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Assume today is Sept 1, 2021. Company IMineGold is a gold mining
company producing gold with plans to increase its size and
valuation over the next few years. The company has invested in
developing goldfields and commenced extracting gold and gold
production from its underground mines. The company is confident
that it will have an output of 100,000 ounces of gold on 1 March
2022 and is willing to sell this output amount on that day.

Following further information is available:

• Profit margin is defined as (Revenue – Cost of Goods Sold) /

• The cost of mining one ounce of gold is $1,420. • The company
has a target profit margin of 18%.

• The minimum acceptable profit margin below which the company
will have difficulties servicing its debt is 14%.

• The spot price of gold on 1 Sept 2021 is $1,800.

• The interest rate curve is flat and the risk-free interest
rate for all maturities is 2% (cont. comp.).

Use the Black-Scholes model to price following options on

• Option 1: A call option with strike price 1680 expiring on 1
March 2022.

• Option 2: A put option with strike price 1680 expiring on 1
March 2022.

• Option 3: A call option with strike price 1850 expiring on 1
March 2022.

• Option 4: A put option with strike price 1850 exp

• The annual gold price volatility is estimated to be 15%.


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