WHICH IS SUPERIOR FOR ASSESSING CAPITAL
INVESTMENTS: NET PRESENT VALUE OR
INTERNAL RATE OF RETURN?
MANAKAH YANG LEBIH SUPERIOR DALAM MENILAI
BERBAGAI PILIHAN INVESTASI: NET PRESENT VALUE ATAU INTERNAL RATE OF RETURN?
Luqman Khakim
Jurusan Administrasi Niaga, Politeknik Negeri Semarang
ABSTRACT
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
where:
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
NPV
$1000
$428.57
0
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
NPV
R
0
 |
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
where:
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
|
Year
|
Projects
|
||||
|
A
|
B
|
C
|
D
|
||||
|
Initial Investment
|
|
0
|
$ 35,282
|
$ 35,282
|
$ 35,282
|
$ 35,282
|
|
|
|
|
1
|
$ 20,000
|
$ 16,691
|
$ 10,949
|
$ 5,000
|
|
|
|
|
2
|
$ 15,000
|
$ 16,691
|
$ 10,949
|
$ 10,000
|
|
|
|
|
3
|
$ 10,000
|
$ 16,691
|
$ 10,949
|
$ 15,000
|
|
|
|
|
4
|
$ 5,000
|
$ 0
|
$ 10,949
|
$ 25,514
|
|
|
|
|
5
|
$ 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
|
|
|
NPV
|
|
|
$ 8,490
|
$ 8,520
|
$ 9,611
|
$ 9,835
|
|
|
IRR (%)
|
|
|
20.000
|
19.781
|
16.692
|
16.183
|
|
|
Proceeds after being reinvested
|
5%
|
|
$ 57,690
|
$ 58,073
|
$ 60,503
|
$ 60,980
|
|
|
7%
|
|
$ 61,391
|
$ 61,435
|
$ 62,965
|
$ 63,278
|
||
|
10%
|
|
$ 66,845
|
$ 66,848
|
$ 66,843
|
$ 66,845
|
||
|
15%
|
|
$ 76,765
|
$ 76,646
|
$ 73,818
|
$ 73,126
|
||
|
20%
|
|
$ 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
|
Year
|
Project Go
|
Project Hold
|
|
|
$
|
$
|
|
0
|
-100,000
|
-50,000
|
|
1
|
40,000
|
20,000
|
|
2
|
40,000
|
20,000
|
|
3
|
40,000
|
20,000
|
|
4
|
40,000
|
20,000
|
|
NPV
|
$26,794.62
|
$13,397.31
|
|
IRR
|
21.860%
|
21.860%
|
Source: (Cheng et al , 1994: 68)
Notes:
a. Minus value on year 0, is the Initial outlay (the
amount of money which has to be paid on the investments.
b.Amount
of dollar ($) on year 1 to year 4 are revenue.
CONCLUSION
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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