Attention!
In Even weeks lecture starts earlier!!!
At 16.00 – 18.00 in room EF. 13-15
In odd weeks at 18.10 -19.40
Midterm exam: 26. October 2010.
Topic: present value calculations
1
Investment
decisions and time value of money
„Res tantum valet quantum vendi protest”
A thing is worth only what someone else will pay for it.
(unknown)
2
Learning goals
1. Discuss the role of time value in finance
2. Understand the concepts of future and present
value
3. Find the future and present value of ordinary
annuity
4. Find the present value of a perpetuity
3
Materials to learn from
Lawrence J. Gitman: Principles of Managerial Finance,
Addison - Wesley 10th Edition – see sharepoint: CH4 +
web
– http://wps.aw.com/aw_gitman_pmf_11
Brealey and Myers: Principles of corporate Finance, West
Publishing Company
www.mhhe.com/business/finance
Lecture material
4
Basic principles of finance
Time value of money - a
dollar today worth more
than a dollar tomorrow
A safe dollar is worth
more than a risky one
5
Basic idea and theories
1. Theory of Present
Value
2. Castle-in-the –air
Theory
6
Castle-in-the-air Theory
Baloon theory by Lord Keynes
(1936)
Investor psychology
Follow others
Succesful investor: identify
timepoint of building castle in the
air, and buy before that point
„Tronics prosperity”
7
Theory of Present Value
Theory by John B.
Williams
Based on : dividends and
assumes long-term
decisions
Compares actual value
and real value
8
Basics
Yield
– Rate of return
– Rate of interest
– Income
Maturity
Nominal/ par/face value-the principal
Future and present value
Simple interest
Compound interest
9
Concept of time value of money postulate
All operations with money must be compared
between alternatives to find the best result.
Interest rate is a simple but prominent equivalent of
any change of time value of money.
10
Rate of return rule
We accept investments that offer rates of return
in excess of their opportunity cost of capital
Cost of capital invested: the return forgone by
NOT INVESTING in other securities
11
Future value and present value
Changing in time value of money gets future and
present nomination
Getting from present value to future value is called
compounding.
Getting from future value to present value is called
discounting.
12
PV and FV
PV – cash in hand today
FV – cash received at given future date
Time line – can be used to depict the cash flows
in time
13
Simple interest
Present value = discount future value by an appropriate
interest rate
Interest rate – opportunity cost of capital
PRINCIPAL – AMOUNT OF MONEY ON WHICH INTEREST IS
PAID
Up to 1 year
PV= FV / (1+ r)
FV = PV ( 1+ r)
14
Where to use simple interest
Money market instruments
–
–
–
–
–
–
Treasury bills (T-bill)
Local authority/ public utility bills
Certificate of deposit (CD)
Commercial paper (CP)
Bill of exchange
Bankers` acceptance (BA)
15
Money market
Short term instruments
Pure discount securities
Contracts up to 1 year
Huge volume and vigorous competition
No physical place
Essentially for professionals ( banks,institutional investors,
brokerage firms, companies)
Liquidity ( fine spreads based on interest rate of lending and
borrowing)
Creditworthiness
16
Money market securities
T-bills
– Domestic instruments issued by governments to raise short term finance
balancing cashflow
– Non-interest bearing and interest-bearing, sold at discount in auction
– Negotiable
– Generally 13,26,52 weeks
Certificate of deposit - CD
–
–
–
–
–
Usually issued by banks, is simple the evidence of time deposit
Negotiable not as time deposit
Sold at discount or pay coupon
Interest payed at maturity
30 days to 3 month or could be longer
17
Money market securities 2
Commercial paper- CP
– Issued by large, safe and well-known companies
bypassing banks to achieve lower borrowing rates
(sometimes below the bank’s prime rate)
– Very short term (max 270 days, most 60days or less)
– Issued at discount
– Unsecured security
18
Money market securities 3
Trade bill, bills of exchange, bankers’acceptance
– Used by companies for trade purposes
– The seller draws up a bill to the buyer to pay and
asks to sign it
– Could be sold at a discount to the bank
– Bank’s signature is a guaranty ( eligible bills in UK
the Bank of England is the guarantor)
19
HELP!!!
Computational tools for
finding PV and FV:
– Financial tables
– Financial Calculators
– Computers and
spreadsheets
20
FV
FV = PV ( 1+ r)t
r = interest rate
PV = recent cashflow
FV = future cashflow
t = time period
FVIF= (1 + r)t
FV = PV ( FVIF)
PV = $100
r = 10%
FV = ?
t = 1 year
t = 3 years
FV = 100 (1 + 0.10) = 110
FV = 100 (1.10)3 = 133.
21
Future value and present value
(1 + r)ⁿ is a future value factor (FVF)
To simplify calculations of FV use table of FVF.
Years
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
1
1,01
1,02
1,03
1,04
1,05
1,06
1,07
1,08
1,09
1,1
2
1,02
1,04
1,06
1,08
1,10
1,12
1,14
1,17
1,19
1,21
3
1,03
1,06
1,09
1,12
1,16
1,19
1,23
1,26
1,295
1,33
4
1,04
1,08
1,13
1,17
1,22
1,26
1,31
1,36
1,41
1,46
5
1,05
1,1
1,16
1,22
1,28
1,34
1,40
1,47
1,54
1,61
6
1,06
1,13
1,19
1,27
1,34
1,42
1,50
1,59
1,68
1,77
7
1,07
1,15
1,23
1,32
1,41
1,50
1,61
1,71
1,83
1,94
8
1,08
1,17
1,27
1,37
1,48
1,59
1,72
1,85
1,99
2,14
9
1,09
1,20
1,30
1,42
1,55
1,69
1,84
1,999
2,17
2,36
10
1,1
1,22
1,34
1,48
1,63
1,79
1,97
2,16
2,37
2,59
22
Nominal and Effective Annual Rate
of Interest (EAR)
EAR = (1+ r/t )t - 1
EAR …?…. with increasing compounding
frequency
23
Compound Interest 1
Invetments for more than 1 year
Contracts in the capital markets
24
Capital market
Instruments
– Bonds
– Government bonds
– Local authority papers
– Mortgage or other assets backed bonds
– Corporate
– Foreign
– Junk
– Shares
– Preferred
– Normal
Innovations
– Convertibles
– Variables
Investment notes
25
Present Value
PV = $125
FV = $132
r=?
PV = FV / DF
DF = discount factor
DF = 1 / 1 + r
DF = PV / FV
DF = 125: 132 = 0.899
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2. Future value and present value
Table of present value factor
Years
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
1
0,99
0,98
0,97
0,96
0,95
0,94
0,935
0,93
0,92
0,91
2
0,98
0,96
0,94
0,92
0,91
0,89
0,87
0,86
0,84
0,83
3
0,97
0,94
0,92
0,89
0,86
0,84
0,82
0,79
0,77
0,75
4
0,96
0,92
0,89
0,85
0,82
0,79
0,76
0,74
0,71
0,68
5
0,95
0,91
0,87
0,82
0,78
0,75
0,71
0,68
0,65
0,62
6
0,94
0,89
0,84
0,79
0,75
0,70
0,67
0,63
0,596
0,56
7
0,93
0,87
0,81
0,76
0,71
0,67
0,62
0,58
0,55
0,51
8
0,92
0,85
0,79
0,73
0,68
0,63
0,58
0,54
0,50
0,47
9
0,914
0,84
0,77
0,70
0,64
0,59
0,54
0,50
0,46
0,42
10
0,905
0,82
0,74
0,68
0,61
0,56
0,51
0,46
0,42
0,39
27
Compound Interest 2
28
Compound Interest 3
DF8 = 0.285
FV8 =CF8 = $ 596
PV = ?
PV = FV (DF) = 596 X 0.285 = $170
29
Valuing more assets
We have plenty of investments:
PV = PV1 + PV2 + PV3 + ….+ PVn
30
Basic patterns of cash flow
Single amount : a lump sum amount
Annuity : A level periodic stream –fixed amount
for fixed period of time
Mixed stream: stream of CF that reflects no
particular pattern
Perpetuity: fixed amount of payments forever
31
Annuities
Asset that pays a fixed sum each year over a
specified period of time
Outflows or inflows
Expl: house mortgage, Installment credit, bond
Types:
– annuity due ( CF at the begining)
– Ordinary annuity ( CF at the end of each period)
32
Annuities 2
End of year
1
2
3
4
5
CF
100
100
100
100
100
33
Annuities 3
The model of annuities present value calculation is:
PVa = cf / (1 + r)¹ + cf / (1 + r)² + cf / (1+ r)³ + … + cf / (1+ r)ⁿ-1;
Matematical expression:
PVIFAr, t = 1 / r X ( 1 - 1/ (1 + r)t
Pva = CF X PVIFA
34
Calculating The Future Value of an Annuity
Fred wishes to determine
how much money he will
have at the end of 5
years, if he puts $1000 at
the end of each year.
The saving account pays
7% interest per annum
35
Future and present value of stream of
cash flow
Table of future value factor of annuity
Years
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
1
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
1,00
2
2,01
2,02
2,03
2,04
2,05
2,06
2,07
2,08
2,09
2,1
3
3,03
3,06
3,09
3,12
3,15
3,18
3,22
3,25
3,28
3,31
4
4,06
4,12
4,2
4,25
4,31
4,38
4,44
4,51
4,57
4,64
5
5,1
5,2
5,3
5,42
5,53
5,64
5,75
5,87
5,99
6,11
6
6,2
6,3
6,5
6,63
6,8
6,98
7,15
7,34
7,52
7,72
7
7,2
7,4
7,7
7,898
8,14
8,39
8,65
8,92
9,2
9,49
8
8,3
8,6
8,9
9,21
9,55
9,897
10,26
10,64
11,03
11,45
9
9,4
9,8
10,16
10,58
11,03
11,49
11,98
12,49
13,02
13,58
10
10,5
10,95
11,46
12,01
12,58
13,18
13,82
14,49
15,19
15,94
36
Calculating The Future Value of an Annuity
CF = $1000
t = 5 years
r = 7%
FVa = CF X FVIFA
FVa = CF X ∑ (1 + r )t-1
Years amount
PV
1.
2.
3
4.
5.
1000
1000
1000
1000
1000
1311
1225
1145
1070
1000
? 5000
5751
37
Table of present value annuity factor
Years
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
1
0,99
0,98
0,97
0,96
0,95
0,94
0,93
0,925
0,917
0,91
2
1,97
1,94
1,91
1,89
1,86
1,83
1,81
1,78
1,76
1,74
3
2,94
2,88
2,83
2,76
2,72
2,67
2,62
2,58
2,53
2,49
4
3,90
3,81
3,72
3,63
3,55
3,47
3,39
3,31
3,24
3,17
5
4,85
4,71
4,58
4,45
4,33
4,21
4,10
3,99
3,89
3,79
6
5,796
5,60
5,42
5,24
5,08
4,91
4,77
4,62
4,49
4,36
7
6,73
6,47
6,23
6,00
5,79
5,58
5,39
5,21
5,03
4,87
8
7,65
7,33
7,02
6,73
6,46
6,21
5,97
5,75
5,53
5,33
9
8,57
8,16
7,79
7,44
7,11
6,8
6,52
6,25
5,99
5,76
10
9,47
8,98
8,73
8,11
7,72
7,36
7,02
6,71
6,42
6,14
38
Thank you 
39