Oleh :
Arwan Apriyono
Paulus Setyo Nugroho
INTRODUCTION
Finansial
Decision Making
Infuence Factor
-Inflation & Deflation
-Tax
-Depreciation
Decision making methods
-NPV/NPW
-ROR/IRR
-B/C
Fundamental knowledge
-Value of money (PV, FV, AV)
-Interest (Rate , Compound)
-Cost and Benefit
-Cast flow diagram
Definition
the internal rate of return is the interest
rate at which the benefits are equivalent to
the costs or the present worth (PW) is 0
PW of benefits - PW of costs = 0
PW of benefits/PW of Cost = 1
Net Present Worth = 0
EUAB- EUAC=0
PW of costs = PW of benefits
Example
1. Instead of lending money, we might invest $8200 in a
machine tool with a 5-year useful life and an equivalent
uniform annual benefit of $2000.
An appropriate question is,What rate of return would we
receive on this investment?
$2000
$8200
Example
Then look at the compound interest tables for the value of
i where (PIA, i, 5) = 4.1;
If no tabulated value of i gives this value, we will then find
values on either side of the desired value (4.1) and
interpolate to find the IRR.
Example
In this example, no interpolation is needed because the
internal rate of return is exactly 7%.
If IRR is not exactly the value (7%), we need to take
interpolation linear as example bellow
Example
With i = 6%  (P/A,i,5) = 4.212
With i = 8%  (P/A,i,5) = 3.993
8%
?
6%
3.993
4.1
4.212
Example
2. An investment resulted in the following cash
flow. Compute the rate of return.
$250
$100
$700
$175
$325
Example
In this situation,we have two different interest factors in
the equation.We wilL not be able to solve it as easily as
Example 1. Since there is no convenient direct method
of solution,we will solve the equation by trial and error.
Example
Try i = 5% first




EUAB- EUAC = 0
100 + 75(A/G, 5%, 4) - 700 (A/P, 5%, 4) = 0
100 + 75(1.439) – 700 (0.2820) = 0
EUAB – EUAC = 208 -197 = + 11
The EUAC is too low. If the interest rate is increased,
EUAC will increase. Try i =8%:
Example
i = 8%




EUAB- EUAC = 0
100 + 75(A/G, 8%, 4) - 700 (A/P, 8%, 4) = 0
100 + 75(1.404) – 700 (0.3049) = 0
EUAB – EUAC = 205 -211 = - 6
This time the EUAC is too large. We see that the true rate
of return is between 5% and 8%. Try i =7%:
Example
i = 7%




EUAB- EUAC = 0
100 + 75(A/G, 7%, 4) - 700 (A/P, 7%, 4) = 0
100 + 75(1.416) – 700 (0.2952) = 0
EUAB – EUAC = 206 -206 = 0
The IRR is 7%
Advantage of
ROR
Rate of return analysis is probably the most frequently used
exact analysis technique in industry.
The advantage to rate of return analysis is no interest rate
introduced into the calculation, instead we compute a rate of
return from the cash flow. Whereas In both present worth
and annual cash flow calculations, one must select an
interest rate for use in the calculations and this may be a
difficult and controversial item.
To decide how to proceed, the calculated rate of return is
compared with a preselected minimum attractive rate of
return, or simply MARR. This is the same value of i used for
present worth and annual cash flow analysis. If the value of
ROR is higher than the MARR, then the project is good.
Incremental
Analysis
When there are two alternatives, rate of return analysis is performed
by computing the incremental rate of return (DIRR) on the
difference between the alternatives.
Since we want to look at increments of investment the cash flow for
the difference between the alternatives is computed by taking the
higher initial-cost alternative minus the lower initial cost
alternative.
Two-Alternative Situation :
 DIRR ≥ MARR  Choose the higher-cost alternative
 DIRR < MARR  Choose the lower-cost alternative
Incremental
Analysis
STEP OF INCREMENTAL ANALYSIS
Step 1: Set up the cash flow of all alternatives in ascending order of
initial investment.
Step 2: Discard all alternatives that have an ROR less than the
MARR. This step can be ignored but performing it will save time
on the rest of the steps.
Step 3: Construct the cash flow of the difference of alternatives two by
two, starting from the two with the lowest ROR. Always subtract
the one with lowest initial investment from the one with the higher
initial investment. A check on this step is that the cash flow at time
zero of the differential should always be negative.
If the ROR of the differential is higher than the MARR, the alternative
with the higher initial investment is preferred, otherwise the one
with the lower initial investment is preferred.
Next we compare the preferred alternative with the next alternative on
the list in the same manner.
Sample
Incremental
Analysis
1. An investor is offered two investment opportunities. Project A is an
investment in frozen yogurt equipment that requires an initial
investment of $40,000 with a life of three years. Its annual
operating costs and annual incomes are presented in table A. The
equipment can be sold at the end of year 3 at a resale value of
$5,000.
Sample
Incremental
Analysis
The second opportunity is purchase of printing equipment with an
initial investment of $200,000. Annual operating costs and annual
incomes are presented in table B. The equipment can be sold at
the end of year 5 at a resale value of $20,000.
If the MARR for this investor is 10%, which project should he invest
in? Ignore tax and depreciation.
Langkah pengerjaan:
1. Hitung IRR project A; apakah layak? Lebih dari MARR ?
2. Hitung IRR project B; apakah layak? Lebih dari MARR ?
3. Tuliskan incremental analysis dari project yang layak
Year
A
0
-40 k
1
25 k
B
-40 k
10 k
-15 k
2
33 k
45 k + 5 k
-20 k
4
-200 k
-200 k
-160 k
110 k
0
0
25 k
10 k
55 k
25 k
90 k
90 k
- 100 k
15 k
-18 k
3
B-A
135 k
-110 k
30 k
170 k
- 115 k
210 k
-120 k
5
230k+20 k 120 k
120 k
-130 k
Gambarkan CFD dari tabel di atas
4. Hitung IRR of incremental CFD; IRR > MARR ? Jika ya ambil yang
investasi lebih besar, jika IRR < MARR ambil yang investasi lebih kecil
Sample
Incremental
Analysis
STEP 1 Calculate ROR of alternative A
NPW = -40000+10000(P/F,i*,1)+15000(P/F,i*,2)+30000(P/F,i*,3)
By trial and error, i* = 14.7% i* > 10% (Acceptable)
Sample
Incremental
Analysis
STEP 2 Calculate ROR of Alternative B
Calculating ROR as we did in the case of project A we obtain
ROR=11% > 10 % (acceptable)
Sample
Incremental
Analysis
STEP 3 Take Incremental Analysis
We have to use the incremental cash flow diagram, i.e.,. B-A. In
calculating ROR, we do not have to equalize the lives. That makes
it easier. The incremental cash flow is
Year Alternative A Alternative B
B-A
0
40000
200000
160000
1
10000
10000
0
2
15000
25000
10000
3
30000
55000
25000
4
0
90000
90000
5
0
120000
120000
Sample
Incremental
Analysis
STEP 4 Calculate ROR of Incremental Cash Flow Diagram
The ROR for this incremental cash flow is calculated as follows:
By trial and error, i* = 10.5. Therefore, i*>10%; hence, project B is
preferred.
This means it is better to invest all the available money ($200,000) in
project B at 10.5% rather than invest $40,000 in project A and the
rest at MARR of 10%.