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 com- pany opens the mine, it will cost $850 million today, and it will have a cash outflow of $120 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 that follows. Bullock has a 12 percent required return on all of its gold mines.

YEAR	CASH FLOW
0 1 2 3 4 5 6 7 8 9	-$850,000,000 165,000,000 190,000,000 225,000,000 245,000,000 235,000,000 195,000,000 175,000,000 155,000,000 -120,000,000

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

1

1

Project
Year	Cash flow stream	Cumulative cash flow
0	-850000000	-850000000
1	165000000	-685000000
2	190000000	-495000000
3	225000000	-270000000
4	245000000	-25000000
5	235000000	210000000
6	195000000	405000000
7	175000000	580000000
8	155000000	735000000
9	-120000000	615000000
Payback period is the time by which undiscounted cashflow cover the intial investment outlay
this is happening between year 4 and 5
therefore by interpolation payback period = 4 + (0-(-25000000))/(210000000-(-25000000))
4.11 Years
Project
IRR is the rate at which NPV =0
IRR	0.153252394
Year	0	1	2	3	4	5	6	7	8	9
Cash flow stream	-850000000	165000000	190000000	225000000	245000000	235000000	195000000	175000000	155000000	-120000000
Discounting factor	1	1.153252394	1.329991085	1.533815403	1.768876287	2.039960813	2.352589692	2.713129695	3.128923317	3.608438307
Discounted cash flows project	-850000000	143073624.5	142858100.4	146693011.1	138506011.9	115198291.3	82887381.8	64501155.37	49537807.19	-33255383.57
NPV = Sum of discounted cash flows
NPV Project =	-3.01749E-07
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	15.33%
Project
Combination approach
All negative cash flows are discounted back to the present and all positive cash flows are compounded out to the end of the project’s life
Thus year 8 modified cash flow=(408533924.09)+(420029467.41)+(444110104.17)+(431773712.38)+(369777049.6)+(273960960)+(219520000)+(173600000)
=2741305217.65
Thus year 0 modified cash flow=-850000000-43273203
=-850000000
Discount rate	12.00%
Year	0	1	2	3	4	5	6	7	8	9
Cash flow stream	-850000000	165000000	190000000	225000000	245000000	235000000	195000000	175000000	155000000	-120000000
Discount factor	1	1.12	1.2544	1.404928	1.57351936	1.762341683	1.973822685	2.210681407	2.475963176	2.773078757
Compound factor	1	2.475963176	2.210681407	1.973822685	1.762341683	1.57351936	1.404928	1.2544	1.12	1
Discounted cash flows	-850000000	0	0	0	0	0	0	0	0	-43273203
Compounded cash flows	-1.17647E-09	408533924.1	420029467.4	444110104.2	431773712.4	369777049.6	273960960	219520000	173600000	0
Modified cash flow	-850000000	0	0	0	0	0	0	0	0	2741305218
Discounting factor (using MIRR)	1	1.138948991	1.297204804	1.477450102	1.682740303	1.916555369	2.182858804	2.486164831	2.831614926	3.225064962
Discounted cash flows	-850000000	0	0	0	0	0	0	0	0	850000000
NPV = Sum of discounted cash flows
NPV=	-2.38419E-07
MIRR is the rate at which NPV = 0
MIRR=	13.89%
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Compounding factor =	(1 + reinvestment rate)^(time of last CF-Corresponding period in years)
Compounded Cashflow=	Cash flow stream*compounding factor

2

Accept project as NPV is positive & IRR & MIRR is more than discount rate