IRR,NPV and PBP

7/21/2019 IRR,NPV and PBP

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Net Present Value (NPV)

Net Present Value of a project is the sum of the present values of all the cash flowspositive as

well as negative, that are expected to occur over the life of the project. In other words, NPV is

the difference between an investments market value and cost. It is a measure of how much

value is created or added today by undertaking an investment.

The formula of NPV is:

Where,

Ct = cash flow at the end of year t

n = Life of the project

k = discount rate (given by the projects opportunity cost of capital which is equal to the

required rate of return expected by investors on investments of equivalent risk).

C0= Initial investment

1 / (1 + k )t= known as discounting factor or PVIF i.e present value interest factor.


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Decision Criteria

I. If the NPV is positive, it means the investment would add value to the firm, so accept the

project

II. If the NPV is negative, it means the investment would subtract the value from the firm, so

reject the projectIII. If the NPV is zero, it means the investment would neither gain nor lose value for the firm,

in such case we should be indifferent whether to accept or reject the project. This project

adds no monetary value. Decision should be based on other criteria such as strategic

positioning or other factors not explicitly included in the calculation.

IV. Assign the higher rank to the project with higher NPV and lower rank to project with

lower NPV.

Advantages of NPV

It considers time value of money.

It is a true measure of profitability as it uses the present values of all cash flows (both

outflows & inflows) & opportunity cost as discount rate.

The NPVs of individual projects can be simply added to calculate the value of the firm.

It is consistent with the shareholders wealth maximization principle as whenever a project

with positive NPV is undertaken, it results in positive cash flows and hence the increase

in the value of the firm.

Disadvantages of NPV

It is difficult to estimate the expected cash flows from a project.

Discount rate to be used is very difficult to determine.

Since this method does not consider the life of the projects, in case of mutually exclusive

projects with different life, the NPV rule, tends to be biased in favour of the longer term

project.

Since NPV is expressed in absolute terms rather than relative terms it does not consider

the scale of investment.


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Internal Rate of Return (IRR)

The discount rate often used in capital budgeting that makes the net present value of all cashflows from a particular project equal to zero. Generally speaking, the higher a project's internalrate of return, the more desirable it is to undertake the project. As such, IRR can be used to rank

several prospective projects a firm is considering. Assuming all other factors are equal amongthe various projects, the project with the highest IRR would probably be considered the best andundertaken first.

IRR is sometimes referred to as "economic rate of return (ERR)".

The formula for calculating IRR is:

Where,

Ct = cash flow at the end of year t

n = Life of the project

r = discount rate

C0= Initial investment

1 / (1 + r )t= known as discounting factor or PVIF i.e present value interest factor.


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IRR Illustrated

Initial outlay = -$200

Year Cash flow1 50

2 100

3 150

Find the IRR such that NPV = 0


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Decision Criteria

I. Accept the project when r(IRR) > k (WACC).

II. Reject the project when r(IRR) < k (WACC).

III. May accept the project when r = k.

IV. In case of independent projects, IRR and NPV rules will give the same results if the firm

has no shortage of funds.

V. In case of projects with equal IRR & different NPV, select project with higher NPV as it

is consistent with firms wealth maximisation objective.

Advantages of IRR

It considers time value of money.

It is a true measure of profitability as it uses the present values of all cash flows (both

outflows & inflows) rather than any other arbitrary assumption or subjective

consideration.

In case of conventional independent projects NPV & IRR methods gives the same

decision.

Whenever a project with higher IRR than WACC is undertaken, it results in the increase

in the shareholders return. Hence, the value of the firm also increases.

Problems with IRR

Lending & Borrowing projects: Project with initial outflow followed by inflows is a

lending type project whereas a project with initial inflow followed by outflows is a

borrowing project. Since IRR does not differentiate between lending and borrowing

projects, a higher IRR may not always be a desirable thing.

Multiple IRR: In case of projects with non-normal or unconventional cash flows more

than one IRR are generated which are misleading.

Mutually Exclusive projects: In case of mutually exclusive projects the results of NPV &

IRR methods may conflict each other. This is because the IRR method does consider the

scale of investment.

Different short term & Long term interest rates: Since the cash flows are discounted at

the opportunity cost of capital, there arises a confusion regarding what rate is to be used

for discounting, if the short term and long term lending rates are different.


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Payback Period (PBP)

The payback period is the length of time that it takes for a project to recoup its initial cost out of

the cash receipts that it generates. This period is sometimes referred to as" the time that it takes

for an investment to pay for itself." The basic premise of the payback method is that the more

quickly the cost of an investment can be recovered, the more desirable is the investment. The

payback period is expressed in years.

PBP is calculated as:

For even cashflow:

For uneven cashflow:

There are four important points to be understood about payback period calculations:

1. This is an approximate, rather than an exact, economic analysis calculation.

2. All costs and all profits, or savings of the investment, prior to payback are included

without considering differences in their timing.

3. All economic consequences beyond the payback period are completely ignored.

4. Being an approximate calculation, payback period may or may not select the correct

alternative. That is, the payback period calculations may select a different alternative

from that found by exact economic analysis techniques.

Example:A company wants to buy a production device for their new factory. They have two

alternatives, whose cash flows are given in the following table. According to these cash flows,

determine the no return payback period of these alternatives.


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Alternative A Alternative B

Cost 3 000 000 TL 3 500 000 TL

Annual income 1 200 000 TL first year,

decreasing by 300.000 TL

per year thereafter

100 000 TL for the first year,

increasing 300 000 TL per

year thereafter.

Useful life 4 years 8 years

Alternative A

Years 0 1 2 3 4

Cash Flow -3 000 000 1 200 000 900 000 600 000 300 000

Cumulative value -3 000 000 -1 800 000 -900 000 -300 000 0

PBA= 4 years

Alternative B

Years 0 1 2 3 4 5

Cash Flow -3 500 000 100 000 400 000 700 000 1 000 000 1 300 000

Cumulative value -3 500 000 -3 400 000 -3 000 000 -2 300 000 -1 300 000 0

PBB= 5 years

According to the payback periods, alternative A should be preferred

Decision Criteria of PBP

For independent project, accept those whose PBP standard PBP set by the firm.

For mutually exclusive project, accept those which meets above condition and which one

has shortest PBP.

Project that has shortest PBP is ranked 1.


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Advantages

The calculations can be easily made by people unfamiliar with economic analysis,

especially in analysis of no-return payback period. One does not need to know how to use

gradient factors, or even to have a set of compound interest tables. Second, payback

period is a readily understood concept.

Payback period does give us a useful measure, telling us how long it will take for the cost

of the investment to be recovered from the benefits of the investment. Businesses and

industrial firms are often very interested in this time period: a rapid return of invested

capital means that it can be re-used sooner for the other purposes by the firm.

The payback period may not be used as a direct figure of merit, but it may be used as

constraint: no project may be accepted unless its payback is shorter than some specified

period of time.

Disadvantages

Ignores the time value of money

Ignores cash flow beyond the payback period

Biased against long-term projects such as research and development, and new projects

Requires an arbitrary cutoff point.

Discounted Payback Period

The length of time until the accumulated discounted cash flows from the investment equals or

exceeds the original cost. We will assume that cash flows are generated continuously during a

period.

Simple Payback Period method does not considers the time value of money but we must consider

the time value of money because of inflation, uncertainty, and opportunity cost. Therefore,

discounted cash flow method is used to calculate the payback period (discounted payback

period).

Discounted PBP is calculated as:


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Advantages of Discounted PBP

Includes time value of money.

Easy to understand.

Does not accept negative estimated NPV investments.

Biased toward liquidity.

Disadvantages of Discounted PBP

May reject positive NPV investments.

Requires an arbitrary cutoff point.

Ignores cash flows beyond the cutoff date.

Biased against long-term projects, such as research and development and new projects.

Example:

The initial cost is $600 million. The appropriate discount rate for these cash flows is 20%. Usingthe discounted payback rule, should the firm invest in the new product?

Year Cash Flow Present Value

Discounted

Accumulated

Cash Flow

1 $200.00 166.67 166.67

2 $220.00 152.78 319.45

3 $225.00 130.21 449.66

4 $210.00 101.27 550.93

Here the project never pays back, so the project should not be selected.


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NPV Vs IRR

The net present value (NPV) and the internal rate of return (IRR) could as well be defined as two

faces of the same coin as both reflect on the anticipated performance of a firm or business over a

particular period of time. The main difference however should be more evident in the method or

should I say the units used. While NPV is calculated in cash, the IRR is a percentage value

expected in return from a capital project.

Due to the fact thatNPV is calculated in currency, it always seems to resonate more easily with

the general public as the general public comprehends monetary value better as compared to other

values. This does not necessarily mean that the NPV is automatically the best option when

evaluating a firms progress. The best option would depend on the perception of the individual

doing the calculation, as well as, his objective in the whole exercise. It is evident that managers

and administrators would prefer the IRR as a method, as percentages give a better outlook that

can be used to make strategic decisions over the firm.

Another major shortfall associated with the IRR method is the fact that it cannot be conclusively

used in circumstances where the cash flow is inconsistent. While working out figures in such

fluctuating circumstances may prove tricky for the IRR method, it would pose no challenge for

the NPV method since all that it would take is the collection of all the inflows-outflows and

finding an average over the entire period in focus.

Evaluating the viability of a project using the IRR method could cloud the true picture if the

figures on the inflow and outflow remain to fluctuate persistently. It may even give the false

impression that a short term venture with high return in a short time is more viable as compared

to a bigger long-term venture that would otherwise make more profits.

In case of independent project, IRR and NPV give the same decision. However, in case of

mutually exclusive projects, the decision is rather conflicting. It is simply because; sometimes

comparison must be made between projects with different lives. And in such situation, NPV

usually favors projects with longer life.

The NPV and IRR rules leads to identical decisions provided two conditions are satisfied. First,

the cashflow of the project must be conventional, implying that the initial cashflows are negative
http://www.differencebetween.net/business/difference-between-npv-and-roi/http://www.differencebetween.net/business/difference-between-npv-and-roi/


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and the subsequent cashflows are positive. Second, the project must be independent meaning that

the project can be accepted or rejected without reference to any other project.

In order to make a decision between any of the two methods, it is important to take note of the

following significant differences.

Summary:

1. While the NPV will work better in helping other people such as investors in understanding the

actual figures in so far as the evaluation of a project is concerned, the IRR will give percentages

which can be better understood by managers.

2. As much as discrepancies in discounts will most likely lead to similar recommendations from

both methods, it is important to note that the NPV method can evaluate big long-term projects

better as opposed to the IRR which gives better accuracy on short term projects with consistent

inflow or outflow figures.

NPV vs Payback

In every business, it is crucial to evaluate the value of a proposed project before actually

investing on it. There are a number of solutions to evaluate this on a financial perspective and

among them are Net Present Value (NPV) and Payback methods. These two can measure thesustainability and value of long-term projects. However, they differ in their computation, factors,

and thus vary in terms of limitations and benefits.

NPV, also known as Net Present Worth (NPW), is a standard method for using the time value of

money to appraise long-term projects. It calculates a time series of cash flows, both incoming

and outgoing, in terms of currency. NPV equates to the sum of the present values of the

individual cash flows. The most important thing to remember about NPV is present value. Put

simply, NPV = PV (Present value) I (Investment). For instance, given $ 1, 000 for I, $ 10, 000

for PV; $ 10,000- $ 1,000 = $ 9, 000 = NPV. When choosing between alternative investments,

NPV can help determine the one with highest present value, specifically with these conditions: if

NPV > 0 accept the investment, if NPV < 0, reject the investment, and if NPV= 0, the investment

is marginal.


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Payback method, conversely, is used to evaluate a purchase or expansion project. It determines

the period, commonly in years, in which therell be a payback on investments made. It is equal

to the initial investment divided by annual savings or revenue or in math terms, Payback period =

I/CF (Cash flow per year. For example, given $10, 000 for I and $ 1, 000 for CF, 10,000/ 1, 000

= 10 (years) = Payback period. The shorter the payback period, the better the investment is. A

long payback means that the investment will be locked up for a long time; hence the project is

relatively unsustainable.

Net present value analysis removes the time element in weighing alternative investments, while

Payback method is focused on the time required for the return on an investment to repay the total

initial investment. Given this, Payback method doesnt properly assess the time value of money,

inflation, financial risks, etc. as opposed to NPV, which accurately measures an investments

profitability. In addition, although Payback method indicates the maximum acceptable period the

investment, it doesnt take into consideration any probabilities that may occur after the payback

period nor measure total incomes. It doesnt indicate whether purchases will yield positive

profits over time. Thus, NPV provides better decisions than Payback when making capital

investments. Relying solely on Payback method might result in poor financial decisions. Most

businesses usually pair it with NPV analysis. As far as advantages are concerned, Payback period

method is simpler and easier to calculate for small, repetitive investment and factors in tax and

depreciation rates. NPV, on the other hand, is more accurate and efficient as it uses cash flow,

not earnings and results in investment decisions that add value. On the downside, it assumes a

constant discount rate over life of investment and is limited in predicting cash flows. Moreover,

the cons of Payback include the fact that it doesnt take into account cash flows and profits after

the payback period and money value along with financial risks prior or during investment.


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Summary:

NPV and Payback methods measure the profitability of long-term investments.

NPV calculates an investment present value, but eliminates time element and assumes

constant discount rate overtime.

Payback determines the period on which a payback on a specific investment will be

made. However, it disregards time value of money and the projects profitability after the

payback period.

Most businesses use a combination of the two to come up with an optimal financial

decision.

Conclusion

The examination of the three different investment appraisals presented here has clearly shownthat the various methods entail the risk of misinterpretation. It is possible to get three differentchoices using the three different methods. And this may not always match the companysstrategy. Adopting the payback rule, for example, only the cash flows to the recovery period areobserved. All subsequently incurred cash flows are ignored. In addition, all predominant cashflows are on equal weight, regardless of whether an investment has a faster return or not. Eventhe method of internal rate of return viewed on its own provides no reliable results for aninvestment decision. IRR itself has many flaws like multiple IRRs, misleading the decision incase of different scale of investment. Net Present Value also has many pitfalls but in comparisonto the other two methods, the use of NPV is rather beneficial. This is because NPV is the onlymethod that concerns the actual objective of the organization i.e value maximization of the firm.

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IRR,NPV and PBP