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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Environmental Engineering Questions and Answers

1.       Define environment (in terms of mining).

Environment is Conditions that affect working atmosphere and development of mining. Or is the physical condition that exists in mines.

2.       What is mining?

It is the extraction of minerals from the earth.

3.       Why does environment become a subject to mining?

Because serious mine closure issues remain after mine is closed so by taking environment as a subject to mining, the mine closure issues can be addressed and must be known to the local people of what is going on and what preventive measures that can be taken to protect people and the natural environment.

4.       What are main sources of physical impacts by mining operations?

They are: exploration, development and extraction.

5.       What are main sources of chemical pollution due to mining?

Main sources of chemical pollution are cyanide and sulfuric acid for (leaching) and organic reagents (flotation agents) from ore separation processes. Others include mercury, toxic blast chemicals and hydrocarbon products run – off.

6.       What particular problem exists with both ferrous and precious metallic ores?

Acid mine drainage is a particular problem in many mines and both ferrous and precious metallic ores are the main sources of ARD.

7.       What is the main concern of trace metal concentrations?

The main concern of trace metal concentration is that, when they are leached into the river systems and streams it cause bioaccumulation which is a concern to the river systems.

8.       State the magnitude of mineral’s contributions to economic growth in developed and developing nations.

High proportions of minerals are mined in developing countries and so the economy of poor countries depends largely on minerals whereas minerals contribute a small portion to the economy of developed countries like USA, Japan and Great Britain.

9.       What are the effects of increased demand for minerals?

The demand for minerals increased as there was an increased in technology, development and human civilization. As a result, environmental impacts of earth based resource extraction increases.

10.   Why is every mine different and related environmental effects?

Because every mine has different characteristics with respect to environment. These characteristics include;

      Amount of materials removed.

      Deposit depth.

      Ore chemical composition

      Ore process technology/techniques

      Degree of stewardship practiced.

11.   Describe very briefly how mineral is extracted by surface mining methods and underground methods.

In surface mining method, the mineral is extracted by removing the overburden, drilled, blasted, loaded and hauled to the processing plant.

In underground mining methods, mineral deposits are extracted at certain depths. Ore is drilled and blasted stopes, marked and hauled to the surface via hoisting systems or diesel units.

12.   What aspect of operation distinguish surface from underground mining?

Underground mine operations are complex compared to surface operations. Surface mining is easy and cheap to operate because the ore deposit is near surface whereas underground mining is hard and expensive to operate because mineral deposit is at certain depth.

13.   State the natures of environmental impacts caused by mill operation, underground and surface mining respectively.

Riverine Tailings from mill operation is dangerous as most mineral deposits are associated with sulfur. In addition, smelting generate large amount of toxic gas. Smelters cause regional pollutions where SO2 can travel considerable distances and cause “acid rain” and climate change.

Potential sources of water pollution include drainage from surface and underground mines, waste water from beneficiation, and contaminated surface water from toxic blast chemicals and hydrocarbon products run – off.

14.   Why is chemical pollution more serious than physical?

Because chemical means are hard to reverse and these must be controlled at process stage. But environmental impacts through physical impacts can be reclaimed through rehabilitation during mining and post – mine period.

15.   Differentiate tailings and waste rock and describe respectively environmental impacts.

Tailings compose mostly of mud and slurry containing high proportion of fine particles. Mud and slurry tailings once exposed to air and rain cause oxidation, releasing sulfuric acid, causing acid rock drainage. The suspended solids cause river bed sedimentation, diversion of watercourses, flooding and destruction of aquatic life.

Waste rock is solid coarse materials from both surface and underground mines. Waste rock dump occupy large portions of land, often outside the special mining lease under lease for mining Purposes.

16.   If Frieda Copper mine is predicted to produce 1million/year ore at 0.45%Cu, what is the annual waste material generated?

Data: production = 1,000,000 tonness/year

       grade = 0.45%

Annual waste generated =????

Copper concentrate = production x grade = 1,000,000 x 0.0045 = 4500 tonnes copper.

Annual wastes = 1,000,000 – 4,500 = 995,500 tonnes of waste.

17.   If Hidden Valley mine has minable ore of 5minllion tones grading 2.5g/t Au, for mine life of 10 years, the tailings dam should be designed to what capacity?

Data: mineable ore = 5 million

Ore grade = 2.5g/t     mine life = 10 years.

 /year x 2.5g/t = 12,500,000 grams/year.

Total value mineral = 10 years x 12,500,000 gram/year = 125,000,000 grams

 In terms of tonnes = 125 tonnes.

Waste and value minerals = 5,000,000 tonnes /year x 10 years = 50,000,000 tonnes of ore.

Therefore; total waste generated would be = 50,000,000 tonnes – 125 tonnes = 49,999,875 tonnes.

So the tailings dam should be designed in such a way that will cater for 49,999,875 tonnes of waste over the ten year period. If tonnage factor was given then the answer would be expressed in volume.

18.   What is beneficiation? Describe it?

Is the entire process of crushing, grinding, sizing and separation of ore into valuable mineral and waste

In other words it is the process that liberates mineral grains locked in rock/ore which can be separated physically and chemically.

19.   State the two types of mineral separation and examples of each.

Two basic means of separation are physical and chemical.

·         Physical separation involves; - (a) magnetic and (b) gravity separation.

·         Chemical separation methods are: (a) floatation (b) cyanidation (c) amalgamation and (d) heap leaching.

20.   Briefly describe the processes: (a) heap leaching (b) cyanidation & (c) amalgamation.

      Heap leaching – is a process used to extract metal values from run – of – mine ore. The ore is usually porous and readily soluble in aqueous solvent.

      Cyanidation – is a process for extracting gold or silver from ore by treating the ore with a weak solution of sodium cyanide and recovering the metal particles from the resulting solution.

         Amalgamation – is a method of extracting a precious metal from an ore by using mercury to form an amalgam (an alloy of mercury and another metal) with the metal.

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Calculations of Inflation/Escalation/Interest Rates - Mineral Economics Questions and Answers

1.      If inflation in 2009 is 6% and NASFUND’s net profit after tax is A$150 million. What is the real net profit?

Nominal profit  = A$150 million

Profit when inflation occurred = $150M  x 6%  = $9M

 Real profit is when the inflated amount is removed.

So, Real net profit = A$150million – A$9M = A$141million.

2.      What is the real interest rate if inflation is 7% and interest rate is 15%?

 Data: inflation = 7%; interest rate = 15%

 Real interest rate = (1+ nominal rate)/ (1+ inflation rate) – 1

                             = (1+ 0.15)/ (1+ 0.07) – 1 = 7.48% real interest rate.

3.      Given the Australian CPI for years 1990 to 2000, (i) calculate its inflation rate, (ii) average inflation over the period, calculate nominal annual escalation and annual escalation if real escalation is 5%.

Data: use CPI for yrs 1990 to 2008.

        i.            Inflation rate in 2008   = (CPI Dec 2008/ CPI Dec 1990) – 1.

                                                  = (166/106) – 1 = 56.6% nominal inflation in 2008.

      ii.            Average inflation over the period (1990 – 2008).

Average inflation  = (CPI Dec 2008 / CPI Dec 1990)^1/n – 1, i.e. n = 18

                                           = (166/106)^1/18 – 1 = 2.5%/ yr for 18 years

    iii.            (a).nominal annual escalation   = (1+inflation 1990 – 2008)*(1+real escalation)ⁿ – 1.

                                                              = (1+0.566)*(1+0.05)¹⁸ – 1

                                                              = 276.9% escl. Over the 18 years.

            (b). annual escalation (1990 – 2008) = (1+ 2.769)^1/18 – 1

                                                                       = 7.65 %/ yr escl. Over 18 years.

                         

4.      Cost of a drill rig was A$1 million in 1990 in Australia. What could be the price in 2000 if equipment was escalated by 5% per year in real terms?

(i). inflation in 2008 = (CPI Dec 2008/ CPI Dec 1990) – 1    =166/106 – 1   = 56.6%

(ii). Nominal escalation = (1+ infl.1990 – 2008 )*(1+real escl)ⁿ – 1

                                        = (1+0.566)*(1+0.05)18 – 1

                                        = 276.9% escalation over the 18 year period.

(iii). Price in 2008 = Cost (Dec1990)A$1M*(1+2.769) = A$3.769million(Dec 2008)

Therefore the price of equipment in December 20008 was A$3.769 million. This shows prices of goods and services increase but standard of services or consumption could eventually decrease, if serviceability is standardized.

5.      Banks A, B and C offer the following interest rates on A$10,000 loan. Which bank offers the lowest interest rates?

Loan = $ 10000, lowest interest rate =?

A)    A nominal interest rate of 12% compounded monthly.

              E = (1+i/n)ⁿ – 1 = (1+0.12/12)¹² – 1 = 0.1268 or 12.68%

B)    A nominal interest rate of 12% compounded quarterly.

              E = (1+i/n)ⁿ – 1 = (1+0.12/4)⁴ – 1 = 12.55%

C)    A nominal interest rate of 12% compounded continuously.

              E = e^r – 1 = e^0.12 – 1 = 12.75%

Therefore, nominal interest rate compounded quarterly has the lowest interest rate so bank B offers the lowest interest rate.

6.      A mining engineer wants to determine the discount rate. He does a research and finds the following details listed below. What is the discount rate?

-          Risk free rate of return is 5.5%(R_f) and beta is 1%.

-          Global mining industry rate of return is 8%

-          Assume finance is sourced from 60% commercial loan with 12% interest rate and the other 40% capital is sourced from equity financing

-          Effective tax rate is 30%.

i.                    Expected rate of return on stock investment;

                  E (Ri) = R_f + β [E (R_m - R_f)] =  5.5% + 1%[8% – 5.5%] = 8%

ii.                  Weighted average cost of capital;

                 WACC = E(Ri)*[D/(D+E)] + [D/(D+E)]*(1-t)*i

                              = 8%*[60/(60+40)]+[60/(60+40)]*(1-0.3)*12%  =9.84%

Normally mining industry discount rate is 10% to 15%. Thus WACC discount rate is widely accepted because it is highly risk weighted rate.

7.      A company purchases 10 fleets of haul trucks for a mine operation at total cost of US$15 million. If the lives of the equipment are 10 years,(i) what is the aggregate depreciation per year,(ii) written down value(WDV) on year 7 applying Straight Line method. (iii) Apply Double Declining Balance method for the same and discuss which method is favorable to the company in terms of recovering the capital cost.

Data: 10 fleets of haul trucks – cost = US$15million

Equipment life = 10 yrs. Cost of 1 truck =US $1.5M

i.                    Depreciation = $15M/10yrs =$1.5M/yr for 10 haul trucks.

                                          =$1.5M/10yrs = 0.15M/yr for 1 haul truck

ii.                  Written down value (WDV)  on year 7 applying straight line method;

                    

                WDV  = cost – annual Depr * No. of years

                             = $15M - $ 1.5M/yr * 7 yrs   = $ 4.5 M for 10 haul trucks.

   WDV for 1 haul truck = $1.5M - $0.15M*7yrs = $0.45M

iii.                Using Double Declining Balance method.

DB = (150%/n) * original cost – Depr.amount)

Year	Method	Rate  * Adjusted value	Depreciated amount
1	1.5DB	1.5/7  x15,000,000x(1/2)	1607142.857
2	1.5DB	1.5/7  x13392857.14	2869897.959
3	1.5DB	1.5/7  x10522959.18	2254919.824
4	1.5DB	1.5/7  x8268039.356	1771722.719
5	1.5DB	1.5/7  x6496316.637	1392067.851
6	1.5DB	1.5/7  x5104248.786	1093767.597
7	1.5DB	1.5/7  x4010481.189	859388.8262

$4010481.189 is the written down value after depreciation deductions in 7 years. Therefore, $4.0M is the written down value after depreciation deduction in 7 years.

NB: Double Declining Balance method enhance fast and early recover of initial capital investment and it improves net present values, rate of return and payback period and project operates on profit in later years.   Declining balance ensures depreciation value is greater in the first year and progressively decreases over successive years.

8.      Would you rather have a savings account that pays 5% annual interest rate compounded semi-annually or one that pays 5% annual interest compounded daily? Explain why?

I would have a savings account that pays 5% interest daily or continuously compounded because I could have a fortune if interest is compounded daily. That is, by continuously adding the interest onto the existing one, the amount also increases.

9.      What is rate of return?

Is the amount of income generated in a year by capital invested, expressed as a percentage of the total sum invested?

10.  What is risk and averse person?

Risk is the possibility of loss in an investment or speculation and risk averse person is someone who seeks to avoid risk as much as possible.

  

11.   What are the effects of high interest rate and low interest rate? What is interest rate?

During high interest rate sparked by high inflation, people tend to save money in the bank because cash – holding has low buying power which results in people buying few good with more cash.

Whereas fall in interest rate encourage investment, attributed to low cost of production.

 Interest rate concepts are complex but there are two main types:

i.                    First, interest rate is the return on the bond investment, commonly known as financial security. E.g. interest added to one’s account periodically. 

ii.                  Second, interest becomes a cost if you borrowed money from a bank or often referred to as cost of capital borrowed from the bank.

12.  What are the effects of high inflation and low inflation?

High inflation lead to increasing the interest rate that in turn discourage investments, especially small business sector, which is the single largest employer in an economy of the world.

 Whereas, when inflation is low, it induces interest rate to fall and encourage investment, attributed to low cost of production which is beneficial to consumers.

However, deflation is bad when there is rapid asset price decline, real estate, manufacturers close and hard to negotiate for low labor wages.

13.  What is weighted average cost of capital?

Weighted average cost of capital is a risk – weighted rate, which takes into consideration percentage of debt to equity proportion of financing a project.

14.  What is the purpose of Government adopting a depreciation rate?

The sole purpose of Government in imposing depreciation is to allow mining companies to recover their capital cost before imposing tax on net income.

15.  Why does the Government impose taxes?

Tax is an amount of money levied by a government on its citizens. The Government imposes taxes because this money collected is then used to run the government, the country, a state, a county, or a municipality.

Definitions:

Levy - use government authority to impose or collect a tax

county - : a unit of local government and one of the administrative subdivisions that the states of the United States and, excepting major cities, all of England and Wales are divided into

Municipality - the appointed or elected members of a local government

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