Question

Your mining company is considering an expansion of operations into iron ore. Your engineers surveyed a particular piece of land (the survey costs $200,000) and concluded the following:

• You can extract 100,000 tons of iron ore per year.

• There are 2 million tons of iron ore underneath this land (hint: 20 years' cash flows)

As you dig deeper, the operating cost to extract the ore will increase. So assume that costs will grow by 6.5 percent per year. The operating cost in the first year will be 6 million dollars (hint: the operating cost can be viewed as the COGS or expense).

Your business associates tell you the following additional information:

• The ore will sell $100 per ton for the first year, and the price is forecasted to grow by 3.3 percent per year for the next 20 years.

• We can invest in the equipment for this project right now for 15 million dollars.

The equipment is depreciated straight-line over 20 years, with an assumed salvage value of zero.(hint: the annual depreciation is 15/20=0.75 million).

Assume a constant tax rate of 40%, and an after-tax cost of capital of 10% (hint: 10% can be viewed as the discount rate for future cash flows). All numbers are nominal. You will need to use Solver in Excel to answer (b) and (c).

a) What is the net present value of this project? (Hint: the annual cash flow=(revenue-cost-depreciation)*(1-tax)+depreciation)

surveying cost will have no role to play in our NPV analysis because it has already happened.

b) Suppose you are uncertain about the growth rate for the operation cost. What growth rate for the operating cost would you need in order to break even(net present value of zero) from this project?

c) Go back to assuming the original growth rate in costs. How high would the initial investment in the equipment have to be in order for you to break even from the project?   

(In Chegg Study, it has an answer to this question, but I think the answer neglect the discount rate for future cash flows, please show the the right answer and the complete process of calculating it. Thank you:)

Answer 1

a.

b. Using a solver, maximum possible growth rtae of operating cost per year should be 6.92%.

c. Using solver, maximum cost of equipment can be $17,129,438