Showing posts with label Mine Management. Show all posts
Showing posts with label Mine Management. Show all posts
Tuesday, 31 July 2018
Discounted Cash Flow Modeling(Simple)  Mineral Economics
Las KuriJuly 31, 2018Educational, Mine Management, Mineral Economics, Mines in PNG, Mining Engineering
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
Ã˜ Mining
Operations Cost Involving disposal of waste and ore extraction and handling
Ã˜ 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
Ã˜ 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.
Ã˜ Income
Tax Rate = 30% of the corporate income
Ã˜ 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.
Ã˜ Real
escalation = 14 years
Ã˜ Risk
free rate of return = 4 %
Ã˜ Beta
= 1.0%
Ã˜ 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 (1t)X i
=6%
x 60/(60+40) + 60/(60+40)x (10.3)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, straightline
depreciation method is used and so the depreciation value is constant. During
the exploration stage, in year 0 to 1, there was only cash outflowing only but
from year two and upwards, there is cash inflow.
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
Sunday, 29 July 2018
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 }+ Î² [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)]*(1t)*i
=
8%*[60/(60+40)]+[60/(60+40)]*(10.3)*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
semiannually 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