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)$41,667
E)This problem cannot be solved.

Question

Quizplus · Accepted Answer

This problem can be solved using the formula for the present value of a perpetuity with declining growth: $PV = \frac{C}{r - g}$, where $C$ is the initial cash flow ($10,000), $r$ is the discount rate (6% or 0.06), and $g$ is the growth rate (-8% or -0.08, since it's a decline). Plugging in the values, we get $PV = \frac{10,000}{0.06 - (-0.08)} = \frac{10,000}{0.14} = \$71,429$.

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