Question

Seth Bullock, the owner of Bullock Gold Mining, is evaluating a new gold mine in South Dakota. Dan Dority, the company’s geologist, has just finished his analysis of the mine site. He has estimated that the mine would be productive for eight years, after which the gold would be completely mined. Dan has taken an estimate of the gold deposits to Alma Garrett, the company’s financial officer. Alma has been asked by Seth to perform an analysis of the new mine and present her recommendation on whether the company should open the new mine. Alma has used the estimates provided by Dan to determine the revenues that could be expected from the mine. She has also projected the expense of opening the mine and the annual operating expenses. 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 area surrounding it. The expected cash flows each year from the mine are shown in the table. Bullock Mining has a required return of 12 percent on all of its gold mines.

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

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?

Answer 1

Answer: Payback period:

Payback period = initial investment - Opening Cumulative cash flowClosing cumulative cash flow - Opening cumulatie cash flow

Initial investment = 635000000

Cumulative cash flow till 4^th year = 497000000

Cumulative cash flow till 5^th year = 702000000

Payback period is between 4^th and 5^th year.

Opening cumulative cash flow = 497000000

Closing cumulative cash flow = 702000000

Payback period after 4^th year = (635 – 497)/(702 – 497)

Payback period after 4^th year = 0.673170732

Payback period = 4.67 years

Answer : Internal Rate of return

The guess I R R using excel formula is 13%

Calculations are made for 13.01 , 13.015 and 13.02%

Year	Cash flow	cumulative	[email protected]	[email protected]	[email protected]
0	-635000000		-635000000	-635000000	-635000000
1	89000000	89000000	78754093	78747124.4	78750608
2	105000000	194000000	82215850	82201301.37	82208575
3	130000000	324000000	90072606	90048699.16	90060651
4	173000000	497000000	106066589	106029055.1	106047820
5	205000000	702000000	111216567	111167373.8	111191967
6	155000000	857000000	74409853	74370359.43	74390103
7	145000000	1002000000	61595627	61557486.92	61576553
8	122000000	1124000000	45859027	45826575.73	45842798
9	-45000000	1079000000	-14967892	-14955976.95	-14961933
Total			222319.13	-8000.944102	107143.71

The I R R is approximately 13.015%

Answer: Modified Internal rate of retrun

Using the excel MIRR function, the MIRR = 12%

Answer NPV

Year	Cash flow	NPV @12%
0	-635000000	-635000000
1	89000000	87944664
2	105000000	102524645
3	130000000	125430113
4	173000000	164939264
5	205000000	193130693
6	155000000	144294116
7	145000000	133384208
8	122000000	110895961
9	-45000000	-40419217
Total		387124448

The NPV of the Cash flows at 12% is 387124448

Answer 2

Since the NPV @ 12% is $ 387124448, the company should open the mine.