Question

The Ore Mining Company is attempting to decide whether or not a certain piece of land should be purchased. The land cost is Rs. 3,00,000. If there are commercial ore deposits on the land, the estimated value of the property is Rs. 5,00,000. If no ore deposits exist, however, the property value is estimated at Rs. 2, 00,000. Before purchasing the land, the property can be cored at a cost of Rs. 20,000 . The coring will indicate if conditions are favorable or unfavorable for one mining. If the coring report is favorable, the probability of recoverable ore deposits on the land is 0.8 , while if the coring report is unfavorable the probability is only 0.2 . Prior to obtaining any coring information, management estimates that the odds are 50-50 that ore is present on the land. Management has also received coring reports on places of land similar to the one in question and found that 60% of the coring reports were favorable.

Construct a decision tree and determine whether the company should purchase the land, decline to purchase it, or take a coring test before making its decision. Specify the optimal course of action and EMV.

Answer 1

To determine if the Ore Mining Company should purchase a piece of land, a decision tree is utilized to evaluate the Expected Monetary Value (EMV) of purchasing without coring, declining the purchase, or coring first. Calculations are based on varying probabilities of discovering ore and the costs associated with coring.

Step-by-step explanation:

Decision Tree Analysis for Ore Mining Company Land Purchase

To determine whether the Ore Mining Company should purchase the land, decline to purchase, or take a coring test, we construct a decision tree. The land costs Rs. 3,00,000, and its value depends on whether it holds ore deposits. With ore, the value is Rs. 5,00,000, and without, it is Rs. 2,00,000. Coring costs Rs. 20,000 and can give favorable (indicating an 0.8 probability of ore) or unfavorable (indicating an 0.2 probability of ore) reports. With no prior coring, there's a 50% chance that ore is present, and historically, 60% of coring reports in similar situations have been favorable.

Using these probabilities and costs, the Expected Monetary Value (EMV) for each action can be calculated:

• Purchase the land without coring: EMV = 0.5 * (5,00,000 - 3,00,000) + 0.5 * (2,00,000 - 3,00,000) = Rs. 50,000.
• Decline to purchase: EMV = Rs. 0, since the company neither gains nor loses money.
• Coring first:
• If favorable: EMV = 0.8 * (5,00,000 - 3,00,000 - 20,000) + 0.2 * (2,00,000 - 3,00,000 - 20,000).
  
• If unfavorable: EMV = 0.2 * (5,00,000 - 3,00,000 - 20,000) + 0.8 * (2,00,000 - 3,00,000 - 20,000).
• Weighted EMV for coring: (0.6 * favorable EMV) + (0.4 * unfavorable EMV).

After calculating these EMVs, the highest EMV will indicate the optimal course of action.