2. Contents
Capital budgeting
Discounted and non-discounted method
Methods of capital budgeting
Net Present Value and its formula
Pros and cons of NPV
Positive and negative NPV
Example of NPV
Probability Index and its formula
PI interpretation
Advantages and disadvantages of PI
Example of PI
Payback period and its formula
Payback and capital budgeting
Example of payback period
Internal Rate of Return and its formula
IRR vs. CAGR and ROI
Example of IRR
3. Capital budgeting
In capital budgeting, projects that improve business are selected. Almost everything,
including the acquisition of land or the purchase of fixed assets like a new vehicle or
machinery, can be included in the capital budgeting process. There are several approaches
to capital budgeting, and businesses employ multiple criteria to monitor the performance
of proposed projects.
4. Capital budgeting
Investors estimate the worth of new investment projects using capital budgeting.
Payback period (PB), internal rate of return (IRR), and net present value (NPV) are the
three methods of project selection that are most frequently used.
Payback period: It helps to calculate how long would it take a business to generate enough
cash flow to recoup the initial investment.
IRR-The predicted return on a project is measured by its internal rate of return; if it
exceeds the cost of capital, the project is good.
NPV-The net present value, compares a project's profitability against alternatives, and is
likely the most useful of the three techniques.
5. Discounted and Non-Discounted Methods
Non-Discounted Methods:
• Non-discounted methods do not take into account the time value of money.
• They focus on the absolute dollar amounts rather than the timing of cash flows.
• Common non-discounted methods include the Payback Period and the Accounting Rate of
Return (ARR).
• These methods are relatively simple to calculate and understand but have limitations.
Discounted Methods
• Discounted methods consider the time value of money by discounting cash flows to their present
value.
• They use a discount rate to reflect the opportunity cost of capital and calculate the Net Present
Value (NPV) or Internal Rate of Return (IRR).
• Discounted methods provide a more accurate assessment of project profitability.
• Common discounted methods include NPV, IRR, and Profitability Index (PI).
6. Methods used in capital budgeting
1. Discounted Cash flow analysis:
Companies frequently utilise discounted cash flow methodologies to evaluate
both the timing and consequences of the amount invested since a capital budget
will frequently cover multiple periods and maybe many years.
The inflows and outflows of a project are included in discounted cash flow as
well. Companies frequently have to make an initial financial investment for a
project (a one-time outflow). At times, there could be a string of outflows that
are used to pay for ongoing projects. Companies may aim to determine a target
discount rate or a certain net cash flow amount at the conclusion of a project.
7. Methods used in capital budgeting
2. Payback analysis:
Payback techniques of capital budgeting make plans around the timing of when
specific benchmarks are reached rather than just focusing on cash and returns. Some
businesses seek to monitor when they become profitable (or has paid for itself).
Others are more focused on when a capital project will start to generate a particular
level of profit.
Capital budgeting necessitates the requirement for meticulous cash flow forecasts for
payback strategies. This strategy needs a little more scheduling attention since any
variation in an estimate from one year to the next may significantly affect when a
firm may meet a payback measure. If a business wishes to combine capital budget
approaches, it may also combine the payback method with the discounted cash flow
analysis method.
8. Methods used in capital budgeting
3. Throughput analysis:
Throughput analysis-based solutions for capital planning represent a vastly
different approach. Throughput techniques examine revenue and expenditures
across the board, not just for particular initiatives. Operational or non-capital
budgeting can also employ throughput analysis through cost accounting.
Throughput techniques include deducting variable costs from a company's
revenue. By using this technique, it is possible to determine how much of each
sale's profit may be attributed to fixed expenses. Any throughput is retained by
the firm as equity once all fixed costs have been covered by the business.
9. Net Present Value (NPV)
Net present value (NPV) is used to evaluate the current worth of a future stream of
payments from a company, project, or investment.
You must predict the timing and size of future cash flows in order to determine NPV,
and you must choose a discount rate that is equal to the minimum rate of return.
Your cost of capital or the rewards offered by substitute investments with equivalent
risk may be reflected in the discount rate.
Positive NPV indicates that the rate of return on a project or investment will be
higher than the discount rate.
10. Net Present Value (NPV) formula
If there’s one cash flow from a project that will be paid one year
from now, then the calculation for the NPV of the project is as
follows:
11. Positive NPV vs. Negative NPV
A project or venture has a positive net present value (NPV) if its expected
profits, discounted for their present value, are more than their
discounted expected expenses. An investment with a positive NPV is
presumed to be successful.
A negative NPV investment will result in a net loss.
The net present value rule, which states that only investments with a
positive NPV should be taken into consideration, is based on this idea.
12. Pros and cons of NPV
PROS CONS
Takes into account the temporal worth of money. strongly depends on inputs, predictions, and
estimations in the long run.
Incorporates discounted cash flow utilising the
cost of capital for the organisation
does not take project size or return on investment
into account (ROI)
Returns a single amount with a comparatively
clear meaning.
Manual calculation may be challenging,
particularly for projects with long cash flow
histories.
Straightforward to calculate using spreadsheets or
financial calculators
It is motivated by numerical inputs and ignores
non-financial indicators
13. Example of NPV
Consider a business that decides to purchase $1 million worth of equipment that will provide
$25,000 a month in income for the next five years. As an alternative, the business might put that
money into assets with an 8% predicted yearly return. Management regards the equipment and
securities as equivalent investment risks.
For estimating the NPV of an equipment investment, there are two essential steps:
Step 1 - NPV of the Initial Investment
Because the equipment is paid for up front, this is the first cash out flow considered in the
computation. There is no need to deduct the $1 million instant cost because there is no time to
account for.
14. Example of NPV
Step 2: NPV of Future Cash Flows
Determine the period count (t): Since the equipment is predicted to provide monthly cash flow for five years, the
calculation will take into account 60 periods once the number of years of cash flows is multiplied by the number
of months in a year.
The discount rate (i) is: The estimated return on the alternative investment is 8% annually. The annual discount
rate must be converted into a periodic, or monthly, compound rate since the equipment produces a monthly
stream of cash flows. We calculate the periodic monthly compound rate to be 0.64% using the formula below.
Periodic rate = ((1 + 0.08)1/12) – 1 = 0.64%
Assume that the first payment is made exactly one month after the equipment purchase and that the monthly
cash flows are earned at the end of the month. Given that this payment is in the future, the time value of money
must be taken into account. This computation may be done quickly and easily by an investor using a spreadsheet
or calculator. The first five payments are shown in the table below to explain the idea.
16. Example of NPV
The present value of all 60 potential future cash flows, less the $1 million
investment, is equal to the total computation of the present value. If the equipment
was anticipated to retain any value at the end of its useful life, the computation may
be more challenging; nevertheless, in this case, it is presumed to be worthless.
That formula can be simplified to the following calculation:
NPV = −$1,000,000 + $1,242,322.82 = $242,322.82
In this case, the NPV is positive; the equipment should be purchased. If the present
value of these cash flows had been negative because the discount rate was larger or
the net cash flows were smaller, then the investment would not have made sense.
17. Profitability Index (PI)
The profitability index (PI) quantifies the allure of a project or investment.
The present value of anticipated future cash flows is divided by the project's original
investment to determine the PI.
A PI of at least 1.0 is considered to be a decent investment, with higher levels indicating
more alluring enterprises.
Only projects with the greatest PIs should be completed when there are capital limits and
projects that cannot be done simultaneously.
18. Profitability Index (PI) formula
The profitability index can be computed using the following ratio:
19. Profitability Index (PI) interpretation
Calculations larger than 1.0 are ordered based on the top calculation
when just utilising the profitability indicator. The project with the
greatest profitability index should be chosen when funds are limited and
projects are mutually incompatible since it will make the best use of the
available resources.
The benefit-cost ratio is another name for the profitability index because
of this. Even if some projects have larger net present values, those
projects could not be chosen because they don't have the greatest
profitability index or the best use of the company's resources.
20. Advantages of Profitability Index (PI)
The profitability index takes into consideration the time value of money:
Because of the possibility of generating interest, money now is worth more than
the same amount in the future. Compared to merely looking at the overall
predicted cash flows, this makes it a more accurate indicator of investment
attractiveness.
It makes it possible to compare projects with various lifespans: The profitability
index, which considers the present value of future cash flows rather than just
the total predicted cash flows, may be used to evaluate projects with various
lifespans.
Making choices when facing financial restrictions is facilitated by: The
profitability index can be used to decide which initiatives to undertake first
when a business has limited resources.
21. Disadvantages of Profitability Index
(PI)
The profitability index only takes into account the initial investment
necessary for a project and ignores any current or potential future
investments. Because of this, comparing projects with various
investment requirements can be challenging.
A large project with lower profit margins may have a lower profitability
index than a smaller project with better profit margins since the
profitability index does not account for the size of the project.
The profitability index depends on precise future cash flow and discount
rate forecasts, both of which can be challenging to anticipate with
precision. The calculated probability index could not effectively represent
how appealing the idea is if the underlying assumptions were erroneous.
22. Example of Profitability Index (PI)
Imagine that a business is debating between expanding an existing plant
or creating a new one. With a 10% discount rate, the factory expansion
project is anticipated to cost $1 million and provide cash flows of
$200,000 year for the following five years. With a 10% discount rate, the
new manufacturing project is anticipated to cost $2 million and provide
$300,000 in cash flows annually over the following five years.
The following method would be used to determine the present value of
the future cash flows in order to get the profitability index for the
industrial expansion project:
PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + ... + CFn / (1 + r)^n
23. Example of Profitability Index (PI)
Where PV is the present value, CF is the cash flow in a given year, r is the discount rate, and n
is the number of years.
Plugging in the values for this example, we get:
PV = $200,000 / (1 + 0.10)^1 + $200,000 / (1 + 0.10)^2 + ... + $200,000 / (1 + 0.10)^5
PV = $750,319
The profitability index for the factory expansion project is then calculated as:
PI = PV / Initial Investment
PI = $750,319 / $1,000,000
PI = 0.75
24. Example of Profitability Index (PI)
To calculate the profitability index for the new factory project, the present value of
the future cash flows would be calculated using the same formula:
PV = $300,000 / (1 + 0.10)^1 + $300,000 / (1 + 0.10)^2 + ... + $300,000 / (1 + 0.10)^5
PV = $1,125,479
The profitability index for the new factory project is then calculated as:
PI = PV / Initial Investment
PI = $1,125,479/ $2,000,000
PI = 0.56
25. Payback period
The payback period is the time required to recoup the cost of an
investment or the amount of time required for an investor to break even.
Longer payback times are unfavourable, whereas shorter paybacks make
investments more appealing.
Divide the investment amount by the yearly cash flow to determine the
payback time.
The payback period is a factor that account and fund managers consider
when deciding whether to proceed with an investment.
The payback period's disregard for the time worth of money is one of its
drawbacks.
26. Payback period formula
Investors, financial experts, and businesses frequently utilise the
payback time as a way to estimate investment returns. It aids in
calculating how long it takes for an investment's original
expenditures to be recouped. Before making any judgements, this
statistic is helpful, especially when a quick assessment of a
potential investment initiative is required.
You can figure out the payback period by using the following
formula:
Payback period = Cost of investment / Average annual cash flow
27. Payback period and Capital budgeting
The computation of the payback period has one flaw. In contrast to other capital budgeting
strategies, the payback period disregards the time value of money (TVM). This is the notion that
the earning potential of the existing money makes it more valuable today than it would be
tomorrow.
The TVM is taken into account by the majority of capital budgeting methods, including net
present value (NPV), internal rate of return (IRR), and discounted cash flow. So, if you give an
investor a payment tomorrow, it must also account for an opportunity cost. This potential cost is
given a value by the TVM concept.
The payback period is calculated by counting the number of years it takes to recoup the money
invested, disregarding the time value of money. The payback time, for instance, is five years if it
takes five years to recoup the cost of an investment.
It disregards the entire profitability of an investment. As a result, NPV is a popular tool used by
managers and investors when making investment choices. The NPV is the difference between
the current value of cash flowing out over time and the present value of cash coming in.
28. Example of payback period
Here is a fictitious illustration of how the payback period functions. Let's say Company A invests
$1 million in a project that will save it $250,000 annually. We arrive at a payback time of four
years for this investment if we divide $1 million by $250,000.
Consider another project that will cost $200,000 and generate $2 million in additional revenue
for the firm over the course of 20 years, but with no corresponding financial savings. The
second project can undoubtedly provide twice as much revenue for the business, but how long
will it take for the investment to be returned?
Divide $100,000 by $200,000 to get the answer, which is two years. The second project's
payback period will be shorter, and the company's profits potential will be higher. If the
corporation intends to prioritise recouping its capital expenditure as soon as feasible, the
second project is a better investment based purely on the payback period technique.
29. Internal Rate of Return (IRR)
The predicted yearly rate of growth from an investment is known as the internal rate
of return (IRR).
Similar to how net present value (NPV) is determined, IRR does so by setting NPV to
zero.
The ultimate objective of IRR is to determine the rate of discount, which brings the
initial net cash expenditure for the investment's investment to the present value of
the total of its initial nominal yearly cash inflows.
IRR is the best tool for examining capital budgeting projects in order to comprehend
and contrast probable annual rates of return over time.
IRR may assist investors in calculating the investment return of various assets, in
addition to being utilised by businesses to choose which capital projects to deploy.
31. Formula and calculation of IRR
How to Determine IRR
1. To find the discount rate, or IRR, one would use the formula, setting NPV
equal to zero.
2. Due to the fact that it represents an outflow, the initial investment is
always negative.
3. Depending on the projected future benefits or capital infusion needs,
each succeeding cash flow may be either positive or negative.
4. IRR must be computed iteratively by trial and error or by utilising
software designed to calculate IRR due to the nature of the formula,
which makes it difficult to calculate analytically (e.g., using Excel).
32. IRR vs. Compound Annual Growth Rate
The CAGR calculates the yearly return on investment over time. The
CAGR normally employs simply a beginning and ending value to
generate an expected annual rate of return, but the IRR typically
includes both.
IRR differs in that it takes into account numerous periodic cash
flows, reflecting the fact that when it comes to investments, cash
inflows and outflows frequently happen continuously. Another
difference is that CAGR is straightforward enough to be computed.
33. IRR vs. ROI
When deciding how much money to allocate for capital expenditures, businesses and analysts
may additionally consider the return on investment (ROI). ROI informs a potential investor of
the investment's overall growth from beginning to end. The rate of return is not yearly. The
yearly growth rate is disclosed to the investor through the IRR. Over the course of a year, the
two values would typically be the same, but not for longer periods of time.
ROI is the overall percentage growth or decline of an investment. It is determined by dividing
the initial value by the difference between the present or anticipated future value and the
beginning value, then multiplying the result by 100.
For almost every activity where an investment has been made and an outcome can be
quantified, ROI values may be generated. However, ROI may not always be the most beneficial
for long time periods. It has limits in capital planning as well because the emphasis there is
frequently on recurring cash flows and returns.
34. Example of IRR
Assume a company is reviewing two projects. Management must decide whether to move forward with
one, both, or neither. Its cost of capital is 10%. The cash flow patterns for each are as follows:
Project A ($) Project B ($)
Initial outlay 5000 2000
Year 1 1700 400
Year 2 1900 700
Year 3 1600 500
Year 4 1500 400
Year 5 700 300
35. Example of IRR
The company must calculate the IRR for each project. Initial outlay (period = 0) will be negative.
Solving for IRR is an iterative process using the following equation:
$0 = Σ CFt ÷ (1 + IRR)t
where:
CF = net cash flow
IRR = internal rate of return
t = period (from 0 to last period)
-or-
$0 = (initial outlay * −1) + CF1 ÷ (1 + IRR)1 + CF2 ÷ (1 + IRR)2 + ... + CFX ÷ (1 + IRR)X
Using the above examples, the company can calculate IRR for each project as:
36. Example of IRR
IRR Project A
$0 = (−$5,000) + $1,700 ÷ (1 + IRR)1 + $1,900 ÷ (1 + IRR)2 + $1,600 ÷ (1 + IRR)3 + $1,500 ÷ (1 + IRR)4
+ $700 ÷ (1 + IRR)5
IRR Project A = 16.61 %
IRR Project B
$0 = (−$2,000) + $400 ÷ (1 + IRR)1 + $700 ÷ (1 + IRR)2 + $500 ÷ (1 + IRR)3 + $400 ÷ (1 + IRR)4 + $300
÷ (1 + IRR)5
IRR Project B = 5.23 %
Given that the company’s cost of capital is 10%, management should proceed with Project A and
reject Project B.
