Question

Bullock Gold Mining

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	−$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. Use investment, cash-flows and discount rate as presented in the chapter 9. Prepare the following: 1. Payback analysis 2. NPV analysis 3. IRR analysis

2. a. Change the cash-flows as follows:

investment $600,000,000

year 1 $79,000,000

year 2 $95,000,000

year 3 $120,000,000

year 4 $163,000,000

year 5 $195,000,000

year 6 $145,000,000

year 7 $135,000,000

year 8 $112,000,000

year 9 ($55,000,000) Salvage value

B. Answer the same quests as #1 above.

3.

A. Use the same data from #2 above and change the discount rate to 12.5%.

B. answer the same question from #1

Answer 1

1. Payback analysis :-

Payback period may be analyzed using two different approaches- 1. Normal payback period

      2. Discounted payback period

• Normal Payback period:

Cash Outflow :

Particulars	Cash Outflow
Year 0	$635,000,000
Year 9	$45,000,000
Total	$680,000,000

    

      Cash Inflows :

Year	Cash Inflow	Cummulative
1	$89,000,000	$89,000,000
2	$105,000,000	$194,000,000
3	$130,000,000	$324,000,000
4	$173,000,000	$497,000,000
5	$205,000,000	$702,000,000
6	$155,000,000	$857,000,000
7	$145,000,000	$1,002,000,000
8	$122,000,000	$1,124,000,000
Total	$1,124,000,000

Payback period : As there is cumulative cash inflow of $497,000,000 in year 4 and $702,000,000 in year 5, the payback period for the project under consideration would be between year 4 & 5, as calculated below:

      Analysis :- This payback period of 4.89 years implies that the total outflow of the project would be recovered in 4.89 years, without considering the time value of money i.e. discounting factor.

• Discounted payback period :- This shows the time period within which, the project would earn cash inflows equivalent to the total cash outflows of the project, considering the discount factors. Hence, this approach considers the present value of the cash flows.

Table-1 - Cash Outflows:

Particulars	Cash Outflow	Discount factor @12%	Present value
Year 0	$635,000,000	1	$635,000,000
Year 9	$45,000,000	0.3606	$16,227,000
Total	$680,000,000		$651,227,000

Table-2 - Cash Inflows:

Year	Cash Inflow	Discount factor @12%	Present Value	Cumulative PV of cash inflows
1	$89,000,000	0.8929	$79,464,286	$79,464,286
2	$105,000,000	0.7972	$83,705,357	$163,169,643
3	$130,000,000	0.7118	$92,531,432	$255,701,075
4	$173,000,000	0.6355	$109,944,628	$365,645,703
5	$205,000,000	0.5674	$116,322,505	$481,968,208
6	$155,000,000	0.5066	$78,527,824	$560,496,032
7	$145,000,000	0.4523	$65,590,636	$626,086,668
8	$122,000,000	0.4039	$49,273,754	$675,360,422
Total	$1,124,000,000		$675,360,422

Discounted Pay back period :-

Present value of total outflow = $651,227,000

Cumulative PV of inflows equivalent to PV of outflows would be between year 7 & 8 :

2. Net Present Value [NPV] :-

= Present value of cash inflow - Present value of cash outflow

= $675,360,422 - $651,227,000

= $ 24,133,422

3. IRR :-

• IRR is the rate at which, the NPV of the project = 0.
• To find the IRR, we shall find NPV using different discounting rates as Trial & Error and then using interpolation of two rates, we can get the IRR as below :-

• NPV @12% = $ 24,133,422
• NPV @13% :

  Year	Cash Inflow	Discount factor @12%	Present Value
  0	-$635,000,000	1.0000	-$635,000,000
  1	$89,000,000	0.8850	$78,761,062
  2	$105,000,000	0.7831	$82,230,402
  3	$130,000,000	0.6931	$90,096,521
  4	$173,000,000	0.6133	$106,104,140
  5	$205,000,000	0.5428	$111,265,787
  6	$155,000,000	0.4803	$74,449,372
  7	$145,000,000	0.4251	$61,633,793
  8	$122,000,000	0.3762	$45,891,503
  9	-$45,000,000	0.3329	-$14,979,818
  NPV			$452,762

  

• Here, 1% increase in the Discount rate leads to $452,762 decrease in the NPV.
• For IRR, we shall decrease NPV to NIL.

Note : As per HOMEWORKLIB RULES, I have answered first question only, as there are multiple questions.