A landowner is looking to develop a coal mine on their property. She determines that a surface mine is the best option, as the coal seam she is targeting is close to the surface. The cost to start the mine is $20 million and the annual cost to operate is $16 million. She estimates that they can remove 450,000 tons of coal a year and sell the coal for $38.50 per ton. How long will it take before she is able to pay off her investment and start to make a profit?

Question

Quizplus · Accepted Answer

To calculate the time it takes to pay off the investment and start making a profit, we need to calculate the total revenue generated and subtract the total costs.

The total revenue generated each year is calculated by multiplying the amount of coal removed (450,000 tons) by the selling price ($38.50 per ton):

Total revenue = 450,000 x $38.50 = $17,325,000

The total annual costs include both the operating costs and the cost of paying back the initial investment:

Total annual costs = $16,000,000 + ($20,000,000 / x years)

Now we can set up an equation to solve for x (the number of years it takes to pay off the initial investment and start making a profit):

$17,325,000 - $16,000,000 - ($20,000,000 / x) = 0

Simplifying this equation, we get:

$1,325,000 = $20,000,000 / x

x = 15.09

Therefore, it will take approximately 15 years to pay off the initial investment and start making a profit.

A Landowner Is Looking to Develop a Coal Mine on Their