$1,500		$1,620	$1,700
	Total revenues		$		$	$
b.	The futures price of gold for 1-month-ahead delivery is $1,630. What will be the firm’s total revenues at each gold price if the firm enters a 1-month futures contract to deliver $4,000 ounces of gold?

			Gold price
			$1,500		$1,620	$1,700
	Total revenues		$		$	$

        

c.	What will total revenues be if the firm buys a 1-month put option to sell gold for $1,620 an ounce? The puts cost $8 per ounce.

			Gold price
			$1,500		$1,620	$1,700
	Total revenues		$		$	$

Answer 1

a.

b. futures price of gold for 1-month-ahead delivery is $1,630.
Therefore, no matter what the gold prices are the firm will generate revenue of $1630*4000 = $6,520,000

c. 1-month put option to sell gold for $1,620 an ounce? The puts cost $8 per ounce.
Here, when the spot price will be less than 1620, put option will be exercised

at $1500, Revenue = $1620 * 4000 - $8*4000 = $6,448,000
at $1620, Revenue = $1620 * 4000 - $8*4000 = $6,448,000
at $1700, Revenue = $1700 * 4000 - $8*4000 = $6,768,000

Gold price
	$       1,500.00	$       1,620.00	$       1,700.00
Total revenues	$64,48,000.00	$64,48,000.00	$67,68,000.00

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