CAPITAL BUDGETING - All you need to know
Capital Budgeting: A Complete Guide

CAPITAL BUDGETING

Contents: Capital Budgeting, Meaning, Characteristics of Capital Budgeting, Significance, Process, Types of Capital Budgeting decisions, Capital rationing (Theory Only), Techniques of Capital Budgeting: (Including Examples) Pay Back Period (PBP), Accounting Rate of Return (ARR), Net Present Value (NPV), Profitability Index (PI) & Internal Rate of Return (IRR)

INTRODUCTION

Capital Budgeting is the process of evaluating and selecting long-term investments that are consistent with the goal of Shareholders Wealth Maximization.

One of the important aspects of Financial Management is proper decision making in respect of investment of funds. Successful operation of any business depends upon the investment of resources in such a way as to bring in benefits or best possible returns from any investment. An investment can be simply defined as expenditure in cash or its equivalent during one or more time periods in anticipation of enjoying a net inflow of cash or its equivalent in some future time period or periods. An appraisal of investment proposals is necessary to ensure that the investment of resources will bring in desired benefits in future.

If the financial resources were in abundance, it would be possible to accept several investment proposals which satisfy the norms of approval or acceptability. Since resources are limited, a choice has to be made among the various investment proposals by evaluating their comparative merit. It is apparent that some techniques should be followed for making appraisal of investment proposals. Capital Budgeting is one of the appraising techniques of investment decisions. Capital Budgeting is defined as the firm’s decision to invest its current funds most efficiently in long term activities in anticipation of an expected flow of future benefits over a series of years. It should be remembered that the investment proposal is common both for fixed assets and current assets.

Capital budgeting decision may be defined as “Firms decisions to invest its current funds most efficiently in long term activities in anticipation of an expected flow of future benefits over a series of year. The firm’s capital budgeting decisions will include addition, disposition, modification and replacement of fixed assets”.

DEFINITIONS:

  • Charles T. Horngren defined capital budgeting as “Long term planning for making and financing proposed capital outlay”.
  • According to Keller and Ferrara, “Capital Budgeting represents the plans for the appropriation and expenditure for fixed asset during the budget period”.
  • Robert N. Anthony defined as “Capital Budget is essentially a list of what management believes to be worthwhile projects for the acquisition of new capital assets together with the estimated cost of each product”.
  • Prof. I. M. Pandey defines Capital Budgeting decision as “the firms decision to invest its current funds most efficiently in long term activities in expectations of expected flow of future benefits over a series of years.

NEED OF CAPITAL

The selection of the most profitable project of capital investment is the key function of Financial Manager. The decisions taken by the management in this area affect the operations of the firm for many years. Capital budgeting decisions may be generally needed for the following purposes:

a) Expansion; b) Replacement; c) Diversification; d) Buy or lease and e) Research and Development

Expansion:

The firm requires additional funds to invest in fixed assets when it intends to expand the production facilities in view of the increase in demand for their product in near future. Accordingly, the current assets will increase. In case of expansion the existing infrastructure like plant, machinery and other fixed assets is inadequate, to carry out the increased production volume. Thus, the firm needs funds for such project. This will include not only expenditure on fixed assets (infrastructure) but also an increase in working capital (current assets).

Replacement:

The machines and equipment used in production may either wear out or may be rendered obsolete due to new technology. The productive capacity and competitive ability of the firm may be adversely affected. The firm needs funds or modernization of a certain machines or for renovation of the entire plant etc. to make them more efficient and productive. Modernization and renovation will be a substitute for total replacement, where renovation or modernization is not desirable or feasible, funds will be needed for replacement.

Diversification:

If the management of the firm decided to diversify its production into other lines by adding a new line to its original line, the process of diversification would require large funds for long-term investment. For example, ITC and Philips company for their diversification.

Buy or lease

This is a most important decision area in Financial Management whether the firm acquire the desired equipment and building on lease or buy it”. If the asset is acquired on lease, there have to be made a series of annual or monthly rental payments. If the asset is purchased, there will be a large initial commitment of funds, but not further payments. The decision-making area is which course of action will be better to follow? The costs and benefits of the two alternative methods should be matched and compared to arrive at a conclusion.

Research and Development

The existing production and operations can be improved by the application of new and more sophisticated production and operations management techniques. New technology can be borrowed or developed in the laboratories. There is a greater need of funds for continuous research and development of new technology for future benefits or returns from such investments.

CHARACTERISTICS OF CAPITAL BUDGETING

In financial decision-making, capital budgeting decisions are of paramount importance since they affect the working and profitability of the firm for many years to come. The crucial importance of capital budgeting decisions is on account of the following characteristics:

  • Long-Term Effects: The capital budgeting decisions have long-term impact on the future profitability and cost structure of the firm. They influence the rate and direction of firms growth. An appropriate decision can yield amazing returns, while a wrong investment decision can endanger the survival of the firm.
  • High Degree of Risk: Long-term investment of funds is exposed to different types of risk. The risk may be due to the changes in taste and preferences of customers or because of technology advancement and continuous research. The longer is the period of the project, the greater may be the risk and uncertainty.
  • Huge Funds: Capital budgeting decisions involve spending large amount of funds for acquisition of fixed asset or for implementing certain big projects. It is known that capital funds of a firm are limited and hence, it is essential that they should be invested in most profitable alternatives through proper appraisal.
  • Irreversible Decision: Capital Budgeting decisions are irreversible and the amount invested cannot be realized back. The reason is that there may neither be any market for such second-hand assets nor there is any possibility of conversion of such assets into other profitable use. The only remedy is to dispose the same at heavy loss to the firm.
  • Most Difficult Decision: Capital Budgeting decisions are difficult to make as their assessment depends on the uncertainty of future events and activities of the firm. Similarly, it is practically not feasible to estimate and calculate the future benefits and cost relating to a particular investment decision accurately in monetary and quantitative terms. Such decision is, therefore, not simple to take.
  • Impact on Firms Competitive Strength: The capital budgeting decisions affect the capacity and strength of a firm to face the competition. It is because, the capital investment decisions determine the future profits and cost for the firm that ultimately affect the competitive position of the firm. For example, a firm may lose competitiveness if the decision to modernize the plant is delayed or not taken in right perspective.
  • Impact on Cost Structure: As a result of Capital budgeting decisions, a firm commits itself to a sizable amount of fixed cost such as supervisor’s charges, insurance, rent of premises, interest and so on. If the investment turns out to be unsuccessful or generates less than anticipated profits, the firm will have to bear the burden of these fixed costs. This will ultimately affect the profitability of the firm.

SIGNIFICANCE OF CAPITAL BUDGETING DECISIONS

Investment decisions require special attention because of following reasons:

  1. They influence the firm’s growth in long run.
  2. They affect the risk of firm.
  3. They involve commitment of large amount of funds.
  4. They are irreversible.
  5. They are most difficult to make.

The following aspects focus on the significance of capital budgeting decisions:

  • Growth: The capital budgeting decisions have long-term impact on the future profitability and cost structure of the firm. They influence the rate and direction of firms growth.
  • Risk: Long-term investment of funds is exposed to different types of risk. The risk may be due to the changes in taste and preferences of customers or because of technology advancement and continuous research. The longer is the period of the project, the greater may be the risk and uncertainty. Thus, these decisions shape the basic character of the firm.
  • Funding: Capital budgeting decisions involve spending large amount of funds for acquisition of fixed asset or for implementing certain big projects. It is known that capital funds of a firm are limited and hence, it is essential that they should be invested in most profitable alternatives through proper appraisal.
  • Irreversibility: Capital Budgeting decisions are irreversible and the amount invested cannot be realized back. The reason is that there may neither be any market for such second-hand assets nor there is any possibility of conversion of such assets into other profitable use. The only remedy is to dispose the same at heavy loss to the firm. Hence, such decisions should be taken after great evaluation and with proper care.
  • Complexity: Capital Budgeting decisions are difficult to make as their assessment depends on the uncertainty of future events and activities of the firm. Similarly, it is practically not feasible to estimate and calculate the future benefits and cost relating to a particular investment decision accurately in monetary and quantitative terms. Such decision are, therefore, not simple to take.
  • Shareholders Wealth Maximization: The basic objective of financial management is to maximize the wealth of shareholders. Therefore, the objective of capital budgeting is to select those long term plans that which will increase the wealth of shareholders. Thus, appropriate decisions can add value to the wealth, while improper decisions can destruct the wealth.
  • Capital Structure Planning: Capital Budgeting decisions help the firm in making policy on various sources of funds required to finance the projects. The surplus generated by the project also depends on the cost of capital which in turn is dependent on capital structure of the firm. Thus, it helps in capital structure planning.

CAPITAL BUDGETING PROCESS

The capital budgeting is the total process of generating, evaluating, selecting and following up of capital expenditure alternatives. Accordingly, the capital budgeting process involves following steps:

1. Project Generation

The capital budgeting process begins with the generation identification of investment proposal. The proposal or idea about protentional investment opportunities may originate within the firm or outside the firm. Within the firm it may come from top management or bottom level worker. It may also generate from outside sources such as trade fairs, people in industry, R & D institutes, conferences etc. Projects may be classified into five categories:

  • New products or expansion of existing products.
  • Replacement of equipment or buildings.
  • Research and development.
  • Exploration.
  • Others like acquisition of a pollution control device etc.

Investment proposals should be generated for the productive employment of firm’s funds. However, a systematic procedure must be evolved for generating profitable proposals to keep the firm healthy.

2. Project Evaluation

The evaluation of the project may be done in two steps. First the costs and benefits of the project are estimated in terms of cash flows and secondly the desirability of the project is judged by an appropriate criterion. It is important that the project must be evaluated without any prejudice on the part of the individual. While selecting a criterion to judge the desirability of the project, due consideration must be given to the market value of the firm.

3. Project Screening and Selection

After evaluation of the project, the project with highest return should be selected. There is no hard and fast rule set for the purpose of selecting a project from many alternative projects. Normally the projects are screened at various levels. However, the final selection of the project vests with the top-level management.

4. Project Execution

After selection of a project, the next step in capital budgeting process is to implement the project. Thus, the funds are appropriated for capital expenditures. The funds are spent in accordance with appropriations made in the capital budget funds for the purpose of project execution should be spent only after seeking format permission for the controller. A control over such capital expenditure is very much important and for that purpose periodical reports should be prepared and submitted to the top management.

5. Performance Review or Follow-up

Finally, a systematic procedure should be developed to review the performance of projects during their life time and after completion. The follow-up or review is made by the way of comparison of actual performance with the budgeted estimates. It will ensure better forecasting and will also help in improving the technique of future forecasting.

TYPES OF CAPITAL BUDGETING DECISIONS

A firm may face several investment proposals for consideration. It may adopt one of them, some of them or all of them depending upon whether they are independent or dependent or mutually exclusive. The firm may face basically with three types of major decisions:

  1. Accept/Reject Decisions
  2. Mutually exclusive Project Decisions
  3. Capital Rationing Decision

1. Accept/Reject Decisions

A firm may accept a project if the expected returns are more than the cut-off rate fixed by the management. The cut-off rate is usually the cost of capital of the firm. A firm may reject a project if the expected returns are lower than the cut-off rate. The decision making techniques are many which includes pay-back period method, NPV method, IRR method etc. These accept/reject decision is important because if the firm accepts the project, it will invest heavy funds in it.

  • Independent Proposals (Projects): Independent proposals are those proposals which do not compete with each other in a way that acceptance of one eliminate the possibility of acceptance of another. In case of such proposal, the firm may straight away “accept or reject” a proposal on the basis of a minimum return of investment required. All those proposals which give higher return than a certain desired rate of return are accepted and the rest are rejected.
  • Dependent Proposals (Projects): These are those proposals whose acceptance depends on the acceptance of one or more other proposals. If the other dependent project is accepted based on the above stated technique, this project would be accepted.

2. Mutually Exclusive Project Decisions

These are proposals which compete with each other in way that acceptance of one eliminates the possibility of acceptance of another. For example, if a company is considering investment in one of the two temperature control systems, acceptance of one system will rule out the acceptance of another. Thus, two or more mutually exclusive projects cannot both or all be accepted. The capital appraisal technique will be used for selected the best alternative and once this is done, other alternatives will be straight-away eliminated.

3. Capital Rationing Decision

In the real world, there is a constraint to the supply of capital particularly from external sources. In view of the availability of limited amount of capital, a company sets an absolute limit on the extent of capital budget for a year. Such a state or situation is called as capital rationing. Under capital rationing the company has a fixed capital budget that it may not exceed. So, when the company has more acceptable projects than it can afford to invest, it will rank the available projects in descending order of profitability index or the rate of expected returns and then will decide on the best ones.

Capital Rationing

Capital rationing refers to the situation where a company has more acceptable projects (i.e., projects with positive net present value or NPV) than it has capital available to invest. This forces the company to select among these projects, choosing only those that are most profitable or strategically aligned.

Firms engage in capital rationing when they invest in only a select group of projects rather than every single one available. Rationing is the controlled distribution of scarce resources, goods and services. It controls the size of the ration.

The technique to artificially control the supply and demand of commodities in economics is referred to as rationing. It’s executed to ensure adequate distribution of resources without their inadequate utilization or wastage.

This rationing refers to a situation where a firm is not in a position to invest in all the projects present. This inability to invest in all the projects, even though they may be profitable, is due to the limited funds available.

The funds here are referred to as capital, a limited resource. It can be raised from debt or equity resources. Debt is limited due to the credit that can be taken on, and equity is limited due to the constraints on the issuance of shares. The demand for these funds far exceeds the limited availability.

For this reason, a firm can’t take on all the projects available, even after they are profitable. Instead, the company should select the most profitable project, or a combination of projects, that yields the greatest profit.

Capital Rationing Assumptions

The first of the two assumptions about capital rationing is that there are restrictions on capital expenditure (CAPEX) such as internal financing restrictions or investment budget restrictions. Secondly, we have to assume that the rationing can come out with an optimal return.

Types

  • Hard Capital Rationing: External restrictions on raising funds, such as tight credit markets, bank limits, or government regulations.
  • Soft Capital Rationing: Internally imposed constraints, such as management-set budget ceilings, fear of diluting ownership, or limits on managerial capacity.

Common Decision Techniques

  • Profitability Index (PI): The ratio of the present value of future cash flows to the initial investment. If projects are divisible, they are ranked by PI from highest to lowest and partially funded until the capital runs out.
  • NPV Approach: If projects are indivisible, combinations of available projects are tested to identify which exact set yields the absolute highest aggregate NPV within the budget

The advantages of Capital Rationing are:

  • The rationing can help to ensure a budget is followed. Accepted projects can help management prepare financial statements and ensure budgets are prepared accordingly.
  • By putting restrictions on investment policies, the firm promotes optimal utilization of resources with less wastage.
  • As the number of active projects decreases, the management of those few may become more effective and efficient. Naturally, the workload reduces, hence leading to better analysis and results.
  • Eliminates projects that have lower returns or are unprofitable.

Similarly, there are certain disadvantages of Capital Rationing, such as:

  • This method will aid only in maximizing short-term profits rather than long-term growth. It can also lead to the rejection of extremely profitable projects simply because it may take a long time to see the returns.
  • Using the rate of returns should be done with utmost care. Using the wrong capital cost can dilute a company’s profits.
  • Maximizing NPV is impossible since rationing favors short-term profitable growth. Moreover, the intermediate cash flows aren’t maximized since the cash flows might be generated in later years.

TECHNIQUES OF CAPITAL BUDGETING

[Diagram representation from original document: Techniques of Capital Budgeting categorized into Traditional Techniques (Pay-Back Period, Average Rate of Return) and Modern Techniques (Net Present Value, Internal Rate of Return, Profitability Index)]

1. Pay-Back Period

It is the most popular and widely recognized traditional methods of evaluating the investment proposals. It can be defined as “the number of years to recover the original capital invested in a project”. According to Weston and Brigham, “the pay-back period is the number of years it takes for the firm to recover its original investment by net returns before depreciation, but after taxes:

a) When cash flows are uniform:
If the proposed project’s cash inflows are uniform the following formula can be used to calculate the payback period,

$$Payback\ period = \frac{Initial\ Investment}{Annual\ Cash\ Inflow}$$

b) When cash flows are not uniform:
When the project’s cash inflows are not uniform, but vary from year to year pay-back period is calculated by the process of cumulating cash inflows till the time when cumulative cash flows become equal to the original investment outlay.

The payback period can be used as an accept or reject criterion as well as a method of ranking projects. The payback period is the number of years to recover the investment made in a project. If the payback period calculated for a project is less than the maximum payback period set-up by the company, it can be accepted. As a ranking method it gives the highest rank to a project which has the lowest payback period, and the lowest rank to a project with the highest payback period. Whenever a company faces the problem of choosing among two or more mutually exclusive projects, it can select a project on the basis of payback period, which has shorter period than the other projects.

Merits:

  • Easy to calculate: It is one of the easiest methods of evaluating the investment projects. It is simple to understand and easy to compute.
  • Knowledge: The knowledge of payback period is useful in decision-making, the shorter the period better the project.
  • Protection from loss due to obsolescence: This method is very suitable to such industries where mechanical and technical changes are routine practice and hence, shorter payback period practice avoids such losses.
  • Easily availability of information: It can be computed on the basis of accounting information, what is available from the books.
  • Liquidity Oriented: This method gives an insight to the liquidity of investment. Therefore, for the firms having liquidity problems, it is good method as it emphasizes the earliest recovery of investment. That is why, it is called liquidity concept, rather than a profitability concept.
  • Risk Curtailment: In a broader sense, PBP deals with risk also. The project with higher PBP is riskier as compared to project with lower PBP. The risk of a project can be curtailed by selecting project with shorter PBP.

Demerits:

  • Failure in taking cash flows after payback period: This method is not taking into account the cash flows received by the company after the payback period.
  • Not considering the time value of money: It does not take into account the time value of money.
  • Non-considering of interest factor: It does not take into account the interest factor involved in the capital outlay.
  • Maximization of market value not possible: It is not consistent with the objective of maximizing the market value of share.
  • Failure in taking magnitude and timing of cash inflows: It fails to consider the pattern of cash inflows i.e. the magnitude and timing of cash inflows.

2. Accounting or Average Rate of Return (ARR)

This technique uses the accounting information revealed by the financial statements to measure the profitability of an investment proposal. It can be determined by dividing the average income after taxes by the average investment. According to Soloman, Accounting Rate of Return can be calculated as the ratio, of average net income to the initial investment. On the basis of this method, the company can select all those projects whose ARR is higher than the minimum rate established by the company. It can reject the projects with an ARR lower than the expected rate of return. This method also helps the management to rank the proposal on the basis of ARR.

$$ARR = \frac{Average\ Profit\ After\ Tax}{Average\ Investment} \times 100$$
$$Average\ PAT = \frac{Total\ PAT\ for\ Economic\ Life}{Economic\ Life} \times 100$$
$$Average\ Investment = \frac{1}{2}(Initial\ Investment – Salvage\ Value) + Salvage\ Value + Net\ Working\ Capital$$

Or alternatively:

$$Average\ Investment = \frac{1}{2}(Initial\ Investment + Salvage\ Value) + Net\ Working\ Capital$$

Acceptance Rule: The project which gives the highest rate of return over the minimum required rate of return is acceptable.

Merits:

  • It is very simple to understand and calculate;
  • It can be readily computed with the help of the available accounting data;
  • It uses the entire stream of earnings to calculate the ARR.
  • This Method considers the profitability of project.
  • In this method, right decision can be taken by comparing ARR with the cost of capital.

Demerits:

  • It is not based on cash flows generated by a project;
  • This method does not consider the objective of wealth maximization;
  • It ignores the length of the project’s useful life;
  • It does not take into account the fact that the profile can be re-invested; and
  • It ignores the time value of money.
  • It is difficult to determine the minimum rate of return/cost of capital

3. Net Present Value (NPV)

The net present value method is a classic method of evaluating the investment proposals. It is one of the methods of discounted cash flow techniques, which recognizes the importance of time value of money. It correctly postulates that cash flows arising at time periods differ in value and are comparable only with their equivalents i.e. present values.

It is a method of calculating the present value of cash flows (inflows and outflows) of an investment proposal using the cost of capital as an appropriate discounting rate. The net present value will be arrived at by subtracting the present value of cash outflows from the present value of cash inflows.

According to Ezra Solomon, “it is a present value of the cost of the investment.” The NPV is thus defined as, “the aggregate of present value of expected inflows minus the total present value of outflows; where the inflows and outflows are discounted for timing a rate of discount equivalent to the cost of capital of the firm.”

Steps to compute net present value:

  1. Estimation of future cash inflows
  2. An appropriate rate of interest should be selected to discount the cash flows. Generally, this will be the “cost of capital” of the company, or required rate of return.
  3. The present value of inflows and outflows of an investment proposal has to be computed by discounting them with an appropriate cost of capital.
  4. The net value is the difference between the present value of cash inflows and the present value of cash outflows.
$$NPV = \frac{C_1}{(1+r)^1} + \frac{C_2}{(1+r)^2} + \frac{C_3}{(1+r)^3} + \dots + \frac{C_n}{(1+r)^n} – I$$

Where:
NPV = Net Present Value
$C_1$, $C_2$… = Cash Flow for $n$ years
$I$ = Initial Investment
$r$ = Discount Factor or Cost of Capital
$n$ = Number of Years

Acceptance Rule:

If the NPV is positive or at least equal to zero, the project can be accepted. If it is negative, the proposal can be rejected. Among the various alternatives, the project which gives the highest positive NPV should be selected.

  • NPV is positive = Cash inflows are generated at a rate higher than the minimum required by the firm.
  • NPV is zero = Cash inflows are generated at a rate equal to the minimum required.
  • NPV is negative = Cash inflows are generated at a rate lower than the minimum required by the firm.

The market value per share will increase if the project with positive NPV is selected. The accept/reject criterion under the NPV method can also be put as:

  • NPV > Zero: Accept
  • NPV < Zero: Reject
  • NPV = 0: May accept or reject

Merits:

  • Consideration to total Cash Inflows: The NPV methods consider the total cash inflows of investment opportunities over the entire life-time of the projects unlike the payback period methods.
  • Recognition to the Time Value of Money: This method explicitly recognizes the time value of money, which is investable for making meaningful financial decisions.
  • Changing Discount Rate: Due to change in the risk pattern of the investor different discount rates can be used.
  • Best decision criteria for Mutually Exclusive Projects: This Method is particularly useful for the selection of mutually exclusive projects. It serves as the best decision criteria for mutually exclusive choice proposals.
  • Maximization of the Shareholders Wealth: Finally, the NPV method is instrumental in achieving the objective of the maximization of the shareholders’ wealth. This method is logically consistent with the company’s objective of maximizing shareholders’ wealth in terms of maximizing market value of shares, and theoretically correct for the selections of investment proposals.
  • Comparison of Relative Profitability: This method enables the comparison of relative profitability between projects of different life span and cash inflows occurring at different times.

Demerits:

  • Difficult to Understand: This method is difficult to understand as compared to PBP and ARR.
  • Difficult to Determine Cost of Capital: In this method, cash flows are discounted at a predetermined rate of return, known as cost of capital. It is not easy to determine COC. Moreover, if wrong COC is determined, NPV may give wrong results.
  • Unsuitable for Projects having Different Costs: This method does not provide satisfactory results when projects compared involve different amount of investment.
  • Unsuitable for Projects of Different Economic Life: A project having higher NPV with larger economic life may be less desirable than a project with a shorter economic life as an alternative. Thus, under such circumstances may give misleading results.
  • Estimation of Cash Inflows: It involves estimation of cash inflows which is a difficult task.

4. Profitability Index (PI)

This method is also known as Benefit-Cost Ratio’. According to Van Horne, the profitability Index of a project is “the ratio of the present value of future net cash inflows to the present value of cash outflows”. PI is based on the concept of discounting the future cash flows and is a ratio of present value of future cash inflows discounted at an expected rate of return to the initial cost of the investment or present value of the future outflows.

$$Profitability\ Index = \frac{Total\ Present\ Values\ of\ Cash\ Inflows}{Initial\ Investment\ (or\ PV\ of\ Outflows)}$$

Decision criteria: If the Profitability Index is greater than or equal to one, the project should be accepted otherwise reject.

Merits:

  • It takes into account the time value of money
  • It helps to accept / reject investment proposal on the basis of value of the index.
  • It is useful to rank the proposals on the basis of the highest / lowest value of the index.
  • It takes into consideration the entire stream of cash flows generated during the life of the asset.

Demerits:

  • It is somewhat difficult to compute.
  • It is difficult to understand the analytical of the decision on the basis of profitability index.

5. Internal Rate of Return (IRR)

IRR method follows discounted cash flow technique which takes into account the time value of money. The internal rate of return is the interest rate which equates the present value of expected future cash inflows with the initial capital outlay. In other words, it is the rate at which NPV is equal zero.

Whenever a project report is prepared, IRR is to be worked out in order to ascertain the viability of the project. This is also an important guiding factor to financial institutions and investors.

It is known by several names like Efficiency of Capital, “Time Adjusted ROR”, “Marginal ROR” or “Marginal Efficiency of Capital.”

Computation of IRR

The Internal rate of return is to be determined by trial and error method. The following steps can be used for its computation.

  1. Compute the present value of the cash flows from an investment, by using arbitrary selected rate.
  2. Then compare the present value so obtained with capital outlay.
  3. If the present value is higher than the cost, then the present value of inflows is to be determined by using higher rate
  4. This procedure is to be continued until the present value of the inflows from the investment are approximately equal to its outflow.
  5. The interest rate that brings about equality is the internal rate of return.

In order to find out the exact IRR between two near rates, the following formula is to be used.

$$IRR = LDR + \frac{PV_{LDR} – Investment}{PV_{LDR} – PV_{HDR}} \times (HDR – LDR)$$

Where:
LDR = Lower rate of interest
$PV_{LDR}$ = Present value at lower rate of interest
$PV_{HDR}$ = Present value at higher rate of interest

Acceptance Rule

If the internal rate of return exceeds the required rate of return, then the project will be accepted. If the project’s IRR is less than the required rate of return, it should be rejected. In case of ranking the proposals the technique of IRR is significantly used. The projects with highest rate of return will be ranked as first compared to the lowest rate of return projects.

Thus, the IRR acceptance rules are:

  • Accept if IRR > k
  • Reject if IRR < k
  • May accept or reject if IRR = k

Where, K is the cost of capital.

MERITS

  • Consideration of Time of Money: It considers the time value of money.
  • Consideration of total Cash Flows: It taken into account the cash flows over the entire useful life.
  • Maximizing of shareholders’ wealth: It is in conformity with the firm’s objective of maximizing owner welfare.
  • Provision for risk and uncertainty: This method automatically gives weight to money values which are nearer to the present period than those which are distant from it. Conversely, in case of other methods like ‘Payback Period’ and ‘Accounting Rate of Return’, all money units are given the same weight which is unrealistic. Thus, the IRR is more realistic method of project valuation. This method improves the quality of estimates reducing the uncertainty to minimum.
  • Project Ranking: The IRR is a convenient method for choosing from mutually exclusive projects or in selecting projects when capital rationing prevails. Comparison between alternatives is simplified by ranking projects according to their ROR.
  • Elimination of pre-determined discount rate: Unlike the NPV method, the IRR method eliminates the use of the required rate of return which is usually a pre-determined rate of cost of capital for discounting the cash flow consistent with the cost of capital. Therefore, the IRR is more reliable measure of the profitability of the investment proposals.

DEMERITS

  • It is very difficult to understand and use
  • It involves a very complicated computational work
  • It may not give unique answer in all situations.
  • The assumption of re-investment of cash flows may not be possible in practice.
  • In evaluating the mutually exclusive proposals, this method fails to select the most profitable project which is consistent with the objective of maximization of shareholders wealthy.
  • The result of this method may be inconsistent compare to NPV method, if the projects differ in their (a) expected lives (b) investment or (c) timing of cash inflows.

IRR vs. NPV: Comparison of both the techniques

  • Both techniques use Discounted Cash Flow (DCF) method.
  • Both recognize the time value of money.
  • Both take into account the cash flows over the entire life of the project.
  • Both are consistent with the objective of maximizing the wealth of shareholders.
  • Both are difficult to calculate.
  • Both techniques may often give contradictory result in the case of alternative proposals which are mutually exclusive.

Contrast, i.e. Points of difference

  1. Interest Rate: NPV uses the firm’s cost of capital as Interest Rate. Unless the cost of capital is known, NPV method cannot be used. Calculating cost of capital is not required for computing IRR.
  2. NPV may mislead when dealing with alternative projects or limited funds under the conditions of unequal lives. IRR allows a sound comparison of the project having different lives.
  3. NPV may give different ranking in case of complicated projects as compared to IRR method.
  4. NPV assumes that intermediate cash flows are re-invested at firm’s cost of capital whereas IRR assumes that intermediate cash inflows are reinvested at the internal rate of the project.
  5. The results of IRR method may be inconsistent compared to NPV method, if the projects differ in their (a) expected lives or (b) investment or (c) timing of cash inflow.
  6. IRR method favours short-lived project so long as it promises return in excess of cut-off rate whereas NPV method favours long-lived projects.
  7. Sometimes IRR may give negative rate or multiple rates. NPV does not suffer from the limitation of multiple rates.

Recommendation

The NPV method is generally considered to be superior theoretically because:

  • It is simple to calculate as compared to IRR.
  • It does not suffer from the limitation of multiple rates.
  • NPV assumes that intermediate cash flows are reinvested at firm’s cost of capital. The reinvestment assumption of NPV is more realistic than IRR method.

But IRR method is favored by some scholars because:

  • It is easier to visualize and to interpret as compared to NPV.
  • Even in the absence of cost of capital, IRR gives an idea of project’s profitability.

Note:
Unless the cost of capital is known, NPV cannot be used.
IRR method is preferable to NPV in the evaluation of risky projects.


PRACTICAL EXAMPLES

Question: 1

Cost of Project = ₹ 10,00,000, $N$ = 5 years

Year12345
CFAT3,00,0002,00,0004,00,0001,00,0005,00,000

Find Pay Back Period.

Question: 2

Cost of Project = ₹ 10,00,000
$N$ = 5 years
Annual Cash Flow = ₹ 3,50,000

Find Pay Back Period.

Question: 3

Cost of Project = ₹ 12,00,000
$N$ = 5 years

Year12345
CFAT4,00,0003,50,0002,50,0003,50,0003,00,000

Find Pay Back Period.

Question: 4

Cost of Project = ₹ 15,00,000

Year12345
CFBT4,00,0005,00,0006,00,0007,00,0008,00,000

Salvage ₹ 3,00,000
$N$ = 5 years
Depreciation is on SLM.
Tax = 0.50

Find Accounting Rate of Return.

Question: 5

Cost of Machine: ₹ 20,00,000
Scrap Value: ₹ 2,00,000

Year12345
CFBT4,50,0005,50,0006,50,0007,50,0008,50,000

Tax Rate is 50%.
Dep. Method is on SLM.

Find Accounting Rate of Return.

Question: 6

Cost of Machine: ₹ 20,00,000

Year12345
CFBT4,50,0005,50,0006,50,0007,50,0008,50,000

Tax Rate is 50%.
Dep. Method is on SLM.

Find Accounting Rate of Return.

Question: 7

Cost of Machine = ₹ 20,00,000
Scrap Value = ₹ 5,00,000

Year12345
CFBT4,50,0005,50,0006,50,0007,50,0008,50,000

Tax Rate is 50%.
Depreciation Method is on SLM.

Find Accounting Rate of Return.

Question: 8

Cost Value is ₹ 10,00,000
The required Rate of Return is 10%.

Year12345
CFAT2,00,0003,50,0004,50,0004,00,0005,00,000

Find NPV (Net Present Value).

Question: 9

Cost Value is ₹ 10,00,000
The require Rate of Return is 15%.

Year12345
CFAT2,00,0003,50,0004,50,0004,00,0005,00,000

Find Net Present Value.

Question: 10

Cost of Project: ₹ 10,00,000
The required Rate of Return is 10%.

Year12345
CFAT2,00,0003,50,0004,50,0004,00,0005,00,000

Find Internal Rate of Return and Profitability Index.

Question: 11

Two alternative capital expenditure proposals each costing ₹ 10,00,000. Providing the following expected net cash inflows:
Discounting factor is 10%.

YearProject XProject Y
13,00,0001,00,000
24,00,0003,00,000
35,00,0004,00,000
43,00,0006,00,000
52,00,0004,00,000

Evaluate the proposal on the basis of:
1. Pay Back Period
2. Net Present Value
3. Profitability Index
4. Internal Rate of Return

Question: 12

Two alternative Capital expenditure proposal each costing 10,00,000. Providing following expected Cash Flow are before tax and depreciation:
There is Dep. method – SLM.
Tax rate is on 50%.

YearProject XProject Y
13,00,0001,00,000
24,00,0003,00,000
35,00,0004,00,000
43,00,0006,00,000
52,00,0004,00,000

Calculate:
ARR, NPV, PBP, IRR, PI

Question: 13

By investing ₹ 50,000 in a project the following Cash Flow is available.
The cost of capital is 10%.

YearCash Flow
122,000
218,000
314,000
416,000
510,000

Calculate:
1. NPV, 2. PI, 3. PBP

Question: 14

Aman Co. Ltd. wants to purchase a machine the particulars are as under:

ParticularsValue
Capital Investment / Cost1,30,000 ₹
Estimated life5 Yrs
Scrap Value10,000 ₹
Tax Rate50%

Estimated profit before dep. & tax are as under:

Year12345
CFBT24,00035,00065,00048,00078,000

Calculate:
1. PBP
2. ARR

Question: 15

Cost of Investment: ₹ 5,20,000
Life of Project: 5 yrs.
Salvage Value: ₹ 20,000
Discounting Factor: 10%
Tax Rate: 50%

Year-wise Data (CFBT)

YearSalesExp.
14,00,0002,40,000
24,00,0002,40,000
33,50,0002,00,000
45,00,0002,40,000
55,20,0002,40,000

Calculate all the Method.

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