1. Calculate the NPV of continuing to operate the mine by working your way backwards through the tree and taking into account the option to abandon.

2. Based on your answer in (2), what should HBP do with the iron ore mine?

## NPV Calculation

The prices of copper for the year end 1, 2, and 3 have been computed as shown in the decision tree in requirement 1 above. There are eight probable prices of copper finally arrived at the end of year 3, which make eight nodes for the purpose of computation of NPV. The computation of net present values for each node is given as under:

Price of copper in year 1 is $68.75; therefore, the cash inflows will be $5.50 million (80000 tones*$68.75). The company incurs $5 million operating cost. Thus, the net cash flows for year 1 work out to be $0.50 million. In same way, the net cash flows for year 2 are worked out to be $18.75 million and the net cash flows from third year and onwards will be $35.94 million. The project’s life is 90 years, thus, the net cash flows of $35.94 million will accrue for 88 years. Using these figures and cost of capital of 12%, the NPV has been computed as under:

Year |
Net Cash flows ($M) |
PV factor |
PV($M) |

1 |
0.50 |
0.89 |
0.45 |

2 |
18.75 |
0.80 |
14.95 |

3 to 90 |
35.94 |
8.33 |
299.48 |

NPV |
314.88 |

NPV at Node-2

At node-2, the price of copper in year 1 and 2 remains the same as it was at node-1, therefore, the net cash flows will also remain same. However, the price of copper for year 3 and onwards changes to $73.05, which changes the net cash also to $0.84 million. The NPV has been computed as under:

Year |
Net Cash flow ($M) |
PV factor |
PV ($M) |

1 |
0.50 |
0.89 |
0.45 |

2 |
18.75 |
0.80 |
14.95 |

3 to 90 |
0.84 |
8.33 |
7.00 |

NPV |
22.39 |

NPV at Node-3

In the light of the changes in the price of copper, the computation of net cash flows is given as follows:

Year |
Price |
Net cash flows ($M) |

[(Price*80000 tones)-$5M] |
||

1 |
68.75 |
0.50 |

2 |
58.44 |
(0.32) |

3 to 90 |
73.05 |
0.84 |

Considering the above cash flows, the net present value has been computed as under:

Year |
Net Cash flow ($M) |
PV factor |
PV ($M) |

1 |
0.50 |
0.89 |
0.45 |

2 |
(0.32) |
0.80 |
(0.26) |

3 to 90 |
0.84 |
8.33 |
7.03 |

NPV |
7.22 |

NPV at Node-4

In the light of the changes in the price of copper, the computation of net cash flows is given as follows:

Year |
Price |
Net cash flows ($M) |

[(Price*80000 tones)-$5M] |
||

1 |
68.75 |
0.50 |

2 |
58.44 |
(0.32) |

3 to 90 |
49.67 |
(1.03) |

Considering the above cash flows, the net present value has been computed as under:

Year |
Net Cash flow ($M) |
PV factor |
PV ($M) |

1 |
0.50 |
0.89 |
0.45 |

2 |
(0.32) |
0.80 |
(0.26) |

3 to 90 |
(1.03) |
8.33 |
(8.55) |

NPV |
(8.37) |

Since, the net present value to operate mine at this node is $-8.37 million, while, the cost of option to abandon is $5 million. Thus, the company will go for exercising the option to abandon rather than continuing mining operations in this case. Thus, the net present value for this node becomes $-5.00 million.

NPV at Node-5

In the light of the changes in the price of copper, the computation of net cash flows is given as follows:

Year |
Price |
Net cash flows ($M) |

[(Price*80000 tones)-$5M] |
||

1 |
46.75 |
(1.26) |

2 |
58.44 |
(0.32) |

3 to 90 |
73.05 |
0.84 |

Considering the above cash flows, the net present value has been computed as under:

Year |
Net Cash flow ($M) |
PV factor |
PV ($M) |

1 |
(1.26) |
0.89 |
(1.13) |

2 |
(0.32) |
0.80 |
(0.26) |

3 to 90 |
0.84 |
8.33 |
7.03 |

NPV |
5.65 |

NPV at Node-6

Year |
Price |
Net cash flows ($M) |

[(Price*80000 tones)-$5M] |
||

1 |
46.75 |
(1.26) |

2 |
58.44 |
(0.32) |

3 to 90 |
49.67 |
(1.03) |

Considering the above cash flows, the net present value has been computed as under:

Year |
Net Cash flow ($M) |
PV factor |
PV ($M) |

1 |
(1.26) |
0.89 |
(1.13) |

2 |
(0.32) |
0.80 |
(0.26) |

3 to 90 |
(1.03) |
8.33 |
(8.55) |

NPV |
(9.94) |

Since, the net present value to operate mine at this node is $-9.94 million, while, the cost of option to abandon is $5 million. Thus, the company will go for exercising the option to abandon rather than continuing mining operations in this case. Thus, the net present value for this node becomes $-5.00 million.

NPV at Node-7

Year |
Price |
Net cash flows ($M) |

[(Price*80000 tones)-$5M] |
||

1 |
46.75 |
(1.26) |

2 |
39.74 |
(1.82) |

3 to 90 |
49.67 |
(1.03) |

Considering the above cash flows, the net present value has been computed as under:

Year |
Net Cash flow ($M) |
PV factor |
PV ($M) |

1 |
(1.26) |
0.89 |
(1.13) |

2 |
(1.82) |
0.80 |
(1.45) |

3 to 90 |
(1.03) |
8.33 |
(8.55) |

NPV |
(11.13) |

Since, the net present value to operate mine at this node is $-11.13 million, while, the cost of option to abandon is $5 million. Thus, the company will go for exercising the option to abandon rather than continuing mining operations in this case. Thus, the net present value for this node becomes $-5.00 million.

NPV at Node-8

Year |
Price |
Net cash flows ($M) |

[(Price*80000 tones)-$5M] |
||

1 |
46.75 |
(1.26) |

2 |
39.74 |
(1.82) |

3 to 90 |
33.78 |
(2.30) |

Considering the above cash flows, the net present value has been computed as under:

Year |
Net Cash flow ($M) |
PV factor |
PV ($M) |

1 |
(1.26) |
0.89 |
(1.13) |

2 |
(1.82) |
0.80 |
(1.45) |

3 to 90 |
(2.30) |
8.33 |
(19.15) |

NPV |
(21.72) |

Since, the net present value to operate mine at this node is $-21.72 million, while, the cost of option to abandon is $5 million. Thus, the company will go for exercising the option to abandon rather than continuing mining operations in this case. Thus, the net present value for this node becomes $-5.00 million.

Now, using the probabilities, the estimated net present value for the company in respect of mining project has been computed in the statement given below:

Node |
NPV ($M) |
Joint Probability |
Expected NPV |

1 |
314.88 |
0.091125 |
28.69 |

2 |
22.39 |
0.111375 |
2.49 |

3 |
7.22 |
0.111375 |
0.80 |

4 |
(5.00) |
0.136125 |
(0.68) |

5 |
5.65 |
0.111375 |
0.63 |

6 |
(5.00) |
0.136125 |
(0.68) |

7 |
(5.00) |
0.136125 |
(0.68) |

8 |
(5.00) |
0.166375 |
(0.83) |

Expected NPV |
29.75 |

Requirement 3

The expected net present value as worked in requirement 2 given above depicts that the company will be benefited by $29.75 million by undertaking the mining operations. Therefore, it is recommended that the company undertakes the mining operations on the iron ore mine.

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