Fins5511 Corporate Finance - Computation Assessment Answers
HBP's risk management department believes that (given current economic conditions) the price of iron ore has a 45% probability of going up by 25%, and 55% probability of going down by 15% every year for the next three years. After three years, economic conditions will have stabilised so that the price of iron ore will remain constant for the remaining life of the mine. They have also estimated HBP's cost of capital to be 12%.
Requirements:
2. 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.
3. Based on your answer in (2), what should HBP do with the iron ore mine?
We ask that you keep all your formulas as simple as possible - don't go overboard and make them unnecessarily complicated. It makes your assignment difficult to understand which can lead to us not allocating you part marks for your effort, particularly if your answer is incorrect! The decision tree can be done in Excel or attached to the report.
Answer
Corporate Finance: Decision tree and Computation of Net Present Value
Requirement 1
Requirement 2: Computation of NPV
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:
NPV at Node-1
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 $1.88 million and the net cash flows from third year and onwards will be $3.59 million. The project’s life is 90 years, thus, the net cash flows of $3.59 million will accrue for 88 years. Using these figures and cost of capital of 12%, the NPV has been computed as under:
Year |
Price |
Net cash flows ($M) |
|
|
|
[(Price*80000 tones)-$5M] |
|
1 |
$68.75 |
0.50 |
|
2 |
$85.94 |
1.88 |
|
3 |
$107.42 |
3.59 |
|
4 to 90 |
$107.42 |
3.59 |
Year |
Net Cash flow ($M) |
PV factor |
PV ($M) |
|
1 |
0.50 |
0.89 |
0.45 |
|
2 |
1.88 |
0.80 |
1.49 |
|
3 |
3.59 |
0.71 |
2.56 |
|
4 to 90 |
3.59 |
5.93 |
21.32 |
|
|
NPV |
25.81 | |
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 flow also to $0.84 million. The NPV has been computed as under:
Year |
Price |
Net cash flows ($M) |
|
|
|
[(Price*80000 tones)-$5M] |
|
1 |
$68.75 |
0.50 |
|
2 |
$85.94 |
1.88 |
|
3 |
$73.05 |
0.84 |
|
4 to 90 |
$73.05 |
0.84 |
Year |
Net Cash flow ($M) |
PV factor |
PV ($M) |
|
1 |
0.50 |
0.89 |
0.45 |
|
2 |
1.88 |
0.80 |
1.49 |
|
3 |
0.84 |
0.71 |
0.60 |
|
4 to 90 |
0.84 |
5.93 |
5.00 |
|
|
NPV |
7.55 | |
NPV at Node-3
In the light of the changes in the price of copper, the computation of net cash flows is given as follows:
Year |
Price |
Net cash flows ($M) |
|
|
|
[(Price*80000 tones)-$5M] |
|
1 |
$68.75 |
0.50 |
|
2 |
$58.44 |
(0.33) |
|
3 |
$73.05 |
0.84 |
|
4 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 ($M) |
|
1 |
0.50 |
0.89 |
0.45 |
|
2 |
(0.33) |
0.80 |
(0.26) |
|
3 |
0.84 |
0.71 |
0.60 |
|
4 to 90 |
0.84 |
5.93 |
5.00 |
|
|
NPV |
5.79 | |
NPV at Node-4
In the light of the changes in the price of copper, the computation of net cash flows is given as follows:
Year |
Price |
Net cash flows ($M) |
|
|
|
[(Price*80000 tones)-$5M] |
|
1 |
$68.75 |
0.50 |
|
2 |
$58.44 |
(0.33) |
|
3 |
$49.67 |
(1.03) |
|
4 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 |
(0.33) |
0.80 |
(0.26) |
|
3 |
(1.03) |
0.71 |
(0.73) |
|
4 to 90 |
(1.03) |
5.93 |
(6.09) |
|
|
NPV |
(6.63) | |
Since, the net present value to operate mine at this node is $-6.63 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 |
(0.33) |
|
3 |
$73.05 |
0.84 |
|
4 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 ($M) |
|
1 |
(1.26) |
0.89 |
(1.13) |
|
2 |
(0.33) |
0.80 |
(0.26) |
|
3 |
0.84 |
0.71 |
0.60 |
|
4 to 90 |
0.84 |
5.93 |
5.00 |
|
|
NPV |
4.22 | |
NPV at Node-6
In the light of the changes in the price of copper, the computation of net cash flows is given as follows:
Year |
Price |
Net cash flows ($M) |
|
|
|
[(Price*80000 tones)-$5M] |
|
1 |
$46.75 |
(1.26) |
|
2 |
$58.44 |
(0.33) |
|
3 |
$49.67 |
(1.03) |
|
4 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 |
(0.33) |
0.80 |
(0.26) |
|
3 |
(1.03) |
0.71 |
(0.73) |
|
4 to 90 |
(1.03) |
5.93 |
(6.09) |
|
|
NPV |
(8.20) | |
Since, the net present value to operate mine at this node is $-8.20 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 $-5.00 million.
NPV at Node-7
In the light of the changes in the price of copper, the computation of net cash flows is given as follows:
Year |
Price |
Net cash flows ($M) |
|
|
|
[(Price*80000 tones)-$5M] |
|
1 |
$46.75 |
(1.26) |
|
2 |
$39.74 |
(1.82) |
|
3 |
$49.67 |
(1.03) |
|
4 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 |
(1.03) |
0.71 |
(0.73) |
|
4 to 90 |
(1.03) |
5.93 |
(6.09) |
|
|
NPV |
(9.39) | |
Since, the net present value to operate mine at this node is $-9.39 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 $-5.00 million.
NPV at Node-8
In the light of the changes in the price of copper, the computation of net cash flows is given as follows:
Year |
Price |
Net cash flows ($M) |
|
|
|
[(Price*80000 tones)-$5M] |
|
1 |
$46.75 |
(1.26) |
|
2 |
$39.74 |
(1.82) |
|
3 |
$33.78 |
(2.30) |
|
4 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 |
(2.30) |
0.71 |
(1.64) |
|
4 to 90 |
(2.30) |
5.93 |
(13.63) |
|
|
NPV |
(17.84) | |
Since, the net present value to operate mine at this node is $-17.84 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 |
25.81 |
0.091125 |
2.35 |
|
2 |
7.55 |
0.111375 |
0.84 |
|
3 |
5.79 |
0.111375 |
0.65 |
|
4 |
(5.00) |
0.136125 |
(0.68) |
|
5 |
4.22 |
0.111375 |
0.47 |
|
6 |
(5.00) |
0.136125 |
(0.68) |
|
7 |
(5.00) |
0.136125 |
(0.68) |
|
8 |
(5.00) |
0.166375 |
(0.83) |
|
|
NPV |
1.43 | |
Requirement 3
The expected net present value as worked out in requirement 2 given above depicts that the company will be benefited by $1.43 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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