Capital Budgeting
Capital Budgeting also
known as "investment appraisal", is the planning process used to
determine whether a firm's long term investments are worth pursuing. It is
budget for major capital, or investment expenditures such as those in property,
plant, machinery and equipment, research and development projects, large
advertising campaigns, or projects of expanding business or introducing a new
product. Ideally, businesses should pursue all projects and opportunities that
enhance shareholder value. However, because the amount of capital
available at any given time for new projects is limited, management needs to
use capital budgeting techniques to determine which projects will yield the
most return over an applicable period of time. Capital budgeting is
essential in undertaking projects that require large capital expenditures and
have a significant impact on the financial performance of the firm.
Capital budgeting is very obviously a vital
activity in business. Vast sums of money can be easily wasted if the investment
turns out to be wrong or uneconomic. The subject matter is difficult to grasp
by nature of the topic covered and also because of the mathematical content
involved. However, it seeks to build on the concept of the future value of money
which may be spent now.
A capital investment project can be distinguished
from current expenditures by two features: (a) a) such projects are relatively
large, and (b) a significant period of time (more than one year) elapses
between the investment outlay and the receipt of the benefits. As a result,
most medium-sized and large organizations have developed capital budgeting as a
set of special procedures and methods for dealing with these decisions. A
systematic approach to capital budgeting implies:
a) the
formulation of long-term goals
b) the
creative search for and identification of new investment opportunities
c) classification
of projects and recognition of economically and/or statistically dependent
proposals
d) the
estimation and forecasting of current and future cash flows
e) a
suitable administrative framework capable of transferring the required
information to the decision level
f) the
controlling of expenditures and careful monitoring of crucial aspects of
project execution
g) a
set of decision rules which can differentiate acceptable from unacceptable
alternatives is required.
Investment projects may be classified under different criteria and different types of project need different approaches in capital budgeting. For example,
a)
If classified by project size: Small projects may be
approved by departmental managers; more careful analysis and Board of
Directors' approval is needed for large projects of, say, half a million
dollars or more.
b) If
classified by type of benefit to the firm: approaches need to be defined based
on an increase in cash flow, a decrease in risk or an indirect benefit (showers
for workers, etc).
c)
If classified by degree of dependence: the decision
variables are mutually exclusive projects (can execute project A or B, but not
both), complementary projects: taking project A increases the cash flow of
project B and substitute projects: taking project A decreases the cash flow of
project B.
d) If
classified by degree of statistical dependence; there can be Positive
dependence, Negative dependence, or Statistical independence.
e)
If classified by type of cash flow: only one change in the cash flow sign e.g.
-/++++ or +/----, etc, in Conventional cash flow but more than one change in
the cash flow sign e.g. +/-/+++ or -/+/-/++++, etc.
Often, it would be good to know what the present
value of the future investment is, or how long it will take to mature (give
returns). It could be much more profitable putting the planned investment money
in the bank and earning interest, or investing in an alternative project.
Capital budgeting helps a company in achieving
long-term goals, ensuring soundness of high volume and long-term investments,
minimizing risks and uncertainties at inception, balancing its liquidity,
profitability and value, discovering alternative investment opportunities, and
matching investment decisions with decisions in some other important aspects of
business. But the most significant point is: capital budgeting leads to finding
ways for increase in income and also, decrease in expenditure.
Capital budgeting decisions are of three types:
Accept-Reject decision: relates to
reviews of a project for accepting it (for investment) or rejecting. Usually,
if the returns expected from the investment are found higher than the cost of
capital, the project is accepted for investment. This type of capital budgeting
decision analyzes projects individually.
Mutually exclusive Project decisions:
A number of projects are simultaneously analyzed to select one and reject the
others. The process has some similarity with accept-reject decisions but in
case of accept-reject decisions any or all of the projects can be rejected
where in case of mutually exclusive Project decisions usually the best among
the comparable projects is accepted.
Capital rationing decisions: This is
a case of allocating the available (limited) funds in selective (one or at a
few) among the competing investment projects based on their ranking according
to definite capital budgeting criteria.
Issues related
to capital budgeting include consideration of prospective investment, costs
of the projects, life of the projects, cash inflows and outflows in them,
salvage value, risks, the discounting rate, and (choice of) technique/method of
evaluation.
The capital budgeting exercise is restricted
by factors like unavailability of data or lack of reliable and adequate data,
problem of measuring future risks (anticipation of the future trends), timing
of the project, problem of quantification and personal biases in evaluation. Steps in capital budgeting are:
identification of the (set of alternative) projects, estimation of cash flows,
evaluation of the alternative project proposals, selection of the project(s),
implementation of the project and continuous evaluation of the project(s) under
implementation.
Key estimation
tools used in capital budgeting:
1. Cost of fund: The amount of money paid to owners of funds collected from various sources. Cost of fund may comprise interest on a loan or part of profit to be paid in different forms. Expenditures in issue of common stocks are also considered as cost of fund. The cost of funds is an expense for both personal and business loans. The concept is pretty simple: money isn’t free! Cost of funds is the cost of borrowing money.
2. Cost of
capital is the minimum expected
return that the provider of capital plans to earn on their investment.
Investors earn profits only if the cost of capital is higher than the cost of
fund. In other words, for an investment to be worthwhile, the risk adjusted return
on capital must be greater than the cost of capital. Since capital can be both
debt and equity, cost of capital is to be estimated for both categories. The cost
of debt is relatively simple: it is the rate of interest paid and this rate
includes the risk-free rate plus a risk component, which itself incorporates a
probable rate of default (and amount of recovery given default). But the cost
of equity is more challenging to calculate as equity does not pay a set return
to its investors. The cost of equity is usually inferred by comparing
the investment to other investments with similar risk profiles to determine the
"market" cost of equity. The cost of capital is often used as the discount
rate, the rate at which projected cash flow will be discounted to give a present
value or net present value.
3. Return on investment indicates cash flow from an
investment to the investor over a specified period of time, usually a year. ROI
is a measure of investment profitability, not a measure of investment size.
While compound interest and dividend reinvestment can increase the size of the
investment (thus potentially yielding a higher dollar return to the investor), ROI is a percentage return based on
capital invested. In general, the higher the investment risk, the greater the
potential investment return, and the greater the potential investment loss.
In finance,
ROI is also known as rate of return
(ROR), rate of profit
or sometimes just return and the concept is used to represent
the ratio of money gained or lost (whether realized or unrealized) on an investment
relative to the amount of money invested. The amount of money gained or lost
may be referred to as interest, profit/loss, gain/loss, or net income/loss. The
money invested may be referred to as the asset, capital, principal, or the cost
basis of the investment. ROI is usually expressed as a percentage rather than a
fraction. ROI may take the form of profit, interest, dividends, or capital
gain/loss and ROI in stocks is calculated as
(a)
dividend
income + capital gain, or
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ROI is a measure of cash generated by or lost due to the investment. It measures the cash flow or income stream from the investment to the investor, relative to the amount invested.
Different forms of ROI include IRR the discoount rate that makes the NPV =0) and annual and annualized returns (not annual or a single-period return but multi-period, geometric average return for a year).
ROI ratio is one of the profitability ratios used by financial analysts compare a company’s profitability over time
or compare profitability between companies (the other profitbility
ratios are Gross Profit Margin, Operating Profit Margin, Dividend yield, Net
profit margin, Return on equity, and Return on assets]. During capital
budgeting, companies compare the rates of return of different projects to
select which projects to pursue in order to generate maximum return or wealth
for the company's stockholders. Companies do so by considering the average rate
of return, payback period, net present value, profitability index, and internal
rate of return for various projects.
4. Discounting rate is
the rate used for converting the future cash flows in present values A firm's weighted
average cost of capital (after tax) is often used as the discount rate, but
many people believe that it is appropriate to use higher discount rates to
adjust for risk for riskier projects or other factors like reflecting the yield
curve premium for long-term debts. Another approach to choosing the discount
rate factor is to decide the rate which the capital needed for the project
could return if invested in an alternative venture. Related to this concept is
to use the firm's Reinvestment Rate, which can be defined as the rate of return
for the firm's investments on average. The reinvestment rate reflects opportunity
cost of investment, rather than the possibly lower cost of capital.
To some extent, the selection of the discount rate is
dependent on the use to which it will be put. For some professional investors,
their investment funds are committed to target a specified rate of return. In
such cases, that rate of return should be selected as the discount rate for the
NPV calculation. In this way, a direct comparison can be made between the
profitability of the project and the desired rate of return.
5. Cash inflows and outflows Cash outflows
are investments (cash expenditures) made in the project at different times and
outflows in different heads are different. They are also different in the same
head at different times. Cash inflows are the money received by the company as
profits, capital gains, realization of bad debts etc.
6. Opportunity cost or economic
opportunity loss is the value of the next best alternative forgone as
the result of making a decision.
Opportunity cost analysis is an important part of a company's decision-making
processes but is not treated as an actual cost in any financial statement. The
next best thing that a person can engage in is referred to as the opportunity
cost of doing the best thing and ignoring the next best thing to be done.
When applied
in finance, opportunity cost implies the choice between desirable, yet mutually
exclusive investment opportunities. In economics it has been described as
expressing "the basic relationship between scarcity and choice." The
notion of opportunity cost plays a crucial part in ensuring that scarce
resources are used efficiently. Opportunity costs are not restricted to
monetary or financial costs only. They apply to the real cost of output forgone,
lost time, swag, pleasure or any other benefit that provides utility should
also be considered opportunity costs.
The real value of capital
budgeting is to rank projects. Most organizations have many projects that could
potentially be financially rewarding. Once it has been determined that a
particular project has exceeded its hurdle, then it should be ranked against
peer projects (e.g. - highest profitability index to lowest profitability
index). The highest ranking projects should be implemented until the budgeted
capital has been expended.
Criteria for Capital Budgeting Decisions
Potentially, there is a wide array of criteria for
selecting projects. Some shareholders may want the firm to select projects that
will show immediate surges in cash inflow, others may want to emphasize
long-term growth with little importance on short-term performance. Viewed in
this way, it would be quite difficult to satisfy the differing interests of all
the shareholders. Fortunately, there is a solution.
The goal of the firm is to maximize present shareholder
value. This goal implies that projects
should be undertaken that result in a positive net present value,
that is, the present value of the expected cash inflow less the present value
of the required capital expenditures. Using net present value (NPV) as a
measure, capital budgeting involves selecting those projects that increase the
value of the firm because they have a positive NPV. The timing and growth rate
of the incoming cash flow is important only to the extent of its impact on NPV.
Using NPV as the criterion by which to select projects
assumes efficient capital markets so that the firm has access to whatever
capital is needed to pursue the positive NPV projects. In situations where this
is not the case, the capital rationing and the capital budgeting process
becomes more complex.
Note that it is not the responsibility of the firm to
decide whether to please particular groups of shareholders who prefer longer or
shorter term results. Once the firm has selected the projects to maximize its
net present value, it is up to the individual shareholders to use the capital
markets to borrow or lend in order to move the exact timing of their own cash
inflows forward or backward. This idea is crucial in the principal-agent
relationship that exists between shareholders and corporate managers. Even
though each may have their own individual preferences, the common goal is that
of maximizing the present value of the corporation.
Alternative Methods of Capital Budgeting
Popular methods of capital budgeting
include (a) Accounting Rate of Return (b) Payback Period, (c) Net Present Value
(NPV), (d) Internal Rate of Return (IRR), and (d) Profitability Index
The Accounting Rate of Return (ARR)
The ARR method (also called the return on capital employed
(ROCE) or the return on investment (ROI) method) of appraising a capital
project is to estimate the accounting rate of return that the project should
yield. If it exceeds a target rate of return, the project will be undertaken.
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Average Capital is estimated as
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Example:
A project has an initial outlay of Tk 50,000 and the
salvage value is Tk 10,000. The pre-tax and depreciation incomes from the
project during the years 1 to 5 are Tk 10,000, 12,000, 14,000, 16,000 and
20,000 respectively. Calculate the ARR of the project if tax rate is assumed
50% and depreciation is calculated on a straight line method.
Year
|
1
|
2
|
3
|
4
|
5
|
Average
|
The
pre-tax and depreciation income
Less Depreciation*
|
10,000
8000
|
12,000
8000
|
14,000
8000
|
16,000
8000
|
20,000
8000
|
14,400
8,000
|
Pre-tax
net income
|
2000
|
4000
|
6000
|
8000
|
12000
|
6,400
|
Les tax (@50%)
|
1000
|
2000
|
3000
|
4000
|
6000
|
3,200
|
After
tax net income
|
1000
|
2000
|
3000
|
4000
|
6000
|
3,200**
|
*Depreciation:
(Initial outlay – Salvage value) ÷ 5 = (50,000 – 10,000) ÷ 5 = 8000 each year
**Average
Annual net Profit = 3,200
Average Capital
|
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Disadvantages of ARR
·
It does not take account of the timing of the profits from an investment.
· It implicitly assumes stable cash receipts
over time.
· It is based on accounting profits and not
cash flows. Accounting profits are subject to a number of different accounting
treatments.
· It is a relative measure rather than an
absolute measure and hence takes no account of the size of the investment.
· It takes no account of the length of the
project.
· it ignores the time value of money.
Payback
Period
Payback period measures the time required for the
cash inflows to equal the original outlay. It measures risk, not return. When
exactly do we get our money back, when does our project break-even. Salvage
value is not taken into account in calculating payback period. The calculation
is pretty simple:
Payback Period = C/A, where
C = Net cash outlay and A = Annual cash inflow. For example, if a project
having an initial investment of Tk 10 million and the annual return in next 8
years is expected to be Tk 2 million, the payback period is 10/2
= 4 years.
But inflows are usually not equal in all years. In
that case cumulative totals for successive years are calculated until the sum
equals the investment.
Year
|
Cash flow
|
Cumulative
inflows
|
0
|
– 100,000
|
-100,000
|
1
|
+ 15,000
|
+
15,000
|
2
|
+ 20,000
|
+
35,000
|
3
|
+ 20,000
|
+
55,000
|
4
|
+25,000
|
+
80,000
|
5
|
+25,000
|
+
105,000
|
So the break-even is
reached sometime after the 4th and before the end of the 5th year.
But, exactly when? The answer is: find the amount yet to recover after the 4th
year and divide it by the amount recovered in the 5th year to get
the fraction of a year needed to recover the remainder. Add this fraction with
4 years to get the total time required.
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When deciding between two or more competing
projects, the usual decision is to accept the one with the shortest payback.
The company might have a target payback, and so it would reject a capital
project unless its payback period were less than a certain number of years.
Advantage of the payback method:
Payback can be important - long payback means capital tied up and high
investment risk; The method involves a quick, simple calculation; it is an
easily understood concept.
Disadvantages
of the payback method:
· It ignores the timing of cash flows within
the payback period, the cash flows after the end of payback period and
therefore the total project return.
·
It ignores the time value of money. This means that it does not take into
account the fact that $1 today is worth more than $1 in one year's time. An
investor who has $1 today can either consume it immediately or alternatively
can invest it at the prevailing interest rate, say 30%, to get a return of
$1.30 in a year's time.
·
It is unable to distinguish between projects with the same payback period.
·
It may lead to excessive investment in short-term projects.
Discounted
Payback - is almost the same as payback, but before you figure it, you
first discount your cash flows. You reduce the future payments by your cost
of capital. Why? Because it is money you will get in the future, and will be
less valuable than money today. (See Time Value of Money if you don't
understand). For this example, let's say the cost of capital is 10%.
Year
|
Cash flow
|
Discounted cash flow | Running Total |
0
|
– 15,000
|
-15,000 | -15,000 |
1
|
+ 7,000
|
6,363 | -8,637 |
2
|
+ 6,000
|
4,959 | -3,678 |
3
|
+ 3,000
|
2,254 | -1,424 |
4
|
+ 2,000
|
1,366 | -58 |
5
|
+ 1,000
|
621 | 563 |
| Negative Balance/Cash flow from the Break Even Year | = | When in the final year we break even |
| -58 / 621 | = | .093 |
So using the Discounted Payback Method we break even after 4.093 years.
The payback and ARR methods in practice
Despite the limitations of the payback method, it is the method most
widely used in practice. There are a number of reasons for this:
· It is a particularly useful approach for
ranking projects where a firm faces liquidity constraints and requires fast
repayment of investments.
·
It is appropriate in situations where risky investments are made in uncertain
markets that are subject to fast design and product changes or where future
cash flows are particularly difficult to predict.
·
The method is often used in conjunction with NPV or IRR method and acts as a
first screening device to identify projects which are worthy of further
investigation.
·
it is easily understood by all levels of management.
·
It provides an important summary method: how quickly will the initial
investment be recouped?
DISCOUNTED
CASH FLOW METHOD
The traditional
methods like ARR and Payback period do not consider the time value of money,
which is limitation. This limitation is overcome by discounted cash flow method
which in fact is not one method but comprises three major methods: (a) The Net
Present Value, (b) Internal Rate of Return and (c) Profitability Index.
Example DCF
To show how discounted cash flow analysis is performed,
consider the following simplified example:
John Doe buys a house for $100,000. Three years later,
he expects to be able to sell this house for $150,000.
Simple subtraction suggests that the value of his
profit on such a transaction would be $150,000 − $100,000 = $50,000, or 50%. If
that $50,000 is amortized over the three years, his implied annual return
(known as the internal rate of return) would be about 14.5%. Looking at those
figures, he might be justified in thinking that the purchase looked like a good
idea since, 1.1453 x 100000 = 150000 approximately.
However, since three years have passed between the
purchase and the sale, any cash flow from the sale must be discounted
accordingly. At the time John Doe buys the house, the 3-year US Treasury Note
rate is 5% per annum. Treasury Notes are generally considered to be inherently
less risky than real estate, since the value of the Note is guaranteed by the
US Government and there is a liquid market for the purchase and sale of T-Notes. If
he hadn't put his money into buying the house, he could have invested it in the
relatively safe T-Notes instead. This 5% per annum can therefore be regarded as
the risk-free interest rate for the relevant period (3 years).
Using the DPV formula above, that means that the value
of $150,000
received in three years actually has a present value of $129,576
(rounded off). Those future dollars aren't worth the same as the dollars we
have now. Subtracting the purchase price of the house ($100,000) from the present
value results in the net present value of the whole transaction, which would be $29,576
or a little more than 29% of the purchase price.
Another way of looking at the deal as the
excess return achieved (over the risk-free rate) is
(14.5%-5.0%)/(100%+5%) or approximately 9.0% (still very respectable). (As a
check, 1.050 x 1.090 = 1.145 approximately.)
But what about risk?
We assume that the $150,000 is John's best estimate of
the sale price that he will be able to achieve in 3 years time (after deducting
all expenses, of course). There is of course a lot of uncertainty
about house prices and the outturn may end up higher or lower than this
estimate. [The house John is buying is in a "good neighborhood", but
market values have been rising quite a lot lately and the real estate market
analysts in the media are talking about a slow-down and higher interest rates.
There is a probability that John might not be able to get the full $150,000 he
is expecting in three years due to a slowing of price appreciation, or that
loss of liquidity in the real estate market might make it very hard for him to
sell at all.]
In this example, only one future cash flow was
considered. For a decision which generates multiple cash flows in multiple time
periods, all the cash flows must be discounted and then summed into a single net
present value.
Real options
Real options analysis has become important since the
1970s as option pricing models have gotten more sophisticated. The discounted
cash flow methods essentially value projects as if they were risky bonds, with
the promised cash flows known. But managers will have many choices of how to
increase future cash inflows, or to decrease future cash outflows. In other
words, managers get to manage the projects - not simply accept or reject them.
Real options analysis tries to value the choices - the option value - that the
managers will have in the future and adds these values to the NPV.
NET PRESENT VALUE (NPV)
NPV, also called net present worth (NPW)
is the total present value (PV) of a time series of cash flows. It is a
standard method for using the time value of money to appraise long-term
projects. Used for capital budgeting, it measures the excess or shortfall of
cash flows, in present value terms, once financing charges are met. NPV is an
indicator of how much value an investment or project adds to the firm.
A project's NPV is estimated
using a discounted cash flow (DCF) valuation which requires estimating
the size and timing of all of the incremental cash flows from the project.
These future cash flows are then discounted to determine their present value.
These present values are then summed, to get the NPV. The NPV method is used
for evaluating the desirability of investments or projects. A common practice
in choosing a discount rate for a project is to apply a weighted average cost
of capital (WACC) that applies to the entire firm and reflects the risk of the
cashflows, but a higher discount rate may be more appropriate when a project's
risk is higher than the risk of the firm as a whole.
The discount rate reflects two things:
1.
The time value of money (risk rate) - investors would
rather have cash immediately than having to wait and must therefore be
compensated by paying for the delay.
2.
A risk premium (risk premium rate) - reflects the extra
return investors demand because they want to be compensated for the risk that
the cash flow might not materialize after all.
The discounted
cash flow formula is derived from the future value formula for calculating the time
value of money and compounding returns.
where
- DPV is the discounted present value of the future cash flow (FV), or FV adjusted for the delay in receipt;
- FV is the nominal value of a cash flow amount in a future period;
- i is the interest rate, which reflects the cost of tying up capital and may also allow for the risk that the payment may not be received in full;
- d is the discount rate, which is i/(1+i), ie the interest rate expressed as a deduction at the beginning of the year instead of an addition at the end of the year;
- n is the time in years before the future cash flow occurs.
Where multiple cash flows in multiple time
periods are discounted, it is necessary to sum them as follows:
for each future cash flow (FV) at any time
period (t) in years from the present time, summed over all time periods.
The sum can then be used as a net present value figure. If the amount to be
paid at time 0 (now) for all the future cash flows is known, then that amount
can be substituted for DPV and the equation can be solved for i,
that is the internal rate of return.
All the above assumes that the interest rate remains constant throughout
the whole period.
The
NPV decision rule is to accept all positive NPV projects in an unconstrained
environment, or if projects are mutually exclusive, accept the one with the highest
NPV. Basically NPV and Discounted Payback are the same
idea, with slightly different answers. Discounted Payback is a period of time,
and NPV is the final dollar amount you get by adding all the discounted cash
flows together. When investors and managers perform DCF analysis, the important
thing is that the net present value of the decision after discounting all
future cash flows at least be positive (more than zero). If the NPV is positive, then
approve the project. It shows that you are making more money on the investment
than you are spending on your cost of capital. If NPV is negative, that
means that the investment decision would actually lose money even if it
appears to generate a nominal profit. In that case do not approve the project
because you are paying more in interest on the borrowed money than you are
making from the project.
where: Ct = the net cash receipt at the end of year t; Io = the initial investment outlay;
r = the discount rate/the required minimum rate of return on investment
n = the project/investment's duration in years.
The discount factor r can be calculated using:
examples: or,
or,
Example: A corporation must decide
whether to introduce a new product line. The new product will have startup
costs, operational costs, and incoming cash flows over six years. (see table on the next page) This project
will have an immediate (t=0) cash outflow of $100,000 (which might include
machinery, and employee training costs). Other cash outflows for years 1-6 are
expected to be $5,000 per year. Cash inflows are expected to be $30,000 each
for years 1-6. All cash flows are after-tax, and there are no cash flows
expected after year 6. The required rate of return is 10%. The present value
(PV) can be calculated for each year. The sum of all these present values is
the net present value, which equals $8,881.52. Since the NPV is greater than
zero, it would be better to invest in the project than to do nothing, and the
corporation should invest in this project if there is no alternative with a
higher NPV.
Year
|
Cashflow
|
Present Value
|
T=0
|
  |
-$100,000
|
T=1
|
 |
$22,727
|
T=2
|
 |
$20,661
|
T=3
|
 |
$18,783
|
T=4
|
 |
$17,075
|
T=5
|
 |
$15,523
|
T=6
|
 |
$14,112
|
The NPV is greatly affected by the discount rate, so selecting the proper rate - sometimes called the hurdle rate - is critical to making the right decision. The hurdle rate is the minimum acceptable return on an investment. It should reflect the riskiness of the investment, typically measured by the volatility of cash flows, and must take into account the financing mix. Managers may use models such as the CAPM or the APT to estimate a discount rate appropriate for each particular project. The following sums up the NPVs in various situations.
If...
|
It means...
|
Then...
|
NPV > 0
|
the investment would add
value to the firm
|
the project may be accepted
|
NPV < 0
|
the investment would
subtract value from the firm
|
the project should be
rejected
|
NPV = 0
|
the investment would
neither gain nor lose value for the firm
|
We should be indifferent in
the decision whether to accept or reject the project. This project adds no
monetary value. Decision should be based on other criteria, e.g. strategic
positioning or other factors not explicitly included in the calculation.
|
However, NPV = 0 does not mean that a project is only
expected to break even, in the sense of undiscounted profit or loss (earnings).
It will show net total positive cash flow and earnings over its life.
Exercise: A
firm intends to invest $1,000 in a project that generated net receipts of $800,
$900 and $600 in the first, second and third years respectively. Should the
firm go ahead with the project?
INTERNAL RATE OF RETURN
The internal rate of
return (IRR) is a rate of return used in capital budgeting to
measure and compare the profitability of investments. It is also called the discounted
cash flow rate of return (DCFROR) or simply the rate of return (ROR). In
the context of savings and loans the IRR is also called the effective interest
rate. The term internal refers to the fact that its calculation does not
incorporate environmental factors (e.g. the interest rate or inflation).
IRR is defined as the discount rate that gives a net
present value (NPV) of zero i.e., the present value of the sum of all
cash inflows for the project in different years would equal the sum of present
value of its outflows in all the years. It is a commonly used measure of
investment efficiency. In more familiar terms, the IRR of an investment is the
interest rate at which the costs of the investment lead to the benefits of the
investment. IRR may be taken as the break-even discount rate. This means
that all gains from the investment are inherent to the time value of money and
that the investment has a zero net present value at this interest rate. The IRR
on an investment or potential investment is the annualized effective
compounded return rate that can be earned on the invested capital.
In most realistic cases, all independent projects
that have an IRR higher than the hurdle rate should be accepted. If IRR exceeds
cost of capital, project is worthwhile, i.e. it is profitable to undertake.
Nevertheless, for mutually exclusive projects, the decision rule of taking the
project with the highest IRR - which is often used - may select a project with
a lower NPV.
An investment is considered acceptable if its
internal rate of return is greater than an established minimum acceptable rate
of return. In a scenario where an investment is considered by a firm that has equity
holders, this minimum rate is the cost of capital of the investment (which may
be determined by the risk-adjusted cost of capital of alternative investments).
This ensures that the investment is supported by equity holders since, in
general, an investment whose IRR exceeds its cost of capital adds value for the
company (i.e. it is profitable). IRR is calculated by using the formula
where r = IRRThe IRR is found by trial and error.
Exercise: Find the IRR of this project for a firm with a 20% cost of capital:
| Year |
0
|
1
|
2
|
| Cash flow $ |
─10,000
|
8000
|
6000
|
a) Try 20%; b) Try
27%; c) Try 29%
Calculation
Given the (period, cash flow) pairs (n, Cn)
where n is a positive integer, the total
number of periods N, and the net present
value NPV, the IRR is given by r in:
Note that the period is usually given in years,
but the calculation may be made simpler if r
is calculated using the period in which the majority of the problem is defined
(e.g. using months if most of the cash flows occur at monthly intervals) and
converted to a yearly period thereafter.
Example
If an investment may be given by the sequence of cash flows| Year (n) | 0 | 1 | 2 | 3 | 4 |
| Cash flow (Cn) | ─100 | 40 | 59 | 55 | 20 |
.
In this case, the answer is 29%.
IRR assumes consumption
of positive cash flows during the project. If positive cash flows can be
reinvested back into the project, then a suitable reinvestment rate is required
in order to calculate the reinvestment cash flow and hence the IRR with cash
flows reinvested. When the calculated IRR is different from the true
reinvestment rate for interim cash flows, the measure will accurately reflect
the annual equivalent return from the project. The company may have additional
projects, with equally attractive prospects, in which to invest the interim
cash flows.
Since IRR does not consider cost of capital, it
should not be used to compare projects of different duration. Modified
Internal Rate of Return (MIRR) does consider cost of capital and
provides a better indication of a project's efficiency in contributing to the
firm's discounted cash flow.
NPV vs IRR
NPV and IRR methods are closely related because: (a)
both are time-adjusted measures of profitability, and (b) their mathematical
formulas are almost identical. So, which method leads to an optimal decision:
IRR or NPV?
Because the IRR is a rate quantity, it is an indicator of the efficiency,
quality, or yield of an investment. This is in contrast with the net present
value, which is an indicator of the value or magnitude of an investment.
Despite a strong academic preference for NPV,
surveys indicate that executives prefer IRR over NPV, although they should be
used in concert. In a budget-constrained environment, efficiency measures
should be used to maximize the overall NPV of the firm. Some managers find it
intuitively more appealing to evaluate investments in terms of percentage rates
of return than dollars of NPV.
NPV vs discount rate comparison for two mutually exclusive projects.
Project 'A' has a higher NPV (for
certain discount rates), even though its IRR is lower than for project 'B' i.e.,
in cases where one project has a higher initial investment than a second
mutually exclusive project, the first project may have a lower IRR (expected
return), but a higher NPV (increase in shareholders' wealth) and should thus be
accepted over the second project (assuming no capital constraints).
Three concepts:- Internal rate of return (IRR): which calculates the rate of return of a project without making assumptions about the reinvestment of the cash flows (hence internal).
- Modified internal rate of return (MIRR): similar to IRR, but it makes explicit assumptions about the reinvestment of the cash flows. Sometimes it is called Growth Rate of Return.
- Accounting rate of return (ARR): a ratio similar to IRR and MIRR
Modified
Internal Rate of Return - MIRR
One shortcoming of the
IRR method is that it is commonly misunderstood to convey the actual annual
profitability of an investment. However, this is not the case because
intermediate cash flows are almost never reinvested at the project's IRR; and,
therefore, the actual rate of return is almost certainly going to be lower.
Accordingly, a measure called Modified Internal Rate of Return
(MIRR) is often used.
MIRR is basically the
same as the IRR, except it assumes that the revenue (cash flows) from the
project are reinvested back into the company, and are compounded by the
company's cost of capital, but are not directly invested back into the project
from which they came.
MIRR assumes that the
revenue is not invested back into the same project, but is put back into the
general "money fund" for the company, where it earns interest. We
don't know exactly how much interest it will earn, so we use the company's cost
of capital as a good guess.
How
to get MIRR?
We've
got these cash flows coming in. The money is going to be invested back into the
company, and we assume it will then get at least the
company's-cost-of-capital's interest on it. So we have to figure out the future
value (not the present value) of the sum of all the cash flows. This, by the
way is called the Terminal Value. Assume, again, that the
company's cost of capital is 10%. Here goes...
Cash
Flow
|
Times
|
=
|
Future Value
of that year’s cash flow. |
Note
|
|
7000
|
X
|
(1+.1) 4
|
=
|
10249
|
compounded for 4 years
|
6000
|
X
|
(1+.1) 3
|
=
|
7986
|
compounded for 3 years
|
3000
|
X
|
(1+.1) 2
|
=
|
3630
|
compounded for 2 years
|
2000
|
X
|
(1+.1) 1
|
=
|
2200
|
compounded for 1 years
|
1000
|
X
|
(1+.1)0
|
=
|
1000
|
not compounded at all
because this is the final cash flow
|
TOTAL
|
=
|
25065
|
this is the Terminal Value
|
The final MIRR is 10.81%. [Initial
investment 15000 and 15000 (1 + 0.1081)5 = 25065
Profitability
Index (PI)
This is a variant of the NPV
method and PI = PV/I0 where
I0 = investment in the year 0
Decision rule: PI > 1;
accept the project; PI < 1; reject the project
If NPV = 0, we have: NPV = PV - Io = 0 and PV = Io
Dividing both sides by Io
we get: PV/I0 > 1
PI = 1.2 means
that the project's profitability is 20%. Example:
|
|
PV of cash
flows
|
I0
|
PI
|
Project A
|
100
|
50
|
2.0
|
Project B
|
1,500
|
1,000
|
1.5
|
Decision:
Choose option B because it maximizes the firm's profitability by $1,500.
Disadvantage
of PI: Like IRR it is a percentage and
therefore ignores the scale of investment.
Profitability Index
|
equals
|
NPV
|
divided by
|
Total Investment
|
plus
|
1
|
PI
|
=
|
563
|
/
|
15,000
|
+
|
1
|
So
in our example, the PI = 1.0375. For every dollar borrowed and invested we get
back $1.0375, or one dollar and 3 and one third cents. This profit is above and
beyond our cost of capital.
Decision Time- Do we approve the project?
Well, let's review.
Decision Method
|
Result
|
Approve?
|
Why?
|
Payback
|
2.66 years
|
Yes
|
We get our money back
|
Discounted Payback
|
4.195 years
|
Yes
|
We get our money back, even
after discounting our cost of capital.
|
NPV
|
$500
|
Yes
|
NPV is positive (reject the
project if NPV is negative)
|
Profitability Index
|
1.003
|
Yes
|
We make money
|
IRR
|
12.02%
|
Yes
|
The IRR is more than the
cost of capital
|
MIRR
|
10.81%
|
Yes
|
The MIRR is more than the
cost of capital
|
- Cost-benefit analysis, which includes issues other than cash, such as time savings.
- Real option method, which attempts to value managerial flexibility that is assumed away in NPV.
One of the important variables in different methods of capital
budgeting is Cash Flow and in order to understand the concept, let us assume
that a project spends 15,000 dollars in the year zero and it may get the money
(including profit or loss) in 5 years as shown in the table.
Year
|
Cash flow
|
0
|
– 15,000
|
1
|
+ 7,000
|
2
|
+ 6,000
|
3
|
+ 3,000
|
4
|
+ 2,000
|
5
|
+ 1,000
|
The expenditure
made in year zero is the cash outflow and the incomes in different years are
cash inflows. Cash outflows make take place in any year after the initial
expenditures, too.
Key terms
Accounting rate of return Interest rateAnnuities Internal rate of return
Capital budgeting Investment decision
Cash flow Net present value
Classification of investment projects Payback period
Compound interest Perpetuity
Current cost accounting (CCA) Present value
Current purchasing power (CPP) Rates of return
Dependent projects The time value of money
Independent projects
Inflation
