Question

Barrick is comparing two gold mines.

Mine A: The mine is expected to make $3.5 billion in year 1, $4.5 billion in year 2, and $5.5 billion in years 3-6 and $4.25 billion in years 7-10. At the end of year 10, Barrick will need to spend $202 million on environmental clean-up costs and expects the residual value to be $200 billion.

Mine B: The mine is currently in operation and produces $4.1 billion per year. At the end of 10 years the residual value would be $200 billion and no environmental clean-up costs would be necessary.

Which mine should Barrick buy for $142 billion. (To simplify things, assume Net Income is earned one time per year at the end of the year.) The appropriate discount rate is 6.22% compounded quarterly.

Answer 1

Step 1

The annual discount rate provided in the question is compounded quarterly. Since, the cash flows are assumed to be incurred at the end of the year, the discount rate without compounding has to be considered.
Such rate is computed as follows-

Hence, the annual discount rate to be used is 6.08%

Step 2

Conclusion

The total discounted cash inflow under Mine A is $ 145.246 billions and under Mine B is $ 140.902 billions. Hence, Mine A could be purchased for $ 142 billions due to positive NPV ($ 3.246 billions).