How do you calculate the NPV in the table. You own an idle silver mine in Chile.
Question:
How do you calculate the NPV in the table.
You own an idle silver mine in Chile. You can reopen the mine now and extract the
remaining silver at an investment cost of
500
million pesos. The present value of the
silver is PV =
600
million pesos. However, technological progress will gradually reduce
extraction costs by 20% over the next 5 years. At the same time, the market price of
silver is increasing at 4% per year.
3
When should you invest if the cost of capital is 14 percent? What if the cost of capital is
20 percent?
Note: The correct numbers (matching the table) are in bold red letters.
Mine
reopened
Cost x100
million
PV x100
million
NPV x100
million
Now
5
6
1
Year 1
4.8
6.24
1.44
Year 2
4.6
6.49
1.89
Year 3
4.4
6.75
2.35
Year 4
4.2
7.02
2.82
Year 5
4
7.30
3.30
The solution is shown in the following table:
Mine reopened
Cost x100
million
PV x100
million
NPV x100
million
NPV
discounted at
14%
NPV
discounted at
20%
Now
5
6
1
1
1
Year 1
4.8
6.24
1.44
1.26
1.2
Year 2
4.6
6.49
1.89
1.45
1.312
Year 3
4.4
6.75
2.35
1.59
1.359
Year 4
4.2
7.02
2.82
1.67
1.360
Year 5
4
7.30
3.30
1.71
1.326
Because revenues are expected to increase (due to increasing price) and costs are expected to
decrease, NPV at the time the mine is opened is seen to be steadily increasing
But this (increasing) value is postponed in time. Hence its present value could be decreasing.
This is precisely what is happening.
If the cost of capital is 14%, we should reopen the mine in Year 5.
If the cost of capital is 20%, we should reopen the mine in Year 4.
With a higher discount rate, the effect of discounting is stronger; we must open the mine earlier
Fundamentals of Corporate Finance
ISBN: 978-0133400694
1st canadian edition
Authors: Jonathan Berk, Peter DeMarzo, Jarrad Harford, David A. Stangeland, Andras Marosi