Question

Boondock Silver Mining

Beth Boondock, owner of Boondock Silver Mining, is reviewing the details of a new silver mine in South Dakota. According to the company's geologist, Dory Donovan, a detailed analysis of the mine suggests it would be productive for eight years. After that amount of time, all of the silver ore would be completely mined. Dory sent an estimate of the silver deposits to Gina Albert, the company's chief financial officer. Beth has contacted Gina to request a full financial analysis of the new mine and to present her recommendations on whether the company should open the new mine.

Gina used the estimates provided by Dory to determine the revenues that could be expected from the mine. She has projected both the annual operating expenses of the new mine and the expense of opening the mine. If the company opens the mine, it will cost $635 million today, and it will have a cash outflow of $45 million nine years from today in costs associated with closing the mine and reclaiming the surrounding area. The expected cash flows each year each year from the mine are shown below:

Year	Cash Flow
0	- $635,000,000
1	89,000,000
2	105,000,000
3	130,000,000
4	173,000,000
5	205,000,000
6	155,000,000
7	145,000,000
8	122,000,000
9	- 45,000,000

Questions:

1. Construct a spreadsheet to calculate the payback period, internal rate of return, modified internal rate of return, and net present value of the proposed mine.
2. Based on your analysis, should the company open the mine? Why or why not?

Answer 1

Pay back period is the time taken by a project to fetch all the cash outflows.

In this question, total outflow is $635 million+$45 million= $680 million

Time taken by project to get this amount is 4 years 11 months.

After 4 years the project will fetch 89+105+130+173= 497.

5th year to get the balance of 183, it will take 11 months.

So payback period is 4 years and 11 months.

IRR= Lower Discount rate+ (NPV@ lower discount rate/PV @lower discount rate - PV@ higher discount rate)× difference of discount rates

Two discount rates selected are 13% and 15%

Year. PVF@13%. PV. PVF@15%. PV.   

1. .885. 78.65. 0.87. 77.43

2. .783. 82.215. .756. 79.38

3. .693. 90.09. .658. 85.54

4. .613. 106.049. .572. 98.956

5. .543. 111.315. .497. 101.885

6. .480. 74.4. .432. 66.96

7. .425. 61.625. .376. 54.52

8. .376. 45.872. .327. 39.894

Total. 650.216. 604.565

PV of Cash outflow at 13% = 635+14.985=649.985

(14.985 is obtained by 45×0.333)

NPV= 650.216-649.985= 0.231

PV of Cash outflow at 15% = 635+12.78= 647.78

(12.78 is obtained by 45×0.284)

NPV= 604.565- 647.78= -43.215

Now, IRR= 13%+ (0.231/650.216-604.565)×(15-13)= 13%+ (0.231/45.651)×2= 13%+ 0.01=13.01%

Modified IRR is given by n√(FVCF/PVCF) -1 where FVCF is the future value of positive cash flows discounted at reinvestment rate. PVCF is the present value of negative cash flows discounted at financing rate. n is the number of years.

Here in this question, we don't have these rates, so modified IRR cannot be calculated.

Also, to find out NPV separately, we need to be given with a discount rate which is not provided in the question.