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Sunday, 5 August 2018

Consumer Price Index(CPI) - Mineral Economics Questions and Answers


                          CPI for USA  from Year 1990 to 2010

Year
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Annual
2010
216.687
216.741
217.631
218.009
218.178
217.965
218.011
218.312
218.439
218.711
218.803
219.179
218.055
2009
211.143
212.193
212.709
213.24
213.856
215.693
215.351
215.834
215.969
216.177
216.33
215.949
214.537
2008
211.08
211.693
213.528
214.823
216.632
218.815
219.964
219.086
218.783
216.573
212.425
210.228
215.303
2007
202.416
203.499
205.352
206.686
207.949
208.352
208.299
207.917
208.49
208.936
210.177
210.036
207.342
2006
198.3
198.7
199.8
201.5
202.5
202.9
203.5
203.9
202.9
201.8
201.5
201.8
201.6
2005
190.7
191.8
193.3
194.6
194.4
194.5
195.4
196.4
198.8
199.2
197.6
196.8
195.3
2004
185.2
186.2
187.4
188
189.1
189.7
189.4
189.5
189.9
190.9
191
190.3
188.9
2003
181.7
183.1
184.2
183.8
183.5
183.7
183.9
184.6
185.2
185
184.5
184.3
184
2002
177.1
177.8
178.8
179.8
179.8
179.9
180.1
180.7
181
181.3
181.3
180.9
179.9
2001
175.1
175.8
176.2
176.9
177.7
178
177.5
177.5
178.3
177.7
177.4
176.7
177.1
2000
168.8
169.8
171.2
171.3
171.5
172.4
172.8
172.8
173.7
174
174.1
174
172.2
1999
164.3
164.5
165
166.2
166.2
166.2
166.7
167.1
167.9
168.2
168.3
168.3
166.6
1998
161.6
161.9
162.2
162.5
162.8
163
163.2
163.4
163.6
164
164
163.9
163
1997
159.1
159.6
160
160.2
160.1
160.3
160.5
160.8
161.2
161.6
161.5
161.3
160.5
1996
154.4
154.9
155.7
156.3
156.6
156.7
157
157.3
157.8
158.3
158.6
158.6
156.9
1995
150.3
150.9
151.4
151.9
152.2
152.5
152.5
152.9
153.2
153.7
153.6
153.5
152.4
1994
146.2
146.7
147.2
147.4
147.5
148
148.4
149
149.4
149.5
149.7
149.7
148.2
1993
142.6
143.1
143.6
144
144.2
144.4
144.4
144.8
145.1
145.7
145.8
145.8
144.5
1992
138.1
138.6
139.3
139.5
139.7
140.2
140.5
140.9
141.3
141.8
142
141.9
140.3
1991
134.6
134.8
135
135.2
135.6
136
136.2
136.6
137.2
137.4
137.8
137.9
136.2
1990
127.4
128
128.7
128.9
129.2
129.9
130.4
131.6
132.7
133
133.8
133.8
130.5

1.  PRODUCTION

Data-
30 000 000 tonnes Cu ore/day for 350 days for 20 years
Mill recovery 87% for every 1 tonnage mined
Cu grade is 0.8% tone Cu per mill tonnage produce.
The price of Cu is projected to be US$1.25/lb

Production = 30 000 x 350 x 20 = 210 000 000 metric tones of Cu ore for 20 years.

Mill trough put Recovery =  87% x 210 000 000 = 182 700 000 Mill tonnage
                                               100

 Cu ore grade is 0.8% tonne Cu per mill tonnage produced

                0.8% x 182 700 000 = 1 461 600 tonnes Cu produced
               100

Price of Cu is projected to be US$ 1.25/lb
1 lb = 0.4535924 kg = 0.000453924 tonnes (Using Calculator Conversion)
                       US$ 1.25 = 0.000453924 tonnes                                                                                 
                          xUS$   = 1 tonne
                      1 tonne    = US$ 2755.778095

Therefore price of Cu projected is US$ 2755.778095/tonne

 Gross Revenue = US$ 2755.778095 x 1 461 600 tonnes of Cu = US$ 4 027 845 264  

2. Capital Cost

Data-
Capital cost projected to be US$600 million (1990)
Working Capital is US$ 70 million (1990)

NB: expected to be incurred in year 2

 Salvage value is 20% of the capital cost.

Capital Cost – 60% debt with 12% interest
                     -  40% equity raising 
Real escalation is 4%

Calculation

·         Inflation in 2010 =   CPI Dec 2010  - 1       =   US$ 219.179 - 1 =  63.81 %
        CPI Dec 1990                   US$ 133.80
                                           = 63.81%  nominal inflation in 2010

    
·         Nominal escalation    = (1+ inf 1990 -2010)* (1 + real esc.)n -1
= (1+ 0.6381)* (1+0.04)20 – 1
= 258.9 % over the 20  years period
Therefore,
·         Capital Cost (Dec 1990) US$ 600 M x (1+2.589) = US$ 2 153 400 000 (Dec 2010)

·         Working Capital ( Dec 1990) US$ 70M x (1 + 2.589) = US$ 251 230 000 (Dec 2010)

·         Capital Cost financed through debt  60% with 12% interest
      60%/100 x US$ 2 153 400 000 =  US$ 1 292 040 000 with 12% interest

·         Capital cost financed through equity of 40 %
      40% / 100 x US$ 2 153 400 000 =  US$ 861 360 000
·         Salvage
20%/100 x US$ 2 153 400 000 =   US$ 430 680 000

Annual Interest plus principle payment
A = P x    i x (1 + i) n = US$ 1 292 040 000 x 0.12(1 +0.12)10 =  US$ 228 670 619.5
                 (1 + i)n – 1                                      (1 + 0.12 )10 -1

                                   = US$ 228 670 619.5

Principle = US$ 1 292 040 000 = US$ 129 204 000
                            10

Interest = Annual payment – principle
             = US$ 228 670 619.5  – US$ 129 204 000 = US$ 67 201 632.5

3.      Operating Cost

i)              Mining Operation Cost

Data

Total ore & waste tonnage is 90 000 tonnes mined per day for 350 days for 20 years
 It cost US$1.0/tonne to remove both waste and ore.

Total cost = US$ 1.0/tonnes x 90 000 x 350
                  =US$ 31 500 000 (1990 value)
Therefore;
·         Mining operating Cost
 (Dec 1990) US$ 31 500 000 x (1+2.589) = US$ 113 053 500 (Dec 2010)

ii)             Milling, Severance and administration operating cost
 a)      Milling
Milling Cost = US$1.60/tonne x 30 000 x 350 = US$ 16 800 000 (1990 value)
        (Dec 1990) US$ 16 800 000 x (1 + 2.589) = US$ 60 295 200 (Dec 2010)
b)      Severance
Severance Cost = US$0.10/tonne x 30 000 x 350   = US$ 1 050 000 (Dec 1990)
                 (Dec 1990) US$1 050 000 x (1 + 2.589) = US$ 3 768 450 (Dec 2010)
c)      Administration
Administration Cost = US$ 0.20/tonne x 30 000 x 350 = US$ 2 100 000 (Dec 1990)
                        (Dec 1990) US$ 2 100 000 x (1+2.589) = US$ 7 536 900 (Dec 2010)

d)     1 tonne Cu smelter-charged is imposed on every 0.87 tonne mill production =
  1tonne/ 0.87tonne x US$1.60 x 30 000 x 350 =US$ 19 310 344.83 (Dec 1990)
           (Dec 1990) US$ 19 310 344.83 x (1+2.589) = US$ 69 304 827.59 (Dec 2010) 


Total Operating Cost = US$ 253 958 877.6

4. Development Cost (Capital Cost)
     Year 0 to Year 1 amount used is US$300 million (1990)
  (Dec 1990)US$ 300M x (1+2.589) = US$ 1 076 700 000 (2010 value)

Year 1 to Year 2 amount used is US$300 million (1990 value)
    (Dec 1990)US$ 300M x (1+2.589) = US$ 1 076 700 000  (2010 value)

5. Royalty
 2% + 0.25% = 2.25% from Year 2 to Year 12
2.25% - 0.25% = 2.0 % from Year 13 to Year 22
 6.      Income Tax
 PNG Income Tax rate is 30% of the corporate income.

7.      Depreciation
Year 2 – 14 Apply Double Declining Balance Method (1/2 convention)
Year 15 – 22 Switch to Straight line depreciation.
 i)                    Double Declining Balance Method
Year
Method
Rate x Adjusted Basis
Depreciated Amount  (US$)
1
2
1.5 DB
1.5/13 x 2,153,400,000  x 1/2
124,234,615.4
3
1.5 DB
1.5/13 x 2,029,165,385
234,134,467.5
4
1.5 DB
1.5/13 x1,795,030,918
207,118,952
5
1.5 DB
1.5/13 x1,587,911,966
183,220,611.5
6
1.5 DB
1.5/13 x1,404,691,355
162,079,771.7
7
1.5 DB
1.5/13 x 1,242,611,583
143,378,259.6
8
1.5 DB
1.5/13 x 1,099,233,323
126,834,614.2
9
1.5 DB
1.5/13 x 972,398,708.8
112,199,851
10
1.5 DB
1.5/13 x 860,198,857.8
99,253,714.36
11
1.5 DB
1.5/13 x 760,945,143.4
29,267,120.9
12
1.5 DB
1.5/13 x 731,678,022.5
84,424,387.21
13
1.5 DB
1.5/13 x 647,253,635.3
74,683,111.76
14
1.5 DB
1.5/13 x 572,570,523.5
66,0665,829.64
ii)                  Straight Line Depreciation

      Annual Depreciation = US$ 41 064 561.09 = US$ 5 133 070.137/year
                                                  8 years

8.      Discount Rate
Step 1
   E(Ri) = Rf + ßi [E (Rm – Rf )]
             =  5% + 1% * [ 6% – 5% ]
            =  6% is expected rate of return on the stock investment
Step 2
  WACC =   E(Ri) *     D    +      D      *  (1 – t )* i
                               (D + E)   (D + E)

  WACC = 6% *        60        +           60       * (1 – 0.3)*  12      
                            (40 + 60)           (40 + 60)

             = 8.64%

Therefore the discount rate is 8.64%



                                           Summary of the Calculation

·         Gross Revenue   US$ 4 027 845 264
·         Royalty -  2%  + 0.25% = 2.25% from Year 2 to Year 12
-          2.25% - 0.25% = 2.0 % from Year 13 to Year 22

·         Capital CostUS$ 2 153 400 000
                i) US$ 1 076 700 000  (Year 0-1)
               ii) US$ 1 076 700 000 (Year 1-2)

·         Operating Cost  US$ US$ 253 958 877.6

·         Working Capital - US$ 251 230 000
·         Salvage Value - US$ 430 680 000
·         Depreciation
·         Interest Expense
·         Tax  30%
·         Discount Rate  8.64%


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