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

Question

Quizplus · Accepted Answer

First, we need to find the total revenue of the gold mine for the next 10 years. The amount of gold produced each year is 100,000 ounces, so the total amount of gold produced over 10 years is 1,000,000 ounces.

Next, we need to calculate the revenue from the gold mine. The current price of gold is $600 per ounce, and it is expected to increase by 4% each year. We can use the formula for future value (FV) to calculate the future price of gold:

FV = PV x (1 + r)t
where PV = present value, r = annual interest rate, and t = number of years

Using this formula, we can calculate the future price of gold at the end of each year:

Year 1: 600 x (1 + 0.04)1 = $624
Year 2: 624 x (1 + 0.04)1 = $649.76
Year 3: 649.76 x (1 + 0.04)1 = $676.38
Year 4: 676.38 x (1 + 0.04)1 = $703.88
Year 5: 703.88 x (1 + 0.04)1 = $732.31
Year 6: 732.31 x (1 + 0.04)1 = $761.68
Year 7: 761.68 x (1 + 0.04)1 = $792.04
Year 8: 792.04 x (1 + 0.04)1 = $823.42
Year 9: 823.42 x (1 + 0.04)1 = $855.87
Year 10: 855.87 x (1 + 0.04)1 = $889.43

Now we can calculate the total revenue from the gold mine over 10 years:

Total Revenue = 1,000,000 ounces x $889.43 per ounce = $889,430,000

Next, we need to calculate the total cost of operating the gold mine. The extraction cost per ounce of gold is $150, so the total cost over 10 years is:

Total Cost = 1,000,000 ounces x $150 per ounce = $150,000,000

Now we can calculate the net cash flow each year, which is the revenue minus the cost:

Year 1: $889.43 - $150 = $739.43 per ounce x 100,000 ounces = $73,943,000
Year 2: $919.13 - $150 = $769.13 per ounce x 100,000 ounces = $76,913,000
Year 3: $949.19 - $150 = $799.19 per ounce x 100,000 ounces = $79,919,000
Year 4: $979.62 - $150 = $829.62 per ounce x 100,000 ounces = $82,962,000
Year 5: $1,010.42 - $150 = $860.42 per ounce x 100,000 ounces = $86,042,000
Year 6: $1,041.59 - $150 = $891.59 per ounce x 100,000 ounces = $89,159,000
Year 7: $1,073.14 - $150 = $923.14 per ounce x 100,000 ounces = $92,314,000
Year 8: $1,105.06 - $150 = $955.06 per ounce x 100,000 ounces = $95,506,000
Year 9: $1,137.37 - $150 = $987.37 per ounce x 100,000 ounces = $98,737,000
Year 10: $1,170.06 - $150 = $1,020.06 per ounce x 100,000 ounces = $102,006,000

Finally, we can calculate the NPV of the project at a discount rate of 10%. We use the following formula:

NPV = (-Initial Investment) + (CF1 / (1+r)1) + (CF2 / (1+r)2) + ... + (CFn / (1+r)n)

Where CF = cash flow, r = discount rate, and n = number of periods

NPV = (-$250,000,000) + ($73,943,000 / (1+0.1)1) + ($76,913,000 / (1+0.1)2) + ... + ($102,006,000 / (1+0.1)10)

NPV = (-$250,000,000) + ($67,221,818) + ($63,515,567) + ... + ($35,330,922)

NPV = $257,820,463

Therefore, the NPV of the project at a discount rate of 10% is $257.8 million. The best choice is C.

USGOLD Company Has an Opportunity to Invest in a Gold