# Mine Waste Management

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## 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 = er – 1 = e0.12 – 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%(Rf) 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) = Rf + β [E (Rm - Rf)] =  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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