You are considering investing in a new gold mine in South Africa. Gold in South

Question

You are considering investing in a new gold mine in South Africa. Gold in South Africa is buried very deep, so the mine will require an initial investment of $ 255$255 million. Once this investment is made, the mine is expected to produce revenues of $ 31 million$31 million per year for the next 2020 years. It will cost $ 10.5 million$10.5 million per year to operate the mine. After 2020 years, the gold will be depleted. The mine must then be stabilized on an ongoing basis, which will cost $ 5.2 million$5.2 million per year in perpetuity. Calculate the IRR of this investment. (Hint: Plot the NPV as a function of the discount rate.) The IRR of this investment is:(Select the best choice below.) A. There are multiple IRRs. B. No positive IRR exists since the NPV, calculated as a function of various discount rates, never equals or exceeds zero. C. The IRR is about 10.3 %10.3%. D. The IRR is infinite as a result of the perpetuity. You are considering investing in a new gold mine in South Africa. Gold in South Africa is buried very deep, so the mine will require an initial investment of $ 255$255 million. Once this investment is made, the mine is expected to produce revenues of $ 31 million$31 million per year for the next 2020 years. It will cost $ 10.5 million$10.5 million per year to operate the mine. After 2020 years, the gold will be depleted. The mine must then be stabilized on an ongoing basis, which will cost $ 5.2 million$5.2 million per year in perpetuity. Calculate the IRR of this investment. (Hint: Plot the NPV as a function of the discount rate.) The IRR of this investment is:(Select the best choice below.) A. There are multiple IRRs. B. No positive IRR exists since the NPV, calculated as a function of various discount rates, never equals or exceeds zero. C. The IRR is about 10.3 %10.3%. D. The IRR is infinite as a result of the perpetuity. You are considering investing in a new gold mine in South Africa. Gold in South Africa is buried very deep, so the mine will require an initial investment of $ 255$255 million. Once this investment is made, the mine is expected to produce revenues of $ 31 million$31 million per year for the next 2020 years. It will cost $ 10.5 million$10.5 million per year to operate the mine. After 2020 years, the gold will be depleted. The mine must then be stabilized on an ongoing basis, which will cost $ 5.2 million$5.2 million per year in perpetuity. Calculate the IRR of this investment. (Hint: Plot the NPV as a function of the discount rate.) You are considering investing in a new gold mine in South Africa. Gold in South Africa is buried very deep, so the mine will require an initial investment of $ 255$255 million. Once this investment is made, the mine is expected to produce revenues of $ 31 million$31 million per year for the next 2020 years. It will cost $ 10.5 million$10.5 million per year to operate the mine. After 2020 years, the gold will be depleted. The mine must then be stabilized on an ongoing basis, which will cost $ 5.2 million$5.2 million per year in perpetuity. Calculate the IRR of this investment. (Hint: Plot the NPV as a function of the discount rate.) You are considering investing in a new gold mine in South Africa. Gold in South Africa is buried very deep, so the mine will require an initial investment of $ 255$255 million. Once this investment is made, the mine is expected to produce revenues of $ 31 million$31 million per year for the next 2020 years. It will cost $ 10.5 million$10.5 million per year to operate the mine. After 2020 years, the gold will be depleted. The mine must then be stabilized on an ongoing basis, which will cost $ 5.2 million$5.2 million per year in perpetuity. Calculate the IRR of this investment. (Hint: Plot the NPV as a function of the discount rate.) $ 255$255 $ 31 million$31 million 2020 $ 10.5 million$10.5 million 2020 $ 5.2 million$5.2 million (Hint: The IRR of this investment is:(Select the best choice below.) A. There are multiple IRRs. B. No positive IRR exists since the NPV, calculated as a function of various discount rates, never equals or exceeds zero. C. The IRR is about 10.3 %10.3%. D. The IRR is infinite as a result of the perpetuity. The IRR of this investment is:(Select the best choice below.) A. There are multiple IRRs. B. No positive IRR exists since the NPV, calculated as a function of various discount rates, never equals or exceeds zero. C. The IRR is about 10.3 %10.3%. D. The IRR is infinite as a result of the perpetuity. The IRR of this investment is:(Select the best choice below.) A. There are multiple IRRs. B. No positive IRR exists since the NPV, calculated as a function of various discount rates, never equals or exceeds zero. C. The IRR is about 10.3 %10.3%. D. The IRR is infinite as a result of the perpetuity. A. There are multiple IRRs. B. No positive IRR exists since the NPV, calculated as a function of various discount rates, never equals or exceeds zero. C. The IRR is about 10.3 %10.3%. D. The IRR is infinite as a result of the perpetuity. A. There are multiple IRRs. A. There are multiple IRRs. There are multiple IRRs. IRRs. B. No positive IRR exists since the NPV, calculated as a function of various discount rates, never equals or exceeds zero. B. No positive IRR exists since the NPV, calculated as a function of various discount rates, never equals or exceeds zero. No positive IRR exists since the NPV, calculated as a function of various discount rates, never equals or exceeds zero. NPV, C. The IRR is about 10.3 %10.3%. C. The IRR is about 10.3 %10.3%. The IRR is about 10.3 %10.3%. 10.3 %10.3%. D. The IRR is infinite as a result of the perpetuity. D. The IRR is infinite as a result of the perpetuity. The IRR is infinite as a result of the perpetuity.

Explanation / Answer

NPV=-255+(31-10.5)/(1+x)+(31-10.5)/(1+x)^2........(31-10.5)/(1+x)^20+5.2/(1+x)^21+5.2/(1+x)^22...........

IRR is the rate at which NPV=0

So, 0=-255+20.5/(1+x)*(1-1/(1+x)^20)/(1-1/(1+x))+5.2/(1+x)^21/(1-1/(1+x))

=>0=-255+20.5/x*(1-1/(1+x)^20)+5.2/(1+x)^21*(1+x)/x

IRR=6.257% and -3.0044%

hence, option A

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