Attention!

In Even weeks lecture starts earlier!!!At 16.00 – 18.00 in room EF. 13-15In odd weeks at 18.10 -19.40

Midterm exam: 26. October 2010.

Topic: present value calculations

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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)

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Learning goals

1. Discuss the role of time value in finance2. Understand the concepts of future and present

value3. Find the future and present value of ordinary

annuity4. Find the present value of a perpetuity

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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 Companywww.mhhe.com/business/finance

Lecture material

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Basic principles of finance

Time value of money - a dollar today worth more than a dollar tomorrowA safe dollar is worth more than a risky one

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Basic idea and theories

1. Theory of Present Value

2. Castle-in-the –air Theory

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Castle-in-the-air Theory

Baloon theory by Lord Keynes (1936)Investor psychologyFollow others Succesful investor: identify timepoint of building castle in the air, and buy before that point„Tronics prosperity”

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Theory of Present Value

Theory by John B. WilliamsBased on : dividends and assumes long-term decisionsCompares actual value and real value

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Basics

Yield– Rate of return– Rate of interest– Income

MaturityNominal/ par/face value-the principalFuture and present valueSimple interestCompound interest

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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.

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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

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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.

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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

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Simple interest

Present value = discount future value by an appropriate interest rateInterest rate – opportunity cost of capitalPRINCIPAL – AMOUNT OF MONEY ON WHICH INTEREST IS PAIDUp to 1 yearPV= FV / (1+ r)

FV = PV ( 1+ r)

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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)

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Money market

Short term instrumentsPure discount securitiesContracts up to 1 yearHuge volume and vigorous competitionNo physical placeEssentially for professionals ( banks,institutional investors, brokerage firms, companies)Liquidity ( fine spreads based on interest rate of lending and borrowing)Creditworthiness

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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

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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

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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)

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HELP!!!

Computational tools for finding PV and FV:– Financial tables– Financial Calculators– Computers and

spreadsheets

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FV

FV = PV ( 1+ r)t

r = interest ratePV = recent cashflowFV = future cashflowt = time periodFVIF= (1 + r)t

FV = PV ( FVIF)

PV = $100r = 10%FV = ?t = 1 yeart = 3 yearsFV = 100 (1 + 0.10) = 110FV = 100 (1.10)3 = 133.

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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 2,5922

Nominal and Effective Annual Rate of Interest (EAR)

EAR = (1+ r/t )t - 1

EAR …?…. with increasing compounding frequency

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Compound Interest 1

Invetments for more than 1 yearContracts in the capital markets

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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

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Present Value

PV = $125FV = $132r = ?PV = FV / DFDF = discount factorDF = 1 / 1 + r

DF = PV / FVDF = 125: 132 = 0.899

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2. Future value and present value

Table of present value factorYears 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

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Compound Interest 2

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Compound Interest 3

DF8 = 0.285

FV8 =CF8 = $ 596

PV = ? PV = FV (DF) = 596 X 0.285 = $170

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Valuing more assets

We have plenty of investments:PV = PV1 + PV2 + PV3 + ….+ PVn

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Basic patterns of cash flow

Single amount : a lump sum amountAnnuity : A level periodic stream –fixed amount for fixed period of timeMixed stream: stream of CF that reflects no particular patternPerpetuity: fixed amount of payments forever

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Annuities

Asset that pays a fixed sum each year over a specified period of timeOutflows or inflowsExpl: house mortgage, Installment credit, bondTypes: – annuity due ( CF at the begining)– Ordinary annuity ( CF at the end of each period)

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Annuities 2

End of year CF1 1002 1003 1004 1005 100

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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

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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

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Future and present value of stream of cash flow

Table of future value factor of annuityYears 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

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Calculating The Future Value of an Annuity

CF = $1000t = 5 yearsr = 7%

FVa = CF X FVIFAFVa = CF X ∑ (1 + r )t-1

Years amount PV

1. 1000 13112. 1000 12253 1000 11454. 1000 10705. 1000 1000

? 5000

5751

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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

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Thank you

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