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 $850 million today, and it will have a cash outflow of $75 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 following table. Bullock Mining has a 12 percent required return on all of its gold mines. 

Year	Cash Flow
0	-$850,000,000
1	170,000,000
2	190,000,000
3	205,000,000
4	265,000,000
5	235,000,000
6	170,000,000
7	160,000,000
8	105,000,000
9	-75,000,000

 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? Explain in detail the different measures which you have calculated for this case. Specifically, provide an explanation of payback period, IRR, MIRR and NPV. Also, explain how business' use these for decisions and the potential advantages/disadvantages of each.

Answer 1

1) Payback Period.

Payback Period is the time in which the investment in the project is recouped (Gross Cash Flow Terms).

  Since this project will require an outflow of cash in 9th year, let us calculate the present value of cash outflow in 9th year and add it to the initial investment.

PV of 75000000 in 9th year is =75000000/(1+0.12)^9 = $ 27,045,751.87\-

  Total Cash Outflow is $ 877,045,751.9\-

Year	Cash Flows	Cumulative Cash Flow
	(877,045,751.9)
1	170,000,000	170,000,000
2	190,000,000	360,000,000
3	205,000,000	565,000,000
4	265,000,000	830,000,000
5	235,000,000	1,065,000,000

We can see that total amount was recouped sometime in 5th year.

Amount to be recovered in 5th year to recover total investment = 877,045,751.9-830,000,000 = 47,045,752\-

No of days in 5th year taken to recoup = 47045752 = 47045752/1065000000*365 = 16.12 Days = 17 Days.

Payback Period = 4 yrs 17 days.

2. IIR (Internal Rate of Return)

It is the discount rate at which NPV of a project will equal to zero. Or in other words, the rate of return provided by the project.

Year	Cash Flows
0	(850,000,000)
1	170,000,000
2	190,000,000
3	205,000,000
4	265,000,000
5	235,000,000
6	170,000,000
7	160,000,000
8	105,000,000
9	(75,000,000)

IRR = 14.48%, IRR can be calculated in a spreadsheet by the formula =IRR(B21:29).

3. MIRR (Modified Rate of Return).

MIRR assumes that cash flows from the project are reinvested at the cost of capital of the firm (12% in this case).

MIRR can be calculated in a spreadsheet by the formula =IRR(B21:29,Cost of capital,Reinvestment rate).

MIRR = 13.15%.

4. NPV (Net Present Value ).

Explains the present value all cash flows (Both Inflows and outflows), by discounting the future cash flows with Cost of Capital of the Firm.

The higher the NPV the better, a project should be taken only is NPV is positive, and if multiple projects are being compared, the project with higher NPV should be chosen.

Year	Cash Flows	PV Factor @ 12%	PV of Cash Flows @12%
0	(850,000,000)	1.00	(850,000,000)
1	170,000,000	0.893	151,785,714
2	190,000,000	0.797	151,466,837
3	205,000,000	0.712	145,914,951
4	265,000,000	0.636	168,412,291
5	235,000,000	0.567	133,345,311
6	170,000,000	0.507	86,127,291
7	160,000,000	0.452	72,375,874
8	105,000,000	0.404	42,407,739
9	(75,000,000)	0.361	(27,045,752)
		Net Present Value	74,790,256

NPV : The higher the better.

IIR :  The higher the better.

MIRR: The higher the better.

Pay Back Period : The LESSER the better.