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Capital budgeting is the process of analyzing and ranking proposed projects to
determine which ones are deserving of an investment. The result is intended to be a
high return on invested funds. There are three general methods for deciding which
proposed projects should be ranked higher than other projects, which are (in declining
order of preference):
1. Throughput analysis. Determines the impact of an investment on the throughput of an
entire system.
2. Discounted cash flow analysis. Uses a discount rate to determine the present value of
all cash flows related to a proposed project. Tends to create improvements on a
localized basis, rather than for the entire system, and is subject to incorrect results if
cash flow forecasts are incorrect.
3. Payback analysis. Calculates how fast you can earn back your investment; is more of
a measure of risk reduction than of return on investment.
These capital budgeting decision points are outlined in the following sections.
Throughput Analysis
Under throughput analysis, the key concept is that an entire company acts as a single
system, which generates a profit. Under this concept, capital budgeting revolves
around the following logic:
1. Nearly all of the costs of the production system do not vary with individual sales; that
is, nearly every cost is an operating expense; therefore,
2. You need to maximize the throughput of the entire system in order to pay for the
operating expense; and
3. The only way to increase throughput is to maximize the throughput passing through
the bottleneck operation.
Consequently, you should give primary consideration to those capital budgeting
proposals that favorably impact the throughput passing through
the bottleneck operation.
This does not mean that all other capital budgeting proposals will be rejected, since
there are a multitude of possible investments that can reduce costs elsewhere in a
company, and which are therefore worthy of consideration. However, throughput is
more important than cost reduction, since throughput has no theoretical upper limit,
whereas costs can only be reduced to zero. Given the greater ultimate impact on
profits of throughput over cost reduction, any non-bottleneck proposal is simply not
as important.
Discounted Cash Flow Analysis
Any capital investment involves an initial cash outflow to pay for it, followed by a
mix of cash inflows in the form of revenue, or a decline in existing cash flows that
are caused by expenses incurred. We can lay out this information in a
spreadsheet to show all expected cash flows over the useful life of an investment,
and then apply a discount rate that reduces the cash flows to what they would be
worth at the present date. This calculation is known as net present value. Net
present value is the traditional approach to evaluating capital proposals, since it
is based on a single factor – cash flows – that can be used to judge any proposal
arriving from anywhere in a company.
For example, ABC Company is planning to acquire an asset that it expects will
yield positive cash flows for the next five years. Its cost of capital is 10%, which it
uses as the discount rate to construct the net present value of the project. The
following table shows the calculation:
Cash Flow
10% Discount Factor
Present Value
Net Present Value
The net present value of the proposed project is negative at the 10% discount rate, so
ABC should not invest in the project.
In the “10% Discount Factor” column, the factor becomes smaller for periods further
in the future, because the discounted value of cash flows are reduced as they progress
further from the present day. The discount factor can be derived from the following
Present value of a
future cash flow
Future cash flow
= --------------------------------------------------------------------------(1 + Discount rate)squared by the number of periods of
Payback Analysis
The simplest and least accurate evaluation technique is the payback method. This
approach is still heavily used, because it provides a very fast “back of the envelope”
calculation of how soon a company will earn back its investment. This means that it
provides a rough measure of how long a company will have its investment at risk,
before earning back the original amount expended. Thus, it is a rough measure of risk.
There are two ways to calculate the payback period, which are:
1. Simplified. Divide the total amount of an investment by the average resulting cash
flow. This approach can yield an incorrect assessment, because a proposal with cash
flows skewed far into the future can yield a payback period that differs substantially
from when actual payback occurs.
2. Manual calculation. Manually deduct the forecasted positive cash flows from the
initial investment amount, from Year 1 forward, until the investment is paid back.
This method is slower to calculate, but ensures a higher degree of accuracy.
For example, ABC Company has received a proposal from a manager, asking to spend
$1,500,000 on equipment that will result in cash inflows in accordance with the
following table:
Cash Flow
The total cash flows over the five-year period are projected to be $2,000,000, which is
an average of $400,000 per year. When divided into the $1,500,000 original
investment, this results in a payback period of 3.75 years. However, the briefest
perusal of the projected cash flows reveals that the flows are heavily weighted toward
the far end of the time period, so the results of this calculation cannot be correct.
Instead, the cost accountant runs the calculation year by year, deducting the cash
flows in each successive year from the remaining investment. The results of this
calculation are:
Cash Flow
Net Invested Cash
The table indicates that the real payback period is located somewhere between Year 4
and Year 5. There is $400,000 of investment yet to be paid back at the end of Year 4,
and there is $900,000 of cash flow projected for Year 5. The cost accountant assumes
the same monthly amount of cash flow in Year 5, which means that he can estimate
final payback as being just short of 4.5 years.
The payback method is not overly accurate, does not provide any estimate of how
profitable a project may be, and does not take account of the time value of money.
Nonetheless, its extreme simplicity makes it a perennial favorite in many companies.
Definition of Capital Budgeting
Capital budgeting is the process that a business uses to determine which proposed fixed asset
purchases it should accept, and which should be declined. This process is used to create a
quantitative view of each proposed fixed asset investment, thereby giving a rational basis for
making a judgment.
Capital Budgeting Methods
There are a number of methods commonly used to evaluate fixed assets under a formal
capital budgeting system. The more important ones are:
Net present value analysis. Identify the net change in cash flows associated with a fixed asset
purchase, and discount them to their present value. Then compare all proposed projects with
positive net present values, and accept those with the highest net present values until funds
run out.
Constraint analysis. Identify the bottleneck machine or work center in a production
environment and invest in those fixed assets that maximize the utilization of the bottleneck
operation. Under this approach, you are less likely to invest in areas downstream from the
bottleneck operation (since they are constrained by the bottleneck operation) and more likely
to invest upstream from the bottleneck (since additional capacity there makes it easier to
keep the bottleneck fully supplied with inventory).
Payback period. Determine the period required to generate sufficient cash flow from a
project to pay for the initial investment in it. This is essentially a risk measure, for the focus is
on the period of time that the investment is at risk of not being returned to the company.
Avoidance analysis. Determine whether increased maintenance can be used to prolong the
life of existing assets, rather than investing in replacement assets. This analysis can
substantially reduce a company's total investment in fixed assets.
The Importance of Capital Budgeting
The amount of cash involved in a fixed asset investment may be so large that it could lead to
the bankruptcy of a firm if the investment fails. Consequently, capital budgeting is a
mandatory activity for larger fixed asset proposals. This is less of an issue for smaller
investments; in these latter cases, it is better to streamline the capital budgeting process
substantially, so that the focus is more on getting the investments made as expeditiously as
possible; by doing so, the operations of profit centers are not hindered by the analysis of their
fixed asset proposals.
Capital Budgeting
Capital budgeting (or investment appraisal) is the process of determining the viability to longterm investments on purchase or replacement of property plant and equipment, new product
line or other projects.
Capital budgeting consists of various techniques used by managers such as:
Payback Period
Discounted Payback Period
Net Present Value
Accounting Rate of Return
Internal Rate of Return
6. Profitability Index
All of the above techniques are based on the comparison of cash inflows and outflow of a
project however they are substantially different in their approach.
A brief introduction to the above methods is given below:
1. Payback Period measures the time in which the initial cash flow is returned by the
project. Cash flows are not discounted. Lower payback period is preferred.
2. Net Present Value (NPV) is equal to initial cash outflow less sum of discounted cash
inflows. Higher NPV is preferred and an investment is only viable if its NPV is positive.
3. Accounting Rate of Return (ARR) is the profitability of the project calculated as
projected total net income divided by initial or average investment. Net income is not
4. Internal Rate of Return (IRR) is the discount rate at which net present value of the
project becomes zero. Higher IRR should be preferred.
5. Profitability Index (PI) is the ratio of present value of future cash flows of a project to
initial investment required for the project.
The above techniques are explained in detail in next pages.
1. Net Present Value (NPV)
Net present value (NPV) of a project is the potential change in an investor's wealth
caused by that project while time value of money is being accounted for. It equals
the present value of net cash inflows generated by a project less the initial
investment on the project. It is one of the most reliable measures used in capital
budgeting because it accounts for time value of money by using discounted cash
flows in the calculation.
Net present value calculations take the following two inputs:
1. Projected net cash flows in successive periods from the project.
2. A target rate of return i.e. the hurdle rate.
Net cash flow equals total cash inflow during a period, including salvage value if
any, less cash outflows from the project during the period.
Hurdle rate is the rate used to discount the net cash inflows. Weighted average
cost of capital (WACC)is the most commonly used hurdle rate.
Calculation Methods and Formulas
The first step involved in the calculation of NPV is the estimation of net cash flows
from the project over its life. The second step is to discount those cash flows at
the hurdle rate.
The net cash flows may be even (i.e. equal cash flows in different periods) or
uneven (i.e. different cash flows in different periods). When they are even, present
value can be easily calculated by using the formula for present value of annuity.
However, if they are uneven, we need to calculate the present value of each
individual net cash inflow separately.
Once we have the total present value of all project cash flows, we subtract the
initial investment on the project from the total present value of inflows to arrive at
net present value.
Thus we have the following two formulas for the calculation of NPV:
When cash inflows are even:
1 − (1 + i)-n
− Initial Investment
the above formula,
is the net cash inflow expected to be received in each period;
is the required rate of return per period;
are the number of periods during which the project is expected to operate and
generate cash inflows.
When cash inflows are uneven:
(1 + i)1
(1 + i)2
+ ...
(1 + i)3
− Initial Investment
is the target rate of return per period;
is the net cash inflow during the first period;
is the net cash inflow during the second period;
is the net cash inflow during the third period, and so on ...
Decision Rule
In case of standalone projects, accept a project only if its NPV is positive, reject it
if its NPV is negative and stay indifferent between accepting or rejecting if NPV is
In case of mutually exclusive projects (i.e. competing projects), accept the project
with higher NPV.
Example 1: Even Cash Inflows: Calculate the net present value of a project which
requires an initial investment of $243,000 and it is expected to generate a cash
inflow of $50,000 each month for 12 months. Assume that the salvage value of
the project is zero. The target rate of return is 12% per annum.
We have,
Initial Investment = $243,000
Net Cash Inflow per Period = $50,000
Number of Periods = 12
Discount Rate per Period = 12% ÷ 12 = 1%
Net Present Value
$562,754 − $243,000 = $319,754
Example 2: Uneven Cash Inflows: An initial investment of $8,320 thousand on
plant and machinery is expected to generate cash inflows of $3,411 thousand,
$4,070 thousand, $5,824 thousand and $2,065 thousand at the end of first,
second, third and fourth year respectively. At the end of the fourth year, the
machinery will be sold for $900 thousand. Calculate the net present value of the
investment if the discount rate is 18%. Round your answer to nearest thousand
PV Factors:
Year 1 = 1 ÷ (1 + 18%)^1 ≈ 0.8475
Year 2 = 1 ÷ (1 + 18%)^2 ≈ 0.7182
Year 3 = 1 ÷ (1 + 18%)^3 ≈ 0.6086
Year 4 = 1 ÷ (1 + 18%)^4 ≈ 0.5158
The rest of the calculation is summarized below:
Net Cash Inflow
Salvage Value
Total Cash Inflow
× Present Value Factor
Present Value of Cash Flows $2,890.68
Total PV of Cash Inflows
− Initial Investment
− 8,320
Net Present Value
$ 2,568 thousand
Or NVP =
(1.18) 1
(1.18) 2
(1.18) 3
(1.18) 4
=$10,888 - $8320 = $2,568
Strengths and Weaknesses of NPV
Net present value accounts for time value of money which makes it a sounder
approach than other investment appraisal techniques which do not discount future
cash flows such payback period and accounting rate of return.
Net present value is even better than some other discounted cash flows
techniques such as IRR. In situations where IRR and NPV give conflicting
decisions, NPV decision should be preferred.
NPV is after all an estimation. It is sensitive to changes in estimates for future
cash flows, salvage value and the cost of capital.
Net present value does not take into account the size of the project. For example,
say Project A requires initial investment of $4 million to generate NPV of $1 million
while a competing Project B requires $2 million investment to generate an NPV of
$0.8 million. If we base our decision on NPV alone, we will prefer Project A
because it has higher NPV, but Project B has generated more shareholders’ wealth
per dollar of initial investment ($0.8 million/$2 million vs $1 million/$4 million).
2. (Simple) Payback Period
Payback period is the time in which the initial cash outflow of an investment is expected to be
recovered from the cash inflows generated by the investment. It is one of the simplest
investment appraisal techniques.
The formula to calculate payback period of a project depends on whether the cash flow per
period from the project is even or uneven. In case they are even, the formula to calculate
payback period is:
Payback Period =
Initial Investment
Cash Inflow per Period
When cash inflows are uneven, we need to calculate the cumulative net cash flow for each
period and then use the following formula for payback period:
Payback Period = A + B
In the above formula,
is the last period with a negative cumulative cash flow;
is the absolute value of cumulative cash flow at the end of the period A;
is the total cash flow during the period after A
Both of the above situations are applied in the following examples.
Decision Rule
Accept the project only if its payback period is LESS than the target payback period.
Example 1: Even Cash Flows
Company C is planning to undertake a project requiring initial investment of $105 million. The
project is expected to generate $25 million per year for 7 years. Calculate the payback period
of the project.
Payback Period = Initial Investment ÷ Annual Cash Flow = $105M ÷ $25M = 4.2 years
Example 2: Uneven Cash Flows
Company C is planning to undertake another project requiring initial investment of $50
million and is expected to generate $10 million in Year 1, $13 million in Year 2, $16 million in
year 3, $19 million in Year 4 and $22 million in Year 5. Calculate the payback value of the
(cash flows in millions)
Cash Flow
Cumulative Cash Flow
Payback Period
= 3 + (|-$11M| ÷ $19M)
= 3 + ($11M ÷ $19M)
≈ 3 + 0.58
≈ 3.58 years
Advantages and Disadvantages
Advantages of payback period are:
1. Payback period is very simple to calculate.
2. It can be a measure of risk inherent in a project. Since cash flows that occur later in a
project's life are considered more uncertain, payback period provides an indication of
how certain the project cash inflows are.
3. For companies facing liquidity problems, it provides a good ranking of projects that would
return money early.
Disadvantages of payback period are:
1. Payback period does not take into account the time value of money which is a serious
drawback since it can lead to wrong decisions. A variation of payback method that
attempts to remove this drawback is called discounted payback period method.
2. It does not take into account, the cash flows that occur after the payback period.
3. Discounted Payback Period
One of the major disadvantages of simple payback period is that it ignores the time value of
money. To counter this limitation, an alternative procedure called discounted payback period
may be followed, which accounts for time value of money by discounting the cash inflows of
the project.
Formulas and Calculation Procedure
In discounted payback period we have to calculate the present value of each cash inflow
taking the start of the first period as zero point. For this purpose the management has to set
a suitable discount rate. The discounted cash inflow for each period is to be calculated using
the formula:
Discounted Cash Inflow =
Actual Cash Inflow
(1 + i)n
is the discount rate;
n is the period to which the cash inflow relates.
Usually the above formula is split into two components which are actual cash inflow and
present value factor ( i.e. 1 / ( 1 + i )^n ). Thus discounted cash flow is the product of actual
cash flow and present value factor.
The rest of the procedure is similar to the calculation of simple payback period except that we
have to use the discounted cash flows as calculated above instead of actual cash flows. The
cumulative cash flow will be replaced by cumulative discounted cash flow.
Discounted Payback Period = A + B
A = Last period with a negative discounted cumulative cash flow;
B = Absolute value of discounted cumulative cash flow at the end of the period A;
C = Discounted cash flow during the period after A.
Note: In the calculation of simple payback period, we could use an alternative formula for
situations where all the cash inflows were even. That formula won't be applicable here since
it is extremely unlikely that discounted cash inflows will be even.
The calculation method is illustrated in the example below.
Decision Rule
If the discounted payback period is less that the target period, accept the project. Otherwise
An initial investment of $2,324,000 is expected to generate $600,000 per year for 6 years.
Calculate the discounted payback period of the investment if the discount rate is 11%.
Step 1: Prepare a table to calculate discounted cash flow of each period by multiplying the
actual cash flows by present value factor. Create a cumulative discounted cash flow column.
Year Cash Flow
$ −2,324,000
Present Value Factor
Discounted Cash Flow
Cash Flow
$ −2,324,000
$ −2,324,000
− 857,771
− 462,533
Step 2: Discounted Payback Period = 5 + |-106,462| / 320,785 ≈ 5.32 years
Advantages and Disadvantages
Advantage: Discounted payback period is more reliable than simple payback period since it
accounts for time value of money. It is interesting to note that if a project has negative net
present value it won't pay back the initial investment.
Disadvantage: It ignores the cash inflows from project after the payback period
4. Internal Rate of Return (IRR)
Internal rate of return (IRR) is the discount rate at which the net present value of an
investment becomes zero. In other words, IRR is the discount rate which equates the present
value of the future cash flows of an investment with the initial investment. It is one of the
several measures used for investment appraisal.
Decision Rule
A project should only be accepted if its IRR is NOT less than the target internal rate of return.
When comparing two or more mutually exclusive projects, the project having highest value of
IRR should be accepted.
IRR Calculation
The calculation of IRR is a bit complex than other capital budgeting techniques. We know that
at IRR, Net Present Value (NPV) is zero, thus:
NPV = 0; or
PV of future cash flows − Initial Investment = 0; or
+ ... − Initial Investment = 0
( 1 + r ) 1 ( 1 + r )2 ( 1 + r ) 3
r is the internal rate of return;
CF1 is the period one net cash inflow;
CF2 is the period two net cash inflow,
CF3 is the period three net cash inflow, and so on ...
But the problem is, we cannot isolate the variable r (=internal rate of return) on one side of
the above equation. However, there are alternative procedures which can be followed to find
IRR. The simplest of them is described below:
1. Guess the value of r and calculate the NPV of the project at that value.
2. If NPV is close to zero then IRR is equal to r.
3. If NPV is greater than 0 then increase r and jump to step 5.
4. If NPV is smaller than 0 then decrease r and jump to step 5.
5. Recalculate NPV using the new value of r and go back to step 2.
Find the IRR of an investment having initial cash outflow of $213,000. The cash inflows during
the first, second, third and fourth years are expected to be $65,200, $96,000, $73,100 and
$55,400 respectively.
Assume that r is 10%.
NPV at 10% discount rate = $18,372
Since NPV is greater than zero we have to increase discount rate, thus
NPV at 13% discount rate = $4,521
But it is still greater than zero we have to further increase the discount rate, thus
NPV at 14% discount rate = $204
NPV at 15% discount rate = ($3,975)
Since NPV is fairly close to zero at 14% value of r, therefore
IRR ≈ 14%
NVP = $65,200 + $96,000 + $73,100 + $55,400 - $213,000 = $18,372
NVP = $65,200 + $96,000 + $73,100 + $55,400 - $213,000 = $4,521
NVP = $65,200 + $96,000 + $73,100 + $55,400 - $213,000 = $204
NVP = $65,200 + $96,000 + $73,100 + $55,400 - $213,000 = ($3,975)
5. Accounting Rate of Return (ARR)
Accounting rate of return (also known as simple rate of return) is the ratio of
estimated accounting profit of a project to the average investment made in the
project. ARR is used in investment appraisal.
Accounting Rate of Return is calculated using the following formula:
ARR = Average Accounting Profit
Average Investment
Average accounting profit is the arithmetic mean of accounting income expected to
be earned during each year of the project's life time. Average investment may be
calculated as the sum of the beginning and ending book value of the project
divided by 2. Another variation of ARR formula uses initial investment instead of
average investment.
Decision Rule
Accept the project only if its ARR is equal to or greater than the required
accounting rate of return. In case of mutually exclusive projects, accept the one
with highest ARR.
Example 1: An initial investment of $130,000 is expected to generate annual cash
inflow of $32,000 for 6 years. Depreciation is allowed on the straight line basis. It
is estimated that the project will generate scrap value of $10,500 at end of the 6th
year. Calculate its accounting rate of return assuming that there are no other
expenses on the project.
Annual Depreciation = (Initial Investment − Scrap Value) ÷ Useful Life in Years
Annual Depreciation = ($130,000 − $10,500) ÷ 6 ≈ $19,917
Average Accounting Income = $32,000 − $19,917 = $12,083
Accounting Rate of Return = $12,083 ÷ $130,000 ≈ 9.3%
Example 2: Compare the following two mutually exclusive projects on the basis of
ARR. Cash flows and salvage values are in thousands of dollars. Use the straight
line depreciation method.
Project A:
Cash Outflow
Cash Inflow
Salvage Value
Project B:
Cash Outflow
Cash Inflow
Salvage Value
Project A:
Step 1: Annual Depreciation = ( 220 − 10 ) / 3 = 70
Step 2: Year
Cash Inflow
Salvage Value
Accounting Income
Step 3: Average Accounting Income = ( 21 + 60 + 45 ) / 3 = 42
Step 4: Accounting Rate of Return = 42 / 220 = 19.1%
Project B:
Step 1: Annual Depreciation = ( 198 − 18 ) / 3 = 60
Step 2: Year
Cash Inflow
Salvage Value
Accounting Income
Step 3: Average Accounting Income = ( 27 + 50 + 42 ) / 3 = = 39.666
Step 4: Accounting Rate of Return = 39.666 / 198 ≈ 20.0%
Since the ARR of the project B is higher, it is more favorable than the project A.
Advantages and Disadvantages
1. Like payback period, this method of investment appraisal is easy to calculate.
2. It recognizes the profitability factor of investment.
1. It ignores time value of money. Suppose, if we use ARR to compare two
projects having equal initial investments. The project which has higher annual
income in the latter years of its useful life may rank higher than the one
having higher annual income in the beginning years, even if the present value
of the income generated by the latter project is higher.
2. It can be calculated in different ways. Thus there is problem of consistency.
3. It uses accounting income rather than cash flow information. Thus it is not
suitable for projects which having high maintenance costs because their
viability also depends upon timely cash inflows.
6. Profitability Index
Profitability index is an investment appraisal technique calculated by dividing the
present value of future cash flows of a project by the initial investment required for
the project.
Profitability Index
= Present Value of Future Cash Flows
Initial Investment Required
1 + Net Present Value
Initial Investment Required
Profitability index is actually a modification of the net present value method. While
present value is an absolute measure (i.e. it gives as the total dollar figure for a
project), the profitability index is a relative measure (i.e. it gives as the figure as a
Decision Rule
Accept a project if the profitability index is greater than 1, stay indifferent if the
profitability index is 1 and don't accept a project if the profitability index is below
Profitability index is sometimes called benefit-cost ratio too and is useful in capital
rationing since it helps in ranking projects based on their per dollar return .
Company C is undertaking a project at a cost of $50 million which is expected to
generate future net cash flows with a present value of $65 million. Calculate the
profitability index.
Profitability Index = PV of Future Net Cash Flows / Initial Investment Required
Profitability Index = $65M / $50M = 1.3
Net Present Value = PV of Net Future Cash Flows − Initial Investment Required
Net Present Value = $65M-$50M = $15M.
The information about NPV and initial investment can be used to calculate
profitability index as follows:
Profitability Index = 1 + (Net Present Value / Initial Investment Required)
Profitability Index = 1 + $15M/$50M = 1.3
Trust in the LORD with all your heart and lean not on your own understanding; in all your ways submit to
him, and he will make your paths straight. - Proverbs 3:5-6
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