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(R_i) = R_f + ß_i [E (R_m – R_f )]

             =  5% + 1% * [ 6% – 5% ]

            =  6% is expected rate of return on the stock investment

Step 2

  WACC =   E(R_i) *     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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Discounted Cash Flow Modeling(Simple) - Mineral Economics

PRODUCTION

·         30,000 tons copper per day for 350 days for 20 years

·         Through put recovery is 87 % for every 1 tonne mined.

·         Cu ore grade is 0.8 % tone Cu per mill tonnage produced

·         Price of Cu is projected to be US$ 1.25/lb

Now: 30,000 x 350 = 10 500 000 tonnes/year of Copper  ore

For 20 years = 10500000

Now: 87% through put recovery for every 1 tonne mined:

0.87 x 10 500 000 tonnes = 9 135 000 tonnes recovery from through put per year

0.8% tones copper per mill tonnage produced (is the Cu grade)

0.008 % x 9 135 000 = 73 080 tonnes of Cu recovered per year

Now conversion of 1.25/lb to price/tonnage

2204.62 lb = 1 tonne

1 b = x

2204.62 x = 1

x = 1/2204.62 = 4.536x10 -⁴

Price of Cu =  US $ 1.25/4.536x10 -⁴  tonnes

Now :  1.25 = 4.536x10 -⁴

x = 1

1.25 = x 4.536x10 -⁴

x = 1.25 / 4.536x10 -⁴

= 2, 733.775

Price of Cu = US$ = 2,755.775/tonnage

Therefore the value is:

73080 x 2755.77 = US$ 201, 392, 037.00

CAPITAL COST

Real escalation = 4/Inflation in 2010 = CPI Dec. 2010     – 1      = 219.2   -1    = 0.6832 =    68.32 %

                                                                      CPI Dec. 1990                  133.8

Nominal escalation

(1+0.6832) (1+0.04)²⁰ - 1

= 2.589 = 258.9 %

Cost (Capital Cost 2010) = 600 M x (1+2.589) = 2 153 400 000

Working Capital 2010 = 70 M x (3.589) = 251 230 000

Salvage Value = 2 153 400 000 x 20% = 430 680 000

Now: 60% of Capital Cost is Debt = 1 292 040 000

(Debt Life = 10 years)

A = 0.12 (1 +0.12)¹⁰ x 1 292 040 000 = 228 670 619.5 (annual repayment

       (0.12 +1)¹⁰ - 1

Equity: 2 153 400 000 – 1 292 400 000 = 861 360 000

So now: 1 292 040 000/ 10 yrs = 129 204 000 (principal)

228 670 619.5 – 129 204 000 = 99 466619.5 (interest expense)

Total Capital COST = 2 153 400 000

Equity = 861 360 000

Working Capital = 251 230 000

Salvage Value = 430 680 000

Interest Expense = 99 466 619.5

Principal (Repayment) = 129 204 000

                                                                                           

OPERATION COST

Cost Projected From two cost parameters

Ø  Mining Operations Cost Involving disposal of waste and ore extraction and handling

Ø  Mining, Severance and Adminstration Operation Cost

1.      Total Ore and Waste tonnage is 90000 tonnes mined/day for 350 days and its costs $1 /tone to remove both waste and ore.

Calculate 1990 values and convert to 2010 value

Now: Nominal escalation ( OF 20 years from 1990 -2010) = 258.9% 

Cost (1990) For mining $1 /tone x (1+ 2.589) = 3.5.89/tone (2010 value)

Mining Cost = 90, 000 x 350 x 3.589 = 113 053 500 (2010 value)

2.      Milling, severance and administration

Milling Cost for 2010 = 1.6 x 3.589 = 5.7424 /tone

Severance cost 2010 = 0.1 x 3.589 = 0.3589 /tone

Administration Cost in 2010 = 0.2 x 3.589 = 0.7178 /tone

Therefore the total is give as:  6.8191

Now: 6.8191/ 0.87 = 7.838

NOW: 7.838 x 30 000 x 350 = 82 299 482.76 (milling cost)

Total operation cost = 113053500 + 82 299 482. 76

= US$195, 352, 982.80 per year

ECONOMIC FUNCTIONS

Ø  Royalty is 2% plus MRA levy of 0.25 % from year 2 to 12  and next 10 years PNG Government intends to remove MRA levy starting year 13 at the production years.

Ø  Income Tax Rate = 30% of the corporate income

Ø  In high production periods, year 2 – 14, apply double Declining Balancing method (1/2 year convention) and then switch to straight line depreciation starting year 15 to mine closure in year 22.

Ø  Real escalation = 14 years

Ø  Risk free rate of return = 4 %

Ø  Beta = 1.0%

Ø  Global Mining Industry rate of return is 6%

NB: The initial inflation is applied in year 2 to year 12 will increase by 2.5% from year 13 to 22

Now: the expected rate of return on stock investment

ECRi = Rf + I [Rm –Rf]

         = 5% + 1% (6%-5%)

         = 6%

Weight Average cost of capital

=WACC = E (Ri) x D/(D+E) + D/(D+E)X (1-t)X i

=6% x 60/(60+40) + 60/(60+40)x (1-0.3)x 12%

=8.64% (nominal Discount Rate)

Inflation 2010 = CPI (Dec.2010)   -  = 219.2  -1  = 0.6382 = 63.82%

                              CPI (Dec. 1990)       133.8

 

Average Inflation =   219.2     1/20     - 1 = 0.024989 = 0.025

                                     133.8

Therefore the inflation rate to be used is:  2.5 %

Summary of the Discounted Cash Flow Model

Discounted Cash Flow (DCF) analysis provides useful techniques to assess in terms of value maximization and cost minimization which addresses financial efficiency objectives.

The DCF analysis is a techno – economic technique applied to convert Profit Lost statement to evaluate financial viability of a new project/investment options. The criterion for decision making are not limited to NPV,IRR/ROR,DPP & KE but must also consider other risk such as environment impacts, political and socio – cultural conditions.

Gross revenue increases over the period beginning at year 2 to 22 as seen from our calculation.

Depreciation during Double Declining Balance Method of depreciation, it decreased slowly over the period from year 2 to year 14. In year 15 to year 22, straight-line depreciation method is used and so the depreciation value is constant. During the exploration stage, in year 0 to 1, there was only cash out-flowing only but from year two and upwards, there is cash in-flow.

It is seen from our results that, the NPV is $ 8,058,113,286.68. So the project is viable because NPV is greater than zero (>0). The IRR is 56.29% which exceeded the discount rate, as such it gives and impression that Frieda Copper Project is viable.

Capital Efficiency (KE) is a measure of project profitability on the capital invested. It must be greater than zero (>0) to meet the condition to be viable. Since our calculated KE is 3.74 > 0, it is better.

Scenario analysis applies DCF model variables to investigate likely scenarios if changes occur in the future. These scenarios could be increase or decrease in these variables with respect to DCF model. It is seen from the Scenario Analysis Spider Chart and we conclude that NPV is more sensitive to both positive and negative changes in revenue or price. Therefore if there is a positive increase in price, the NPV improves proportionally and vice versa if decreases

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