# Decision on Opening Gold Mine Using NPV Analysis

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Sub: Finance                                                                          Topic: Capital Budgeting

Question:

Decision on Opening Gold Mine Using NPV Analysis.

You own an unused gold mine that will cost \$100,000 to reopen. If you do open the mine, you expect
to extract 1,000 ounces of gold per year, for the next 3 years. After those 3 years the deposit will be
exhausted. An ounce of gold is currently selling for \$500. For each of the next 3 years, this price is
equally likely to rise or fall by \$50 per year from its level at the start of that year. The extraction cost is
estimated to be around \$460 an ounce, and this cost will not change over the next 3 years.

The demand for gold has increased tremendously in the recent years and there is a good chance that
this demand will continue in the future as well. You are therefore puzzled as to whether to open the
mine now or in one year in the hope that prices will move further up.

Assume that the opportunity cost of the project is 10%.

Questions:
What is the NPV of opening the mine now? What is the NPV of opening the mine one year later?
Should you wait?

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Sub: Finance                                                                          Topic: Capital Budgeting

Solution :

NPV of opening the mine now:                       (\$525.92)

NPV of opening the mine one year later: \$132,907.68

Npv of the cash flows at 10% cost of capital is positive and high \$132907.68 only in case of reopening
gold mine one year from now. And opening the gold mine as of today is negative the same is to be
avoided.

We have to wait one year from now and reopen the gold mine.

Excel workings:

1/
A      B                                 C                                      D                     E                 F
opportunity cost of the
2      project                           0.1
Current Selling price of
3      per ounce gold                    500
For each of the next 3
years,     this    price     is
equally likely to rise or
fall by \$50 per year from
its level at the start of
4      that year

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Sub: Finance                                                                           Topic: Capital Budgeting

Reopening the mine as
5      of today.
6      Initial investment                 100000
Current Selling price of
7      per ounce gold                     500
8      Current Extraction cost            460
Net cash inflows from
extraction one ounce of
9      gold                               =500-460
If you do open the mine,
you expect to extract
1,000 ounces of gold per
year, for the next 3
years. After those 3
years the deposit will be
10     exhausted.
Current          year     cash
inflows on extraction of
11     1000 ounces of gold                =1000*40
12     The next year
Prices of Gold is equally
likely to rise or fall by
\$50 per year from its
level at the start of the
13     year

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Sub: Finance                                                                          Topic: Capital Budgeting

14                                       Price                                  Probability           Expected Price
At increased prices from
the starting price of the
15     \$500 year                         550                                    0.5                   =550*0.5
At the decreased prices
from the starting price
16     of the \$500 year                  =500-50                                0.5                   =450*0.5
One year from now the                                                                          =SUM(275:225
17     prices one ounce Gold                                                                          )
one year from now
Selling     price    of    per
18     ounce gold                        500
Extraction cost after
19     one year from now                 460
20
If you do open the mine,
you expect to extract
1,000 ounces of gold per
year, for the next 3
years. After those 3
years the deposit will be
21     exhausted.
One year from now cash
inflows on extraction of
22     1000 ounces of gold               =1000*40

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Sub: Finance                                                                          Topic: Capital Budgeting

23     Second year from now
Prices of Gold is equally
likely to rise or fall by
\$50 per year from its
level at the start of the
24     year
25                                       Price                                  Probability           Expected Price
At increased prices from
the starting price of the
26     \$500 year                         550                                    0.5                   =550*0.5
At the decreased prices
from the starting price
27     of the \$500 year                  =500-50                                0.5                   =450*0.5
Two year from now the                                                                          =SUM(275:225
28     prices one ounce Gold                                                                          )
Two year from now the
29     prices one ounce Gold             500
Extraction cost from two
30     years from now                    460
Net cash inflows from
extraction one ounce of
gold      after two year
31     from now                          =500-460
32     Two year from             now =1000*40

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Sub: Finance                                                                           Topic: Capital Budgeting

cash      inflows            on
extraction        of        1000
ounces of gold
33     Year                                0                                     1                     2                3
=4000
34     Cash flows                          -100000                               =40000                =40000           0

NPV of the cash inflows =NPV(10%,40000:40000)
35     at 10% cost of capital              +(-100000)
The demand for gold
has                increased
tremendously           in    the
recent years and there
is a good chance that
this       demand            will
continue in the future as
well. You are therefore
puzzled as to whether to
open the mine now or in
one year in the hope
that prices will move
36     further up.
Only prices increased
37     one year from now then

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Sub: Finance                                                                          Topic: Capital Budgeting

only he reopens the
mine assume the prices
at the end of one year
38     from now                          550
Extraction         cost per
ounce gold one year
39     from now                          460
Cash       in    flows       of
extraction of one ounce
40     gold one year from now            =550-460
One year from now cash
inflows on extraction of
41     1000 ounces of gold               =1000*90
42     Second year from now
at the end of one year
43     from now                          550
Prices of Gold is equally
likely to rise or fall by
\$50 per year from its
level at the start of the
44     year
45                                       Price                                  Probability           Expected Price
At increased prices from
46     the starting price of the 600                                            0.5                   =600*0.5

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Sub: Finance                                                                          Topic: Capital Budgeting

\$5500 year
At the decreased prices
from the starting price
47     of the \$550 year                  500                                    0.5                   =500*0.5
Two year from now the                                                                          =SUM(300:250
48     prices one ounce Gold                                                                          )
At the end of two years
49     from now                          550
Extraction cost from two
50     years from now                    460
Cash         inflows         of
extraction of one ounce
gold Two years from
51     now.                              =550-460
Two year from now cash
inflows on extraction of
52     1000 ounces of gold               =1000*90
Prices of Gold is equally
likely to rise or fall by
\$50 per year from its
level at the start of the
53     year
54                                       Price                                  Probability           Expected Price
55     At increased prices from 600                                             0.5                   =600*0.5

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Sub: Finance                                                                          Topic: Capital Budgeting

the starting price of the
\$550 year
At the decreased prices
from the starting price
56     of the \$550 year                  500                                    0.5                   =500*0.5
Three year from           now
the prices one ounce                                                                           =SUM(300:
57     Gold                                                                                           250)
At the end of three
58     years from now                    550
Extraction      cost     from
59     three years from now              460
Cash         inflows         of
extraction of one ounce
gold Three years from
60     now.                              =550-460
Three years from now
cash        inflows         on
extraction        of     1000
61     ounces of gold                    =1000*90
Reopening cost of mine
one year from now            (-
62     100000*1/(1+10%)^1)               =(-100000/(1+10%)^1)
Cash flows of opening
63     mine one year from

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Sub: Finance                                                                          Topic: Capital Budgeting

now.
64    Year                              0                                      1                     2                 3
65    Cash flows                        -90909                                 90000                 90000             90000
NPV of the cash inflows =NPV(10%,90000:90000)+
66    at 10% cost of capital            (-90909)
Npv of the cash
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Description: You own an unused gold mine that will cost \$100,000 to reopen. If you do open the mine, you expect to extract 1,000 ounces of gold per year, for the next 3 years. After those 3 years the deposit will be exhausted. An ounce of gold is currently selling for \$500. For each of the next 3 years, this price is equally likely to rise or fall by \$50 per year from its level at the start of that year. The extraction cost is estimated to be around \$460 an ounce, and this cost will not change over the next 3 years. The demand for gold has increased tremendously in the recent years and there is a good chance that this demand will continue in the future as well. You are therefore puzzled as to whether to open the mine now or in one year in the hope that prices will move further up. Assume that the opportunity cost of the project is 10%. Questions: What is the NPV of opening the mine now? What is the NPV of opening the mine one year later? Should you wait?
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