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 RECONVERY 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 DESPOSE OF THEIR PCS. THE PROJECT WILL LAST FOR FIVE YEARS, AND THE CONTRACT CALLS FRO THE DISPOSAL OF 200,000 PCS PER YEAR. THERE 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 FICE YEARS IS AS FOLLOWS: 2011 $679.40/OUNCE 2012 $715.10/OUNCE 2013 $750.60/OUNCE 2014 $786.90/OUNCE 2015 $822.80/OUNCE S&M ESTIMATES THAT THE FIRMS 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 2010 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 PROCES WILL INVREASE AT A RATE OF 7% PER YEAR OVER THE NEXT FIVE YEARS, WHAT IS THE NPV OF PROJECT USING THE TRADITIONAL WACC METHOD OF ANALYSIS BASED ON EXPECTED PROJECT FREE CASH FLOW, 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 WASS APPROACH AS WITH THE CERTAINTY-EQUIVALENT APPROACH USED IN PART B?

PROBLEM 11-6
Given
Initial investment	$ 450,000
Total PCs scrapped	1,000,000	units
Electronic scrap per PC	6	pounds
Gold content	0.33	ounce per ton
Life of project	5	years
PCs scrapped per year	200,000	units
Tons of scrap per year	600
Current price of gold	$ 592.80	per ounce
Cost/ton for processing	$ 67.50
Tax rate	30.0%
Risk free rate	5.0%
WACC	10.5%
Growth in gold prices	7.0%
Forward Price Curve	Gold Price/Ounce	Expected Prices per Ounce
2011	$ 679.40	$ 634.30
2012	715.10	678.70
2013	750.60	726.21
2014	786.90	777.04
2015	822.80	831.43
Solution
a.
Year	Revenues	Processing Costs	Depreciation/ Depletion	NOI	NOPAT	Plus: Depreciation	Project FCF
2011
2012
2013
2014
2015
b.
NPV
c.
Year	Revenues	Processing Costs	Depreciation/ Depletion	NOI	NOPAT	Plus: Depreciation	Project FCF
2011
2012
2013
2014
2015
NPV
To solve for equivalent growth rate, use the following:
Year	Expected Price	Revenues	Processing Costs	Depreciation/ Depletion	NOI	NOPAT	Plus: Depreciation	Project FCF
2011
2012
2013
2014
2015
NPV
Difference