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Find the net present value (NPV) of a mining project with the following cash flows:-$3,000 at time zero (t=0). This is the initial cost to prepare and build the mine and facilities. This cost is all paid upfront, though the builders will take 3 years to finish construction.$500 paid annually 60 times, where the first payment is made 4 years from now. So there are 60 annual payments from t=4 to t=63 inclusive. These are the positive cash flows from running the mine once it's built.-$800 at t=63. This is the clean-up cost of burying the mine and replanting native vegetation at the end of the project. This cost is paid at the same time as the last positive cash flow is received from running the mine.The required return is 16% pa. All dollar figures above and below are in millions. The NPV of this project is:Question 10Select one:a.$3,124.58b.$124.52c.-$675.42d.-$998.29e.-$1,440.05

Question

Find the net present value (NPV) of a mining project with the following cash flows:-3,000attimezero(t=0).Thisistheinitialcosttoprepareandbuildthemineandfacilities.Thiscostisallpaidupfront,thoughthebuilderswilltake3yearstofinishconstruction.3,000 at time zero (t=0). This is the initial cost to prepare and build the mine and facilities. This cost is all paid upfront, though the builders will take 3 years to finish construction.500 paid annually 60 times, where the first payment is made 4 years from now. So there are 60 annual payments from t=4 to t=63 inclusive. These are the positive cash flows from running the mine once it's built.-800att=63.Thisistheclean−upcostofburyingthemineandreplantingnativevegetationattheendoftheproject.Thiscostispaidatthesametimeasthelastpositivecashflowisreceivedfromrunningthemine.Therequiredreturnis16800 at t=63. This is the clean-up cost of burying the mine and replanting native vegetation at the end of the project. This cost is paid at the same time as the last positive cash flow is received from running the mine.The required return is 16% pa. All dollar figures above and below are in millions. The NPV of this project is:Question 10Select one:a.3,124.58b.124.52c.−124.52c.-675.42d.-998.29e.−998.29e.-1,440.05

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Solution

To calculate the Net Present Value (NPV), we need to discount all cash flows to the present using the required return rate.

Step 1: Identify the cash flows

  • Initial investment at t=0: -$3,000
  • Annual returns from t=4 to t=63: $500
  • Clean-up cost at t=63: -$800

Step 2: Calculate the present value of each cash flow

  • The initial investment is already at present value, so it remains -$3,000.
  • The annual returns start at t=4 and continue for 60 years. We can calculate the present value of these returns using the formula for the present value of an ordinary annuity: PV = C * [(1 - (1 + r)^-n) / r], where C is the cash flow per period, r is the discount rate, and n is the number of periods. Substituting the given values, we get PV = 500 * [(1 - (1 + 0.16)^-60) / 0.16] = $3,124.58.
  • The clean-up cost occurs at t=63, so we need to discount it back to the present. The formula for the present value of a single future cash flow is PV = FV / (1 + r)^n, where FV is the future value of the cash flow. Substituting the given values, we get PV = 800 / (1 + 0.16)^63 = $1.44.

Step 3: Calculate the NPV The NPV is the sum of the present values of all cash flows. So, NPV = -3,000+3,000 + 3,124.58 - 1.44=1.44 = 124.14.

So, the closest answer is (b) $124.52.

This problem has been solved

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