Question

A mining company just purchased land in South Africa and discovered gold there. It takes time to build a gold mine to extract them, so the company expects to dig out 3192000.0 troy ounces of each year for two years, starting two years from now. The 1-year and 2-year future prices for gold are $1380.0/oz and $1391.0/oz, respectively. The 1-year spot rate is 1.0%. Assume that the net convenience yield for gold is zero.

The company needed capital to invest in other projects, and the company decided to sell its claim on the gold. What is the value of the claim in billions?

Answer 1

Extraction started after 2 year from now. Do first year of extraction is 3 year from now and second year extraction is 4 year from now.

Gold extracted in year 1 = 3,192,000 ounce

Futures price in year 1 = $1,380 per aunce

Revenue in year 1 = 3,192,000 × $1,380

= $4,404,960,000

Revenue in year 1 will be $4,404,960,000.

Year 2

Gold extracted in year 2 = 3,192,000 ounce

Futures price in year 2 = $1,391 per aunce

Revenue in year 2 = 3,192,000 × $1,391

= $4,440,072,000

Revenue in year 1 will be $4,440,072,000.

Present value of claim is present value of future revenuw.

So present value of revenue = [$4,404,960,000 / (1 + 1%) ^ 3] + [$4,440,072,000 / (1 + 1%) ^ 4]

= ($4,404,960,000 / 1.0303) + ($4,440,072,000 / 1.0406)

= $4,275,410,778 + $4,266,821,920

= $8,542,232,698

So present value of revenue is $8,542,232,698 or $8.542 billion. So, value of claim is $8,542,232,698 or $8.542 billion.