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D009452333
1. Penggunaan ROR dan B/R
Pertemuan 17 dan 18
Matakuliah : D 0094 Ekonomi Teknik
Tahun : 2007
2. Bina Nusantara
Contoh Soal Rate of Return:
Contoh :
Vincent Gogh’s painting “Irises”
• John Whitney Payson membeli barang seni ini
seharga $80,000.
• John menjual kembali seharga $53.9 juta 40
tahun kemudian.
• Berapa rate of return dari investasi John ?
3. Bina Nusantara
Rate of Return
• Diketahui: P =$80,000, F =
$53.9juta, and N = 40 tahun
• Cari : i
• Solusi:
$80,000
$53.9 Juta
( )
%69.17
1000.90$9.53$
40
=
+=
i
ijuta
0
40
4. Bina Nusantara
Pada 1970, ketika Wal-Mart Stores, Inc.
menjadi Perusahaan terbuka (go public),
suatu investasi dari 100 saham seharga
$1,650. Investasi tersebut akan menjadi
$13,312,000 pada 31 January 2000.
Berapa rate of return pada investasi
tersebut ?
Arti Rate of ReturnArti Rate of Return
6. Bina Nusantara
Seandainya anda menginvestasikan senilai ($1,650)
dalam rekening tabungan 6% per tahun. Kemudian
anda hanya memperoleh $9,477 pada January,
2000.
Apa arti dari 6% interest disini?
Ini adalah opportunity cost jika menyimpan uang
pada rekening tabungan, dan merupakan suatu
tindakan yang terbaik yang dapat dilakukan saat itu.
7. Bina Nusantara
Kemudian, pada tahun 1970, anda memperoleh tawaran
untuk investasi lain dengan interest lebih dari 6% untuk
investasi lain, anda akan mengambil investasi tersebut.
Oleh karena itu, 6% dipandang sebagai minimum
attractive rate of return (rate of return yang dibutuhkan).
Maka, anda dapat menetapkan aturan keputusan berikut
untuk memperoleh investasi yang diusulkan adalah
yang terbaik :
ROR > MARR
8. Bina Nusantara
Rate of Return
• Definisi 1: Rate of return (ROR) merupakan
interest rate yang diperoleh pada
unpaid balance dari angsuran suatu
pinjaman.
• Contoh: Sebuah bank meminjamkan $10,000
dan menerima pembayaran pertahun
sebesar of $4,021 selama 3 tahun.
Bank dikatakan memperoleh
penghasilan kembali (return of) 10%
dari pinjaman sebesar $10,000.
9. Bina Nusantara
Loan Balance Calculation:
A = $10,000 (A/P, 10%, 3)
= $4,021
Unpaid Return on Unpaid
balance unpaid balance
at beg. balance Payment at the end
Year of year (10%) received of year
0
1
2
3
-$10,000
-$10,000
-$6,979
-$3,656
-$1,000
-$698
-$366
+$4,021
+$4,021
+$4,021
-$10,000
-$6,979
-$3,656
0
A return of 10% on the amount still outstanding at the
beginning of each year
10. Bina Nusantara
Rate of Return:
• Definition 2: Rate of return (ROR) is defined
as break-even interest rate, i*
, which equates the
present worth of a project’s cash outflows to the
present worth of its cash inflows.
• Mathematical Relation:
PW i PW i PW i( ) ( ) ( )* * *
= −
=
cash inflows cash outflows
0
11. Bina Nusantara
Return on Invested Capital
• Definition 3: Return on invested capital is
defined as the interest rate earned on the
unrecovered project balance of an investment
project. It is commonly known as internal rate
of return (IRR).
• Example: A company invests $10,000 in a
computer and results in equivalent annual labor
savings of $4,021 over 3 years. The company is
said to earn a return of 10% on its investment of
$10,000.
12. Project Balance Calculation:
0 1 2 3
Beginning
project balance
Return on
invested capital
Payment
received
Ending project
balance
-$10,000 -$6,979 -$3,656
-$1,000 -$697 -$365
-$10,000 +$4,021 +$4,021 +$4,021
-$10,000 -$6,979 -$3,656 0
The firm earns a 10% rate of return on funds that remain internally
invested in the project. Since the return is internal to the project, we
call it internal rate of return.
13. Bina Nusantara
Period
(N)
Project A Project B Project C
0 -$1,000 -$1,000 +$1,000
1 -500 3,900 -450
2 800 -5,030 -450
3 1,500 2,145 -450
4 2,000
Project A is a simple investment.
Project B is a nonsimple investment.
Project C is a simple borrowing.
15. Bina Nusantara
Direct Solution Methods
• Project A • Project B
PW i
i i
x
i
PW i x x
x
x
i
i
i
i
i
i i
( ) $2,
$1,
( )
$1,
( )
,
( ) , , ,
:
.
. .
, *
= − +
+
+
+
=
=
+
= − + +
=
=
+
→ = − =
+
→ = −
− < < ∞ =
000
300
1
500
1
0
1
1
2 000 1300 1500
08
08
1
1
25%, 1667
1
1
160%
100% 25%.
2
2
Let then
Solve for
or -1.667
Solving for yields
Since the project's
$1, $1, ( / , , )
$1, $1, ( )
. ( )
ln .
ln( )
. ln( )
.
.
000 500 4
000 500 1
0 6667 1
0 6667
4
1
0101365 1
1
1
4
4
0 101365
0 101365
=
= +
= +
−
= +
= +
= +
= −
=
−
−
P F i
i
i
i
i
e i
i e
10.67%
16. Bina Nusantara
Trial and Error Method – Project C
• Step 1: Guess an interest
rate, say, i = 15%
• Step 2: Compute PW(i)
at the guessed i value.
PW (15%) = $3,553
• Step 3: If PW(i) > 0, then
increase i. If PW(i) <
0,
then decrease i.
PW(18%) = -$749
• Step 4: If you bracket the
solution, you use a linear
interpolation to
approximate
the solution
3,553
0
-749
15% i 18%
+
+=
749553,3
553,3
%3%15i
%45.17=
17. Bina Nusantara
Graphical Solution – Project D
• Step 1: Create a NPW plot
using Excel.
• Step 2: Identify the point at
which the curve crosses the
horizontal axis closely
approximates the i*.
• Note: This method is
particularly useful for
projects with multiple rates
of return, as most financial
softwares would fail to find
all the multiple i*s.
18. Bina Nusantara
Aturan Keputusan Dasar
If ROR > MARR, terima
Aturan ini tidak berlaku untuk situasi dimana
invesrasi mempunyai ‘multiple rates of
return’
19. Problem Multiple Rates of Return
• Cari rate(s) of return:
PW i
i i
( ) $1,
$2, $1,
( )
= − +
+
−
−
+
=
000
300
1
320
1
0
2
$1,000
$2,300
$1,320
20. Bina Nusantara
Let Then,
Solving for yields,
or
Solving for yields
or 20%
x
i
PW i
i i
x x
x
x x
i
i
=
+
=− +
+
−
+
=− + −
=
= =
=
1
1
000
300
1
320
1
000 300 320
0
10 11 10 12
10%
2
2
.
( ) $1,
$2,
( )
$1,
( )
$1, $2, $1,
/ /
22. Kalkulasi Kesetimbangan Proyek
n = 0 n = 1 n = 2
Beg. Balance
Interest
Payment -$1,000
-$1,000
-$200
+$2,300
+$1,100
+$220
-$1,320
Ending Balance -$1,000 +$1,100 $0
i* =20%
Cash borrowed (released) from the project is assumed
to
earn the same interest rate through external investment
as money that remains internally invested.
23. Bina Nusantara
Critical Issue: Can the company be able to invest the money
released from the project at 20% externally in
Period 1?
If your MARR is exactly 20%, the answer is “yes”, because it
represents the rate at which the firm can always invest
the money in its investment pool. Then, the 20% is also true
IRR for the project.
.
Suppose your MARR is 15% instead of 20%. The assumption
used in calculating i* is no longer valid.
Therefore, neither 10% nor 20% is a true IRR.
24. Bina Nusantara
• If NPW criterion is used at MARR = 15%
PW(15%) = -$1,000
+ $2,300 (P/F, 15%, 1)
- $1,320 (P/F, 15%, 2 )
= $1.89 > 0
Investasi diterima
How to Proceed: If you encounter multiple
rates of return, abandon the IRR analysis
and use the NPW criterion (or use the procedures
outlined in Appendix A).
25. Bina Nusantara
Aturan Keputusan Untuk Nonsimple Investment
• Kemungkinan multiple RORs.
• Jika PW (i) plot looks seperti
berikut, maka, IRR = ROR.
If IRR > MARR, Terima
• Jika PW(i) plot seperti berikut,
maka, IRR ≠ ROR (i*).
• Dapatkan IRR sebenarnya
atau
• Gunakan method PW
PW(i)
i*
i
i
i*
i*
PW(i)
26.
27. Membandingkan Mutually Exclusive
Alternatives Berdasarkan IRR
• Issue: Dapatkah membuat ranking
‘mutually exclusive projects’ dengan
besaran dari IRR?n A1 A2
0
1
IRR
-$1,000 -$5,000
$2,000 $7,000
100% > 40%
$818 < $1,364PW (10%)
28. Incremental Investment
• Assuming MARR of 10%, you can always earn that rate from other
investment source, i.e., $4,400 at the end of one year for $4,000
investment.
• By investing the additional $4,000 in A2, you would make additional
$5,000, which is equivalent to earning at the rate of 25%. Therefore,
the incremental investment in A2 is justified.
n Project A1 Project A2
Incremental
Investment
(A2 – A1)
0
1
-$1,000
$2,000
-$5,000
$7,000
-$4,000
$5,000
ROR
PW(10%)
100%
$818
40%
$1,364
25%
$546
29. Bina Nusantara
Incremental Analysis (Procedure)
Step 1: Compute the cash flows for the difference
between the projects (A,B) by subtracting
the cash flows for the lower investment
cost project (A) from those of the higher
investment cost project (B).
Step 2: Compute the IRR on this incremental
investment (IRR ).
Step 3: Accept the investment B if and only if
IRR B-A > MARR
B-A
30. Bina Nusantara
Contoh - Incremental Rate of Return
n B1 B2 B2 - B1
0
1
2
3
-$3,000
1,350
1,800
1,500
-$12,000
4,200
6,225
6,330
-$9,000
2,850
4,425
4,830
IRR 25% 17.43% 15%
Diketahui MARR = 10%, project mana pilihan terbaik?
Bila IRRB2-B1=15% > 10%, dan juga IRRB2 > 10%, pilih B2.
31. Bina Nusantara
IRR pada Increment Investment:
Tiga Alternatif
n D1 D2 D3
0 -$2,000 -$1,000 -$3,000
1 1,500 800 1,500
2 1,000 500 2,000
3 800 500 1,000
IRR 34.37% 40.76% 24.81%
Step 1: Tetapkan IRR untuk tiap
proyek untuk mngeliminasi tiap
project yang gagal memenuhi
MARR
Step 2: Bandingkan D1 dan D2 berpasangan.
IRRD1-D2=27.61% > 15%,
pilih D1.
Step 3: Bandingkan D1 dan D3.
IRRD3-D1= 8.8% < 15%,
pilih D1.
Kesimpulannya D1 adalah alternatif terbaik.
32. Bina Nusantara
Incremental Borrowing Analysis
Decision Rule:
• If BRR B-A < MARR, select B.
• If BRR B-A = MARR, select
either one.
• If BRR B-A > MARR, select A.
Principle:
• If the difference in flow (B-A)
represents an increment of
investment, then (A-B) is an
increment of borrowing.
• When considering an
increment of borrowing, the
rate i*
A-B is the rate we paid to
borrow money from the
increment.
i*
A B A BBRR− −=
33. Bina Nusantara
Borrowing Rate of Return
n B1 B2 B1-B2
0 -$3,000 -$12,000 +$9,000
1 1,350 4,200 -2,850
2 1,800 6,225 -4,425
3 1,500 6,330 -4,830
34. Bina Nusantara
Incremental Analysis for Cost-Only Projects
Items CMS Option FMS Option
Annual O&M costs:
Annual labor cost $1,169,600 $707,200
Annual material cost 832,320 598,400
Annual overhead cost 3,150,000 1,950,000
Annual tooling cost 470,000 300,000
Annual inventory cost 141,000 31,500
Annual income taxes 1,650,000 1,917,000
Total annual costs $7,412,920 $5,504,100
Investment $4,500,000 $12,500,000
Net salvage value $500,000 $1,000,000
36. Bina Nusantara
Solution:
PW i
P A i
P F i
IRR
FMS CMS
FMS CMS
( ) $8, ,
$1,908, ( / , , )
$2, , ( / , , )
.43%
−
−
= −
+
+
=
= <
000 000
820 5
408 820 6
0
12 15%,
select CMS.
37. Bina Nusantara
Ultimate Decision Rule:
If IRR > MARR, Accept
• Aturan berlaku untuk setiap situasi investasi.
• Dalam beberapa situasi,
IRR = ROR
tapi hubungan ini tidak dapat digunakan untuk
investasi dengan multiple RORs.
38. Bina Nusantara
Predicting Multiple RORs
- 100% < i *
< infinity
• Net Cash Flow Rule of Signs
No. of real RORs (i*s)
<
No. of sign changes in the project
cash flows
39. Bina Nusantara
Example
n Net Cash flowSign Change
0
1
2
3
4
5
6
-$100
-$20
$50
0
$60
-$30
$100
1
1
1
• No. of real i*s ≤ 3
• This implies that the project could have
(0, 1, 2, or 3) i*s but NOT more than 3.
40. Bina Nusantara
Accumulated Cash Flow Sign Test
Find the accounting sum of net cash flows at
the end of each period over the life of the
project
Period Cash Flow Sum
(n) (An ) Sn
If the series S starts negatively and changes sign
ONLY ONCE, there exists a unique positive i*.
S A
S S A
S S A
S S AN N N
0 0
1 0 1
2 1 2
1
=
= +
= +
= +−
A
A
A
AN
0
1
2
0
1
2
N
41. Bina Nusantara
Contoh
n An Sn Perubanhan
tanda
0
1
2
3
4
5
6
-$100
-$20
$50
0
$60
-$30
$100
-$100
-$120
-$70
-$70
-$10
-$40
$60 1
• Jumlah tanda berubah = 1, indicating a unique i*.
• i* = 10.46%
42. Bina Nusantara
Contoh: $2,145
$3,900
$5,030
$1,000
0 1
2
3
• Apakah ini simple investment?
• Berapa RORs (i*s) dapat diharapkan dari menguji
cash flows?
• Apakah Investasi ini mempunyai rate of return yang unik ?
46. Bina Nusantara
General Procedure for Cost-Effectiveness
Studies
Step 1: Establish the goals to be achieved by the analysis.
Step 2: Identify the imposed restrictions on achieving the goals, such
as budget or weight.
Step 3: Identify all the feasible alternatives to achieve the goals.
Step 4: Identify the social interest rate to use in the analysis.
Step 5: Determine the equivalent life-cycle cost of each alternative,
including research and development, testing, capital investment,
annual operating and maintenance costs, and salvage value.
47. Bina Nusantara
• Step 6: Determine the basis for developing the cost-effectiveness
index. Two approaches may be used;
– (1) the fixed-cost approach and
– (2) the fixed-effectiveness approach.
– If the fixed-cost approach is used, determine the amount of
effectiveness obtained at a given cost.
– If the fixed-effectiveness approach is used, determine the cost to
obtain the predetermined level of effectiveness.
• Step 7: Compute the cost-effectiveness ratio for each alternative based
on the selected criterion in Step 6.
• Step 8: Select the alternative with the maximum cost-effective index.
48. Bina Nusantara
Cost-Effectiveness Decision Criterion
• Fixed Effectiveness
Approach
• Fixed Cost Approach
Maximize Effectiveness
Subject to:
Budget Constraint
Minimize Cost
Subject to:
Must meet the minimum
effectiveness
