USGOLD Company has an opportunity to invest in a gold mine. The initial investment is $250 million. Analysts estimate that the mine will produce 100,000 ounces of gold per year for the next 10 years. The extraction cost of gold is $150 per ounce and is expected to remain at that level. The current price of gold is $600 per ounce and is expected to increase 4 percent per year for the next 10 years. What is the NPV of the project at a discount rate of 10 percent? (Ignore taxes.)

Question

Quizplus · Accepted Answer

To calculate the NPV of the project, we need to calculate the present value of all the cash inflows and outflows at a discount rate of 10 percent.

Cash inflows:
The mine will produce 100,000 ounces of gold per year for 10 years, at a price of $600 per ounce in year 1, with a 4% increase each year. The calculation of the annual cash inflows is as follows:

Year 1: 100,000 x $600 = $60 million
Year 2: 100,000 x $600 x 1.04 = $62.4 million
Year 3: 100,000 x $600 x 1.04^2 = $64.9 million
Year 4: 100,000 x $600 x 1.04^3 = $67.5 million
Year 5: 100,000 x $600 x 1.04^4 = $70.2 million
Year 6: 100,000 x $600 x 1.04^5 = $73.1 million
Year 7: 100,000 x $600 x 1.04^6 = $76.1 million
Year 8: 100,000 x $600 x 1.04^7 = $79.2 million
Year 9: 100,000 x $600 x 1.04^8 = $82.5 million
Year 10: 100,000 x $600 x 1.04^9 = $85.9 million

Total cash inflows = $672.6 million

Cash outflows:
Initial investment = $250 million
Annual extraction cost per year for 10 years = 100,000 x $150 = $15 million per year
Total cash outflows = $250 million + ($15 million x 10) = $400 million

Now, we can calculate the NPV as follows:

NPV = - $250 million + ($672.6 million / (1 + 0.1)^1) + ($672.6 million / (1 + 0.1)^2) + ... + ($672.6 million / (1 + 0.1)^10) - $400 million

NPV = $257.8 million

Since the NPV is positive, the project is expected to generate a return greater than the cost of the investment, and therefore it would be a good choice for USGOLD Company to invest in this gold mine.

USGOLD Company Has an Opportunity to Invest in a Gold