evaluating income producing investing

8/8/2019 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


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


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


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


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=

+


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.


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