P9 & P10 cover chapters 5 of the textbook, which discusses time value of money concepts. Specifically: - P9 covers single amounts, annuities, and the role of time value in finance. It provides examples of calculating future value, present value, and net present value. - P10 extends the discussion to mixed cash flow streams, compounding interest more frequently than annually, and special applications of time value. It also provides additional examples of time value calculations. - The key concepts covered are future value, present value, net present value, internal rate of return, and modified internal rate of return. Worked examples are provided to illustrate calculations for each.

2. MANAJEMEN KEUANGAN 1
(P9 -10 :Time Value of Money )
Prof. Dr. H. Aminullah Assagaf, SE., MS., MM., M.Ak
Email : assagaf29@yahoo.com
Hp : 628113543409
Jakarta, 29 Oktober 2019

3. REFERENCE
Principles of Managerial Finance
13th edition, Pearson, Addison Wesley Publishing Company. 2012
by : Gitman, Lawrence J. and Zutter, Chad J.

5. P-1 = Ch. 1 dan 2

6. P-1 = Ch. 1 dan 2

7. P2 & P3 = Ch.3

8. P4 & P5 = Ch. 4

9. P-6 = Ch. 8

10. • P7: Review
• P8: Mid-Term Examination
P7 & P8

11. P9 & P10 = Ch. 5

12. P11 & P12 = Ch.15

13. P13 = Ch. 16

14. P14 & P15
• P14: Review
• P15: Final Examination

16. Manajemen Keuangan 1
1. Ch. 1, 2 = P1…The role of managerial finance & The financial market
invironment
2. Ch. 3 = P2, P3 …Financial statement and ratio analysis
3. Ch. 4 = P4, P5… Cash flow and financial planning
4. Ch. 8 = P6 …Risk and return
Review, UTS = P7, P8
1. Ch. 5 = P9, P10 …Time value of money
2. Ch. 15 = P11, P12 …Working capital and current assets management
3. Ch. 16 = P13 …Current liabilities management
Review, UAS = P14, P15

17. SAP – Manajemen Keuangan 1
Pertemuanke Topi k Tugas
1 1. THE ROLE OF MANAGERIAL FINANCE
2. Finance and Business
3. Goal of the Firm
4. Managerial Finance Function
5. Governance and Agency
6. THE FINANCIAL MARKET ENVIRONMENT
7. Financial Institutions and Markets
8. The Financial Crisis
9. Regulation of Financial Institutions
10. Business Taxes
2 1. FINANCIAL STATEMENTS AND RATIO ANALYSIS
2. The Stockholders' Report
3. Using Financial Ratios
4. Liquidity Ratios
5. Activity Ratios

18. Pertemuanke Topik Tugas
3 1. FINANCIAL STATEMENTS AND RATIO ANALYSIS
2. Debt Ratios
3. Profitability Ratios
4. Market Ratios
5. A Complete Ratio Analysis
4 1. CASH FLOW AND FINANCIAL MANAGEMENT
2. Analyzing the Firm's Cash Flow
3. The Financial Planning Process
4. Cash Planning : Cash Budgets
5 1. CASH FLOW AND FINANCIAL MANAGEMENT
2. Profit Planning : Pro Forma Statements
3. Preparing The Pro Forma Income Statement
4. Preparing The Pro Forma Balance Sheet
5. Evaluating of pro Forma Statements

19. Pertemuanke Topik Tugas
6 1. RISK & RETURN
2. Risk & Return Fundamentals
3. Risk of a Single Asset
4. Risk of a Portfolio
5. Risk & Return: the Capital Asset Pricing Model (CAPM)
7 1. Review
8 1. Mid-Term Examination
9 1. TIME VALUE OF MONEY
2. The Role of Time Value in Finance
3. Single Amounts
4. Annuities
10 1. TIME VALUE OF MONEY
2. Mixed Streams
3. Compounding interest more frequently than annually
4. Special Applications of Time Value

20. Pertemuanke Topik Tugas
11 1. WORKING CAPITAL AND CURRNT ASSETS MANAGEMENT
2. Net Working Capital Fundamentals
3. Cash Conversion Cycle
4. Inventory Management
12 1. WORKING CAPITAL AND CURRNT ASSETS MANAGEMENT
2. Account Receivable Management
3. Management of Receipts and Disbursements
13 1. CURRENT LABILITIES MANAGEMENT
2. Spontaneous Liabilities
3. Unsecured Sources of Short-term Loans
4. Secured Sources of Short-term Loans
14 1. Review
15 1. Final Examination

21. Manajemen Keuangan 1
1. Ch. 1, 2 = P1…The role of managerial finance & The financial market
invironment
2. Ch. 3 = P2, P3 …Financial statement and ratio analysis
3. Ch. 4 = P4, P5… Cash flow and financial planning
4. Ch. 8 = P6 …Risk and return
Review, UTS = P7, P8
1. Ch. 5 = P9, P10 …Time value of money
2. Ch. 15 = P11, P12 …Working capital and current assets management
3. Ch. 16 = P13 …Current liabilities management
Review, UAS = P14, P15

23. Pertemuanke Topik Tugas
6 1. RISK & RETURN
2. Risk & Return Fundamentals
3. Risk of a Single Asset
4. Risk of a Portfolio
5. Risk & Return: the Capital Asset Pricing Model (CAPM)
7 1. Review
8 1. Mid-Term Examination
9 1. TIME VALUE OF MONEY
2. The Role of Time Value in Finance
3. Single Amounts
4. Annuities
10 1. TIME VALUE OF MONEY
2. Mixed Streams
3. Compounding interest more frequently than annually
4. Special Applications of Time Value

24. P9 & P10 = Ch. 5

25. P-9: Time value of money
5.1 The role of value in finance - 161
5.2 Single amounts - 164
5.3 Annuities - 171

26. P-10: Time value of money
5.4 Mixed Streams - 178
5.5 Compounding interest more frequently than annuity - 181
5.6 Special applications of time value - 188

30. 5.1 The role of value in finance - 161

31. Contoh:
….FV= Berapa nilai yad yang sama dengan pengeluaran hari ini ?
….PV= Berapa nilai hari ini yang sama dengan pengeluaran yad ?

32. 5.2 Compunding (bunga berbunga untuk FV) and Discounting
(pengurangan untuk PV)

33. 5.2 Single amounts - 164

34. FUTURE VALUE (FV)

35. PERHITUNGAN FV
FV = PV x DF
DF = (1+r)n
FV = PV (1+r)n
Atau

36. Contoh 1:

37. Contoh 2: FV = 800 (1.06)5
FV = 800 (1.33823) = 1.070.58

38. PRESENT VALUE (PV)

39. Contoh: 1:

40. PERHITUNGAN PV
Semula  FV = PV (1+r)n
PV =
𝐹𝑉
1+𝑟 𝑛
PV = FV
1
1+𝑟 𝑛
PV = FV x DF
DF =
1
1+𝑟 𝑛

41. PERHITUNGAN PV

42. Contoh 2:

43. PERHITUNGAN PV
Semula  FV = PV (1+r)n
PV =
𝐹𝑉
1+𝑟 𝑛
PV = FV
1
1+𝑟 𝑛
PV = FV x DF
DF =
1
1+𝑟 𝑛

44. Contoh

45. NET PRESENT VALUE (NPV)
Alternatif : A
Th CI CO DF PVCI PVCO NPV
15.0%
1 2 3 5 6=2x5 7=3x5 8=6-7
0 100,000 1.000 - 100,000 (100,000)
1 16,000 0.870 13,913 - 13,913
2 17,000 0.756 12,854 - 12,854
3 18,000 0.658 11,835 - 11,835
4 19,000 0.572 10,863 - 10,863
5 20,000 0.497 9,944 - 9,944
6 21,000 0.432 9,079 - 9,079
7 22,000 0.376 8,271 - 8,271
8 23,000 0.327 7,519 - 7,519
9 24,000 0.284 6,822 - 6,822
10 25,000 0.247 6,180 - 6,180
Total 205,000 100,000 0 97,280 100,000 (2,720)
Kesimpulan :
- NPV (2,720) Tdk Layak
- B/C ratio 0.973 Tdk Layak
Contoh 1 :

46. Alternatif : B
Th CI CO DF PVCI PVCO NPV
15%
1 2 3 5 6=2x5 7=3x5 8=6-7
0 100,000 1.000 - 100,000 (100,000)
1 25,000 0.870 21,739 - 21,739
2 24,000 0.756 18,147 - 18,147
3 23,000 0.658 15,123 - 15,123
4 22,000 0.572 12,579 - 12,579
5 21,000 0.497 10,441 - 10,441
6 20,000 0.432 8,647 - 8,647
7 19,000 0.376 7,143 - 7,143
8 18,000 0.327 5,884 - 5,884
9 17,000 0.284 4,832 - 4,832
10 16,000 0.247 3,955 - 3,955
Total 205,000 100,000 0 108,490 100,000 8,490
Kesimpulan :
- NPV 8,490 Layak
- B/C ratio 1.085 Layak
NET PRESENT VALUE (NPV)
Contoh 2 :

47. Alternatif : C
Th CI CO DF PVCI PVCO NPV
15%
1 2 3 5 6=2x5 7=3x5 8=6-7
0 100,000 1.000 - 100,000 (100,000)
1 20,500 0.870 17,826 - 17,826
2 20,500 0.756 15,501 - 15,501
3 20,500 0.658 13,479 - 13,479
4 20,500 0.572 11,721 - 11,721
5 20,500 0.497 10,192 - 10,192
6 20,500 0.432 8,863 - 8,863
7 20,500 0.376 7,707 - 7,707
8 20,500 0.327 6,701 - 6,701
9 20,500 0.284 5,827 - 5,827
10 20,500 0.247 5,067 - 5,067
Total 205,000 100,000 0 102,885 100,000 2,885
Kesimpulan :
- NPV 2,885 Layak
- B/C ratio 1.029 Layak
NET PRESENT VALUE (NPV)
Contoh 3 :

48. INTERNAL RATE OF RETURN (IRR)
Th CI CO NCF DF PVCI PVCO NPV
n 17.4% 17.4%
1 2 3 4=2-3 5 6=2x5 7=3x5 8=6-7
0 100,000 (100,000) 1.000 - 100,000 (100,000)
1 25,000 25,000 0.852 21,297 - 21,297
2 24,000 24,000 0.726 17,417 - 17,417
3 23,000 23,000 0.618 14,219 - 14,219
4 22,000 22,000 0.527 11,586 - 11,586
5 21,000 21,000 0.449 9,421 - 9,421
6 20,000 20,000 0.382 7,644 - 7,644
7 19,000 19,000 0.326 6,186 - 6,186
8 18,000 18,000 0.277 4,992 - 4,992
9 17,000 17,000 0.236 4,017 - 4,017
10 16,000 16,000 0.201 3,220 - 3,220
Total 205,000 100,000 105,000 0 100,000 100,000 0
Kesimpulan :
- NPV 0 Layak 1/(1+i)^n
- B/C ratio 1.000 Layak
- IRR 17.4% Layak
PERHITUNGAN IRR
Contoh 4 :

49. MIRR (Modified IRR)
TH CI =Cash CO = Cash Net 20% DF PV-FVCI PVCO NPV
Inflow outflow Cashflow n DF FVCI 18.99%
1 2 3 4=2-3 5 6=2X5 7=3X5 8=6-7
0 100,000 (100,000) 1.000 - 100,000 (100,000)
1 25,000 25,000 9 5.16 128,995 0.840 22,663 - 22,663
2 24,000 24,000 8 4.30 103,196 0.706 18,131 - 18,131
3 23,000 23,000 7 3.58 82,413 0.594 14,479 - 14,479
4 22,000 22,000 6 2.99 65,692 0.499 11,542 - 11,542
5 21,000 21,000 5 2.49 52,255 0.419 9,181 - 9,181
6 20,000 20,000 4 2.07 41,472 0.352 7,286 - 7,286
7 19,000 19,000 3 1.73 32,832 0.296 5,768 - 5,768
8 18,000 18,000 2 1.44 25,920 0.249 4,554 - 4,554
9 17,000 17,000 1 1.20 20,400 0.209 3,584 - 3,584
10 16,000 16,000 - 1.00 16,000 0.176 2,811 - 2,811
Jumlah 205,000 100,000 105,000 569,174 100,000 100,000 0
Finance rate 15% NPV 0 Layak
Reinvest rate 20% B/C 1.00 Layak
IRR 17.39% Layak
MRRI 18.99% Layak
CASH FLOW
FVCI

50. 5.3 Annuities

52. Contoh:

53. Ordinary (A) 7%
Th n Anunity DF=(1+r)
n
FVA
0 0 -
1 4 1000 1.311 1,310.80
2 3 1000 1.225 1,225.04
3 2 1000 1.145 1,144.90
4 1 1000 1.070 1,070.00
5 0 1000 1.000 1,000.00
Total 5,750.74
Due (B) 7%
Th n Anunity DF=(1+r)
n
FVA
0 5 1000 1.403 1,402.55
1 4 1000 1.311 1,310.80
2 3 1000 1.225 1,225.04
3 2 1000 1.145 1,144.90
4 1 1000 1.070 1,070.00
5 -
Total 6,153.29
Ordinari (CF tiap ahir tahun) Due (CF tiap awal tahun) lebih cepat terima

54. FV-Ordinary Annuity (CF Akhir Tahun)

56. Atau……
FV5 = CFA (5.75074) = 5.750,74 FV5 = 1000 (5.75074) = 5.750,74
DF5
FV - Ordinary Annyity

57. FV - Annuity Due (CF Lebih awal atau cepat)

58. FV - Annuity Due(CF lebih awal atau cepat diterima)
FV5 = 1000 (6.15329) = 6.153,29
x (1+r) (1 +0.07)
5.750,74 x 1,07) = 6.15329

59. PRESENT VALUE OF AN ORDINARY ANNUITY (CF AKHIR TAHUN)

60. PV – Ordinary Annuity (CF akhir th atau dihitung nol pd th pertama)
Ordinary (A) 8%
Th Anunity DF=(1+r)
n
FVA
0 0 -
1 700 0.926 648.15
2 700 0.857 600.14
3 700 0.794 555.68
4 700 0.735 514.52
5 700 0.681 476.41
Total 3.993 2,794.90
PVA- Ordinary= CFA x 3.993 = 700 x 3.993 = 2.794,90
}
}
0.681}
= 3.993

61. PRESENT VALUE OF ANNUITY DUE

62. PRESENT VALUE OF ANNUITY DUE
Due (B) 8%
Th Anunity DF=(1+r)n
FVA
0 700 1.000 700.00
1 700 0.926 648.15
2 700 0.857 600.14
3 700 0.794 555.68
4 700 0.735 514.52
5 -
Total 4.312 3,018.49
PVA- Due= CFA x 4.312 = 700 x 4.312 = 3.018.49
} x (1+r)
} x (1+0.08)
0.681} x (1.08)
= 4.312

63. Point: 5.4

66. Th n CF Compounded Future
(akhir) 8% Value (FV)
1 4 11,500 1.360 15,645.62
2 3 14,000 1.260 17,635.97
3 2 12,900 1.166 15,046.56
4 1 16,000 1.080 17,280.00
5 0 18,000 1.000 18,000.00
72,400 - 83,608.15Total

69. Th CF Disc Fact Future
(akhir) 9% Value (FV)
1 400 0.917 366.97
2 800 0.842 673.34
3 500 0.772 386.09
4 400 0.708 283.37
5 300 0.650 194.98
Total 2,400 - 1,904.76

70. Point: 5.5

72. 4%
Bulan Awal Bunga/6 bln Akhir
6 100.00 4.00 104.00
12 104.00 4.16 108.16
18 108.16 4.33 112.49
24 112.49 4.50 116.99

73. Periode 2 tahun, Pembayaran tiap 3 bulan, bunga 2% per 3 bln
atau 8% pertahun

74. Period 2 tahun, Pembayaran tiap 3 bulan, bunga 2% per 3 bln atau 8%
pertahun
2%
Bulan Awal Bunga/6 bln Akhir
3 100.00 2.00 102.00
6 102.00 2.04 104.04
9 104.04 2.08 106.12
12 106.12 2.12 108.24
15 108.24 2.16 110.41
18 110.41 2.21 112.62
21 112.62 2.25 114.87
24 114.87 2.30 117.17

78. e (euler), bilangan dasar 2,718282 FV =100(e^0.08x2)=
diperoleh dgn menghitung …..dari Ln e 2.718282
=100^(1/ln(100)) 2.718282 0.08x2 0.16
=10^(1/ln(10)) 2.718282 e^0.16 1.1735
atau CF 100
Ln(100) = 4.60517 FV 117.35
Maka bilangan dasar Ln= 100^(1/4.60517)= 2.718282

81. Point: 5.6

83. TH Deposit Bunga FV
6%
1 5321.89 5,321.89
2 5321.89 319.31 10,963.10
3 5321.89 657.79 16,942.78
4 5321.89 1,016.57 23,281.23
5 5321.89 1,396.87 30,000.00

84. FV 30,000
r 6%
n 5
(1+r)^n 1.338225578
(1+r)^n - 1 0.338225578
( (1+r)^n - 1)/r 5.63709296
CF = FV/DFA 5,321.89
Jumlah CF tiap tahun = 5.321,89

87. Pembayaran utang, jumlah yang sama tiap periode $.......

88. Utang $6000, bunga 10%, 4 tahun, Pembayaran tiap periode….?
Akhir TH Awal Bayar Interest Principal Akhir
10%
1 6000.00 1892.82 600.00 1292.82 4707.18
2 4707.18 1892.82 470.72 1422.11 3285.07
3 3285.07 1892.82 328.51 1564.32 1720.75
4 1720.75 1892.82 172.07 1720.75 0.00
Pembayaran yang sama tiap periode = $ 1892,82

89. Menghitung Bunga….%

92. Goal Seek
PV 1000
FV 2500 PV(1+r)^n 2500
r 8%
n??? 11.91