The Utah Mining Corporation is set to open a gold mine near Provo, Utah. Accordi

Question

The Utah Mining Corporation is set to open a gold mine near Provo, Utah. According to the treasurer, Monty Goldstein, “This is a golden opportunity.” The mine will cost $2,900,000 to open and will have an economic life of 11 years. It will generate a cash inflow of $395,000 at the end of the first year, and the cash inflows are projected to grow at 8 percent per year for the next 10 years. After 11 years, the mine will be abandoned. Abandonment costs will be $450,000 at the end of Year 11. a. What is the IRR for the gold mine

Explanation / Answer

Calculation of NPV at different trial rates:
Year   Cash Inflows   Cash Outflows   Net Cash flows   DF 10%   PV @ DF 10%   DF 15%   PV @ DF 15%
0       -2900000   -2900000   1   -2900000   1   -2900000
1   395000       395000   0.909   359091   0.870   343478
2   426600       426600   0.826   352562   0.756   322571
3   460728       460728   0.751   346152   0.658   302936
4   497586       497586   0.683   339858   0.572   284497
5   537393       537393   0.621   333679   0.497   267179
6   580385       580385   0.564   327612   0.432   250916
7   626815       626815   0.513   321655   0.376   235643
8   676961       676961   0.467   315807   0.327   221300
9   731117       731117   0.424   310065   0.284   207829
10   789607       789607   0.386   304428   0.247   195179
11   852775   -450000   402775   0.350   141170   0.215   86574
               NPV   552079   NPV   -181898

At IRR, NPV will be Zero.
Change in Rate = 15-10 = 5%
Change in NPV = 733977
Change in NPV per 1% = 733977/5 = 146795
So IRR = 10% + 552079/146795= 10% + 3.76 = 13.76%
The IRR for the gold mine = 13.76%

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