evaluating income producing investing
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School of Civil, Mining and Environmental Engineering
MINE412 MINING ECONOMICS
EVALUATING INCOME PRODUCING INVESTMENTS
There are two basic classifications of investments requiring decision analysis, namely:
1. Income producing investment alternatives.2. Service producing investment alternatives.
The income producing investments will be examined in this section and the serviceproducing investments in the next section.
The techniques discussed below are on a before tax and a no inflation basis to avoidunnecessary complication at this stage. It should be emphasised that economicevaluation should always be carried out after tax and with inflation effects taken intoaccount.
1. INCOME PRODUCING INVESTMENT
Income producing investment situation may be subdivided into two classifications,
namely:
• Mutually exclusive alternatives.
• Non mutually exclusive alternatives.
MUTUALLY EXCLUSIVE INVESTMENT ALTERNATIVES
Mutually exclusive investment alternatives are those where several alternatives areconsidered from which only one can be selected. This could be the best machine toinstall to improve existing operations or the best way to carry out a mining operationwhere only a single activity is possible.
Any economic analysis involving a comparison of mutually exclusive alternativesmust be carried out on an incremental or marginal basis.
This is demonstrated in the following examples.
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(a) EQUAL PROJECT LIFE ALTERNATIVES
Three mutually exclusive process improvement projects with 7 year lives beingconsidered. The company has $800,000 available for investment and any money notinvested in process improvements will be invested elsewhere at rates of return of 10%(R.O.R.) before taxes.
The optimum investment for the $800,000 is determined as follows:
The details of the three alternatives are:
PROJECT INVESTMENT REVENUEANNUAL
EXPENSESANNUAL
SALVAGEANNUAL
A 400,000 200,000 90,000 120,000
B 600,000 300,000 120,000 150,000
C 800,000 450,000 300,000 300,000
Cash Flows:
PROJECT"A"
0 1 2 3 4 5 6 7
400,000 110,000
PROJECT"B"
0 1 2 3 4 5 6 7
600,000 180,000
PROJECT"C" 0 1 2 3 4 5 6 7
800,000 150,000
The analysis will be carried out using four analytical techniques.
(a) IRR analysis(b) Net PRESENT VALUE analysis
(c) Net ANNUAL VALUE analysis(d) Net FUTURE VALUE analysis
In the analysis of mutually exclusive alternatives, the following steps are carried out:
1. Each alternative is examined to determine that it is economicallysatisfactory in its' own right.
2. Incremental analysis is then examined to see whether the additionalinvestment is justified economically.
Salvage $120,000
Salvage $150,000
Salvage $300,000
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SUMMARY OF ANALYSIS ANALYTICAL METHODS
(a)
(b)
(c)
(d)
Use EXCEL to verify the results in the above table.
From the above summary it can be seen that PROJECT "B" is selected as the perfectalternative by all analytical techniques.
Another example will demonstrate the need to carry out incremental analysis formutually exclusive investment alternatives.
PROJECT INVESTMENT REVENUEANNUAL
EXPENSESANNUAL
SALVAGEVALUE
AB
$ 20,000$200,000
$ 30,000$150,000
$10,000$50,000
$ 5,000$50,000
Assume that $200,000 is available to invest and any unused capital would be investedat 10%. Project life is 7 years.
PROJECT"A"
0 1 2 3 4 5 6 7
C=20,000 20,000
PROJECT"B"0 1 2 3 4 5 6 7
C=200,000 100,000
PROJECTA
PROJECTB (B-A)
PROJECTC (C-B)
IRR
ANALYSIS
22.63% 25.03% 30.23% 11.21% 0%
xN.P.VANALYSIS
$+ 197,064
$+ 353,220
$+ 156,156
$+ 84,160
$- 269,060x
N.A.VANALYSIS
+ 40,485 + 72,566 + 32,081 + 17,295 - 55,271x
N.F.VANALYSIS
+ 389,970 + 688,260 +298,290 +163,850 - 524,440x
Salvage $5,000
Salvage $50,000
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IRR Analysis for these projects is
PROJECT "A"
0.9040 0.0055P.W Equation - 20,000 = 20,000 (P/A i.7.) + 5000 (P/Fi.7)
Try i = 110% = 20,000 (0.9040) + 5000 (0.0055)
= 18,080 + 28= $18,108
i = 90% = 20,000 (1.0987) + 5,000 (0.0112)= 21,974 + 56= 22,030
By Interpolation IRR = 100.35%
PROJECT "B"
P.W. Equation 200,000 = 100,000 (P/Ai.7.) + 50,000 (P/Fi.7.)
Try i = 50% = 100,000 (1.883) + 50,000 (0.0585)=188,300 + 2,925= $191,225
i = 40% = 100,000 (2.263) + 50,000 (0.0949)= 226,300 + 4745= 231,045
By Interpolation IRR = 47.8%
In this example, if IRR analysis is used alone, then Project "A" would be selected with
100% R.O.R. compared with a R.O.R. for Project "B" of 48%.
However, when incremented analysis is used, the incremented IRR is calculated asfollows:
PROJECT B-A
0 1 2 3 4 5 6 7
C=180,000 80,000
P.W.Equation 180,000 = 80,000 (P/Ai.7.) + 45,000(P/Fi.7)
Try i = 50% =80,000 (1.883) + 45,000 (0.0585)=150,640 + 2,633=153,273
i = 40% =80,000 (2.263) + 45,000 (0.0949)
Salvage $45,000
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=181,040 + 4,271=185,311
By Interpolation IRR = 41.66%
This shows that the decision should be to proceed with Project "B" because it is morebeneficial to invest the $180,000 at 42% than at the alternative of 10%.
Use EXCEL to verify the above results
(b) MUTUALLY EXCLUSIVE PROJECTS WITH UNEQUAL INVESTMENT LIFEALTERNATIVES
The following techniques apply to handle mutually exclusive investments whereservice lives are unequal.
It is firstly necessary to find a common basis of comparison, otherwise the economicevaluation will be invalid.
There are generally two possibilities which are illustrated by the following example.
PROJECT “A”
0 1 2 3 4 5 6
2000 960
Investment $2,000
Annual Net cash earnings $ 960Estimated service life 6 YearsInterest Rate 9%
PROJECT “B”
0 1 2 3 4
2000 1200
Investment $2,000Annual Net cash earnings $1,200Estimated service life 4 YearsInterest Rate 9%
The two possibilities are:
a) The investment is a once off and will not be repeated.
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b) The investment will be repeated indefinitely.
The techniques to be adopted for these two possibilities are as follows:
INVESTMENT WILL NOT BE REPEATED
The N.P.V. analysis is valid for this case if it is assumed that funds which are released
from the shorter life project are reinvested at the minimum rate of return adopted inthe evaluation.
The evaluation would favour Project “A” with the largest N.P.V.
PROJECT “A” PROJECT “B”
Investment $2,000 $2,000Annual Net Cash Earnings 960 1,200Service Life 6 Years 4 YearsMinimum R.O.R. 9% 9%Net Present Value
4.486Project “A” 960 (P/A9.6) - 2000 $2,307
3.240Project “B” 1200 (P/A9.4) – 2000 $1.888
Use EXCEL to verify the above results
INVESTMENT WILL BE REPEATED INDEFINETELY
This is typical of equipment replacements which continue as long as the businessenterprise does.
Three techniques may be adopted although the EQUIVALENT ANNUAL VALUEmethod is favoured because of its simplicity of application. The three techniques are:
1. N.P.V. analysis over a time period which is common to both projectsi.e. 12 years in the following example.
2. N.P.V. analysis assuming that each project is repeated in perpetuity.
3. Equivalent Annual Value of each project.
In the following example the same investment decision is reached in favour of
Project “B” with each of the three techniques.
PROJECT A 0 1 2 3 4 5 6
C=2000 960
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0 1 2 3 4
PROJECT B
C=2000 1200
(1) N.P.V. analysis over a common 12 Year period.
PROJECT “A”
0 1 2 3 4 5 6 7 8 9 10 11 12
960C=2000 C=2000
7.161 0.5963N.P.V. = 960 (P/A9.12) – 2000 (P/F9.6) – 2000
= 6875 – 1193 – 2000= $3,682
PROJECT “B”
0 1 2 3 4 5 6 7 8 9 10 11 12
1200C=2000 C=2000 C=2000
7.161 0.5019 0.7084N.P.V. = 1200 (P/A9.12) – 2000 (P/F9.8) – 2000 (P/F9.4) – 2000
= 8593 – 1,004 – 1,417 – 2000= $4,172
(2) N.P.V analysis in perpetuity
PROJECT “A”
11.11 0.223 11.11
N.P.V. = 960 (P/A9⋅∝) – 2000 (A/P9.6) (P/A9⋅∝)= 10,666 – 4955= $5,711
PROJECT “B”
11.11 0.309 11.11
N.P.V. = 1200 (P/A9⋅∝) – 2000 (A/P9.4) (P/A9⋅∝)= 13,332 – 6866= $6,466
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3. EQUIVALENT ANNUAL VALUE
PROJECT “A”
0.223N.A.V. = 960 – 2000 (A/P9.6)
= 960 – 446= $514
0.309N.A.V. 1200 – 2000 (A/P9.4)
= 1200 – 618= $582
Use EXCEL to verify the above results
NON MUTUALLY EXCLUSIVE INVESTMENT ALTERNATIVES
Non mutually exclusive investment alternatives are those investment alternatives fromwhich more that one alternative may be selected within the constraints of budgetrestrictions.
The objective is to select those investment alternatives which will maximiseprofitability.
PRESENT VALUE RATIO ANALYSIS. (P.V.R)
The technique is to rank the investment alternatives by P.V.R. analysis and to selectthose which yield the highest ranking.
PRESENT VALUE RATIO P.V.R. =COSTSINVESTMENT.W.P
V.P.N
The following three investment alternatives where the budget allowance is $100,000.The projects are non mutually exclusive and the minimum rate of return is 9%.
PROJECT “A”
0 1 2 3
50,000100,000
Investment $100,000Net Cash Inflow/Annum $ 50,000Project Life 3 YearsInterest Rate 9%
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PROJECT “B”
0 1 2 3 4 5
20,000
60,000
Investment $60,000Net Cash Inflow/Annum $20,000Project Life 5 YearsInterest Rate 9%
PROJECT “C”
0 1 2 3 4 5 6 7 8
10,000
40,000
Investment $40,000Net Cash Inflow/Annum $10,000Project Life 8 YearsInterest Rate 9%
N.P.V CALCULATION
2.531PROJECT “A” = 50,000 (P/A9.3) – 100,000
= 126,550 – 100,000= 26,550
3.89PROJECT “B” = 20,000 (P/A9.5) – 60,000
= 77,880 – 60,000= 17,800
5.535PROJECT “C” = 10,000 (P/A9.8) – 40,000= 55,350 – 40,000= 15,350
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PRESENT VALUE RATIO ANALYSIS (P.V.R)
38.0000,40
350,15
30.0
000,60
800,17
27.0000,100
550,26
==
==
==
C PROJECT
BPROJECT
APROJECT
Decision – Select Project “C”, then “B”, then “A”.
In this case with a $100,000 budget allowance select projects “B” and “C”.
Collectively this yields a N.P.V. of 33.0000,100
350,15800,17=
+
Use EXCEL to verify the above results
2. SERVICE PRODUCING INVESTMENTS
Service producing investment analysis usually involves an analysis of costs, includingcapital, operating and salvage, with no income differences between the investmentalternatives.
The technique of analysis are similar to income producing investments discussed inthe previous section.
Incremental analysis is necessary in order to calculate IRR. because the IRR with theindividual investments will be negative without income.
In the case of PRESENT WORTH and ANNUAL WORTH calculations, theinvestment opportunity yielding the lowest total cost will be selected.
An example will illustrate the technique.
An investment of $100,000 in automated equipment will provide a service for 3 yearswith zero salvage value and will reduce existing operating costs by $45,000 per year.
Should the expenditure of $100,000 be proceeded with. Assume that the minimum rateof return is 9%.
PROJECT “A” CAPITAL INTENSIVE
0 1 2 3Salvage Zero
100,000
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PROJECT “B” LABOUR INTENSIVE
0 1 2 3
45,000
The analysis will be carried out using the same four analytical techniquesadopted for the income producing investments in the previous section.
a) IRR. ANALYSISb) PRESENT WORTH ANALYSISc) ANNUAL WORTH ANALYSISd) FUTURE WORTH ANALYSIS
a) INCREMENTAL IRR ANALYSIS
PROJECT “A” – “B”
0 1 2 3
100,000 45,000Savings
P.W. Equation
100,000 = 45,000 (P/Ai.3.)
2.283Try i = 15% = 45,000 (P/A15.3)
= 102,735
2.106i = 20% = 45,000 (P/A20.3)
= 94,770
By interpolation IRR = 16.78%
Since IRR of 16.78% is > 9%, the minimum rate of return, the acceptance of Project“A” is satisfactory.
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(b) PRESENT WORTH
P/W. PROJECT A – $100,000
2.531P/W. PROJECT B – 45,000 (P/A9.3) = $113,895
Select “A” with smallest ANNUAL WORTH.
(c) ANNUAL WORTH
0.395A/W. PROJECT A – 100,000 (A/P9.3) = 39,500
A/W. PROJECT B – 45,000
Select “A” with smallest ANNUAL WORTH
(d) FUTURE WORTH
1.295F/W. PROJECT “A” – 100,000 (F/P9.3) = 129,500
3.278F/W. PROJECT “B” – 45,000 (F/A9.3) = 147,510
Select “A” with smallest FUTURE WORTH.
Use EXCEL to verify the above results