Question

MINI CASE (p.475): STRIK-IT-RICH GOLD MINING COMPANY

The Strik-it-Rich Gold Mining Company is considering expanding its operations. To do so, you will need to buy land that your geologists believe is rich in gold. Strik-it-Rich management believes the expansion will allow it to mine and sell an additional 2,000 troy ounces of gold per year. The expansion, including the cost of land, will cost $ 2,500,000. The current price of gold bullion is $ 1,400 per ounce and one-year gold futures are trading at $ 1,484 = $ 1,400 (1.06).

Extraction costs are $ 1,050 per ounce. The company's cost of capital is 10%. At the current gold price, the expansion appears profitable: NPV = ($ 1,400 - 1,050) x 2,000 / .10 - $ 2,500,000 = $ 4,500,000. However, Strik-it-Rich management is concerned about the possibility that the large sales of gold reserves by Russia and the United Kingdom will reduce the price of gold to $ 1,100 in the foreseeable future. On the other hand, management believes that there is some chance that the world will soon return to an international gold reserve monetary system.

In the latter case, the price of gold would rise to at least $ 1,600 per ounce. The course of the future price of gold bullion should be clarified in one year. Strik-it-Rich can postpone the expansion for a year by purchasing a purchase option on the land for $ 250,000. What should Strik-it-Rich management do? Include in your discussion an analysis of how the NPV would be affected if the price of gold increased or decreased significantly. Is it a good idea to buy a call option on land? Why or why not?

Answer 1

Step 1: Calculate NPV if Price of Gold Falls to $1,100 Per Ounce

The NPV is price of gold falls to $1,100 per ounce is calculated as below:

NPV if Price of Gold Falls to $1,100 Per Ounce = (New Price Per Ounce - Extraction Cost Per Ounce)*2,000/.10 = (1,100 - 1,050)*2,000/.10 - 2,500,000 = $1,000,000 = -$1,500,000

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Step 2: Calculate NPV if Price of Gold Increases to $1,600 Per Ounce

The NPV is price of gold increases to $1,600 per ounce is determined as below:

NPV if Price of Gold Increases to $1,600 Per Ounce = (New Price Per Ounce - Extraction Cost Per Ounce)*2,000/.10 = (1,600 - 1,050)*2,000/.10 - 2,500,000 = $1,000,000 = $8,500,000

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Step 3: Calculate Risk-Neutral Probability of Gold Increasing to $1,600 Per Ounce

The company will consider expanding the operations only if the NPV is positive. As such, we don't need to calculate the risk-neutral probability of gold falling to $1,100. The risk-neutral probability of gold increasing to $1,600 is arrived as follows:

Risk-Neutral Probability of Gold Increasing to $1,600 Per Ounce = (1,484 - 1,100)/(1,600 - 1,100) = 0.768

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Step 4: Calculate Value of the Timing Option to Postpone the Decision to 1 Year

The value of the timing option to postpone the decision to 1 year is calculated as below:

Value of the Timing Option to Postpone the Decision to 1 Year = (Risk-Neutral Probability of Gold Increasing to $1,600 Per Ounce*NPV if Price of Gold Increases to $1,600 Per Ounce)/1.06 = (0.768*8,500,000)/1.06 = $6,158,490.57

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Conclusion:

The company should buy the call option on the land. It is because the value of the timing option to postpone the decision to 1 Year of $6,158,490.57 is significantly higher than the cost of purchase option on the land for $250,000. In other words, Strik-it-Rich management should consider buying the option on land and taking the benefit of the timing option to understand how gold will perform in future (that is after 1 years) before arriving at the decision to expand the operations.