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Everything you need to know about the techniques of capital budgeting. Some of the techniques can be grouped in the two categories as mentioned below:

1. Non-Discounted Cash Flow Techniques: (a) Accounting Rate of Return Method (b) Payback Period Method;

2. Discounted Cash Flow Techniques: (a) Net Present Value Method (b) Internal Rate of Return Method (c) Profitability Index Method.

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*Capital budgeting is the most important decision in financial management. Capital budgeting is concerned with long-term investment of funds to create production capacity of a firm in anticipation of an expected flow of benefits over a long period of time.*

* The capital budgeting techniques or evaluation of investment proposals have considerably gained the importance. This is truer in the modern business environment. After the introduction of New Economic Policy, the environment in the industry and service sector have considerably changed. *

**Techniques and Methods used in Capital Budgeting (with advantages, disadvantages, examples, formula and calculations)**

### Techniques of Capital Budgeting – Non-Discounted Cash Flow and Discounted Cash Flow Techniques

Capital budgeting is the most important decision in financial management. Capital budgeting is concerned with long-term investment of funds to create production capacity of a firm in anticipation of an expected flow of benefits over a long period of time.

According to Charles T. Horngren and George Foster, “Capital budgeting is as the making of long-term planning decisions for investments and their financing.”

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Capital budgeting is an important technique widely used for the evaluation of various capital investment proposals and selecting the most appropriate source of finance for the chosen investment proposal. In general, investing in long-term fixed assets is called capital budgeting.

In capital budgeting, we forecast a set of cash flows, find the present value of these cash flows, and make the investment only if the present value of the inflows is greater than the investment’s cost.

A number of capital budgeting techniques (investment criteria) are used in taking a capital investment decision.

**These techniques can be grouped in the two categories as mentioned below: **

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**1. Non-Discounted Cash Flow Techniques: **

(a) Accounting Rate of Return Method

(b) Payback Period Method

**2. Discounted Cash Flow Techniques: **

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(a) Net Present Value Method

(b) Internal Rate of Return Method

(c) Profitability Index Method

The Net Present Value (NPV) is the best method, primarily because it addresses directly the central goal of financial management-maximising the shareholders’ wealth. However, all of the methods provide useful information, and all are used in practice at least to some extent.

**1. Non-Discounted Cash Flow Techniques: **

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**(a)** **Accounting Rate of Return Method****: **

The accounting rate of return, also known as the return on investment, is calculated on the basis of accounting statements. The accounting rate of return is equal to the average net operating profit divided by the average investment.

**It is calculated by applying the following formula: **

**Merits of Average Rate of Return Method: **

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**The average rate of return method has the following merits: **

(i) Simplicity- This method of capital budgeting is simple to understand and use.

(ii) Accounting profitability- In this method, accounting profits over the economic life of the project are considered in evaluating the project. The required data are easily available from the firm’s financial statements.

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**Demerits of Average Rate of Return Method:**

**The average rate of return method has the following demerits: **

(i) No consideration of time value- This method ignores time value of the earnings.

(ii) Overlook of cash flows- Accounting profit is taken into consideration instead of cash flows from the project.

(iii) Inconsistent with the objective- This method is inconsistent with the objective of maximising shareholders’ wealth.

(iv) Arbitrary cut-off- Firms using average rate of return use arbitrary cut-off rate in taking a decision about a project.

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Payback period method is traditional and simple most method of capital budgeting. It is defined as the length of time that is required for a stream of cash inflows from the investment to recover the original cash outlay invested in the project.

**When periodic cash inflows from the investment are equal, the following formula is used to compute payback period: **

**Merits of Payback Period Method: **

**Payback period method has following merits: **

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1. Simplicity- It is simple to understand and easy to calculate.

2. Emphasis on early returns- This method lays emphasis on early returns. Investments with shorter payback period will be less risky.

3. Based on cash flows- The evaluation of capital expenditures is carried out on the basis of cash inflows arising from the investments.

**Limitations of Payback Period Method****: **

**Though the payback period method is simple and lays emphasis on liquidity and risk, it has following limitations: **

I. No consideration of time value- This method ignores time value of the earnings.

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II. Overlook of remaining cash flows- Cash flows from the project after the recovery of cost are ignored.

III. Inconsistent with the objective- This method is inconsistent with the objective of maximising shareholders’ wealth as it does not take into consideration all cash flows.

IV. Supplementary technique- Payback period method does not say anything about selection or rejection of projects. It can be used as supplementary technique to discounted techniques.

**2. Discounted Cash Flow Techniques: **

Net present value technique is most popular and most widely used technique of capital budgeting. This technique lays emphasis on time value of money. This method is consistent with the objective of shareholders’ wealth maximisation.

In this method, present values of all cash flows are computed. Cost of capital (required rate of return) is employed as discount rate. The excess of present value of all inflows over present value of initial investment is equal to net present value of the investment made in the project.

**Merits of Net Present Value Method: **

**Net Present Value method has following merits: **

1. Recognition of time value of money- In net present value method, present values of all cash inflows are computed. Decision is taken on the basis of excess of present value of all cash flows over present value of cash outflows.

2. Consideration of all cash flows- This method considers cash inflows rather than accounting profits. All cash flows are considered.

3. Consistent with objective- Net present value method is consistent with the objective of maximisation of shareholders’ wealth. Net present value of the project is addition to the shareholders’ wealth.

**Demerits of Net Present Value Method: **

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**Net Present value method has following limitations: **

1. Difficult to compute- Net present value method is difficult to understand and calculation of net present value is difficult and requires skills.

2. Work out of appropriate cost of capital difficult- Net present value cannot be computed if cost of capital is unknown. Weight average of capital is used to find the present values of cash inflows. It is particularly difficult to measure cost of equity.

3. Not suitable in capital rationing- Net present value method is not suitable for evaluating capital expenditure when funds are limited.

4. Misleading result in case of mutually exclusive projects- If projects having different life span and capital size are to be evaluated, net present value method can give the misleading results. In such situation, profitability index is more suitable.

**(b)** **Internal Rate of Return Method****: **

A project’s internal rate of return is the discount rate that makes the present value of its inflows equal to its cost. This is equivalent to forcing the net present value to equal to zero. The internal rate of return is an estimate of the project’s rate of return. The internal rate of return is also known as yield on investment and marginal efficiency of capital.

A project is selected if the internal rate of return is more than the required rate of return (cost of capital). Net present value method is preferred in evaluating the capital projects. In small project, the internal rate of return may be higher, but its net present value may be lower than the net present value of large project. Since the objective in financial management is to maximise the shareholders’ wealth, net present value method is preferred to the internal rate of return method of capital expenditure evaluation.

**1. Calculation of IRR when Cash Inflows are Equal: **

When cash inflows are equal, the concept of present value of an annuity is applied.

**We know that: **

P = C × PVFA (r%, n)

Where,

P = present value of an annuity

C = annual cash inflow

PVFA = present value factor for annuity

After finding PVFA, we can read the rate of interest corresponding to the calculated PVFA and the life of the project (number of years) from PVFA table. This rate of interest is the internal rate of return of the project.

**The following steps are needed in computing the internal rate of return of a project: **

(i) Calculate payback period as given below and treat it as PVFA.

(ii) In PVFA table, move in the row which is equal to the life of the project and find the value which is equal to the payback period calculated above. If we get the exact value, the rate of interest corresponding to this value in the PVFA table is equal to the internal rate of return of the project.

(iii) In case we do not find the exact value in the PVFA table, we note down two values from the table, one lower than calculated payback period and another higher than payback period. Then, we find corresponding interest rates to the values from PVFA table. These interest rates are treated as lower discount rate (L) and higher discount rate (H).

**The following formula is used to find exact internal rate of return by interpolation: **

**2. Calculation of IRR when Cash Inflows are Unequal: **

When cash inflows are unequal, the trial and error approach is used to find the discount rate that makes present value of cash inflows from the project equal to the initial investment. This discount rate is the internal rate of return.

**The following steps are used to find the internal rate of return: **

(i) Find the fake payback period by dividing the initial investment by average cash inflows.

(ii) Move in the row which is equal the life of the project in PVFA table, and find the value which is equal to the fake payback period. If exact value is not found, look for the value approximate to fake payback period. Note down the corresponding interest rate to the approximate value from PVFA table.

(iii) Compute the present value of cash inflows at discount rate equal to rate of interest noted above. If the present value is greater than initial investment, designate this as lower discount rate (L). Now, move to higher discount rate and repeat this process until we get the discount rate which makes the present value of cash inflows lower than the initial investment. Designate this rate as higher discount rate (H).

If the present value is lower than initial investment, designate this as higher discount rate (H). Now, move to lower discount rate and repeat this process until we get the discount rate which makes the present value of cash inflows higher than the initial investment. Designate this rate as lower discount rate (L).

(iv) The following formula is used to find exact internal rate of return by interpolation-

**Merits of Internal Rate of Return Method: **

**Internal rate of return method of capital budgeting has following merits: **

1. Recognition of time value of money- In internal rate of return method, present values of all cash inflows are computed. Decision is taken on the basis of equality of present value of all cash flows to present value of cash outflows.

2. Consideration of all cash flows- This method considers cash inflows rather than accounting profits. All cash flows are considered.

3. No requirement of cost of capital- There in no pre-requirement of knowledge of cost of capital. Internal rate of return can be calculated without the required rate of return. However, the decision is taken by comparing the internal rate of return with the cost of capital of investment.

4. Consistent with the objective- In the selected project, internal rate of return is more than cost of capital. So, there is net present value of the project, which is addition to the wealth of shareholders.

**Demerits of Internal Rate of Return Method: **

**The internal rate of return method has following limitations: **

1. Difficult to calculate- The calculation of internal rate of return is complicated.

2. Unrealistic reinvestment assumption- It is assumed that cash flows generated by the project can be reinvested at its internal rate of return. This assumption is unrealistic.

3. Negative or multiple results- In some cases, IRR may be negative. In non-conventional projects there is possibility of multiple internal rate of returns.

**(c)** **Profitability Index Method****: **

Profitability index method of capital expenditure evaluation is a version of net present value method. In this method, the ratio of present value of cash inflows to present value of cash outflow is calculated and the decision is taken on the basis of this.

In situation of capital rationing, profitability index method is preferred to net present value method. If unlimited capital is available, the net present value method is suitable. In case of limited capital, net present method may give misleading decision. Profitability index method removes this limitation of net present value method.

A project is selected if its profitability ratio is greater than one. The profitability index of less than one indicates loss in undertaking the project. In this situation, firm’s cost of capital exceeds the rate of return.

**Techniques of Capital Budgeting (With Examples, Advantages and Disadvantages)**

Capital budgeting decision involves three steps. First, to compute the cash flows associated with the project. Second, to estimate the cost of capital or minimum required rate of return, that is used to calculate present value of cash flows of the project. The third step is to apply some investment evaluation criteria to assess the viability of a project. This Investment assessment criteria is termed as capital budgeting technique.

The decision to accept or reject a project is done by applying some capital budgeting technique.

**These capital budgeting techniques can be classified as: **

1. Traditional (or Non-Discounting) Techniques and

2. Modern (or Discounted Cash Flow- DCF) Techniques.

**1. Traditional or Non-Discounting Cash Flow Techniques****: **

Traditionally, capital projects have been evaluated on the basis of average profits or cash flows without considering time value of money. There are two Non-Discounting techniques- Accounting Rate of Return (ARR) and Pay Back Period (PB Period).

i. Accounting Rate of Return (ARR)

ii. Payback Period (PB Period)

**These techniques are explained below:**

Accounting rate of return is based on accounting profits. This is a simple technique for calculating expected return from a project. This is the simplest way of computing the return from any project. Accounting rate of return, also known as the Average rate of return or ARR calculates the return, generated from average profit of the project. Accounting rate of return is calculated as a percentage of average investment.

**Computation of AAR: **

**Accounting rate of return is computed by dividing the average annual profits after tax by the average investment by using the following formula: **

**Average Annual Profits after Taxes: **

**There are two situations for which we need to compute the average profits after taxes:**

**(a) Equal Annual Profits: **

When the amount of annual profits is expected to be same for all the years, the average annual profit will be equal to the amount of annual profit after taxes. Suppose there is a project which is expected to generate an equal, amount of annual profit after tax of Rs.10,000 for the next five years, then the expected average annual profit for this project will be equal to Rs.10,000.

**(b) Unequal Amount of Annual Profits: **

It is quite unrealistic to assume that the expected annual profits will remain same throughout the life of the project. In reality, expected profits differ in different years and therefore we need to calculate average profit. Average profit is normally calculated using simple average. If annual profits are P1, P2, P3……..PN upto N years than the average profit will be –

**Average Investment:**

Average investment is used in the denominator of ARR formula.

**It can also be computed in different ways as explained below:**

i. Original Cost of Investment – When no information is given regarding the depreciation and salvage value, the original cost of investment can be used as average investment. For example- there is machine costing Rs.1,50,000 and has installation expenses of Rs.50,000. Then the average investment amount for this machine would be Rs.2,00,000.

ii. Average investment after considering depreciation and salvage value

We know that all investments are subject to depreciation and they also have some salvage value. Hence depreciation as well as salvage value should be considered while calculating average investment.

**When the investments are subject to depreciation and salvage value, we calculate average investment by using the following formula: **

Please note that here we assume Straight Line Method (SLM) of depreciation.

**Decision Making Criteria using ARR****: **

Accounting rate of return (ARR) is considered as a measure of return from the project. It is compared with some benchmark or predetermined or minimum required rate of return so as to decide about the acceptability of the project.

**In Case of Independent Projects****: **

If Accounting rate of return is higher than the minimum required rate of return then the project is accepted, if ARR is less than the minimum required rate of return then the project is rejected. When ARR is equal to the minimum required rate of return then there is indifference.

**In Case of Mutually Exclusive Projects (or where Projects Need to be Ranked)****: **

Mutually exclusive projects mean that the selection of one project precludes the selection of others. In essence, we can select only one out of the given mutually exclusive projects. Hence we need to ‘Rank’ projects and select the one with the highest rank. Therefore, In case of mutually exclusive projects, we can rank the projects on the basis of their ARR. The project having highest ARR is given Rank No. 1 and the project with lowest ARR is ranked in the last. Then the project with 1st rank is accepted.

Accept if ARR > Predetermined or Benchmark Rate of Return

Reject if ARR < Predetermined or Benchmark Rate of Return

Indifferent if ARR = Predetermined or Benchmark Rate of Return

Rank the projects from Highest ARR to Lowest ARR

ARR is one of the simplest methods for the evaluation of capital projects.

**This method has the following Advantages: **

i. Simple and Easy – It is simple, easy to compute and understand.

ii. Based on Accounting Data – It is based on accounting data which can be easily accessed from the company’s books of account and future accounting profits can also be estimated using past data.

iii. Expressed in Percentage Terms – It measures the benefits in percentage terms which makes it easily comparable and provides an easy rule to make investment decision.

**Limitations (Disadvantages) of ARR****: **

**Although ARR is the most simple and easy method of capital budgeting, it suffers from serious limitations which are discussed below:**

**i. It is based on Accounting Profits and not on Cash flows and hence is not consistent with objective of shareholders’ wealth maximisation:**** **

The first problem with ARR method is that it is based on accounting profit rather than cash flows. The objective of financial management is to maximize the wealth of the shareholders. To attain this goal, the focus must be on the cash flows rather than on the accounting profits. Further accounting profit is a vague and ambiguous term. Profit can be measured in a variety of ways such as gross profit, net profit, profit before tax, profit after tax, operating profit etc.

**ii. No consideration of Time Factor:**** **

The other major limitation of this method is that it does not take into consideration the time value of money. This method treats all profits generated in different years at par which can be added together for the calculation of Average profit. Thus it does not consider the timing of benefits and a profit of Rs.10,000 in 1st year is considered to have same value as Rs.10,000 profit in 2nd year.

**iii. Not Suitable in Case of Capital Rationing Situation: **

Capital rationing means that limited capital is available for different projects. It is possible that ARR may be same for two projects but they require different amount of investment. Therefore given the capital budget (i.e. limited amount of capital) investment decision cannot be taken just on the basis of ARR. For example for two machines A and B the average profits are Rs.10,000 and Rs.15,000 while average investment is Rs.1,00,000 and Rs.1,50,000 respectively.

Hence both the projects have ARR as 10%. However they differ in terms of their investment requirements. The availability of funds is also another concern which should be taken into consideration while making investment decision.

Another Traditional or Non-Discounting Method is Payback Period Method.

This is also one of the simplest and most commonly used non discounting techniques of capital budgeting. As the term suggests the ‘Payback period’ is the time period required to recover the original cost of investment. Using this method, the firm aims to find out the time period or time span in which the cost of investment will be recovered. Hence Payback period provides a signal about the liquidity of a project.

If payback period is say 3 years then it means that the project will recover its initial cost in 3 years’ time. Beyond three years it will generate only benefits.

Payback period method is based on cash flows i.e. CFAT (Cash flows after tax).

**Payback period may be computed in two ways: **

**I. When Annual Cash Flows are Equal:**** **

The first type of project is one which involves equal amount of cash flows for various years.

**The payback period is computed by using the following formula: **

PB = Investment / Annual NCF

For example- suppose there is a project which is expected to generate Rs.5,000 for the next five years. If the cost of the project is Rs.12,500 then the payback period for the project is –

PB =12,500 / 5,000

PB = 2.5 years

The PB period comes out to be 2.5 years. Thus, it will take 2 years and 6 months for this project to cover the initial investment of Rs.12,500.

**II. When Annual Cash Flows are Unequal****: **

In reality we have different cash flows in different years. In this case the cash flows are unequal. Here we use the concept of cumulative cash inflows. The cash flows are added for various years and cumulative cash inflows are computed until the sum total of cash inflows becomes equals to initial investment.

Let us assume that a project has Rs.4,00,000 of cost of investment and it generates the following cash flows over its five years’ life – i.e. Rs.1,25,000, 1,40,000, 1,35,000, 1,20,000 and Rs.1,25,000 respectively.

**The following table shows the calculation of cumulative CFAT: **

As you can see the payback period is three years because cumulative cash flows are equal to initial investment of Rs.4,00,000 at the end of three years.

In the above example, cumulative cash flows are matched with the cost of investment at the end of a particular year, however, it is also possible that cumulative cash flows are not exactly matching with the cost of the project at the end of a specific year. In such a case we make use of ‘Interpolation’.

The payback period method can also use to take accept-reject decision for any project. The companies usually have some predetermined or target payback period which works as a benchmark. Actual PB period is compared with some benchmark or target or predetermined payback period so as to decide about the acceptability of the project.

**a. In Case of Independent Projects: **

If calculated Payback period is less than the target payback period then the project is accepted. If it is more than the target payback period then the project is rejected. When Payback period is equal to the target payback period then there is point of indifference.

**b. In Case of Mutually Exclusive Projects (or Where Projects Need to be Ranked): **

Mutually exclusive projects mean that the selection of one project precludes the selection of others. In essence, we can select only one out of the given mutually exclusive projects. Hence we need to ‘Rank’ projects and select the one with the highest rank. Therefore, In case of mutually exclusive projects, we can rank the projects on the basis of their PB period. The project having lowest PB period is given Rank No. 1 and the project with highest PB period is ranked in the last. The project with 1st rank is accepted.

**Decision Rule – PB Period: **

Accept if PB period < Predetermined or Target PB period

Reject if PB period > Predetermined or Target PB period

Indifferent if PB period = Predetermined or Target PB period

Rank the projects from Lowest PB period to Highest PB period.

**Advantages of PB Period: **

Payback period is one of the simplest methods for the evaluation of capital projects.

**This method has the following advantages: **

**i. Simple and Easy to Calculate and Understand: **

It is simple, easy to compute and understand. Its calculation does not require special skills in computation and its interpretation is also straight forward. It is expressed in number of years which can be compared across projects.

**ii. Based on Cash Flows: **

Payback period is based on Cash flows unlike ARR method which is based on accounting profit. Cash flows is a precise term and is considered better option in measurement of future benefits.

**iii. Provides an Indication of Liquidity of the Project: **

Payback period is the time period in which the initial cost of the project is recovered. Hence it clearly provides an idea about the liquidity of the project. Most of the firms place very high important on the liquidity. It tells us the time when the original investment will be recovered and companies can arrange funds accordingly.

**iv. Indicates Riskiness of the Project: **

It can give us very good indication of riskiness of the project. The longer the time it takes to recover the initial investment, the more risky is the project. This is because future is uncertain. It helps in identifying the risk of the project on the basis of the time taken to recover the cost.

**Limitations (Disadvantages) of PB Period****: **

**Although PB period is simple and easy method of capital budgeting, it suffers from serious limitations which are discussed below: **

**i. No Consideration of Time Factor and Time Value of Money:**** **

The major limitation of this method is that it does not take into consideration the time value of money. This method treats all cash flows generated in different years at par which can be added together for the calculation of cumulative cash flows. Thus it does not consider the timing of benefits and a cash inflow of Rs.10,000 in 1st year is considered to have same value as Rs.10,000 cash inflow in 2nd year.

For example- there are two projects X and Y, both have the same investment outlay of Rs.20,000.

**The cash flows are given below:**

In this case, both the projects have the same payback period of three years, however, more money is in case of project Y as compared to project X. The money which is received earlier has more value than the money which is received later. Payback period method will put both the projects at par because their PB period is same. However we can see that project Y is better than Project X due to time value of money.

**ii. Does not consider all cash inflows and hence is inconsistent with the objective of shareholders’ wealth maximization:**** **

PB period method does not take into account the cash flows occurring after the payback period. Hence it does not consider all cash flows occurring throughout the life of the project. So, we may get biased results in favour of a project which provides higher cash inflows in initial years. It is quite possible that a project provides higher cash flows in later years, later than its Payback period. However all the cash inflows occurring after payback period are ignored.

Since it does not consider cash flows occurring after payback period, this method is considered to be a method of assessing liquidity of a project rather than its profitability. A project having shorter Payback period is more liquid than a project having longer payback period.

**Consider the case of following two projects which have the same cost of Rs. 2,00,000 and the cash flows are given below:**

Both the projects have the same payback period which is 3 years, on the basis of payback criteria both projects are equally good. However, we can easily see that the project B is far better than project A as the cash flows after payback period are higher for project B. Thus the payback method fails to take into consideration the cash flows occurring after payback period.

**Payback period is a measure of liquidity of a project and not a measure of its profitability****: **

It is true that Payback period method is a measure of liquidity of a project rather than its profitability. This is because it does not consider all cash flows associated with the project. PB period method ignores all cash inflows occurring after PB period. Hence if decision regarding acceptance of a project is undertaken solely on the basis of PB period, we may make an incorrect decision.

Therefore, PB period method is never used in isolation when deciding whether to accept a project or reject. It is always used as a supplementary technique in addition to Net present Value (NPV) or Internal rate of return (IRR).

**Limitations of Traditional or Non Discounting Techniques:**** **

**The two non discounting methods (ARR and Payback period), although easy to calculate and simple to understand, suffer from the following limitations: **

**i. Completely Ignores Time Factor (or Time Value of Money): **

Both the Non Discounting methods do not consider time value of money. Profits or cash flows occurring in different years are added without applying discounting technique or without converting them into their present value.

**ii. Inconsistent with the Objective of Shareholders’ Wealth Maximization:**** **

Both the Non-Discounting methods are not consistent with the objective of shareholders’ wealth maximization. ARR method uses profits rather than cash flows. Payback period method does not consider all cash flows. It ignores all cash flows occurring after the payback period.

**2. Modern or Discounted Cash Flow (DCF) Techniques****: **

The main problem with traditional or Non-discounting techniques is that they ignore timing of cash flows and time value of money and are also inconsistent with the objective of shareholders’ wealth maximisation.

Discounted cash flow techniques overcome these limitations and provide much better criteria for project evaluation. These techniques consider time factor or time value of money by discounting cash flows occurring in future. Hence the name is Discounted Cash flows. We calculate present value of future cash flows by discounting them at an appropriate rate of return (generally cost of capital or minimum required rate of return). These present values can be added together to calculate total present value.

**The followings are three main DCF techniques: **

i. Net Present Value (NPV) method

ii. Profitability Index (PI)

iii. Internal Rate of Return (IRR)

**i. Net Present Value** **(NPV) Method: **

Net Present Value (NPV) method is the most theoretically sound method for evaluation of capital projects. This method is consistent with the objective of shareholders’ wealth maximisation. In NPV method we consider cash flows as well as time value of money.

NPV is excess of present value of all cash inflows over present value of all cash outflows.

NPV = Present Value of all Cash inflows – Present Value of all Cash outflows

The amount of NPV is the net addition to the wealth of the shareholders in present value terms.

NPV of the project is present value of the cash inflows minus present value of cash outflow.

If project involves initial cash outflow and is followed by cash inflows then NPV formula will be –

Where, time ‘t’ is ranging from 1 to ‘n’, CFAT_{t} is the cash flow after tax at the end of time ‘t’, k is the cost of capital which is used as a discount rate, and CO_{o} is the cash outflow arising in the beginning of the year.

If project involves cash outflow not just in initial year but in later years as well then NPV formula will be –

All the terms are same as given above. CO_{t} is cash outflow in year t.

**Decision Making Criteria: **

The NPV technique is most frequently used technique of capital budgeting. NPV is positive when present value of cash inflows is higher than present value of cash outflows. NPV is negative when present value of cash inflows is lower than present value of cash outflows. NPV is zero when present value of cash inflows is equal to present value of cash outflows.

Net present value shows how much present value is added to shareholders’ wealth if the project is taken up. For example if NPV of a project is Rs.12,000, then we can say that shareholders’ wealth will increase by Rs.12,000 if the project is accepted. On the other hand if NPV is negative say -12,000 rupees then we can say that shareholders’ wealth will decrease by Rs.12,000 if the project is accepted.

Therefore we accept a project when NPV is positive, we reject a project when NPV is negative and we are indifferent when NPV is zero.

When the projects are mutually exclusive and we need to rank the projects then 1st rank goes to the project with highest NPV and last rank to the one having lowest NPV.

Accept if NPV > 0 or positive

Reject if NPV < 0 or negative

Indifferent if NPV = 0

Rank the projects from Highest NPV to Lowest NPV

**Advantages of NPV Method: **

**There are several benefits of using NPV method for evaluating capital projects:**

**i. Considers Cash Flows Rather than Accounting Profits****: **

It considers cash flows for the purpose of analysis rather than the accounting profits. Accounting profits do not reflect the true picture of the financial position of the firm. Accounting profits can be a vague term and can be manipulated by using different accounting methods. Cash flows do not suffer from these limitations.

**ii. Considers All Cash Flows throughout the Life of the Project:**** **

NPV calculation is based on all cash flows during the entire life of the project. Hence it reflects true value addition to the shareholders’ wealth.

**iii. Considers Time Factor or Time Value of Money as well as Risk:**** **

One of the biggest advantages of NPV technique is that it takes into consideration the time value of money. Here we convert all cash flows into their present values to find out NPV of the project or asset. We use a discount rate to account for time value of money and risk profile of the project while calculating present value of cash flows from the project.

**iv. Different Discount Rates can be Used in Different Years:**** **

Different discount rates can be easily incorporated into the NPV computations. Thus we can see the sensitivity of the discount rates on the profitability of the project.

**v. Consistent with the Objective of Shareholders’ Wealth Maximization:**** **

NPV shows how much value is added to shareholders’ wealth or to firm value. Thus NPV technique is consistent with the fundamental objective of financial management i.e. shareholders’ wealth maximization. The wealth of the shareholders will be maximized when firm takes up the project which generates extra cash flows in present value terms i.e. the projects having positive NPV.

**vi. NPV Values of Two Projects can be Added to Find Out Total NPV:**** **

NPV values are additive i.e. NPV of two projects can be added together to get total NPV. For example if two projects A and B have NPV as Rs.10,000 and Rs.20,000 respectively then the total NPV of project A and B will be Rs.30,000.

**Limitations (Disadvantages) of NPV Method: **

**Although NPV is theoretically the most sound method of capital budgeting it suffers from the following limitations: **

**i. Somewhat difficult to compute:**** **

It is somewhat difficult to compute as compared to the traditional tools of capital budgeting such as payback method and ARR method. However with the use of computers this limitation can be done away with.

**ii. Determination of appropriate discount rate is difficult:**** **

NPV is based on one very important factor, i.e. discount rate which is normally the weighted average cost of capital (WACC). Computation of WACC itself is a difficult task and may involve subjectivity. Any mistake in calculation of discount rate may change NPV and lead to incorrect decision.

**iii. NPV is an absolute value, does not consider size of investment and hence not suitable in situation of capital rationing: **

NPV is based on absolute amount of cash flows and is expressed in rupees. Given a choice between two projects, we will choose a project with higher NPV, though there is a possibility that the project with higher NPV may also involve huge investment. Under the situation of limited capital i.e. capital rationing, it is not possible for the firm to take up those projects. The NPV analysis fails to take it into account the size of investment and hence is not suitable in situation of capital rationing.

**iv. Does not consider life span of the project: **

When projects are independent then there is no problem because then all projects having positive NPV can be accepted. However when two projects are mutually exclusive and have different life span, then NPV method may not give correct decision.

For example- suppose there are two projects with 4 years and 6 years life having the same NPV of let’s say, Rs.24,000. NPV criteria would suggest that both the projects are equally good; however, we can see that first project provide Rs.24,000 NPV in just 4 years and hence project A is better than project B.

Despite these limitations, NPV is one of the best and most commonly used technique of capital budgeting and represents a significant improvement over the traditional techniques of capital budgeting.

**ii. Profitability Index Method****: **

One of the main limitations of NPV technique is that it is expressed in absolute terms in rupees. There is no problem if the projects are independent and there is unlimited amount of capital for investment. However in reality we have limited amount of capital to be invested in worthy projects.

Therefore we cannot use NPV method when there is situation of capital rationing. Capital rationing means that limited amount of capital is invested in a number of projects so as to maximise NPV. In such a case we, need to use a relative measure such as Profitability index.

Profitability index is a relative measure which is computed by dividing present value of cash inflows by present value of cash outflows.

Profitability index is also known as benefit cost ratio. It is a useful tool for ranking projects in case of capital rationing situation.

PI = Present Value of Cash Inflow / Present Value of Cash Outflows

It must be noted that Profitability Index (PI) is a relative concept. It shows how much present value of cash inflows is generated for every one rupee invested. It is a number not expressed in any unit of measurement unlike NPV which is expressed in absolute value in rupees. If PI is 1.5 then it means that a rupee invested in the project generates Rs.1.5 present value of cash inflows.

It can be seen from the formula of Profitability Index (PI) that when present value of cash inflows is higher than present value of cash outflows PI is more than 1 and hence project should be accepted. When present value of cash inflows is lower than present value of cash outflows then PI is less than 1 and hence project should be rejected. When present value of cash inflows is equal to present value of cash outflows then PI is equal to 1 and here we are indifferent.

Accept if PI > 1

Reject if PI < 1

Indifferent if PI = 1

Rank the projects from Highest PI to Lowest PI

**Relationship between NPV and PI Methods: **

It must be noted that NPV and PI methods are related. Whenever PI is more than one, NPV must be positive because in such a case present value of cash inflows is greater than present value of cash outflows. When PI is less than one, NPV must be negative because here present value of cash inflows is less than the present value of cash outflows. When PI is equal to one, NPV must be zero because here present value of cash inflows is equal the present value of cash outflows.

**Relationship between NPV and PI Method****: **

When PI > 1, NPV is positive

When PI < In NPV is negative

When PI = 1, NPV is zero

**Advantages of PI Method: **

PI technique is a modification to NPV method and hence it contains all the benefits which are applied for NPV method. It is better than NPV method when there is limited amount of capital or situation of capital rationing. In such a case limited capital needs to be distributed over a number of projects so as to maximise NPV. PI method is used to rank and select projects in such a situation.

**The main benefits of PI method are:**

i. Considers Time value of Money and Risk – PI method considers time value of money and risk of the project by using appropriate discount rate.

ii. Based on Cash flows – PI method, like NPV is based on cash flows rather than accounting profit.

iii. Consistent with the objective of financial management – PI method is consistent with the objective of shareholders’ wealth maximization.

iv. Relative Measure – Unlike NPV which is an absolute measure, PI is a relative concept. PI tells the present value of cash inflows generated per rupee of cash outflow. Therefore it can be used to rank and compare projects having different amounts of investment.

v. Useful in situation of capital rationing – PI technique is very useful and better than NPV technique in ranking the projects and choosing projects which maximize shareholders’ wealth in case of capital rationing.

**Limitations (Disadvantages) of PI Method: **

PI method is an improvement over NPV method especially in case of capital rationing situation. PI method like other techniques is not free from limitations. Its main limitation is that it requires a discount rate which is generally weighted average cost of capital. Calculation of WACC is a difficult task and any error in its estimation will result in incorrect PI and hence wrong decision.

**iii. Internal Rate of Return (IRR) Method: **

Another DCF technique is Internal Rate of Return or IRR. Internal Rate of Return (IRR) is defined as that discount rate at which present value of cash inflows is equal to present value of cash outflows i.e. the discount rate at which NPV is zero.

As the term suggests IRR is expressed in percentage terms. It is the rate of return generated by a project internally. It is based on all the cash inflows and outflows of the project throughout its life.

**Computation: **

**The situations under which we compute IRR are classified in two parts: **

(a) When future cash inflows are equal

(b) When future cash inflows are unequal

**(a) When Cash Inflows are Equal: **

When future cash inflows are equal then it means that cash inflows are in the form of an annuity.

**Here we can calculate IRR using the following three steps: **

i. Calculate PB period as follows –

PB = Investment / Annual CFAT

ii. In present value of annuity table (PVFA), search in the row which is equal to the life of the project and look for the value which is equal to the payback period computed in above step. If we get approximate value then we look at the corresponding rate of interest. This rate of interest is IRR.

However, we do not find the exact value and under this situation, we note two values, one greater than payback period and one which is less than the payback period. Then we look at the top of the column and note the rate of interest corresponding to these two values, one is called lower discount rate and another high rate of discount.

iii. Compute the actual value of IRR by interpolation. We use the following formula –

Where, L is the lower discount rate, H is the higher rate of discount, PV of CFAT_{L} is the present value of cash inflows after tax at lower discount rate, PV of CFAT_{H }is the present value of cash inflows after tax at higher discount rate and PV of CO is the present value of cash outflows.

**(b) When Cash Inflows are Unequal: **

When annual cash inflows are not equal, then the process of computing IRR is not simple and is based on trial and error approach.

**Here in place of annual cash flows we use average cash flow as given in following steps: **

i. Calculate the average cash inflows by taking their arithmetic mean. This is called fake annuity.

ii. Use the value of fake annuity to compute fake PB period by dividing the amount of investment by fake annuity amount

Fake PB = Investment / Fake Annuity of CFAT

iii. In present value of annuity table (PVFA), search in the row which is equal to the life of the project and look for the value which is equal to the fake payback period computed in above step. If we get approximate value then we look at the corresponding rate of interest. This is the discount rate to begin with.

iv. In this step compute Present value of cash inflows using the discount rate calculated in step three. If this value is higher than the initial investment then move to a higher discount rate and repeat this process until we get two discount rates such that at one discount rate present value of cash inflows is higher than initial investment and at the other discount rate the present value of cash inflows is lower than the initial investment cost.

On the other hand if this value is lower than the initial investment then move to a lower discount rate and repeat this process until we get two discount rates such that at one discount rate, present value of cash inflows is higher than initial investment and at the other discount rate the present value of cash inflows is lower than the initial investment cost.

v. Compute the actual value of IRR by interpolation. We use the following formula –

Where, L is the lower discount rate, H is the higher rate of discount, PV of CFAT_{L} is the present value of cash inflows after tax at lower discount rate, PV of CFAT_{H} is the present value of cash inflows after tax at higher discount rate and PV of CO is the present value of cash outflows.

**Please Note: **

1. For the calculation of IRR we need two discount rates. At one discount rate present value of cash inflows should be more than the present value of cash outflows and at the second discount rate present value of cash inflows should be lower than the present value of cash outflows. Then we can use interpolation to find out actual IRR.

2. When we are given required rate of return or cost of capital then we can begin with this required rate of return and calculate present value of cash inflows at that rate. If the present value of cash inflows is more than the present value of cash outflows we take a higher discount rate such that at this higher discount rate present value of cash inflows is less than the present value of cash outflows.

Then we can use interpolation. On the other hand if the present value of cash inflows is less than the present value of cash outflows at the given required rate of return then we take a lower discount rate such that at this lower discount rate present value of cash inflows is more than the present value of cash outflows. Then we can use interpolation.

Internal Rate of Return (IRR) does not require the minimum required rate of return or cost of capital for its computation. When we decide about the acceptability of a project using IRR method then we compare IRR of the project with the minimum required rate of return or Cost of capital.

When the project generates internal rate of return which is more than the cost of capital or minimum required rate of return, we should accept the project. On the other hand, when IRR is less than the minimum required rate of return we should reject the project. When internal rate of return is equal to minimum required rate of return or cost of capital then we are indifferent.

We can also rank the projects using IRR. Rank 1 is provided to the project having highest IRR and last rank to the one having lowest IRR.

Accept if IRR > Minimum required rate of return or cost of capital (k)

Reject if IRR < Minimum required rate of return or cost of capital (k)

Indifferent if IRR = Minimum required rate of return or cost of capital (k)

Rank the projects from Highest IRR to Lowest IRR

Besides NPV, IRR is a popular method of capital budgeting.

**Its advantages are explained blow: **

i. Considers Time Value of Money and Risk – IRR method considers time value of money and risk of the project by comparing IRR with the cost of capital or minimum required rate of return.

ii. Based on Cash flows – IRR method like NPV is based on cash flows rather than accounting profit.

iii. Consistent with the objective of financial management – IRR method is also consistent with the objective of shareholders’ wealth maximization. Whenever IRR is greater than cost of capital NPV is positive.

iv. Considers all cash flows – In the calculation of IRR we consider all cash flows during the life of the project. This technique is also based on all the cash flows of a project just like NPV. The complete life of the project is taken into account before any investment decision is made, which results in sound investment decision.

v. Easy to understand by a layman – IRR is expressed in percentage form and hence is easy to understand by a layman. Percentage returns can be compared easily rather than absolute values. Saying that the project generates 25% return is better than saying that the NPV of the project is Rs.2500.

vi. Does not require cost of capital or required rate of return for its calculation – IRR calculation does not require any prior estimation of required rate of return or cost of capital. IRR can be calculated without even having cost of capital or required rate of return

**Limitations (Disadvantages) of IRR Method****: **

IRR is a popular method because it is expressed in percentage and does not require any prior estimation of required rate of return or cost of capital.

**However, it suffers from the following limitations:**

**i. Tedious Calculations: **

Manual calculations of IRR involve trial and error approach which is a time consuming and tedious process.

**ii. Multiple IRR: **

When the projects are non-conventional i.e. involve cash outlays not just in initial year but also in subsequent years then we can have more than one IRR. Hence there are chances that we may get multiple IRRs.

**iii. Unrealistic Reinvestment Rate Assumption: **

The main problem or limitation of IRR is that it is based on the assumption that intermediate cash inflows are reinvested at IRR itself. This is an unrealistic assumption. It is unrealistic to assume that a project A, having IRR as 25% can reinvest all its intermediate cash inflows at 25%.There is a probability that the company may not get any other project providing 25% IRR where cash inflows from project A can be reinvested.

Further let us assume that two projects A and B have IRR as 20% and 25%. Then as per IRR, the cash inflows from project A are reinvested at 20% while those from B are reinvested at 25%. It is quite absurd to assume that the company will reinvest its cash at two rates. Rather the company should reinvest all cash in the investment option that generates 25% IRR.

**Relationship between NPV, IRR and Cost of Capital (k)****: **

NPV and IRR are both discounted cash flow techniques. NPV is the excess of present value of cash inflows over present value of cash outflows. NPV calculation uses required rate of return or cost of capital (k) as discount rate for present value calculations.

IRR is that discount rate at which present value of cash inflows is equal to present value of cash outflows i.e. IRR is that discount rate at which NPV is zero. Therefore when NPV is positive, IRR is greater than cost of capital or required rate of return (k). When NPV is negative, IRR is less than k and when NPV is zero IRR=k.

If IRR > k the NPV is positive

If IRR < k the NPV is negative

If IRR = k the NPV is zero

**Do NPV and IRR Always Provide Same Decision?**** **

There can be two cases- independent projects and mutually exclusive projects. When the projects are independent, then NPV and IRR provide same results regarding the acceptance or rejection of the project.

**However when projects are mutually exclusive the two methods may provide contradictory results:**

**i. Independent Projects: **

When NPV is positive, IRR is greater than cost of capital or required rate of return (k). When NPV is negative, IRR is less than k and when NPV is zero IRR=k. therefore NPV and IRR provide same decision when the projects are independent.

**ii. Mutually Exclusive Projects: **

**When the projects are mutually exclusive then NPV and IRR may provide contradictory results in the following three situations:**

a. Size disparity – When projects have different amount of initial investment.

b. Time disparity – When projects have different pattern of cash inflows.

c. Unequal lives – When projects have different lives.

**Techniques of Capital Budgeting (With Formula, Merits & Demerits)**

The capital budgeting techniques or evaluation of investment proposals have considerably gained the importance. This is truer in the modern business environment. After the introduction of New Economic Policy, the environment in the industry and service sector have considerably changed.

Number of mergers, acquisitions, joint venture and continuous innovation are being experienced in the market. Therefore, it is very difficult to arrive at a decision for financing the project. It is absolutely essential for every business entity to make use of this scarce resource on the most profitable lines. Following are some of the important methods used in practice in evaluating the investment proposals.

There are many methods for evaluating or ranking the capital investment proposals. In all these methods, the basic approach is to compare the investments in the project to the benefits derived therefrom.

**These methods can be categorised as follows: **

(i) Payback period method,

(ii) Payback profitability method or post-payback profitability method, and

(iii) Accounting rate of return method.

**2. Discounted Cash Flow Methods:**

(i) The net present value method

(ii) Internal rate of return

(iii) Profitability index method or Benefit cost ratio method

#### The usage of methods of evaluation of capital investments does not have uniformity. It differs from firm-to-firm. Large-scale business undertakings may use all techniques for evaluating and comparing the projects. Smaller firms may use only one method. The selection of a particular method is mainly based on its merits and demerits and its relevance to the present circumstances.

**Technique # 1. Traditional Methods:**

The term payback period refers to the period in which the project will generate the necessary cash to recover the initial investment. It is a traditional, simple method of evaluating the projects. It does not take the effect of time value of money. It emphasises more on annual cash inflows, economic life of the project and the original investments. Cash inflows refers to profit before depreciation and after taxes. Formula-

**If the annual cash inflows are uniform:**

The selection of the project is based on the earning capacity of a project. Here the financial manager’s aim is to know how soon the original investments are recovered. During the process of comparison be always keeps firm’s cut-off rate (Recovery of investment period) and compares the same with payable period of the proposals. If the payback period is more than the cut-off rate, the proposals are rejected. If the payback period is less than the cut-off rate such proposals are selected for investments.

[Cut-off rate = cost of funds or in terms of period, if a firm’s cost of capital is 15 per cent, payback period = 100/15 = 6.6 years]

a. It is a traditional and old method.

b. It involves simple calculation.

c. Selection or rejection of the project can be made easily.

d. The results obtained under this method is more reliable.

e. It is the best method for evaluating high-risk projects.

a. It is based on the principle of ‘rule of thumb’.

b. It does not recognise the importance of ‘time value of money’.

c. It does not consider the profitability of economic life of the project [earnings till payback period is only considered].

d. It does not recognise the pattern of cash flows and its timing.

e. Payback period concept does not reflect all the relevant dimensions of profitability.

**(ii) Payback Profitability Method or Post-Payback Profitability Method****:**

To remove the drawbacks of payback period, post-payback profitability method was developed. Under this method, the cash inflow generated from a project during the economic life is taken into account, whereas in payback period the cash inflows were considered only to the extent of recovering the original investment. But in the practical situation, after the payback period, a project or a machine is still capable of generating cash inflows. Therefore, to evaluate the project the entire amount of earning or cash inflows must be considered.

a. It is based on simple calculations.

b. Less time-consuming.

c. It is easy to follow and even a non-finance executive can also understand the concept.

d. It takes into account the earnings of the project of entire life.

a. It is also based on the principle, of ‘rule of thumb’.

b. It doesn’t consider the impact of time value of money.

c. It ignores depreciation.

**Accept or Reject Criterion: **

The payback period can be used as an accept or reject criterion. It can also be used as a method of ranking projects. If the payback period calculated for a project is less than the maximum payback period set up by the management of the firm, it would be accepted. A project whose actual payback period is more than what has been predetermined by the management, will be rejected.

**(iii) Accounting Rate of Return Method****: **

Accounting rate of return considers the earnings of the project of the economic life. This method is based on conventional accounting concepts. The rate of return is expressed as percentage of the earnings of the investment in a particular project. This method has been introduced to overcome, the disadvantage of payback period. The profits under this method is calculated as profit after depreciation and tax of the entire life of the project.

This method of ARR is not commonly accepted in assessing the profitability of capital expenditure. Because the method does to consider the heavy cash inflow during the project period as the earnings will be averaged. The cash flow advantage derived by adopting different kinds of depreciation is also not considered in this method.

**Accept or Reject Criterion: **

Under the method, ail projects, having Accounting Rate of return higher than the minimum rate establishment by management will be considered and those having ARR less than the predetermined rate. This method ranks a project as number one, if it has highest ARR, and lowest rank is assigned to the project with the lowest ARR.

a. It is very simple to understand and use.

b. This method takes into account saving over the entire economic life of the project. Therefore, it provides a better means of comparison of project than the payback period.

c. This method through the concept of “net earnings” ensures a compensation of expected profitability of the projects, and

d. It can readily be calculated by using the accounting data.

a. It ignores time value of money.

b. It does not consider the length of life of the projects.

c. It is not consistent with the firm’s objective of maximising the market value of shares.

d. It ignores the fact that the profits earned can be reinvested.

**Technique # **2. **Discounted Cash Flow Method****: **

Discounted cash flow method or time adjusted technique is an improvement over payback method and ARR. An investment is essentially out flow of funds aiming at fair percentage of return in future. The presence of time as a factor in investment is fundamental for the purpose of evaluating investment.

Time is a crucial factor, because, the real value of money fluctuates over a period of time. A rupee received today has more value than a rupee received tomorrow. In evaluating investment projects it is important to consider the timing of returns on investment. Discounted cash flow technique takes into account both the interest factor and the return after the payback period.

**Discounted cash flow technique involves the following steps: **

a. Calculation of cash inflows and outflows over the entire life of the asset.

b. Discounting the cash flows by a discount factor.

c. Aggregating the discounted cash inflows and comparing the total so obtained with the discounted outflows.

**DCF methods of evaluating capital investment: **

(i) The Net present value Method

(ii) Internal Rate and Return Method

(iii) Cost Benefit Ratio and Profitability Index

**(i) The Net Present Value Method****: **

Net present value method recognises the impact of time value of money. It is considered as the best method of evaluating the capital investment proposal. It is widely used in practice. The cash inflow to be received at different period of time will be discounted at a particular discount rate. (Rate of return or interest rate). The present values of the cash inflow are compared with the original investment.

The difference between the two will be used for accept or reject criteria. If the different yields (+) positive value, the proposal is selected for investment. If the difference shows (-) negative values, the proposed project is rejected for investment.

**Steps: **

a. An appropriate rate of interest should be selected to discount cash flows. Generally, it is referred to the cost of capital.

b. The present value of cash inflow will the calculated by using this discounted rate.

c. The discounted cash inflow are used to find its difference with original investment or cash outflows.

**Accept or Reject Criterion: **

Net present value is used as an accept or reject criteria. In case NPV is positive the project is selected for investment. If NPV is negative, the project is rejected.

If NPV > Zero – Accept; If NPV < Zero – Reject.

a. It recognises the time value of money.

b. It considers the cash inflow of the entire project.

c. It estimates the present value of their cash flows by using a discount rate equal to the cost of capital.

d. It is consistent with the objective of maximising the welfare of owners.

**The present value of one rupee received after particular period of time at a particular rate of discount is calculated using the following formula: **

Alternatively, since the cash inflow is the same throughout, the cash inflow can be multiplied with the total of present value of the rupee for six years, to arrive at the present value cash inflows.

That is Rs.6,000 × 4.6228 = Rs.27,736 – 80

a. NPV method is based on discount rate. In a real-life situation, it is very difficult to find and understand the concept of cost of capital.

b. It may not give reliable answers when dealing with alternative projects under the conditions of unequal lives of project.

c. Decision arrived at may not be satisfactory, and when the project being compared involve different amount of investment.

**(ii) ****Internal Rate of Return Method****: **

Internal rate of return is that rate at which the sum of discounted cash inflows equals the sum of discounted cash outflows. It is that rate at which the net present value of the investment is zero. In other words, it is the rate of discount which reduces the net present value of an investment to zero. It is called internal rate because it depends mainly on the outlay and proceeds associated with the project and not on any rate determined outside the investment. This method was advocated by Joel Dean, in which the magnitude and timings of cash flows has been mainly considered.

**This method is also known as: **

(a) Marginal efficiency of capital

(b) Rate of return over cost

(c) Time adjusted rate of return

(d) Yield of an investment

**Accept or Reject Criterion:**

Accept the project if the internal rate of return is higher than or equal to the minimum required rate of return. The minimum required rate of return is also known as cut-off rate or firm’s cost of capital. A project shall be rejected if its IRR, is lower than the cut-off rate.

While evaluating two or more projects, project giving a higher internal rate of return would be preferred.

**Calculation of Internal Rate of Return****: **

IRR can be calculated by locating the Factor in Annuity Table (Annuity Table of Present Value of rupee one received annually for N years).

a. It considers the time value of money.

b. Calculation of cost of capital is not a prerequisite for adopting IRR.

c. IRR attempts to find the maximum rate of interest at which funds invested in the project could be repaid out of the cash inflows arising from the project.

d. It is not in conflict with the concept of maximising the welfare of the equity shareholders.

e. It considers cash inflows throughout the life of the project.

a. Computation of IRR is tedious and difficult to understand.

b. Both NPV and IRR assume that the cash inflows can be reinvested at the discounting rate in the new projects. However, reinvestment of funds at the cut-off rate is more appropriate than at the IRR. Hence, NPV method is more reliable than IRR for ranking two or more projects.

c. It may give results inconsistent with NPV method. This is especially true in case of mutually exclusive project, i.e., projects where acceptance of one would result in the rejection of the other.

Such conflict of results arises due to the following- a. Different in cash outlays. b. Unequal lies of project. c. Different pattern of cash flows.

**Comparison of NPV and IRR Method: **

**NPV Method:**

1. Interest rate is known.

2. It involves computation of the amount that can be invested in a given project so that the anticipated earnings will be sufficient to repay this amount with market rate of interest.

3. It assumes that the cash inflows can be remitted at the discounting rate in the new projects.

4. Re-investment is assumed to be at the cut-off rate.

**IRR Method:**

1. Interest rate is to be calculated.

2. It attempts to find out the maximum rate of interest at which funds are invested in the project. Earnings from the project in the form of cash flow will help us to get back the funds already invested.

3. It also assumes that the cash inflows can be reinvested at the discounting rate in the new projects.

4. Re-investment of funds is assumed to be at the IRR.

The profitability index (PI) refers to the ratio of discounted benefits over the discounted costs, it is an evaluation of the profitability of an investment and can be compared with the profitability of other similar investments which are under consideration. The profitability index is also referred to as benefit-cost ratio, cost-benefit ratio, or even capital rationing. The profitability index is one of the numerous ways used to quantify and measure the efficiency of a proposed investment.

Profitability index is an investment appraisal technique calculated by dividing the present value of future cash flows of a project by the initial investment required for the project.

Accept a project if the profitability index is greater than 1, stay indifferent if the profitability index is zero and don’t accept a project if the profitability index is below 1.

Profitability index is sometimes called benefit-cost ratio too and is useful in capital rationing since, it helps in ranking projects based on their per dollar return.

**Advantages of Profitability Index****: **

**The advantages of profitability index for a firm are listed below: **

(a) The profitability index tells about an investment increasing or decreasing the firm’s value.

(b) The profitability index takes into consideration all cash flows of the project.

(c) The profitability index takes the time value of money into consideration.

(d) The profitability index also considers the risk involved in future cash flows with the help of cost of capital.

(e) The profitability index is also helpful in ranking and picking projects while rationing of capital.

**Disadvantages of Profitability Index****: **

In addition to the aforesaid advantages, there are also certain disadvantages featured by the profitability index.

**These include: **

(a) An estimate about the cost of capital is required so as to calculate the profitability index of a firm.

(b) The profitability index of a firm might not, sometimes, provide the correct decision while being used to compare mutually exclusive projects under consideration.