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# Estimating the Net Present Value of a Project.

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A number of industrial products include gold and silver as a component since they have very good conductive properties. The S&M Smelting Company engages in the recovery of gold from such products and is
considering a contract to begin extracting the gold from the recycling of personal computers. The project involves contracting with the state governments of three Midwestern states to dispose of their PCs. The
project will last for five years, and the contract calls for the disposal of 200,000 PCs per year. Three tons of electronic scrap contains approximately one Troy ounce of gold. Moreover, each PC contains approximately 6 pounds of electronic scrap, and the processing cost involved in extracting the gold is \$67.50 per ton of scrap. In addition, the current (spot) price of gold is \$592.80 and the forward price curve for the price per ounce of gold spanning the next five years is as follows:
2008 \$679.40/ounce
2009 \$715.10/ounce
2010 \$750.60/ounce
2011 \$786.90/ounce
2012 822.8/ounce

S&M estimates that the firm's cost of capital is 10.5%, and the risk-free rate of interest on five-year Treasury bonds is currently 5.0%. In addition, S&M faces 30% tax rate and the entire investment of \$450,000 made in the project in 2007 will be depreciated using straight-line depreciation over five years with a zero salvage value.

a. Estimate the after-tax (certainty-equivalent) project free cash flows for the project over its five-year productive life.
b. Using the certainty-equivalent valuation methodology, estimate the NPV of the project.
c. If we assume that gold prices will increase at a rate of 7% per year over the next five years, what is the NPV of the project using the traditional WACC method of analysis based on expected project free cash flows, where the
WACC is estimated to be 10.5%? What rate of growth in gold prices is required to produce the same NPV using the traditional WACC approach as with the certainty-equivalent approach used in part b?