Luqman Khakim
Jurusan Administrasi Niaga, Politeknik Negeri Semarang


Kajian ini ditujukan untuk mengetahui mana yang lebih superior dalam menilai berbagai pilihan investasi, NPV atau IRR. Hasil investigasi menunjukkan NPV lebih baik  dari IRR. Kriteria  yang digunakan yaitu : Maksimalisasi hasil investasi, nilai waktu uang, akomodasi resiko sistematis dan penentuan ranking yang tepat pada alternatif-alternatif yang ‘mutually exclusive’. Berdasarkan empat area yang penilaian, NPV unggul dalam dua bidang, nilai waktu uang dan identifikasi ranking optimal pada berbagai pilihan yang saling terkait; sementara IRR unggul dalam mengakomodasi resiko sistematis.

Kata kunci : NPV, IRR, Maksimalisasi hasil investasi, nilai waktu uang, akomodasi resiko sistematis dan penentuan ranking yang tepat pada alternatif-alternatif yang ‘mutually exclusive’.

Capital budgeting methods do critical work in modern companies. The companies do need the methods in order to solve their capital allocation problems on limited budgets (Luenberger, 1998: 103). The process of capital budgeting is started by formulating and articulating long-term goals, continued by finding feasible investment funds opportunities. This is followed by planning and constructing the investment preparation, market and financial chances projection, feasibility and controlling budgets preparation, then integrating them into companies’ information system, alternative investments evaluation and the past investments performance assessments (Levy & Sarnat, 1994: 23).

Discussing Net Present Value (NPV) and Internal Rate of Return (IRR) as part of capital budgeting techniques is essential. These techniques are the most popular methods which are used by “a broad range of companies” in the US (Duke University study cited by IOMA Financial Executive’s News, 2003, Tang & Tang, 2003). Therefore, it is essential to compare and choose the superior one, as they produce different results in many cases.

The objective of this paper is to determine which one is the superior investment appraisal method, NPV or IRR. Both methods are compared and assessed in several angles/criteria in order to know their benefits and disadvantages. It will be concluded that the NPV method is superior to the IRR method because NPV is superior in two criteria - the time value of money consideration and optimal rankings production on mutually exclusive investments. In contrast, IRR is superior in a criterion - accommodating systematic risk.

The Concepts of NPV & IRR

1. The concept of NPV

One of several characters of an investment project is a finite sequence of net cash flows. It is symbolized by “αi (i=0,1,2,…, n)” (Beaves, 1988) or “FV” (Bishop et al2004: 193) or “St” (Levy & Sarnat, 1994: 39).

Mathematically, the NPV formula is described as follows:

             n              St
“NPV = ∑                         -  I0
           t = 1      (1 +k )t

St =         the expected net cash receipt at the end of year t
I0 =         the initial investment outlay
k =          the discount rate, i.e., the minimum annual rate of return required on the project.
n =         the project’s duration in years” (Levy & Sarnat, 1994: 39).

In order to determine NPV of an investment, the net cash receipts in the future of the investment have to discount at rates that represent “the value of the alternative use of the funds,” adding all incremental cash flow up along project duration and subtracted by the initial outlays (Levy & Sarnat, 1994: 39).

The NPV profile is a good tool to explain NPV. Figure 1 describes the relationship between NPV and discount rates. For example, a project offers a $2000 proceeds at the end year one, by investing $1000 as its initial outlay:
                           St                            $2000
   NPV =            - I0 =                -     - $1000      (Levy & Sarnat, 1994: 42).
               1 + r                  1 + r

Furthermore, NPV and discount rates have an inverse relationship. It is pointed out by figure 1.
When NPV is on the highest point ($1000), the discount rate is zero, then; it decreases as the discount rate increases (Levy & Sarnat, 1994). In contrast, NPV will value - $1000 if the discount rate approaches infinity, while, when the discount rate is on the middle (reaches 100%), the value of NPV is zero (Levy & Sarnat, 1994: 42).

Under decision making perspective, If NPV of a project is positive (discount rates less than 100%) and rate of return (k) below 100%, the proposed project is feasible to be done (Levy & Sarnat, 1994: 43). For example the rate of return (k) of the project above is 40% (of $1000 = $400), by operating the NPV formula; it is found that NPV of the project is   $428.57 (Levy & Sarnat, 1994: 43). This means that the investment exceeds $600 ($2000 - $1400) and the present value of $600 is $428.57 (Levy & Sarnat, 1994: 43). Since the project’s NPV is positive, the investment should be accepted (Levy & Sarnat, 1994: 43).

Figure 1
NPV Profile





                            40%            100%
                            Discount rates, r

   - $1000

(Levy & Sarnat, 1994: 42)

2. The Concept of Internal Rate of Return ( IRR )
Internal rate of return could be defined as “the discount rate r* which equates the projected net income stream’s present value with the initial investment I0, or, alternatively, that equates their difference to zero” (Trippi, 1989).

The IRR rule simply uses the minimum rate of return (k) as its standard. “If IRR ≥ r, accept the project; If IRR < r, reject the project” (Bishop et al2004: 204).

Figure 2
Relationship between NPV and IRR


                           Discount factor ( r )                                                                           
NPV curve


 (Bishop, et al, 2004: 205)

The IRR formula could be described as follows:

n           St
                           - I0  = 0“       
t = 1    (1 +R)t                                     

R =         the discount rate or the cost of capital, i.e., the minimum annual rate of return required on the project / investment.
“I0 =       the initial investment outlay
n =         the project’s duration in years” (Levy & Sarnat, 1994: 39, 44).


The Criteria for a Superior Investment Appraisal Method

This research uses four criteria to examine the NPV and the IRR superiorities. They are “wealth maximization, consideration of the time value of money, systematic risk accommodation and generation of optimal rankings of mutually exclusive alternatives” (Moyer, McGuigan & Kretlow, 1984, cited by Cheng et al , 1994). The criteria are used in this research, since the criteria are also part of capital budgeting techniques criteria and most differences between NPV and IRR occur on the four areas (Bishop et al, 2004: 248-252, Levy & Sarnat, 1994: 59-102, Beaves, 1988, Cheng et al , 1994). A method which provides the best performance on such criteria probably is the superior one.

The NPV & IRR Comparison

1. Wealth maximization
In term of wealth maximization, maximum profit that probably can be obtained by investors from each alternative “by the terminal date” of the project duration periods (Dudley, 1972), reinvestment rates are good tools to measure the criteria. They are rates of profit which can be obtained by reinvesting “interim cash flow” of projects to other investment opportunities (Levy & Sarnat, 1994: 71, Beaves, 1988). The reinvestment rates of NPV and IRR are compared to know which one provides the highest proceeds.

Under this term, the IRR technique possibly produces profits more than the NPV method. IRR prefers projects with shorter duration periods, less initial outlays and ‘earlier cashflow’, while NPV has inverse preferences (Grant, 1982 cited by Beaves, 1988). Therefore, if these cash flow are reinvested earlier, IRR has chance to obtain reinvestment profits higher than the NPV method.
However, those who support IRR must consider facts that the NPV method has similar opportunity to gain reinvestment revenues higher than IRR. Table 1 shows that in the case where interim cash flows are reinvested, NPV and IRR have their own advantages. If rates of return on investment are less than or equal to the discount rate of NPV, the NPV technique will provide profit higher than the IRR method (Dudley, 1972). In contrast, if the rates of return on reinvestment are higher than that of NPV, IRR offers reinvestment revenue higher than NPV (Dudley, 1972, Cheng et al , 1994).

Table 1
Annual Cash Flow & Terminal Values at a 5 year perspective

Assumed Return on Reinvestment
Initial Investment

$            35,282
$        35,282
$       35,282
$       35,282

$             20,000
$        16,691
$       10,949
$         5,000

$             15,000
$        16,691
$       10,949
$       10,000

$             10,000
$        16,691
$       10,949
$       15,000

$               5,000
$                 0
$       10,949
$       25,514

$                 0
$                 0
$       10,949
$                0
Initial Proceeds

$             50,000
$        50,073
$       54,745
$       55,514
Present Value at 7%

$             43,772
$        43,802
$       44,893
$       45,117

$               8,490
$          8,520
$         9,611
$         9,835
IRR (%)

Proceeds after being reinvested

$             57,690
$        58,073
$       60,503
$       60,980

$             61,391
$        61,435
$       62,965
$       63,278

$             66,845
$        66,848
$       66,843
$       66,845

$             76,765
$        76,646
$       73,818
$       73,126

$             87,800
$      87,494
$       81,483
$       79,867
Source: Dudley , 1972

2. Consideration of the time value of money,

The IRR and the NPV methods both take into consideration time value of money. This is because the techniques are derived from the time value of money concept – a concept which assumes that the current value of money is higher than its value in the future.

Yet, the opinion above should be re-evaluated, as both methods consider time value of money in different ways. Since NPV “measures the change in the net worth of the firm due to the project”, this method is flexible to adjust to the cost of capital variations and the effects of inflation (Cheng et al , 1994). For example, if inflation occurs in year three, NPV will adapt to this case by increasing discount rates on that year. In contrast, IRR only “measures periodic rate of return” required by an investment (Cheng et al , 1994). The IRR rate of return will constant over project duration period and generally cannot adapt to the cost of capital changes. It means the IRR approach is inferior to the NPV method on time value of money consideration.

3. Systematic risk accommodation

NPV is a capable method in considering systematic risk, “the risk that remains after diversifying” (Campsey, B. J. and Brigham, E. F., 1991: 422-423), on its counting. Since NPV is a flexible method to adapt to many changes, it can accommodate systematic risk on its consideration simply by measuring systematic risk costs than add it up on its rates.

However, on this horizon the IRR method is superior. The longer period of projects, the higher systematic risk that should be borne. IRR accommodates the risk by choosing the shorter duration investment periods, while on the same cases NPV prefers the longer ones (Cheng et al , 1994). It means IRR is more protective to the systematic risk than that of NPV.

4. Generation of optimal rankings of mutually exclusive alternatives

Under producing of optimal rankings of mutually exclusive investments perspective, NPV is superior to IRR. The evidence can be pointed out as follows:

Table 2 shows that both projects have similar values of IRR. Since IRR values are produced from comparison of investment variables; therefore, it cannot differ between projects in million dollars and projects in hundred dollars (Cheng et al ; 1994, Levy & Sarnat, 1994: 68). This can lead to erroneous decisions, whereas, this one example lends support to the conclusion that the NPV method treats both projects appropriately.

Table 2
Comparison between NPV & IRR

Project Go
Project Hold


         Source: (Cheng et al , 1994: 68)

a. Minus value on year 0, is the Initial outlay (the amount of money which has to be paid on the investments.
b.Amount of dollar ($) on year 1 to year 4 are revenue.


In conclusion, the NPV method is superior to the IRR method. It is because NPV is more adaptable to many changes on cost of capital and appropriately considers scale of investments. Therefore, the NPV method is superior in two terms - time value of money consideration and optimal rankings production on mutually exclusive investments. In contrast, IRR is only superior in one term - accommodating systematic risks. In addition, in the case of wealth maximization, both methods are equal.


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