CAPITAL BUDGETING TECHNIQUES
1. Introduction
Capital budgeting is the quantitative and qualitative analysis and evaluation of physical investment projects that
generate benefits over multiple years. Capital budgeting is one of the most important areas covered in financial
management as management is required to make decisions on which project is best suitable to receive better returns
out of the many that they can choose from. The financial managers perform capital budgeting procedures as they
forecast on the future cash flows and profits for the proposed and planned projects. Financial managers are looking at
different options and always want to come up with the best where the ultimate goal is to increase the value of the
owners` wealth. As financial managers act and make decisions on behalf of the owners they do feasibility studies
before they make large investment decisions. A key principle undertaken by financial managers during capital
budgeting is that capital projects that do not add value to the business should never be undertaken. When financial
managers perform capital budgeting processes they forecast on the future cash flows and profitability of any future
project. It should be borne in mind that any mistake in the future projections during capital budgeting process will lead
to wrong investment decisions. Capital budgeting is the cornerstone of the investment decision-making process, and
involves quantitative and qualitative analysis and evaluation of physical investment projects that generate benefits
over a number of years. This chapter we will look into other aspects like, capital budgeting process, types of cash
flows, types of projects. This chapter will also deal with the calculation of the initial investment or costs, operating
cash flow and the terminal cash flow. This chapter will also look at the different non-discounting techniques and
discounting techniques and their bearing in capital budgeting decisions. Long-term investments take a large portion of
capital investments and will look at the associated cash outflows. The financial managers have to select the
investments that are viable and that will enable companies to increase the wealth of the business owners.
Capital expenditure is an investment made by a firm with expectations to accrue benefits over a long period of time
which will add value to the business and to the investors (shareholders). The basic objective of capital expenditure is
expansion, replacement and renewal. This chapter also explores the various types of quantitative analysis
management conducts to analyse and evaluate projects. As an essential part also we consider how qualitative factors
should be taken into account during the investment decision-making process. Efficient investment appraisal is
required to ensure that a firm invests its funds (money) in capital (big) projects that will create value for the business
owners.
2. Defining capital budgeting and capital budgeting process, types of projects and cash flows
Capital budgeting is the process of evaluating and selecting long-term investments that are consistent with the goal
of increasing the firm`s value. Capital budgeting is the cornerstone of the investment decision-making process, and
involves quantitative analysis and evaluation of physical investment projects that generate returns over multiple years.
Capital budgeting decisions are broadly divided into two categories: that is projects for replacement of existing
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assets and projects for expansion and or new acquisitions. The difference between the two categories is the risk
associated with each, where replacement risk is lower than the other projects. The primary motive for capital
expenditure is expansion, replacement and renewal.
Expansion: The need to expand the business operations is one of the key motives for capital expenditure and this is
achieved by acquiring non-current assets. A firm following a growth strategy often finds it necessary to acquire new
non-current assets for rapid expansion.
Replacement: is when an asset reaches the end of its useful life and then they are replaced by new and better
assets. The management should periodically examine the need to replace existing assets and weigh it with the
benefits of replacement of existing machine. In most cases technological advancement has become more
pronounced to acquire new machines (assets) that could render currently used assets obsolete.
Renewal: businesses wishing to increase efficiency may find that replacing or renewing existing pieces of machinery
may prove to be the optimum solution. Renewal may involve rebuilding or overhauling a machine or production plant
which sometimes may not have a guarantee for the future.
Some capital expenditure may involve long-term commitment of money (funds) by the firm in expectation of a future
return without necessarily adding new assets to the firm. Expenditure of this nature include funds spent on research
and development (R&D), management consulting services, advertising campaigns, improved safety
measures and/ or equipment to prevent pollution.
The capital budgeting process, in which new projects and investments are analysed and evaluated, consists of
five distinct interrelated steps which are spelled out below. Each step in the process is important and during each of
these steps a great deal of time and effort should be devoted to review, analysis and decision making. The
processes are as follows:
 Proposal generation: all departments in the firm make proposals where potential expenditure is reviewed
together with associated benefits as the project is being identified.
 Review and analysis: proposals are formally reviewed so that their appropriateness to the firm`s overall
objectives and plans can be assessed and their economic viability evaluated.
 Decision making: Looking at the outlay amount a decision is made on whether to accept or to reject the
proposed project
 Implementation: once a proposal has been approved and funding made available, then the implementation
phase begins. Greater control is usually required to ensure that what has been approved is actually acquired
and at the budgeted cost.
 Follow-up: This final step is to continually re-evaluate the company`s investment projects where the
monitoring of results during the operating phase of the project.
In most cases managers are faced with various options when it comes to capital expenditure as they have to choose
between the following types of projects:
2
(i)
Independent projects: means accepting one project does not affect the decision of whether to accept
or reject another project
(ii)
Mutually exclusive project: the acceptance of one project in a group prevents all other projects in a
group from being considered.
(iii)
Divisible projects: is made up of smaller pieces that can be implemented or accepted at the same time
or at different times
(iv)
Indivisible project: cannot be broken down into smaller pieces and therefore the whole project has to
be accepted or implemented at the same time.
When a new project is being evaluated, the financial managers have to determine the new project’s estimated
cash flows which are used to evaluate capital projects. The following are the different cash flow types used when
evaluating capital projects:

Conventional cash flows: involves an initial investment/ cost followed by a series of cash inflows

Unconventional cash flows: is when the initial cost/outflow is not followed by a series of inflows

Annuity cash flows: is a stream of equal annual cash flows that are received or paid

Mixed cash flows: is when irregular inflows of cash are received or outflows are paid
Activity 1
The management of a manufacturing company is investigating whether it is worthwhile to expand the same factory or
to expand by moving to a new location in another region because they have not been able to meet the market demand.
Establish the issues that this proposal should entail in order to meet the market demand and what should be done in
order to be successful with this new venture.
3. Explaining and calculating the initial investment or costs, operating cash flow and terminal cash flows
Capital expenditures needs to be calculated in order to come up with all relevant cash flows for any project. Capital
expenditures with conventional cash flow patterns usually consist of the following major cash flow components:
(i) Initial Investment/ costs: These types of costs occur at the beginning of the project and in most cases it is the
cost that cannot be avoided as it associated with the project. The basic components of the initial investment are the
cost of the new asset, installation costs, transportation costs, custom duties, freight charges and adjustment
of the proceeds from the old asset. All these are added together to give us the total initial cost/ investment. The
basic format for the calculation of the initial investment/ Cost is as follows:
Cost of the new assets
= xxxx
Add: Installation costs
= xxxx
Add: Transportation costs
= xxxx
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Add: Freight charges
= xxxx
Add: shipping costs
= xxxx
Add: Custom duties
= xxxx
Less: Proceeds from sale of an old asset = (xxxx)
Total Initial cost
= xxxx
(ii) Operating cash flow: these refer to the relevant cash inflows that are expected to be generated during the life of
the proposed long-term investment. When dealing with operating cash flow we account cash inflow as opposed to
the accounting profit. Cash inflow is determined by adding any non-cash item of expense which could have been
deducted as an expense in the income statement, back to the expected net profit after tax. The most non-cash item
that is added back is depreciation on a yearly basis of the life span of the asset. The basic format for the
calculation of the operating cash flow: The initial cost of the project is R50000.
Year
NOPAT
Depreciation
Operating cash flow
1
30 000
5 000
35 000
2
35 000
5 000
40 000
3
35 000
5 000
40 000
4
40 000
5 000
45 000 (52500)
(iii)Terminal cash flow: We refer to the expected cash flow being generated once the investment is terminated at
the end of the life of the assets or project. When calculating the terminal cash flow the residual amount or
disposal amount is added to the net cash flow on the year of disposal. The basic format calculating the terminal cash
flow is as follows:
The total cash flow for Year 4 is the operating cash flow plus the terminal cash flow:
Operating cash flow
R45 000
Add: terminal cash flow
R7 500: Sale of the machine
Net cash flow (Year 4)
R52 500.
Activity.2
South Africa has been experiencing serious financial irregularities when it comes to government tendering systems as
billions of rands are lost annually because fraud and theft and largely due to poor working capital management. Some
jobs have been left incomplete as funds totalling billions of rands have gone missing without any trace. Make
suggestions on how the government can improve on this and other issues to even improve service delivery to the
communities.
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TECHNIQUES /METHODS USED TO EVALUATE PROJECTS/
4. Evaluating projects using the Non-Discounted Cash- flow Techniques
There are two most distinct methods that do not discount the cash inflows, where they do not involve the time
value of money concept whenever they evaluate projects. The two basic non-discounting techniques that are used
to evaluate projects are the following:
(i) Average rate of return or Accounting rate of return (ARR)
This method is a simple technique that considers the initial cash investment a project requires and compares this
figure with the average annual cash flow generated by the project over its lifetime. The project with the highest
average rate of return is acceptable. The following formula is used: Assume the Initial cost is R50000
Average rate of return = Average earnings after taxes x 100 = 41875 x 100 = 83.75%
Initial investment(cost)
50000
Advantages
Disadvantages
1.Simple to use and quick to calculate
1. This method tend to insensitive to fluctuations in
cash flows during project lifetime
2.It is easy to understand and apply the principle
2. For projects with relatively long lifetimes, this method
can overlook and result in large errors
3. Can be used to compare investments if projects
3. This method does not take time value of money into
lifespans are the same and cash flows are reasonably
consideration.
stable
The advantage of this method is that it is easy to calculate and the major disadvantage is that it ignores the time
factor in the value of money.
(ii) Payback period (PBP)
This method calculates the expected number of years it takes for the project to recover its initial
investment/cost. It is determined by calculating exactly how long it takes to recoup the initial investment from net
cash flows. The payback period is determined by subtracting the net cash flows from the initial investment on a
yearly basis until the whole amount is recovered. In most cases the cash flow amounts do not match with the
remaining balance therefore leading to interpolate in order to determine the exact period. The decision-making
criterion for PBP in respect of a project is that those projects with a PBP shorter than stipulated by the management
is accepted. The major disadvantage with the payback period is that it ignores the time value of money concept and
also the relevant cash flows involved. The advantage of payback period is that it is easy to calculate.
The formula for calculating the payback period is as follows: Assume the Initial Cost is R50000
Step1. Initial cost – yearly cash flows until the recovery of initial amount. Use the information given above.
5
Step 2. PBP = years before recovery + (uncovered cash flow at beginning of the year ÷ cash flow during the
year) (interpolation)
= 50000 – 35000 = 15000 Year 1
= 15000 – 40000= (25000) Year 2 Interpolate (Apportion the time)
= 1 year + 15000/ 40000 x 12 months
= 1 year + 4.5 months
= 1 year + 4months + 0.5 x 30days
= 1 year + 4months + 15days
Advantages
Disadvantages
1.The PBP is simple to use and quick to calculate
1. The PBP can only be determined subjectively, no
concrete decision criteria to indicate whether an
investment increases the firm`s value.
2. Provides some information on the risk of the
2. The PBP does not take into account the cash flows
investment
beyond the payback period.
3. It serves as an indicator for liquidity because the
3. The PBP ignores the time value of money and the
quicker the initial cost is recovered the earlier cash is
risk of the future cash flows
available for other uses
a. Evaluating projects using the Discounted Cash-flow Techniques
The discounted cash flow techniques (DCF) do take the time value of money into consideration while the major
disadvantages of non-discounted cash flow techniques are that they ignored the time value of money principle. The nondiscounting techniques ignore the timing and the size of the cash flows and this seriously affect the accuracy of these methods.
The discounting techniques take into account the time value of money principle into consideration, where the cash flows are
discounted first before calculations are made. The following are the major discounting methods that are used to evaluate
projects:
(i)The discounted payback period method (DPBP):
This method is a variant of the PBP method and it attempts to address the weakness of the PBP method as it discounts the
cash flows using the firm`s cost of capital. The method then calculates the expected number of years required to recover the
initial investment by considering the discounted net cash flows generated by the project. The formula is the same as the
payback period the only difference is the use of present values instead of cash flows. Formula is as follows:
DPBP = years before full recovery + (unrecovered cash flow at beginning of year ÷ cash flow during the year)
Initial Cost is R50000; The cost of capital is 10%
6
Year
NCFs
Discount Factor
Present Values
1÷(1+r)n (1÷1.10)n
Discounted values
1
35000
0.9091 = (1÷1.10)1
31819
2
40000
0.8264 = (1÷1.10)2
33056
3
40000
0.7513 = (1÷1.10)3
30052
4
52500
0.6830 = (1÷1.10)4
35858
Total present value (TPV)
130785
Less: Initial Cost
50000
Net Present value (NPV)
80785
DF = YR1 = 1/1.10 = 0.9091; YR2 = 0.9091÷1.1 = 0.8265; YR3 = 0.8265÷1.1 = 0.7514; YR 4 = 0.7514÷1.1= 0.6831
YR1= 1÷(1.10)1 = 0.9091; YR2 = 1÷(1.10)2 = 0.8264
DPBP = Initial cost less discounted yearly PV (cash flow) until the initial is totally recovered
= 50000 less 31819 = 18181 YR1
= 18181 less 33056= interpolate (apportion)
= 1 year + 18181÷33056 x 12months
= 1 year + 6.60months
= 1 year + 6months + 18 days (0.6x30days)
Advantages
Disadvantages
1.It is simple to use and quick to calculate
1. Can only be determined subjectively, no concrete
decision criteria that indicate whether the investment
increases the firm`s value
2. It considers the riskiness of the project`s cash flows
2. Does not take into account the cash flows that occur
through the cost of capital
after the DPBP has been reached and is not reliable
measure of profitability.
3. The DPBP takes into account the time value of money
3. The emphasis is on short-term profitability rather than
when calculating
profitability over the entire life of the project. Makes no
distinction between projects of different sizes.
(ii)The net present value method (NPV):
The net present value (NPV) is the difference between the present value (PV) of all expected net cash flows and the PV of all
expected net cash outflows calculated over the expected life of the project. The NPV is calculated by subtracting the initial
investment(II) from the present value of the net cash inflows (NCFs), discounted at the firm`s cost of capital. The formula for
calculating NPV is as follows: NPV = Total present values(TPV) less Initial investment/Cost(II)
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The general criterion of the NPV method states that any project that has the positive or greater than zero should be accepted
as the project will be profitable. The decision-making criteria applied when using the NPV method can be summarised as
follows:
a. Accept projects where the NPV> 0
b. Reject projects where the NPV< 0
c. Projects with an NPV = 0 will increase the scale of the business as management will be indifferent as to whether the project
should be undertaken or not.
Advantages
Disadvantages
1.The NPV is logically consistent with firm`s goal of
1. The NPV method may be difficult to understand for many
maximising owners` wealth
2.Considers all the cash flows during its calculations and
2. The NPV requires an estimate of the cost of capital in
considers the risk of future cash flows through the cost of
order to calculate
capital
3. Considers the time value of money and offers theoretical
3. It is one out of the many techniques that is expressed in
correct decisions.
terms of rand, and not as a percentage.
(iii)The profitability index (PI):
The profitability index (PI) investigates the relationship between the initial investment amount and the expected pay-off of a
proposed project. The PI is the measure of a project`s profitability relative to each rand invested in the project. The PI is a
handy tool for ranking projects because it allows management to identify the amount of value created per rand invested. The
formula for calculating the profitability index is as follows:
PI =
TPV
II
= 130785 = R2.62
50000
The highest profitability index is acceptable, and also the PI value of one (1) is considered the lowest acceptable value of index.
Any value that is less than one, (1) would indicate that the PV of a project`s expected cash flows is less than the initial
investment. The general decision-making criteria for PI are as follows:
a. Accept projects where the PI > 1
b. Reject projects where the PI < 1
c. Projects with a PI = 1 will only increase the scale of the business, management, therefore, will be indifferent as to whether
the project should be undertaken or not.
Advantages
Disadvantages
1.It is one of the easy, best methods to use as it considers
1. The PI is a difficult concept to understand
all cash flows of the project
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2. It shows whether an investment increases the firm`s value
2. It may be problematic as it may not give correct decision
when used to compare mutually exclusive projects
3. It considers the risk of the future cash flows and also the
3. The PI requires an estimate of the cost of capital in order
time value of money
to calculate.
(iv)Internal rate of return (IRR)
The internal rate of return (IRR) is an investment appraisal technique is based on concepts that are similar to the NPV method.
Like the NPV method, a project is evaluated by considering the initial investment it requires and the expected future cash flow
that the project will generate, and it compares the return of the project with the firm`s cost of capital. IRR is the discount rate
that equates the NPV of an investment opportunity of 0. While the IRR is the most difficult to calculate than the NPV and PI, it
also the most popular technique. The common step of calculating IRR is to use the Trial and Error method and then
interpolate. The formula for calculating IRR is as follows:
IRR = A% + (B% - A%) x (NPVA)
10% + (70%-10%) x 80785
(NPVA) +– (NPVB)
=
10% + (60% x 0.9860)
(80785 +1149)(= 81934)
IRR= 10% + 59.16% = 69.16%
Where: A% = lowest estimate of r
B% = highest estimate of r (negative NPV)
NPVA = the present value of the future cash flows discounted at A%
NPVB = the present value of the future cash flows discounted at B%
Initial Cost is R50000; The cost of capital is 70%
Year
NCFs
Discount Factor (70%)
Present Values
1÷(1+I)n (1÷1.70)n
1
35000
0.5882 = (1÷1.70)1
20587
2
40000
0.3460 = (1÷1.70)2
13840
3
40000
0.2035 = (1÷1.70)3
8140
4
52500
0.1197 = (1÷1.70)4
6284
Total present value (TPV)
48851
Less: Initial Cost
50000
Net Present value (NPV)
(1149)
The IRR can also be calculated by using a financial calculator with the functionality available.
Advantages
Disadvantages
9
1.The IRR tells whether an investment increases the firm`s
1.May not give the value- maximizing decision when used to
value
compare mutually exclusive projects
2. Considers the time value of money and all the cash flows
2. The IRR requires an estimate of the cost of capital in
of the project
order to make a decision
3. Considers the risk of the future cash flows through the
3. Cannot be useful in situations in which the sign of the
cost of capital in decision of accept or reject
cash flows of a project change more than once during the
project`s life
6 Summary
Capital budgeting is one of the opaquest subjects in the financial management, as financial managers seldom disclose or
publicise the information that they use to make large investment decisions. Information about an entity`s capital budgeting
process is not readily available, as this information usually includes sensitive business plans and other information that gives a
business its competitive advantage. This chapter has focused on an important aspect of the business capital investment
decision and its determinants. During the capital budgeting process, financial managers analyse and evaluates the
opportunities, risks and financial implications of proposed capital projects, both qualitatively and quantitatively. This chapter has
made a distinction between non-discounted cash flow techniques and the discounted cash flow techniques as these take time
of value into consideration. Before an investment project is subjected to various investment appraisal techniques, it is
important to determine what type of project it is in order to select the most viable and appropriate. Efficient investment appraisal
is required to ensure that a company invests its capital on projects that will create value for the business owners. As the
projects are being appraised they are then ranked in accordance to their viability as firms use different approaches in order to
rank projects and to distinguish viable projects. The capital budgeting techniques are applied to determine if a project will
contribute towards the profitability of the firm and the creation of owners’ wealth. A firm has to identify projects that will
contribute to its main objective and implement them so to increase the value of the firm.
This chapter has covered a number of capital budgeting techniques which were explored in order to make well calculated
decisions for the entire benefit of the business. Before undertaking a project, it is essential to subject it to various capital
budgeting techniques before final making a decision. It is also important when engaging on the capital budgeting techniques to
select the best project. A distinction has to be made between those capital budgeting techniques that take the time value of
money into consideration and those that do not. The non-discounting capital budgeting techniques are the average rate of
return and the payback period, while the discounting techniques are the discounted payback period, the net present value, the
profitability index and the internal rate of return. It is fundamental important to acknowledge these capital budgeting techniques
as they play a major role in the firm`s future plan and objectives.
Self- Test Questions Unit 4
1. Explain the terms the following terms to your friend that is studying industrial technology: (i) capital project (ii) capital
budgeting; (iii) capital investment decisions (iv) Opportunity cost.
[4marks]
2. Differentiate between conventional cash flow and unconventional cash flow.
[4marks]
10
3. Efficient investment appraisal is required to ensure that a firm invests its capital in projects that will create value.
Explain to your friend who is studying computers the capital budgeting process.
[5marks]
4. When evaluating capital investment projects explain why emphasis should be placed on the initial cost and what other costs
are added to it before calculating the final initial cost?
[4marks]
5. Differentiate between profit and cash flow when dealing with investment projects.
[4marks]
6. Discuss the meaning of terminal cash flow and what other items can be added to it?
[4marks]
7. Elaborate on the major differences between non-discounting techniques and the discounting techniques. [4marks]
8. Explain the main differences between the average rate of return (ARR) and the payback period (PBP) as some of the major
techniques used to evaluate projects.
[4marks]
9. Discuss the advantages of average rate of return (ARR) and the payback period (PBP)
[4marks]
10. Discuss the disadvantages of net present value (NPV) and profitability index (PI)
[4marks]
11. Kingdom Limited is intending investing in three independent projects, one in Swaziland, Gauteng Province and
another in Limpopo Province. These projects will require that the company pays for training and establishment fees of
R50 000, R20 000 and R30 000 respectively. Your department has asked you to evaluate these three projects and write
a report to the Board of Directors on which one is the most viable. The following information has been supplied to you
to use. The firm has a 12% cost of capital (WACC).
Year
Swaziland
Gauteng
Limpopo
0
(R950 000)
(R1 300 000)
(R1 000 000)
1
240 000
260 000
300 000
2
210 000
340 000
300 000
3
270 000
470 000
300 000
4
300 000
510 000
300 000
5
420 000
520 000
300 000
(1÷1.12) DF (1÷ 1+r)n = (1÷ 1+ 0.12) = (1÷1.12)
Adjustments: Initial Cost/ Investment:
Swaziland
Gauteng
Limpopo
IC/ II
950000
1300000
1000000
Add T& Est
50000
20000
30000
Total IC
1000000
1320000
1030000
Required:
a. Calculate average rate of return (ARR), for each province
[6marks]
b. Calculate the payback period (PBP), for each province
[6marks]
c. Calculate the Discounted payback period (DPBP), for each province
[6marks]
d. Calculate the net present value (NPV), for each province
[6marks]
e. Calculate the Profitability Index (PI), for each province
[3marks]
f. Calculate the Internal rate of return (IRR), for each province
[6marks]
11
g. Indicate which of the three provinces will be the most viable and why?
[2marks]
Swaziland
ARR = Ave Profits/ II x100 = 288000/1000000 x 100 = 28.80%
G = 420/1320= 31.82% L= 300/1030 = 29.13%
PBP = 1000000 – 240000 = 760000 Yr1
7600000- 210000 = 550000 Yr2
550000 – 270000 = 280000 Yr3
280000 – 300000 interpolate
3 years + 280000/300000 x 12months
3years + 11months + 6days
G= 3yrs 5m26d
Year
NCFs
DF 12%
PV
PV
PV
1
240 000
0.8929
214296
232154
267870
2
210 000
0.7972
167412
271048
239160
3
270 000
0.7118
192186
334546
213540
4
300 000
0.6355
190650
324105
190650
5
420 000
0.5674
238308
295048
170220
TPV
1002852
1456901
1081440
Less: II
1000000
1320000
1030000
NPV
2852
136901
51440
Financial Calculator: NPV
2852
136901
51433
Financial Calculator: IRR
12.10%
15.63%
14.00%
L= 3yrs 5m 6d
DPBP
1000000 – 214296 = 785704 Yr1
4 yrs 6m 13d
4y 8m 12d
785704 -167412 = 618292 Yr2
618292 -192186= 426106 Yr3
426106 -190650 = 235456 Yr4
235456 – 238308 interpolate
4 years + 11 months +26days
PI = TPV / II = 1002852/1000000 = R1.00
G = 1.10
L= 1.05
IRR Method:Trial and Error Method
IRR = A% + (B% - A%) x (NPVA)
(NPVa +NPVb)
=12% + (14% -12%) (2852/ 52728)
12% + (20%-12%) (136901/331197)
12% + (15%-12%) (51440/75780)
= 12% + (2%x 0.054088909)
12% + (8%x 0.413352174)
12% + (3% x 0.678807073)
12
= 12% + 0.1082
12% + 3.31%
12% + 2.04%
= 12.11%
=15.31%
14.04%
Year
NCFs
DF 14%
PV
DF: 20%
PV
DF: 15%
PV
Swazi
Gauteng
Gauteng
Limpopo
Limpopo
1
240 000
0.8772
210528
0.8333
216658
0.8696
260880
2
210 000
0.7695
161595
0.6944
236096
0.7561
226830
3
270 000
0.6749
182223
0.5787
217989
0.6575
197250
4
300 000
0.5921
177630
0.4823
245973
0.5718
171540
5
420 000
0.5194
218148
0.4019
208988
0.4972
149160
TPV
950124
1125704
1005660
Less: II
1000000
1320000
1030000
NPV
(49876)
(194296)
(24340)
Financial Calculator:
NPV
SHARP: Enter 5= N; 12%=I/YR, then followed by: +-1000000 ENT Cf0; ENT, 240 000 ENT:CF1, 210 000 ENT:CF2, 270
000 ENT:CF3, 300 000 ENT:CF4, 420 000 ENT:CF5 then 2nd F CFi, Lower Cursor then. Comp =NPV= R2852
HP: Enter 5=N; 12%=I/YR; +-1000000CFj; 240000CFj; 210000CFj; 270000CF; 300000CFj; 420000CFj Downward arrow
then NPV = R2852
IRR
SHARP: IRR= Enter 5= N; then followed by: +-1000000 ENT Cf0; ENT, 240 000 ENT:CF1, 210 000 ENT:CF2,
270 000 ENT:CF3, 300 000 ENT:CF4, 420 000 ENT:CF5 then 2nd F CFj, then Comp I/YR = 12.10%
HP: Enter 5=N; +-1000000CFj; 240000CFj; 210000CFj; 270000CF; 300000CFj; 420000CFj; Downward arrow then IRR =
12.10%
3. As the financial director New Horizons Computer School, you have been tasked with replacing the old computer
network. Dexter Computer Company Ltd has informed you that they have two types of computer network that you are
looking for, and have priced them as follows:
Computer Network 1 is valued at R250 000, and Computer Network 2 is valued at R300 000
The cash flows expected from the two networks are as follows:
Year
Network1
Network2
1
R120 000
R120 000
2
R125 000
R120 000
3
R130 000
R120 000
4
R140 000
R120 000
13
5
R160 000
R120 000
Transportation and installation will amount to R20 000 for each Network. Management has told you that this new
capital venture must be able to yield 15% return on investment. At the end of year 5 both Computer Networks will be
sold for R10 000 cash each.
1. What is the total initial cost for each network?
2. What is the terminal NCFs for each network?
Required to calculate the following for each network:
a. Average rate of return (ARR)
[4marks]
b. Payback period. (PBP)
[4marks]
c. Discounted payback period (DPBP)
[4marks]
d. Net Present Value (NPV)
[6marks]
e. Profitability Index (PI)
[4marks]
f. Internal rate of return (IRR)
[4marks]
g. Using these techniques which network would you choose and why?
[2marks]
4. Ngwenya Limited would like to replace an existing factory machine with one of the three more efficient equipment
from Germany. The new machines are valued as follows: Machine A costs R400 000 plus R8 000 to install, Machine B
costs R540 000 plus R10 000 to install, and Machine C costs R320 000 plus R6 000 to install. The price of each
machine also indicates the efficiency and its capacity. These machines have a life span of five years and need to be
depreciated. The projected cash flows after accounting for depreciation as an operating expense for each machine are
provided in the table below:
Year
Machine A
Machine B
Machine C
1
210 000+78000
220 000
140 000
2
220 000+78000
250 000
140 000
3
230 000+78000
260 000
140 000
4
240 000+78000
260 000
140 000
5
250 000+18000+78000
260 000+20000
140 000+12000
The company`s required rate of return is 12%. After five years, these can be disposed for cash as follows: Machine A:
R18 000; Machine B: R20 000 and Machine C: R12 000.
Adjustments to be made before calculations are made!
1. What is the total initial cost for each machine?
2. What is the terminal NCFs for each machine?
3. What is the depreciation amount for each machine?
Answers are as follows:
4. Depreciation = Cost –Scrap / No. of years = (400000+8000) – 18000 / 5 = 78000
5. Initial Cost
400000
14
+ Installation cost
Total Initial Cost
8000
408 000
6. Calculate the yearly Cash flows
7. In year 5 Calculate Terminal Cash flow 250000+ 18000+ 78000= 346000
Required:
a. Calculate the average rate of return (ARR) MA = 76.37%
[9marks]
b. Calculate the payback period (PBP)
[9marks]
MA= 1 years + 4months + 25days
c. Calculate the discounted payback period (DPBP) for each machine
[9marks]
d. Calculate the net present value (NPV) for each machine
[6marks]
e. Calculate the profitability index (PI) for each machine
[3marks]
f. Calculate the internal rate of return (IRR) for each machine
[6marks]
g. Write a report to the Board of Directors indicating which of the three machine will be the most viable and why?
[6marks]
SOLUTION
SOLUTIONS TO QUESTIONS
a. ARR = Ave Profits/Initial investment
Network 1 = 137 000/270 000 x 100 = 50.74%
Network 2 = 122 000/ 320 000 x 1000 = 38.13%
[4marks]
b. Payback Period(4marks)
Network 1 = 2 years + 2months+ 10days
Network 2= 2years 8months
Initial investment 270 000
initial investment 320 000
Yr 1 cashflow 120 000 balance 150 000
yr 1 cashflow 120 000 balance 200 000
Yr 2 125 000 balance 25 000
yr 2 120 000 balance 80 000
25 000 – 130 000 interpolate
80 000 – 120 000
2yrs +25000\130 000 *12 months
2 yrs +80 000\120 000 * 12 months
2yrs +2.3077 months
2yrs + 2 months +.3077*30 days
2 years + 8 months
2yrs +2 months + 9 days.
Discounted Payback Period(4marks)
Network 1 = 270000- 104352= 165648
320000- 104352=215648
165648- 94513= 71135
215648-90732 = 124916
71135-85475= interpolation
124916 -78900=46016
15
46016 – 68616= interpolate
NW1= 2 years10months 29days
NW 2= 3years 8months
c.Net Present Value (16/16x6marks)
Disc Factor
NW (1)
NW (2)
1.
0.8696
104 352 
104 352
2
0.7561
94 513
90 732 
3
0.6575
85 475
78 900
4
0.5718
80 052 
68 616
5
0.4972
84 524 
64 636
Total Present Value
448 916
407 236
Less Initial Value
270 000
320 000
Net Present Value
178 916
87 236
Network 1
Discount factor
cashflow
discount factor
present value
Yr 1 0.8696
120 000
0.8696
104 352
Yr 2 : 0.8696\1.15 = 0.7561
125 000
0.7561
94 513
Yr 3: 0.7561\1.15 =0.6575
130 000
0.6575
85 475
Yr 4 : 0.6575\1.15= 0.5718
140 000
0.5718
80 052
Yr 5: 0.5718\1.15 =0.4972
170 000
0.4972
84 524
Total PV
448 916
Less Initial investment 270 000
NPV
d. Profitability Index =
Total Present Value / Initial Investment
Network 1= 448 916/270 000
Network 2 = 407 236/320 000
= R1.66
= R1.27
[4marks]
NPV = Using Financial Calculator =NW1= R178908; NW2= R87230
IRR= Using a Financial Calculator=NW1= 38.94%; NW2 = 25.90%
e. Network 1 is the best option because of the following:
a. ARR: Network 1 has the highest
b. Payback Period :Network 1 has the shortest period
c. NPV: Network 1 has the highest NPV
16
178 916
d. PI : Network 1 has the highest
Therefore choose Network 1 as it is the most viable. (2marks)
IRR Method: Trial and Error Method
IRR = A% + (B% - A%) x (NPVA)
(NPVa +NPVb)
=15% + (40% -15%) (2852/ 52728)
12% + (20%-12%) (136901/331197)
12% + (15%-12%) (51440/75780)
= 12% + (2%x 0.054088909)
12% + (8%x 0.413352174)
12% + (3% x 0.678807073)
= 12% + 0.1082
12% + 3.31%
12% + 2.04%
= 12.11%
=15.31%
14.04%
Year
NCFs
DF40%
PV
DF: 20%
PV
Swazi
Gauteng
Gauteng
1
240 000
0.8772
210528
0.8333
216658
2
210 000
0.7695
161595
0.6944
236096
3
270 000
0.6749
182223
0.5787
217989
4
300 000
0.5921
177630
0.4823
245973
5
420 000
0.5194
218148
0.4019
208988
TPV
950124
1125704
Less: II
1000000
1320000
NPV
Workings
Machine A
Machine B
Machine C
Initial cost.
400 000
540 000
320 000
Installation.
8 000
10 000
6 000
Total Cost
408 000
550 000
326 000
Depreciation: Cost less disposal value
No. of years.
408000-18000
550000-20000
326000-12000
5years
5years
5years
=78000
=106 000
= 62800
a. ARR = MA 1558000/ 5yrs = 311600/408000 = 76.37%
ARR = MA. =1558000/ 5yrs = 311600/408000 = 76.37%
ARR= MB. = 1800000/5 = 360000/550000 = 65.45%
ARR = MC = 1026000/5 = 205200/326000 = 62.94%
PBP = MA 408000 – 288000 = 120000 Yr1.
120000- 298000 = interpolate
MB= 550000-326000
MC = 326000 – 202800 = 123200
326000-356000
123200 – 202800 =
17
I year + 120/298 x 12 months
1 yr + 326/356 x12.
1yr +123200/202800 x12
I YEAR +4.8322 months
1 yr + 10.9months
1 yr + 7.2899
I year +4 months + 0.8322*30 days
1 yr + 10months + 29days 1 yr + 7 months
1 year + 4months + 25days
1 yr + 10months + 29day
1 yr + 7months + 9days
MACHINE A
Year
DF(12%) MA NCFs
PV
MB NCFs
PV
MC NCFs
PV
1
0.8929
288000=210000+78000
257155
326000
291085
202800
181080
2
0.7972
298000= 220000+78000
237566
356000
283803
202800
161672
3
0.7118
308000
219234
366000
260518
202800
144353
4
0.6355
318000
202089
366000
232593
202800
128879
5
0.5674
346000
196330
386000
219016
214800
121878
TPV
1112374
1287015
737862
TIC
408000
550000
326000
NPV
704374
737015
411862
a. Discounted payback period: DPBP
Machine A: 408000 less 257155= 150845 less 237566 (interpolate) =1year + 150845/237566x12months
1 year + 7 months+ 0.6195* 30 months
= 1year + 7months +19days
(2marks)
Machine B: 550 000less 291085=258915 less 283803= 1year + 258915/283803x12month =
1year+ 10months + 29days
(2marks)
Machine C: 326 000less 181080=144920less161672= 1year + 144920/161672x12month =
1year+ 10months + 23days
(2marks)
b. Net Present Value (NPV) Using Financial Calculator
Machine A
Enter N=5years; 12=I/YR, then followed by:-408 000 ENT Cf0; ENT, 288 000 ENT:CF1, 298 000 ENT:CF2, 308 000
ENT:CF3, 318 000 ENT:CF4, 346 000 ENT:CF5 then 2nd F CFj, Lower Cursor then Comp = R704 359 (2marks)
Machine B
Enter N=5years;12=I/YR, then followed by: -550 000 ENT Cf0; ENT, 326 000 ENT:CF1, 356000 ENT:CF2, 366 000
ENT:CF3, 366 000 ENT:CF4, 386 000 ENT:CF5 then 2nd F, then, CFj, Lower Cursor then Comp = R737 010 (2marks)
Machine C
Enter N=5years; 12=I/YR, then followed by: -326 000 ENT Cf0; ENT, 202 800 ENT:CF1, 202 800 ENT:CF2, 202 800
ENT:CF3, 202 800 ENT:CF4, 214 800 ENT:CF5 then 2nd F, then, CFj, Lower Cursor then Comp = R414 858 (2marks)
c. Profitability Index (PI)
18
Machine A: TPV/ II = 1112374/ 408000 = R2.73 (1mark)
Machine B: TPV/ II = 1287015/ 550 000 = R2.34 (1mark)
Machine C: TPV/ II = 737862/ 326000 = R2.26
(1mark)
d. Internal rate of return (IRR): Using financial calculator
Machine A
IRR= Enter N=5years; then followed by: -408 000 ENT Cf0; ENT, 288 000 ENT:CF1, 298 000 ENT:CF2, 308 000 ENT:CF3,
318 000 ENT:CF4, 346 000 ENT:CF5 then 2nd F CFj, then Comp I/YR = 67.95% (2)
Machine B
IRR= Enter N=5years, then followed by: -550 000 ENT Cf0; ENT, 326 000 ENT:CF1, 356000 ENT:CF2, 366 000 ENT:CF3,
366 000 ENT:CF4, 386 000 ENT:CF5 then 2nd F, then CFj, then CompI/YR = 56.66% (2marks)
Machine C
IRR= Enter N=5years, then followed by: -326 000 ENT Cf0; ENT, 202 800 ENT:CF1, 202 800 ENT:CF2, 202 800 ENT:CF3,
202 800 ENT:CF4, 214 800 ENT:CF5 then 2nd F, then CFj, then Comp I/YR = 55.62% (2marks)
e. Report to advice on the most viable machine
To: Board of Directors: Name of the company
From: Financial Manager: Name of the company
Date: ------------------------Re: Most viable machine
Accordingly, Machine A is the most suitable one to acquire as it proves to have the best capacity for our operations.
 Guided by the above-mentioned criteria it is of advantage to buy Machine A.  The second best would be Machine
B which has the second highest NPV R737 010.Machine A has the highest IRR of 67.95%, and best PI of R2.73 as
compared to others and the shortest DPBP by 3months  (3marks)
19