5. financial concepts.pdf
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© MEA 2006 V 1.0 08/2006
Financial Concepts & Discount Cash Flow Techniques
Copyright © 2007-2012 University of New South Wales (UNSW)
This slide presentation was created byAssoc Prof Serkan Saydam The University of New South Wales
Assoc Prof Emmanuel Chanda The University of Adelaide
2011
The moral right of the author has been asserted
The presentation forms part of the Resource Estimation, an MEA Course
All rights reserved. The presentation is licensed to MEA for educational purposes in MEA courses only
Introduction
All capital investment decisions involve the concept ofinvesting funds at the present time with theexpectation of receiving a return at some future date.
Need to be examined estimated future streams ofincome in an attempt to determine value.
Need to be fully understood the role of the time valueof money as this forms the basis for any financialanalysis or valuation.
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Mining is an economic activity The economists tend to be interested in;
1.Forecasting (supply, demand, price and capitalcost),
2.The structure of mineral and commodityindustry and the competitive behavior of thefirms comprising those industries, and
3. In public policy, especially as related to energy,the environment, and land management.
Profits = REVENUES - COSTS
For engineers, profits can be expressed in simple equation form as;
Revenue ($) = Metal Price ($/t) x Grade (%) x Tonnage (t)
Cost ($) = Total Cash Cost ($/t) x Tonnage (t)
Gross Revenue – Operating Cost = Gross Profit (taxable income)
Gross Profit (taxable income) – Tax = Net Profit
Net Profit – Capital Costs = Cash Flow
Cash Flow refers to the net inflow or outflow of money that occursduring a specific time period.
PURPOSE OF EVALUATION PROCESS
Designed to assess the size of return on investment in the project
And the probability of that return occurring
Based on the assumed values of key parameters
THE FINANCIAL EVALUATION CANNOT CONFIRM THE TECHNICAL FEASIBILITY OF THE PROJECT
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EVALUATION GUIDELINES
Made at a point in time
Sunk costs
Constant $ or current $
For comparing alternatives, make sure techniques used permit fair comparisons
Manual evaluations
Computer financial models
Investment decision versus sale/purchase evaluation
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CASHCash is the lifeblood of the enterprise
“Cash flows” are actual $ spent or received
Non-cash items (e.g. depreciation) are important as far as they affect cash flows
Project cash flows for a period are inflows minus outflows - may be +ve or -ve
Periods are usually years; may be quarters or months, depending on the size of the project
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INFLOWS AND OUTFLOWS
Inflows - sales revenue; may include other minor items
Outflows - Initial capital expenditure, working capital, maintaining capital, operating costs, taxes, royalties, rehabilitation costs, etc
Royalties, ? Treat as reductions in revenue
Off site costs, such as realisation costs, ? Treat as reductions in revenue
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WORKING CAPITAL
Component of intial cap. ex. - to fund op. costs until sales revenues arrive - in theory recovered at end of mine life
Required throughout project life but generally supplied by sales revenues
Itemised on a period by period basis in detailed financial models
Avoid double counting in financial model but must be counted in initial funding requirement
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CURRENCY
Local currency
Because costs in local currency
Convert revenues to local currency
Forecast exchange rates can dominate the evaluation
Foreign projects in host country currency
In cases of foreign country hyperinflation, use a stable currency, e.g. US$, if sales revenues in US$
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CONSTANT VS CURRENT $$ change in value over time
Constant $ - generally average value of $ of the day at time of evaluation, preserved throughout project life.
Current $ - $ of the day for each period in the future -requires calculation of the change in value from period to period, i.e. usually inflation rates
Costs affected by local inflation, revenues by world inflation, up to a point. Mineral commodity revenues controlled by supply and demand most of the time.
INTEREST RATES
A function of the time value of money
On debt, represent low risk return
Therefore, risky investments offer higher return
Diversified equity investments offer about 6% above the risk free rate
Government bonds represent risk free rate
Interest rates and discount rates closely linked
Cash Flow TechniquesTime value of moneyA principle based on the timing of cash flows that states $1.00 to be received in the future is less valuable than $1.00 received today.
DiscountingA large future amount of cash is reduced to its smaller current equivalent.
CompoundingA smaller amount of cash earns interest and accumulates to a large amount in the future.
P : Present single sum of money (at time zero)F : Future single sum of moneyA : Amount of each payment in a uniform series of equal payments madeat the end of each periodn : Number of interest compounding periodsi : Period compound interest rateC : Capital investmentL : Salvage valueI : Period income
Discounting TechniquesSimple interest
Simple interest is calculated by application of the rate to the initial investment principal each interest compounding period. Total interest paid over the repayment is proportional to the length of the loan schedule.
Cumulative payment (simple interest) = P × i × n
Example
$1,000 principal at simple interest of 6% per annum for 120 days gives
Solution
Simple interest = $1,000 × 0.06 × (120/365) = $19.73
Compound interest (period, nominal, effective and continuous)
Compound interest is calculated separately for each period within the repayment schedule.
Interest paid in a period is the rate multiplied by the outstanding principal for that period.
Rate = x per cent per TIME FRAME compounded each PERIOD LENGTH
Normally, compound interest rates are expressed using a TIME FRAME of a year. However, the PERIOD LENGTH for compounding is very often a much shorter time such as a day or a month.
Discounting Techniques
P(1+i)n = F
More Examples
Calculate the future worth that $2,000 today will have 4 yrs from now if interest is 5% per yr compounded annually.
P(1+i)n = F
The F/Pi,n factor can be found from interest tables or it can be calculated mathematically to be (1 + 0,05)4=1.216
SIMPLE VS COMPOUND INTERESTExample: Compound Interest
This means earn “interest on interest”
Now:
o F1 = P + P*i = P(1+i) = 100 + 100(0.1) = $110
o F2 = P(1+i) + i[P(1+i)]= 100(1.1)+0.1*100*1.1 = $121 = P(1+i)2
o F3 = P(i+i)2 + i[P(1+i)2] = P(1+i)3 = 100(1.1)3 = $133.10
o In general:
F = P(1+i)n
COMPOUNDING MORE THAN ONCE PER YEARConsider:
10% compounded semi-annually:
Same as 5% compounded every six months!
o F = 100(1+0.05) (1+0.05) (1+0.05) (1+0.05) (1+0.05) (1+0.05)
= 100 (1.34) = $134; compared with $133
NB: first term: 100(1+0.05) = P(1+i) @ end of first 6 months;
100(1+0.05)(1+0.05) = P(1+i) @ end of 2nd six month
o OR F = 100(1+0.10/2)2*3 = 100(1+0.05)6
COMPOUNDING MORE THAN ONCE PER YEARIn general:
o r = nominal rate of interest (% per year)
o m= Times per year interest rate is compounded
o Example: nominal = 10% per compounded semi-annually
=> 5% compounded 6 months!
o The EFFECTIVE RATE, (i) = rate compounded once a year which is equivalent to the nominal rate compunded n times per year
In general:
o i(effective) =
%3.10121.01
11
2
=−⎟⎠⎞
⎜⎝⎛ +=
−⎟⎠⎞
⎜⎝⎛ +
m
mr
COMPOUNDING MORE THAN ONCE PER YEAR
Exercise:
o Calculate the effective interest rate if the nominal rate, r = 18% compounded once per month. Answer: 19.6%
o Calculate the effective interest rate if the nominal rate, r = 10% compounded quarterly. Answer: 10.4%%
o HINT:
11 −⎟⎠⎞
⎜⎝⎛ +
m
mr
COMPOUNDING MORE THAN ONCE PER YEAR
Original Example: Future value of $100 after 3 years,@ nominal interest rate of 10% compounded semiannually.
o F = P(1+r/m)mxn = 100(1+0.1/2)2x3 = $134.01
o Or, we could use the effective rate:
F = P(1+ effective “i”)n = 100(1+0.1025)3 = $134.01
Activity: Determine the effective rate for a nominal of 5% compounded:
Annually
semiannually
Quarterly
Daily
Continuously = Hint: effective i = P(ern)
COMPOUNDING MORE THAN ONCE PER YEAR
INTEREST FORMULASo Future Value F of a present amount P:
F = P (1+i)n ; “find F given P…………………(1)
o Ex.: You deposit $5000 today @10% interest for five years. How much will accumulate of we compound annually?
Answer: $8,052.50
o What if we compound semiannually?
Answer: $8,144.50
o Find P of $5000 received at the end of 5 years.
Answer: $3,104.50
Compound Interest Formulas
ANNUITYSet of money payments made periodically under certain stated conditions.
o Annuity certain = fixed number of payments
o Contingent annuity = number of payments conditional
o Life annuity = made during the life of a person
o F = sum at the end of n periods; P = Present value
o => (F/P, i, n) or to find F given an Annuity A @rate I, and n periods
( )⎥⎦
⎤⎢⎣
⎡ −+=
iiAF
n 11
ANNUITYHow much will accumulate in a fund if $2,500 is invested each year for 5 years at 10%?
Answer: $15,262.5
o HINT:( )
⎥⎦
⎤⎢⎣
⎡ −+=
iiAF
n 11
SINKING FUNDEqual payments which will amount to some Future Value at the end of n years @ i% interest.
o Transpose the equation for Annuity!
⎥⎦
⎤⎢⎣
⎡−+
=1)1( ni
iFA
o (A/F, i, n) => sinking fund factor: Find A given F
UNIFORM SERIESPresent value of an Annuity
o Formula:
⎥⎦
⎤⎢⎣
⎡+
−+= n
n
iiiAP
)1(1)1(
o (P/A, i, n) => sinking fund factor: Find P given A
CAPITAL RECOVERYUsed in typical car and home loan..
o Formula:
⎥⎦
⎤⎢⎣
⎡−+
+=
1)1()1(
n
n
iiiPA
o (A/P, i, n) => Capital Recovery Factor: Find A given P
Determining the Interest Factors:
(1)Use formulas
(2)Read factors from Interest tables (on Moodle)
(3)Use Microsoft Excel
Practice makes perfect (nearly)!
Solve the problems for Tutorial #2 and LG pages from 44. Time Value of Money (upload file from Moodle)
PROJECT PERIODS
Equal length periods cover entire life of project
Permits use of standard compound interest relationships and rules
Periods = years, generally
May be quarters or months for small projects
Project commences with the first period of investment
Evaluation relates to beginning of first period
DEPRECIATION
Depreciation is the means of recovering capital expenditure
Deducted from taxable income because it is recovered capital, not income
But, since dividends cannot be paid out of capital, accountants concentrate on the after tax profit without adding back depreciation
Discounted cash flow evaluations add back depreciation to evaluate total cash flows of the project.
Dividend payments are not part of the project evaluation.
Depreciation in DCF modelling
Depreciation deducted from cash flow to determine taxable income, and thus tax payable
Depreciation then added back to after tax profit to determine period cash flow
Positive NPV of cash flows mean capital has been serviced at the discount rate while invested, has been recovered and excess return has been received
Period cash flows
Project cash flows for each year (or shorter period) made up of:
After tax profit or loss
Plus any depreciation added back
Plus adjustments for any after tax items such as capital expenditures, loan drawdowns or loan repayments made or received during the year.
DCF Modeling TechniquesUndiscounted and Discounted
Undiscounted:
PayBack Period - limited value but still popular.
How long will it take to fully recover the initial investment in a project?
Useful for investment decisions where obsolescence is of importance or for investment in developing countries where instability of tenure is expected.
The weakness of the PbP is that no account of the time value of money and ignores the cash flows after the payback period.
DCF Modeling TechniquesUndiscounted:
Return On Investment or Rate Of Return
For decision making purposes, projects with ROIs equal to or greater than the firm’s target ROI are accepted for development.
Others are rejected.
Projects are ranked from the highest ROI down.
The ROI gives no indication of the value of the project.
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DCF Modeling TechniquesUndiscounted:
ROI and PbP are useful as supplementary measures to assist in corporate decision making.
Many companies will only accept projects which meet certain PbP and, less commonly, ROI measures.
ROI and PbP are of no use where the purpose of the evaluation is to establish the value of a project.
For purposes of evaluation, net cash flow is the measure of profit from the project.
Total Profit is the cumulative net cash flow over the life of the project.
Total Profit takes no account of the time value of money or of the size of capital investment required.
What it does do is alert management to the gross size of the project.
Useful indicator of gross size, usually as a result of long life - can be very useful when companies are using high discount rates.
Two projects may have similar net present values and internal rates of return but one may have a much greater total profit. This greater total profit reflects a longer life and all companies prefer long life mines.
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DCF Modeling Techniques
Discounted:
Net Present Value (NPV)
Internal Rate of Return (IRR)
Present Value Ratio (PVR)
Equivalent Annual Value (EAV)
All four related - based on the same stream of cash flows
DCF Modeling Techniques
NPV - WHAT IS IT?Most important of evaluation measures
Measure of project value at chosen discount rate
Positive NPV - investing in project will add value to the company
Calculate by discounting all cash flows to same point in time
Equal periods
End of period convention
more NPVA project achieves economic acceptability when the sum of discounted receipts exceeds the sum of discounted expenditures.
The NPV of the project is the sum of all the individual period cash flows discounted to the common time datum.
The formula is:Project NPV = ΣCF0 + CF1(1+i)-1 + CF2(1+i)-2 + … + CFn(1+i)-n
Discount RateTheoretically, if the project investment is considered to be riskless, the discount rate should be the highest risk free rate available to the investor.
No mining investment is risk free.
Many companies tend to use their long run weighted average cost of funds as the discount rate, as that reflects a market perception of the required rate of return from such a company.
Some companies increase the discount rate above their cost of capital to take account of the perceived riskiness of a specific project or in the hope of identifying potentially higher earning projects.
In that case, the discount rate is called the hurdle rate.
more Discount RateNPV is a function of discount rate as well as stream of cash flows.
The discount rate represents the discount on the future cash flow.
Discounted cash flows are cash flows that have had their value decreased by the discount rate, compounded by the amount of time until the cash flow is realized.
This accounts for the time value of money when determining the true value of the future cash flow. Summing all appropriately discounted cash flows allows the calculation of the NPV.
IRR
For the most common investment projects, which involve mainly negative cash flows in the early years and predominantly positive cash flow in later years, the NPV is an inverse function of the discount rate and a zero NPV is generated by a unique discount rate, called the Internal Rate of Return (IRR).
In those cases, the NPV goes down as the discount rate goes up
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more NPV
There can be no unique NPV for any project.
For the most common investment projects, which involve mainly negative cash flows in the early years and predominantly positive cash flow in later years.
- If NPV > 0, the project obtains income which is more than anticipated interest rate- If NPV = 0, the project obtains income just for anticipated interest rate- If NPV < 0, the project obtains income which is less than anticipated interest rate
IRR – Internal Rate of Return
Also called Discounted Cash Flow Rate Of Return (DCFROR)
The IRR is simply the discount rate that causes the NPV of a series of cash flows to be zero.
Good for ranking competing projects
No use for valuing projects
Cannot be calculated where all cash flows are positive
NPV is an inverse function of the discount rate and a zero NPV is generated by a unique discount rate, called the Internal Rate of Return (IRR).
NPV vs DCF
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PVR – Present Value RatioPVR measures NPV per unit of discounted investment
Supplements the NPV
2 ways of calculating PVR but both are similar and are used to supplement the info from the NPV
The PVR may be calculated by dividing the NPV of a project by the net present value of the capex outflows, discounted at the same rate as used for the NPV calculation.
So, the PVR is measuring the NPV of the project per unit of investment.
The NPV does not indicate whether the NPV is the result of a large or a small investment.
Does not value project
B/C Ratio = PVR
Instead of looking at the difference in PV + and - flow to analyse projects in NPV calculations, some investors prefer to look at the ratio of PV (PW) net positive cash flows to the present worth of negative cash flows.
This ratio commonly called Benefit Cost ratio (B/C ratio).
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more PVRThe alternative method of calculating the PVR is to divide the present value of all project cash flows excluding capex by the present value of all capital expenditures, both streams being discounted at the same rate.
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EAV - Equivalent Annual Value EAV is the equal net cash flow over each year of the project life which generates the NPV
The Equivalent Annual Value of a project can be calculated by multiplying the NPV of the project by the Capital Recovery Factor for the number of years of the life of the project and for the interest rate (discount rate) used in determining the NPV.
The EAV is a rather specialised tool.
It can be used for choosing between different equipment alternatives, in which cases the EAVs are Equal Annual Costs and the lowest cost alternative is selected.
EAVs of competing projects could be very helpful to management in selecting preferred alternatives, when considered in conjunction with NPV.
Example 1A company must decide whether to introduce a new product line. The new product will have startup costs, operational costs, and incoming cash flows over six years.
This project will have an immediate (t=0) cash outflow of $100,000 (which might include machinery, and employee training costs).
Other cash outflows for years 1-6 are expected to be $5,000 per year. Cash inflows are expected to be $30,000 per year for years 1-6.
All cash flows are after-tax, and there are no cash flows expected after year 6.
The discount rate is 10%. Calculate the PV for each year??
Sum of all present values gives NPV $8,881.52
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Example 1 - Solving with MS Excel
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Example 1
Example 2A five year project requires investments of $120,000 at time zero and $70,000 at the end of year 1 to generate revenues of $100,000 at the end of each of years 2 through 5. The minimum rate of return is 15%. Calculate the project NPV and ROR to determine if the project is economically acceptable.
Net Present value (NPV) @15%
= -120,000-70,000(P/F15%,1)+100,000(P/A15%,4)(P/F15%,1) = $67,389>0 acceptable
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Example 2
Rate of Return (ROR)
0= -120,000 - 70,000(P/Fi,1) + 100,000(P/Ai,4)(P/Fi,1)
@30% =-7,212
@25%=12,928 == by iterating i = 25%+5%(12,928/20,140)=28.2% >15% economically satisfactory
Trial and error basis
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NPV Example
Economic Evaluation
You cannot manage what you cannot measure
How can you measure the value of a project?
Simple cash flow analysis
Discounted Cash Flow Analysis (NPV)
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NPV Analysis
Simple to calculate
Take into account risk
Allows comparison of project with different profiles
Independent of inflation
But;
Does not take into account a project managers ability to adapt to future changes as they occur.
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Decision making behavior
What are the corporate objectives?
The first and immutable objective of a public mining company is to develop the shareholder value
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Corporate Objectives
Lowest quartile of the cost curve
Develop world class deposits
Hedge to protect investors of price market fluctuations
Not hedge to expose investors to the market
Increase value through expansion in reserves
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NPV Curve
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Design Criteria
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Sensitivity Graph of NPV vs Production Rate
-15
-10
-5
0
5
10
15
20
25
0 100 200 300 400 500 600 700 800 900 1000
Production Rate (tonnes/day)
NPV
($ m
illio
n)
NPV $11/g NPV $14/g NPV $18/g
Mine Investment AnalysisThe optimal production rate is
NPV is sensitive to the gold price, and a positive NPV will not be obtained if the market price is not above $11/g and this variable is one that can make or break the mine.
600 tonnes/day
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