Drury (2000) stated, ” The theory of capital budgeting reconciles the goals of survival and profitability by assuming that management takes as its goal the maximization of the market value of the shareholders’ wealth via the maximization of the market value of ordinary share”.
Capital budgeting decisions may be defined as “the firm’s decision to invest its current funds most efficiently in the long term assets in anticipation of an expected flow benefits over a series of years”. (Pandy, 2005)
According to the above definitions of capital budgeting, following features can be identified,
I. Exchange current funds for future benefits
II. Funds are invested in long term assets and
III. Benefit will occur to the firm over a series of years.
Therefore main objective of the capital budgeting decisions are to maximize the wealth of the shareholders by,
â€¢ Determining which specific investment projects to be undertaken
â€¢ Determining the total amount of capital expenditure which the firm should be obtained
â€¢ Determining how this portfolio of projects should be financed.
In capital budgeting process different investment appraisal techniques are used to evaluate the investments. They are mainly traditional and Discounting Factor (DCF) methods. In traditional method consist of Payback and Accounting Rate of Return (ARR) which don’t have the time value adjustment. But in DCF method Net Present Value (NPV) and Internal Rate of Return (IRR) are included and they are adjusting the time value of money to the cash flows. These techniques give different benefits and limitations in investment evaluation process, although as per the theoretical view DCF analysis may give more benefit to the organization.
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However successful completion of a project mainly depends on the selection criteria adopted while choosing the project in the initial phases itself and the choice of a project must be based on a sound financial assessment and not based on impression. DCF techniques are being widely used in both public and private sector. This is the method recommended for evaluating investment proposals. In this method, the incremental cost and benefits of proposals are discounted by a required rate of return in order to obtain the net present value of the proposal.
Investment decisions are essential for a business as they define the future survival, and growth of the organization. The main objective of a business being the maximization of shareholders wealth. Therefore a firm needs to invest in every project that is worth more than the costs. The Net Present value is the difference between the projects value and its costs. Thus to make shareholders happy, a firm must invest in projects with positive NPVs. We shall start this essay with an explanation of investment appraisal, NPV, then compare this method with other investment appraisal methods and finally try to define, based on the works of Tony Davies, Brian Pain, and Brealey/Myers/Allen, which method works best in order to define a good investments.
What is Investment Appraisal?
A means of assessing whether an investment project is worthwhile or not
Investment project could be the purchase of a new PC for a small firm, a new piece of equipment in a manufacturing plant, a whole new factory, etc
Used in both public and private sector
Types of investment appraisal:
Accounting Rate of Return (ARR)
Internal Rate of Return (IRR)
Net Present Value (discounted cash flow)
Why do companies invest?
Importance of remembering investment as the purchase of productive capacity NOT buying stocks and shares or investing in a bank!
Buy equipment/machinery or build new plant to:
Increase capacity (amount that can be produced) which means:
Demand can be met and this generates sales revenue
Increased efficiency and productivity
Investment therefore assumes that the investment will yield future income streams
Investment appraisal is all about assessing these income streams against the cost of the investment
Capital budgeting versus current expenditures
A capital investment project can be distinguished from current expenditures by two features:
a) Such projects are relatively large
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 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.
The classification of investment projects
a) 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) By type of benefit to the firm
· An increase in cash flow
· A decrease in risk
· an indirect benefit (showers for workers, etc).
c) By degree of dependence
· Mutually exclusive projects (can execute project A or B, but not both)
· complementary projects: taking project A increases the cash flow of project B.
· substitute projects: taking project A decreases the cash flow of project B.
d) By degree of statistical dependence
· Positive dependence
· Negative dependence
· Statistical independence.
e) By type of cash flow
· Conventional cash flow: only one change in the cash flow sign
e.g. -/++++ or +/—-, etc
· Non-conventional cash flows: more than one change in the cash flow sign,
e.g. +/-/+++ or -/+/-/++++, etc.
Brief Introduction to Discounted Cash Flow and Methods
This section would give a briefing on the mentioned topic and explain them thoroughly later on in this report.
Discounted cash flow (DCF)
DCF focuses on the time value of money, Rs.1 is worth more today than Rs.1 in the future. The reason being that it could be invested and make a return (yes, even in times of low interest, so long as interest rates are positive).
So that’s the discounting methodology, DCF has two methods.
Net Present Value (NPV)
The annual cash flows are discounted and totaled and then the initial capital cost of
the project is deducted. The excess or deficit is the NPV of the project, it goes
without saying that for the project to be worthwhile the NPV must be positive and the
higher the NPV the more attractive is the investment in the project
Internal Rate of Return (IRR)
The IRR or yield of a project is the rate of return at which the present value of the net cash inflows equals the initial cost, which is the same as the discount rate which produces a NPV of zero. For an investment to be worthwhile the IRR must be greater than the cost of capital.
Due to the following reasons, DCF method is identified as a best method for Investment appraisal processes,
â€¢ They give due weight to timing and size of cash flow
â€¢ Thy take the whole life of the project in to irregular cash flows do not invalidate the result obtained.
â€¢ Estimate of risk and uncertainty can be incorporated
â€¢ Use of discounting methods may lead to move accurate estimating and
â€¢ They rank projects correctly in order of profitability and give better criteria for acceptance or rejection of projects than other method.
Because of that in theoretically said that DCF analysis is best method to evaluate the investment over its rivals. A survey carried out by the Arnold & Hatzopolous (2000) and Graham & Harvey (2000) to identify the practical usage of investment appraisal techniques among the large manufacturing firms of UK had revealed that NPV and IRR are less behind its rivals in practically. Therefore they have commented that there is a gap between usages of appraisal techniques in practically and theoretically.
The economic evaluation of investment proposals
The analysis stipulates a decision rule for:
I) accepting or
II) rejecting Investment projects
The time value of money
Recall that the interaction of lenders with borrowers sets an equilibrium rate of interest. Borrowing is only worthwhile if the return on the loan exceeds the cost of the borrowed funds. Lending is only worthwhile if the return is at least equal to that which can be obtained from alternative opportunities in the same risk class.
The interest rate received by the lender is made up of:
The time value of money: the receipt of money is preferred sooner rather than later. Money can be used to earn more money. The earlier the money is received, the greater the potential for increasing wealth. Thus, to forego the use of money, you must get some compensation.
The risk of the capital sum not being repaid. This uncertainty requires a premium as a hedge against the risk; hence the return must be commensurate with the risk being undertaken.
Inflation: money may lose its purchasing power over time. The lender must be compensated for the declining spending/purchasing power of money. If the lender receives no compensation, he/she will be worse off when the loan is repaid than at the time of lending the money.
Internal Rate of Return
The internal rate of return (IRR) is another widely used method of investment appraisal. It calculates the rate of return, where the difference between the present values of cash inflows and outflows, the NPV, is zero. Thus when would a company undertake the project? Simply when the expected rate of return, the IRR, exceeds the target rate of return of the company. This is called the IRR rule. When the IRR is superior to the target rate of return, the NPV is positive. When IRR is equal to the target rate of return then NPV is equal to 0, and when the IRR is inferior to the target rate of return, then the NPV is negative.
IRR can easily be determined through interpolation, which assumes a linear relationship between the NPVs of a capital investment project obtained using different discount rates. The exact rate is calculated algebraically using the theorem of Thales.
we would have to compute a complex weighted average of these rates to be able to compare it to the IRR. This very much complicates the task, and gives us yet another reason to stick to the simple NPV method to better appraise investments.
It has been shown that NPV proves to be much more reliable and simple of use than IRR. IRR is indeed subject to many pitfalls developed above. Nevertheless, a very important proportion of managers still use the IRR method to define attractive investments. Why could this be?
It can be argued that managers do not trust the cash flow forecasts they receive. In the case of two projects A and B having the same NPV, IRR plays an important role. Project A requires an investment of 8,000 and project B necessitates an investment of 80,000. As said earlier both NPVs are the same. In such a situation where the NPVs are similar, managers would go for the project, whose initial investment is the lowest. If the project were to be dysfunctional, it is always easier to recover from a small initial loss than from a bigger one. By looking at the IRR the choice is quickly made. The project with the highest IRR is the one with the less risk.
To summarize we have seen that although easy to use when used correctly, there are many drawbacks to the use of the IRR.
IRR ignores the size of investment projects. That is two projects may have the same IRR but one project can return many times the cash flow returned by the other project.
If the project cash flows are alternatively positive and negative, then we obtain two or more IRRs, or even no IRR, which can be disconcerting for interpretation.
IRR should not be used to make a choice between mutually exclusive projects because it proves to be unreliable when it comes to ranking investment projects of different scale.
So Forth, the IRR rule is difficult to apply when the discounting factors used over the years are different. Indeed, it is not easy to define what opportunity cost IRR should be compared to.
Modified Internal Rate of Return (MIRR)
Modified internal rate of return (MIRR) is a financial measure of an investment’s attractiveness. It is used in capital budgeting to rank alternative investments. As the name implies, MIRR is a modification of the internal rate of return (IRR) and as such aims to resolve some problems with the IRR.
Problems with the IRR
While there are several problems with the IRR, MIRR resolves two of them.
First, IRR assumes that interim positive cash flows are reinvested at the same rate of return as that of the project that generated them. This is usually an unrealistic scenario and a more likely situation is that the funds will be reinvested at a rate closer to the firm’s cost of capital. The IRR therefore often gives an unduly optimistic picture of the projects under study. Generally for comparing projects more fairly, the weighted average cost of capital should be used for reinvesting the interim cash flows.
Second, more than one IRR can be found for projects with alternating positive and negative cash flows, which leads to confusion and ambiguity. MIRR finds only one value.
MIRR is calculated as follows:
Where n is the number of equal periods at the end of which the cash flows occur (not the number of cash flows), PV is present value (at the beginning of the first period), FV is future value (at the end of the last period).
The formula adds up the negative cash flows after discounting them to time zero, adds up the positive cash flows after factoring in the proceeds of reinvestment at the final period, then works out what rate of return would equate the discounted negative cash flows at time zero to the future value of the positive cash flows at the final time period.
Spreadsheet applications, such as Microsoft Excel, have inbuilt functions to calculate the MIRR. In Microsoft Excel this function is “=MIRR”.
If an investment project is described by the sequence of cash flows:
Then the IRR r is given by
In this case, the answer is 25.48% (the other solutions to this equation are -593.16% and -132.32%, but they will not be considered meaningful IRRs).
To calculate the MIRR, we will assume a finance rate of 10% and a reinvestment rate of 12%. First, we calculate the present value of the negative cash flows (discounted at the finance rate):
Second, we calculate the future value of the positive cash flows (reinvested at the reinvestment rate):
Third, we find the MIRR:
The calculated MIRR (17.91%) is significantly different from the IRR (25.48%).
Lefley and Morgan have developed a financial appraisal model, which has extended the traditional appraisal methodologies so as to provide more considered comparison for individual investment projects. The Lefley and Morgan model creates a profile, which combines the uses of NPV, Discounted payback period, and the discounted payback index, (DPBI). The discounted payback period is interesting to take into consideration as the entity proceeding with the investment might be lacking money and would prefer having a quick return of the funds invested. DPBI is used to assess the number of times the initial cost of the investment will be recovered over the project’s life. It is calculated by dividing the accumulated present values by the initial capital cost. Combined these methods give a fairly accurate view of an investment.
Net present value vs internal rate of return
Independent vs dependent projects
NPV and IRR methods are closely related because:
Both are time-adjusted measures of profitability, and their mathematical formulas are almost identical. So, which method leads to an optimal decision: IRR or NPV?
a) NPV vs. IRR: Independent projects
Independent project: Selecting one project does not preclude the choosing of the other.
With conventional cash flows (-|+|+) no conflict in decision arises; in this case both NPV and IRR lead to the same accept/reject decisions.
NPV vs. IRR Independent projects
If cash flows are discounted at k1, NPV is positive and IRR > k1: accept project.
If cash flows are discounted at k2, NPV is negative and IRR < k2: reject the project.
Mathematical proof: for a project to be acceptable, the NPV must be positive, i.e.
Similarly for the same project to be acceptable:
Where R is the IRR.
Since the numerators Ct are identical and positive in both instances:
· Implicitly/intuitively R must be greater than k (R > k);
· If NPV = 0 then R = k: the company is indifferent to such a project;
· Hence, IRR and NPV lead to the same decision in this case.
b) NPV vs. IRR: Dependent projects
NPV clashes with IRR where mutually exclusive projects exist.
Agritex is considering building either a one-storey (Project A) or five-storey (Project B) block of offices on a prime site. The following information is available:
Initial Investment Outlay
Net Inflow at the Year End
Assume k = 10%, which project should Agritex undertake?
Both projects are of one-year duration:
$11,500 = $9,500 (1 +RA)
Therefore IRRA = 21%
$18,000 = $15,000(1 + RB)
Therefore IRRB = 20%
Assuming that k = 10%, both projects are acceptable because:
NPVA and NPVB are both positive
IRRA > k AND IRRB > k
Which project is a “better option” for Agritex?
If we use the NPV method:
NPVB ($1,363.64) > NPVA ($954.55): Agritex should choose Project B.
If we use the IRR method:
IRRA (21%) > IRRB (20%): Agritex should choose Project A. See figure below.
NPV vs. IRR: Dependent projects
Up to a discount rate of ko: project B is superior to project A, therefore project B is preferred to project A.
Beyond the point ko: project A is superior to project B, therefore project A is preferred to project B
The two methods do not rank the projects the same.
Differences in the scale of investment
NPV and IRR may give conflicting decisions where projects differ in their scale of investment. Example:
Assume k= 10%.
NPVA = $1,500 x PVFA at 10% for 3 years
= $1,500 x 2.487
= $3,730.50 – $2,500.00
NPVB == $7,000 x PVFA at 10% for 3 years
= $7,000 x 2.487
= $17,409 – $14,000
Therefore IRRA = 36% (from the tables)
Therefore IRRB = 21%
· NPV prefers B to A
· IRR prefers A to B
See figure below.
Scale of investments
To show why:
The NPV prefers B, the larger project, for a discount rate below 20%
The NPV is superior to the IRR
a) Use the incremental cash flow approach, “B minus A” approach
b) Choosing project B is tantamount to choosing a hypothetical project “B minus A”.
“B minus A”
IRR”B Minus A”
c) Choosing B is equivalent to: A + (B – A) = B
d) Choosing the bigger project B means choosing the smaller project A plus an additional outlay of $11,500 of which $5,500 will be realized each year for the next 3 years.
e) The IRR”B minus A” on the incremental cash flow is 20%.
f) Given k of 10%, this is a profitable opportunity, therefore must be accepted.
g) But, if k were greater than the IRR (20%) on the incremental CF, then reject project.
h) At the point of intersection,
NPVA = NPVB or NPVA – NPVB = 0, i.e. indifferent to projects A and B.
i) If k = 20% (IRR of “B – A”) the company should accept project A.
· This justifies the use of NPV criterion.
Advantage of NPV:
· It ensures that the firm reaches an optimal scale of investment.
Disadvantage of IRR:
· It expresses the return in a percentage form rather than in terms of absolute dollar returns, e.g. the IRR will prefer 500% of $1 to 20% return on $100. However, most companies set their goals in absolute terms and not in % terms, e.g. target sales figure of $2.5 million.
The profitability index – PI
This is a variant of the NPV method.
PI > 1; accept the project
PI < 1; reject the project
If NPV = 0, we have:
NPV = PV – Io = 0
PV = Io
Dividing both sides by Io we get:
PI of 1.2 means that the project’s profitability is 20%. Example:
PV of CF
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.
The Payback Period (PP)
The CIMA defines payback as ‘the time it takes the cash inflows from a capital investment project to equal the cash outflows, usually expressed in years’. When deciding between two or more competing projects, the usual decision is to accept the one with the shortest payback.
Payback is often used as a “first screening method”. By this, we mean that when a capital investment project is being considered, the first question to ask is: ‘How long will it take to pay back its cost?’ The company might have a target payback, and so it would reject a capital project unless its payback period was less than a certain number of years.
For a project with equal annual receipts:
= 4 years
Payback period lies between year 2 and year 3. Sum of money recovered by the end of the second year
= $7,500, i.e. ($5,000 + $2,500)
Sum of money to be recovered by end of 3rd year
= $10,000 – $7,500
= 2.625 years
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 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.
Advantages of the payback method
Payback can be important: long payback means capital tied up and high investment risk. The method also has the advantage that it involves a quick, simple calculation and an easily understood concept.
Discounted Payback Method
Some companies require that the initial outlay on any project should be recovered within a specific period. The discounted payback appraisal method requires a discount rate to be chosen to calculate the present values of cash inflows and then the payback is the number of years required to repay the initial investment. Yet payback can give misleading answers.
Project Year 0 Year 1 Year 2 Year 3
A -4,000 2,500 500 5,500
B -4,000 2,500 1,800 0
C -4,000 3,180 500 0
The cost of capital is 10% per annum
Year Net cash Discount factor Present Cumulative
flow at 10% values present values
0 -2,000 1.00 -2,000 -2,000
1 500 0.91 455 -1,545
2 500 0.83 415 -1,130
3 5,000 0.75 3,750 2,620
Year Net cash Discount factor Present Cumulative
flow at 10% values present values
0 -2,000 1.00 -2,000 -2,000
1 500 0.91 455 -1,545
2 1,800 0.83 1,494 -51
3 0 0.75 0 -51
Year Net cash Discount factor Present Cumulative
flow at 10% values present values
0 -2,000 1.00 -2,000 -2,000
1 1,800 0.91 1,638 -362
2 500 0.83 415 53
3 0 0.75 0 53
The payback rule does not take into consideration any cash inflow that occurs after the cut-off date. For example if the cut-off date is two years, project A, although clearly the most profitable on the long term will be rejected. Thus if a firm uses the same cut-off regardless of project life then it will tend to accept many poor short lived projects and reject many good long lived ones.
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.
Note that net annual profit excludes depreciation.
A project has an initial outlay of $1 million and generates net receipts of $250,000 for 10 years.
Assuming straight-line depreciation of $100,000 per year:
We here see that ARR is based on profits rather than cash flows and that it ignores the time value of money. It therefore just gives a brief overview of a new project, and should not be recommended as a primary investment appraisal method. As said earlier the impact of cash flows and the time value of money are essential in making an investment decision. Another disadvantage of the ARR is the fact it is dependent on the depreciation policy adopted by the business.
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.
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?
limitations of NPV when evaluating alternative investment proposals
NPV is not that flexible and only uses information available at the time of the decision. It does not account for changes to the projects after the initial decision is made. NPV factors in risk by using a single discount rate, but in reality choices in the future concerning the project will likely change its payoffs and risk. Try real option analysis instead if you want to get around this problem.
NPV only evaluates tangible and quantifiable projects. Some projects with negative NPVs are carried out anyway because they have some kind of strategic value, e.g. it shows the firm in a good light, builds goodwill or allows access to as yet unknown earnings in the future.
In conclusion it can thus be stated that only discounted cash flow methods should be used for appraising investments. This leaves us with the discounted payback method, the IRR, and the NPV. The Discounted payback method, ignoring cash flows that occur after the payback point, cannot be used on its own as it simply provides an overview. Concerning the IRR, although easy to understand it has many pitfalls that have been developed above. Thus the NPV rule proves to be the safest and most reliable. Yet the ideal
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