You are thinking about investing in a mine that will produce $10,000 worth of ore in the first year.As the ore closest to the surface is removed it will become more difficult to extract the ore.Therefore,the value of the ore that you mine will decline at a rate of 8% per year forever.If the appropriate interest rate is 6%,then the value of this mining operation is closest to:
A)$71,429.
B)$500,000.
C)$166,667.
D)This problem cannot be solved.

Question

Quizplus · Accepted Answer

The value of the mining operation can be calculated using the formula for the present value of a perpetuity with a growth rate: PV = C / (r - g), where C is the cash flow in the first year, r is the interest rate, and g is the growth rate. Here, C = $10,000, r = 6% (0.06), and g = -8% (-0.08). Plugging in these values, PV = $10,000 / (0.06 - (-0.08)) = $10,000 / 0.14 = $71,429.

You Are Thinking About Investing in a Mine That Will