Valuing Gold Reclaimed from Old Personal Computers A number of industrial produc

Question

Valuing Gold Reclaimed from Old Personal Computers A number of industrial products include gold and silver as a component because 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 (PCs). 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:

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 a 30% tax rate, and the entire investment of $450,000 made in the project in 2015 will be depreciated using straight-line depreciation over five years with a zero salvage value.

Estimate the after-tax (certainty-equivalent) project free cash flows for the project over its five-year productive life.

Using the certainty-equivalent valuation methodology, estimate the NPV of the project.

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 Problem 11-10(b)?

Explanation / Answer

Answer (a) Year Revenues Processing Cost Depreciation NOI NOPAT Plus: Depreciation Projected FCF 2016 134521 40500 90000 4021 2815 92815 80359 2017 141649 40500 90000 11149 7804 97804 73314 2018 148528 40500 90000 18028 12619 102619 66600 2019 155806 40500 90000 25306 17714 107714 60525 2020 162914 40500 90000 32414 22690 112690 54824 (b) Total Cash Flow 335622 Initial Investment 450000 NPV -114378 (c) Year Revenues Processing Cost Depreciation NOI NOPAT Plus: Depreciation Projected FCF 2016 125591 40500 90000 -4909 -3436 86564 78340 2017 134383 40500 90000 3883 2718 92718 69501 2018 143790 40500 90000 13290 9303 99303 64447 2019 153854 40500 90000 23354 16348 106348 59757 2020 164623 40500 90000 34123 23886 113886 55406 NPV -122548 (d) Year Expected Price Revenues Processing Cost Depreciation NOI NOPAT Plus: Depreciation Projected FCF 2016 677.57 134159 40500 90000 3659 2561 92561 83768 2017 774.46 153344 40500 90000 22844 15991 105991 86806 2018 885.21 175272 40500 90000 44772 31340 121340 89937 2019 1011.80 200336 40500 90000 69836 48885 138885 93150 2020 1156.48 228984 40500 90000 98484 68939 158939 96476 NPV 137

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