1. Baseline AnalysisCalculate the NPV of this investment assuming that you will open the mine, operate itfully for 6 years, and sell the product at each year’s current price (adjusting the startingprice for projected annual increases). Use the discount rate, r = 12%/year.DCFYear 1 2 3 4 5 6Costs -6000000 -6000000 -6000000 -6000000 -6000000 -6000000Copper Sold 5000 5000 5000 5000 5000 5000Price of Copper $2,600 2704 2812.16 2924.6464 3041.632256 3163.297546Revenue $13,000,000 $13,520,000 $14,060,800 $14,623,232 $15,208,161 $15,816,488 Profit $7,000,000 $7,520,000 $8,060,800 $8,623,232 $9,208,161 $9,816,488 Present Value 6250000 5994897.959 5737518.222 5480219.83 5224958.002 4973338.185NPV $33,660,932 2. Modeling UncertaintyNow bring recognition of uncertainty into the analysis. Assume that the annual standarddeviation is 15% (i.e., the volatility). On this basis, calibrate the binomial model for thisanalysis, and present the range of future copper prices.OUTCOME LATTICE2500.00 2904.59 3374.65 3920.78 4555.30 5292.50 6149.012151.77 2500.00 2904.59 3374.65 3920.78 4555.301852.05 2151.77 2500.00 2904.59 3374.651594.07 1852.05 2151.77 2500.001372.03 1594.07 1852.051180.92 1372.031016.42 On the same graph, plot theprobability density function of copper prices at all times from year 0 to year 6.PDF of copper prices0.000.200.400.600.801.001.200.00 2000.00 4000.00 6000.00 8000.00Copper Price ($)ProbabilityYear 0Year 1Year 2Year 3Year 4Year 5Year 63. Analysis recognizing UncertaintyUse the above results to calculate the NPV of the mine on the assumption that youoperate the mine regardless of the evolution of the price of copper. Does the NPVcalculated this way agree with the NPV you calculated using the DCF approach?EXPECTED REVENUE LATTICE6500000.00 5397854.42 4361375.41 3455895.04 2699170.74 2085068.98 1596916.541744911.56 3018888.89 3760505.25 4051233.16 4012678.13 3760844.57438319.51 1215621.72 2103159.26 2910909.62 3527948.8897131.05 407150.12 940981.26 1628001.0615547.39 112779.94 354559.90-632.39 21662.70-2230.56Year 1 2 3 4 5 6Average Expected Revenue 7142765.98 7818583.81 8529153.05 9276260.68 10061785.53 10887703.08Present Value 6377469.625 6232927.14 6070882.67 5895231.36 5709327.33 5516049.22NPV 35801887.35The NPV does not agree with the DCF approach. This is because of the “flaw of averages”. This is an illustration that E[f(x)] != f(E[x])4. Valuation of Option to closeYour analysis should now recognize that you have the option to permanently close themine if it is optimal to do so. What is the value of the mine on this basis? Therefore,what is the value of the option on this basis (i.e., what is the additional value of theflexibility to close down) ?NET PRESENT VALUE LATTICE WITH OPTION35801887.35 47210309.21 50423915.19 51091920.37 48090662.34 39947532.1727813412.73 31076510.80 32559669.46 31443165.65 26650295.2116743601.11 18830640.31 19110396.77 16799459.788659925.36 9974056.87 9501781.413205689.80 4095528.3190477.50The value of the mine is also $35801887.35. The value of the option is $0Assuming you did the analysis on a spreadsheet similar to the one shown in the lecture andrecitation, it should be easy to repeat it for current price of copper at (1) $4000/ton and (2)$1000/ton. How significant is the flexibility to close down the mine in each case?(1) $4000/tonEXPECTED REVENUE LATTICE14000000.00 10916567.07 8422200.66 6443965.39 4897877.63 3702939.86 2787391.804111858.49 6502222.22 7605208.40 7823288.61 7482159.82 6824376.171185311.22 2864594.75 4529881.48 5886994.65 6812780.50332876.35 1101022.42 2217408.53 3506463.8189946.94 386506.43 958807.0222847.58 125326.075179.55Year 1 2 3 4 5 6Average Expected Revenue 15028425.57 16109734.09 17246644.89 18442017.09 19698856.85 21020324.92Present Value 13418237.11 12842581.4 12275821.2 11720235.3 11177660.4 10649550.8NPV 72084086.12NET PRESENT VALUE LATTICE WITH OPTION72084086.12 92113689.06 95212721.95 93993665.16 86629243.42 70730337.1961078654.69 64256874.94 64342063.70 59993248.71 49454758.0541324219.43 42375617.06 40260818.50 33693421.3726102473.14 25642674.67 22017135.9714813287.36 13367131.006959049.71In this case, the value of the option is $0.(2) $1000EXPECTED REVENUE LATTICE-1000000.00 -120858.23 300550.16 467824.68 500463.85 467198.11 406441.28-622035.38 -464444.44 -84197.90 279177.71 543196.44 697312.97-308672.20 -433351.31 -323562.96 -65175.41 243117.25-138614.25 -286722.17 -335446.02 -250461.70-58852.15 -160946.54 -249687.23-24112.37 -82000.67-9640.67Year 1 2 3 4 5 6Average Expected Revenue -742893.61 -472566.48 -188338.78 110504.27 424714.21 755081.23Present Value -663297.864 -376727.102 -134055.822 70227.4622 240994.25 382547.651NPV -480311.425NET PRESENT VALUE LATTICE WITH OPTION1003315.45 2756445.28 5746576.52 8190175.58 9552081.26 9164727.15-1696460.12 -923322.30 1117759.58 2893082.59 3845832.37-2295908.90 -1696460.12 -1000000.00 -94501.80-2811859.24 -2295908.90 -1696460.12-3255941.82 -2811859.24-3638167.24In this case, the value of the option is $1003315.45-(-480311.425)=$
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