Question

A mining company is evaluating when to open a gold mine. The mine has 100,000 ounces of gold left that can be mined and mining operations will produce 10,000 ounces per year. The price of gold from the mine will be guaranteed for the remaining life of the mine through the gold futures contracts. If the mine is opened today, each ounce of gold will generate an after-tax cash flow (= total or net cash flow) of $1,300 per ounce. If the company waits one year, there is a 70 percent probability that the contract price will generate an after-tax cash flow of $1,550 per ounce and a 30 percent probability that the after-tax cash flow will be $1,200 per ounce. The required return on the gold mine is 15 percent and it will cost $30,000,000 to open the mine regardless of whether the mine is open today or in one year. Compute the value of the option to wait today.

Answer 1

The value of the option to wait today = $2,500,000

Step-by-step explanation:

a) Data and Calculations:

Quantity of gold left in the mine = 100,000 ounces

Quantity of gold to be produced yearly = 10,000 ounces

Estimated life of mine = 10 years (100,000/10,000)

After-tax cash flow if mine is opened today = $1,300 per ounce

After-tax cash flow if mine is opened a year later:

Expected value = ($1,550 * 70%) + ($1,200 * 30%) = $1,325 per ounce

Comparison of the values of opening options:

Mine opened Mine opened

today a year later

After-tax cash flow per ounce $1,300 $1,325

Quantity of gold in the mine 100,000 100,000

Total after-tax cash flows $130,000,000 $132,500,000

Cost of opening mine 30,000,000 30,000,000

Required return (15%) 4,500,000 4,500,000

Actual returns from mine $100,000,000 $102,500,000

Therefore, the value of option to wait:

Returns from mine opened next year = $102,500,000

Returns from mine opened today = 100,000,000

Value of the option to wait today = $2,500,000