Capital Budgeting Techniques
Management need to understand
capital budgeting techniques to
correctly analyze the relevant cash
flows of proposed projects and
decide whether to accept or reject
them.
Several methods of evaluating investment
projects as follows:
1. Payback period.
2. Net present value (NPV).
3. Internal rate of return (IRR) and MIRR
4. Profitability index (PI)
Bennett Company is currently contemplating
two projects: Project A requires an initial
investment of $42,000, project B an initial
investment of $45,000.
The relevant operating cash flows for the two
projects are presented as follow:
Payback period method
The payback period is the exact amount of time
required to recover the firm’s initial investment in a
project.
In the case of an annuity, the payback is calculated by
dividing the initial investment by the annual cash
inflow.
In the case of a mixed stream, the cash inflows are
added until their sum equals the initial investment in
the project.
Paybacks:
Year before full recovery
+
Unrecovered cost at start of year
Cash flow during year
Project B an initial investment of
$45,000:
Year
0
1
2
3
Cash Inflows
- $ 45,000
$ 28,000
$ 12,000
$ 10,000
Investment Balance
- $ 45,000
- $ 17,000
- $ 5,000
Payback period:
- Project A = 3 years
- Project B = 2.5 years
The maximum acceptable payback period is
determined by management.
If the payback period is less than the
maximum acceptable payback period,
accept the project.
If the payback period is greater than the
maximum acceptable payback period, reject
the project.
The payback method is widely used by large firms
to evaluate small projects and by small firms to
evaluate most projects.
It is simple, intuitive, and considers cash flows
rather than accounting profits.
It also gives implicit consideration to the timing of
cash flows and is widely used as a supplement to
other methods such as NPV and IRR.
The weaknesses of using the payback
period are :
(1) no explicit consideration of shareholders’
wealth;
(2) failure to take fully into account the time
value of money; and
(3) failure to consider returns beyond the
payback period
It fails to consider the principle of wealth
maximization because it is not based on
discounted cash flows and thus provides no
indication as to whether a project adds to firm
value. Thus, payback fails to fully consider the
time value of money.
Discounted Payback Period
Project Gold:
Tahun Arus Kas
0
PVIF
10%
- $ 50,000
1
PV Arus kas
- $ 50,000
1
5,000
0,909
4,545
2
5,000
0,826
4,130
3
40,000
0,751
30,040
4
10,000
0,683
6,830
5
10,000
0,621
6,210
Discounted Paybak Period = 4,72 year
Year
0
1
2
3
4
5
PV Arus kas Investment Balance
- $ 50,000
- $ 50,000
4,545
- $ 45,455
4,130
- $ 41,325
30,040
- $ 11,285
6,830
- $ 4,455
6,210
Project Silver:
Tahun Arus Kas
PVIF 10%
0
- $ 50,000
1
1
40,000
0,909
2
2,000
0,826
3
8,000
0,751
4
10,000
0,683
5
10,000
0,621
PV Arus kas
- $ 50,000
36,360
1,652
6,008
6,830
6,210
Discounted Paybak Period = 3,87
tahun
Year
0
1
2
3
4
5
PV Arus kas
Investment Balance
- $ 50,000
- $ 50,000
36,360
- 13,640
1,652
- 11,988
6,008
- 5,980
6,830
6,210
Cost of Capital
Suatu investasi dapat didanai oleh berbagai
sumber, dan masing-masing sumber dana
mempunyai biaya yang berbeda-beda.
Sehingga perlu dihitung biaya modal rata-rata
tertimbang, biaya ini dapat digunakan untuk
penentuan tingkat pengembalian yang layak
dalam perhitungan NPV dan sebagai cut-off
rate dalam penilaian kelayakan investasi
dengan menggunakan IRR method.
Net Present Value (NPV)
NPV is found by subtracting a project’s initial investment
from the present value of the after-tax inflows discounted
at a rate equal to the firm’s cost of capital.
NPV = Total present value of cash flows – initial investment.
Acceptance criterion for the NPV method is
if NPV > 0, accept;
if NPV < 0, reject.
If the firm undertakes projects with a positive NPV, the
market value of the firm should increase by the amount of
the NPV.
n
CFt
NPV = ∑
−
I
0
t
t =1 (1 + r )
Internal Rate of Return (IRR)
IRR is the discount rate that will equate the present
value of the outflows with the present value of the
inflows. TPVCF = Initial Investment
The IRR is the project’s intrinsic rate of return.
If a project’s IRR is greater than the firm’s cost of
capital, the project should be accepted; otherwise,
the project should be rejected.
If the project has an acceptable IRR, the value of the
firm should increase. Unlike the NPV, the amount of
the expected value increase is not known.
n
Σ
t=1
CF
= CF0
(1+IRR)t
IRR = r1 +
NPV1
NPV1 – NPV2
(r2 – r1)
Project A: IRR = 19,86%
NPV = 0 $ 42,000 = $ 14,000 x PVIFAIRR,n
PVIFAIRR,5 = 3
19% NPV = $ 812
20% NPV = - $ 126
Project B:
Year
0
1
2
3
4
5
Cash Flow
PVIF 20%
- $ 45,000
1
$ 28,000
0,833
12,000
0,694
10,000
0,579
10,000
0,482
10,000
0,402
PV Cash Flow
- $ 45,000
23,324
8,328
5,790
4,820
4,020
Project B:
Year Cash Flow PVIF 25% PV Cash Flow
0 - $ 45,000
1
- $ 45,000
1
$ 28,000
0,800
20,000
2
12,000
0,640
7,680
3
10,000
0,512
5,120
4
10,000
0,410
4,100
5
10,000
0,328
3,280
Projek B:
20% , NPV = $ 1,282
25%, NPV = - $ 4,820
20% + $ 1,282
5%
$ 1,282 + $ 4,820
IRR = 21,05%
Modified IRR (MIRR)
The discount rate at which the present value of
a project’s cost is equal to the present value of
its terminal value.
Terminal value is found as the sum of the future
values of the cash inflows, compounded at the
firm’s cost of capital.
Investment = PV of terminal/future value
compounded at the cost of capital
MIRR projek A
Tahun
1
2
3
4
5
Arus Kas
$ 14,000
$ 14,000
$ 14,000
$ 14,000
$ 14,000
FVIF 10%
1, 464
1,331
1,210
1,100
1
FV Arus Kas
$ 20,496
$ 18,634
$ 16,940
$ 15,400
$ 14,000
$ 85,470
Terminal Value projek A $ 85,470
FVIFA 10%, 5 x Cash Flow
6,105 x $ 14,000
MIRR :
$ 85,470 = $ 42,000 (1 + MIRR)⁵
(1 + MIRR)⁵ = 2,035 antara 15% dan 16%
MIRR projek B
Tahun
1
2
3
4
5
Arus Kas
$ 28,000
$ 12,000
$ 10,000
$ 10,000
$ 10,000
FVIF 10%
1, 464
1,331
1,210
1,100
1
FV Arus Kas
$ 40,992
$ 15,972
$ 12,100
$ 11,000
$ 10,000
$ 90,064
MIRR :
$ 45,000 = $ 90,064 / (1 + MIRR)⁵
1 / (1 + MIRR)⁵ = 0,4996
MIRR terletak antara 14% dan 15%
Profitability Index
The profitability index which is also sometimes
called the benefit/cost ratio, is the ratio of the
present value of the inflows to the present
value of the outflows.
PI =
TPV Inflows
TPV Outflows
PI =
n
Σ
t=1
CF
(1+r)t
CF0
Decision Criteria:
• If PI > 1, accept the project
• If PI < 1, reject the project
• If PI = 1, indifferent
Net Present Value Profiles
• NPV Profiles are graphs that depict project
NPVs for various discount rates and provide an
excellent means of making comparisons
between projects.
To prepare NPV profiles for Bennett Company’s
projects A and B, the first step is to develop a number
of discount rate-NPV coordinates and then graph
them as shown in the following table and figure.
Discount Rate–NPV Coordinates for
Projects A and B
NPV Profiles
Problems with Discounted Cash Flow Techniques
• Capital rationing occurs whenever a company is
constrained in its profitable (positive NPV) activities
by a lack of funding.
• Smaller firms tend to face these obstacles more
often because they have even more limited access to
funds.
• One problem with NPV and IRR is that it is difficult to
rank projects.
• In this case, the higher NPV should always be
chosen.
A project’s risk reflects the variability of a
project’s future cash flows. One must
consider all factor’s - both internal and
external - that can impact an investment’s risk.
Once these risks have been identified, the risk
adjusted discount rate is selected for the
purpose of project evaluation.
Conflicting Rankings
• Conflicting rankings between two or more projects using NPV
and IRR sometimes occurs because of differences in the
timing and magnitude of cash flows.
• This underlying cause of conflicting rankings is the implicit
assumption concerning the reinvestment of intermediate
cash inflows—cash inflows received prior to the termination
of the project.
• NPV assumes intermediate cash flows are reinvested at the
cost of capital, while IRR assumes that they are reinvested at
the IRR.
NPV vs IRR
• NPV mengasumsikan bahwa CF yang diterima
sebelum berakhirnya umur projek diinvestasikan
pada tingkat diskonto, sedangkan IRR
mengasumsikan bahwa CF diinvestasikan pada
tingkat IRR, dalam hal ini seringkali tidak realistis.
• Pada projek yang mempunyai pola arus kas nonkonvensional dapat diperoleh IRR lebih dari satu, hal
ini terjadi karena aspek matematis.
Reinvestment Rate Comparisons for a
Project
A project requiring a $170,000 initial investment
is expected to provide cash inflows of
$52,000, $78,000 and $100,000.
The NPV of the project at 10% is $16,867 and it’s
IRR is 15%.
The calculation of the project’s future value at
the end of it’s 3-year life, assuming both a
10% (cost of capital) and 15% (IRR) interest
rate.
If the future value in each case were viewed as
the return received 3 years from today from
the $170,000 investment, then the cash flows
would be those given in on the following slide.
Project Cash Flows After Reinvestment
Bennett Company’s projects A and B were found
to have conflicting rankings at the firm’s 10%
cost of capital.
If we review the project’s cash inflow pattern,
we see that although the projects require
similar investments, they have dissimilar cash
flow patterns.
Project B has higher early-year cash inflows than
project A, would be preferred over project A
at higher discount rates.
Which Approach is Better?
• On a purely theoretical basis, NPV is the better approach
because:
– NPV assumes that intermediate cash flows are reinvested
at the cost of capital whereas IRR assumes they are
reinvested at the IRR,
– Certain mathematical properties may cause a project with
non-conventional cash flows to have zero or more than
one real IRR.
• Despite its theoretical superiority, however, financial
managers prefer to use the IRR because of the preference for
rates of return.