Fundamental Basic. Fundamentals. Fundamental PV Principle. Time Value of Money. Fundamental. Chapter 2. How to Calculate Present Values

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1 McGraw-Hill/Irwin Chaper 2 How o Calculae Presen Values Principles of Corporae Finance Tenh Ediion Slides by Mahew Will And Bo Sjö 22 Copyrigh 2 by he McGraw-Hill Companies, Inc. All righs reserved. Fundamenal Basic A firm mus pull in more money han i pays ou over ime The mos imporan concep The cash flow Definiion cash flow money (cash) in money (cash) ou during a period. Cashmoneypoenial consumpion uliy value Free cash flow: he cash flow in each period which can be used o pay dividends on equiy or ineres on deb. Here is he value of he firm. 2-2 Fundamenals 2-3 Fundamenal Principle 2-4 Price is wha you pay. Value is wha you ge. In you privae life, as in he life of a firm: Esimae fuure ne cash flows in periods Calculae he ne presen value oday of hese flows Then, make a decision. If you don do i some else will do i for you, aking heir own ineres ino accoun, no yours. Find ou wha ype of cash flow Find he simplyfing formula Find he correc discoun rae for each ype of cash flow Required reurn on deb (Yield o Mauriy) Required reurn on Equiy (Asse pricing model, such as CAPM) Calculae he presen value, or fuure value. Fundamenal 2-5 Time Value of Money 2-6 The goal of he firm Max value of he firm by maximizing he presen value of all fuure free cash flows adjused for he ime value of money including risk. Each decision o pay ou or recieve money, including invesmen decisions, should be filered hrough a Ne Presen Value (N) Anlysis. Value Based Managemen (VBM) le his principle be ransparen and open hrough he whole firm and o all sakeholders. I means saisfy all sakeholders wihou favouring one over he oher. Take all facs ino accoun. Consumion oday does no have he same value as consumpion omorrow. You can choose, and maximise uiliy from consumpion over your whole life if you wan. People decide on how much o save and consume oday. Thereby hey creae an ineres rae, he alernaive cos of consuming oday compared wih omorrow. Presen and fuure cash flows can only be compared by aking he ime value of money ino accoun, as ha value is manifesed by peoples decions (marke yields).

2 2-7 Topics Covered Valuaion 2-8 Fuure Values and Presen Values One fuure period or many Sar wih one period, a cerain cash flow Nex more han one period Followed by many periods and risk cash flows Sring of cash flows, perhaps infinie Therefore, look for Shorcus Perpeuiies and Annuiies Growing Perpeuiies and Growing Annuiies Economic values vs. Accouing values Never use book/accouning values Economic decisions are aken on economic values no book values Value of deb/bonds/money marke insrumens/fixed income insrumens Value of socks/equiy/shares The value of a firm Value of invesmen projecs Value vs. Price 2-9 and FV? 2- Value is wha you ge, price is wha you pay The price of he sock on he sock marke oday is he value on he marke I is he price you pay. If you ask how much do I ge? You need o do your own valuaion, calculae he inrinisc value. The inrinisic value is a valuaion of an asse based on available informaion abou he cash flows he owner can recieve. If markes are fully efficien marke value and inrinsic values are he same. So how o do i? We sar wih he mechanics. So how o do i? We sar wih he mechanics. For his course: Memorize some formulas, do no use financial calculaors, ables or Excel. Valuaion 2- Presen and Fuure Value 2-2 Always ) Idenify he cash flows, 2) Simplify? Type of flows? 3) Idenify he discoun rae 4) Use he correc formula o calculae Laer we will learn o calculae he correc discoun rae in each siuaion Now, le us ravel hrough ime... Presen Value Value oday of a fuure cash flow. Fuure Value Amoun o which an invesmen will grow afer earning ineres

3 2-3 Fuure Values (Compounding) Fuure Values 2-4 Fuure Value (FV) of $ is FV, you have $ oday and inves (save), a he end of nex period you have FV $ ( + ) - FV r FV $ ( + ) r Wha is he fuure value of $ if ineres is compounded annually a a rae of 7% for wo years? FV $ (.7) (.7) 4.49 FV $ ( +.7) 2 $4.49 Fuure Values wih Compounding 2-5 Convenion 2-6 FV of $ % 5% % 5% Ineres Raes Ineres raes and yields, are always qoued on an annual basis, o make hem comparable. The hree-monh ineres rae is quoued as 6%, meaning ha you pay (or recieve).6/4.5, or.5% per quarer Number of Years There are no excepions from his rule Presen Value (Discouning) of a fuure cash flow C a ime. 2-7 Presen Value 2-8 Presen Value Discoun facor C Discoun Facor DF of $ DF ( + r ) Discoun Facors can be used o compue he presen value of any cash flow, if you know he correc r of course.

4 2-9 Presen Value wo periods Presen Values wih Compounding 2-2 Given any variables in he equaion, you can solve for he remaining variable. Also, you can reverse he prior example. of Cash flow coi ming wo periods from now: DF C 2 2 (+.7) of $ Ineres Raes % 5% % 5% Number of Years Valuing an Office Building 2-2 Valuing an Office Building 2-22 Sep : Forecas cash flows Cos of building C 37, Sale price in Year C 42, Sep 2: Esimae opporuniy cos of capial If equally risky invesmens in he capial marke offer a reurn of 5%, hen Cos of capial r 5% Sep 3: Discoun fuure cash flows C 42, ( +r ) ( +. 5) 4, Sep 4: Go ahead if of payoff exceeds invesmen N 4, 37, 3, N Do you ge he money back, in erms of real economic value? 2-23 Risk and Presen Value 2-24 N - required invesmen Higher risk projecs require a higher rae of reurn Higher required raes of reurn cause lower s I is worh less oday compared wih less risky invesmens N C C + + r of C $42, a 5% 42, 4, +.5

5 2-25 Risk and Presen Value Risk and Ne Presen Value 2-26 of C $42, a 2% 42, 375, +.2 of C $42, a 5% 42, 4, +.5 N - required invesmen N 375, - 37, $5, Wha is risk? 2-27 Ne Presen Value Rule 2-28 Risk is he variaion (variance) around he esimae of he fuure cash flow. The pracical meaning is ha when you need o exchange asses ino money, o consume in he fuure, you don know how much you will ge. You canno plan fuure consumpion exacly. The bigger he variance, he bigger he risk, he higher is he discoun rae. Accep invesmens ha have posiive ne presen value Use he original example. Should we accep he projec given a % expeced reurn? 42, N -37,+ $3,.5 Rae of Reurn Rule 2-29 Muliple Cash Flows 2-3 Accep invesmens ha offer raes of reurn in excess of heir opporuniy cos of capial For muliple periods we have he Discouned Cash Flow (DCF) formula In he projec lised below, he foregone invesmen opporuniy is 2%. Should we do he projec? C C (+ r) (+ r) + C (+ r) profi 42, 37, Reurn.35 or 3.5% invesmen 37, N C + T C (+ r )

6 2-3 Ne Presen Values Shor Cus 2-32 Presen Value Year 2,/.2 - $37, $2, $ 42, Year 2 -$37, $7,9 Someimes here are shorcus ha make i very easy o calculae he presen value of an asse ha pays off in differen periods. These ools allow us o cu hrough he calculaions quickly. 42,/.2 2 $334,8 Toal - $7,3 Shor Cus 2-33 Perpeuiy 2-34 Perpeuiy - Financial concep in which a cash flow is heoreically received forever. Reurn r cash flow presen value C The firm is ypically seen a Going concern meaning ha we assume ha i will run forever. Therefore he firm s, asses deb, ec are all perpeuiies. +Prefered sock and consols Mahemaically i is easier o work wih infinie cash flows han finie flows. Shor Cus 2-35 Presen Values 2-36 Perpeuiy - Financial concep in which a cash flow is heoreically received forever. Wha is he presen value of $ billion every year, for all eerniy, if you esimae he perpeual discoun rae o be %?? cash flow of Cash Flow discoun rae C r $ bil. $ billion

7 2-37 Presen Values Shor Cus - Annuiy coninued Wha if he invesmen does no sar making money for 3 years? Two-sep. Annuiy - An asse ha pays a fixed sum each year for a specified number of years. (Bonds, loans, deb) Asse Year of Paymen Presen Value Perpeuiy (firs paymen in year ) C r ( 3 ) $7.5billion $ bil.. Perpeuiy (firs paymen in year + ) Annuiy from year o year C r ( + r) C C r r ( + r) Presen Values Tiburon Auos offers you easy paymens of $5, per year, a he end of each year for 5 years. If ineres raes are 7%, per year, wha is he cos of he car? Presen Value a year 5, /.7 4, , /(.7) 4, , /(.7) 4,8 4 5, /(.7) 3,84 5 5, /(.7) 3,565 Toal N 2,5 5, 5, 5, 5, 5, Year 2-39 Shor Cus Annuiy - An asse ha pays a fixed sum (C) each year for a specified number of years. (Please memorize his formula) of annuiy C r r ( + r) 2-4 Annuiy Shor Cu 2-4 Annuiy Shor Cu 2-42 You agree o lease a car for 4 years a $3 per monh. You are no required o pay any money up fron or a he end of your agreemen. If your opporuniy cos of capial is.5% per monh, wha is he cos of he lease? - coninued You agree o lease a car for 4 years a $3 per monh. You are no required o pay any money up fron or a he end of your agreemen. If your opporuniy cos of capial is.5% per monh, wha is he cos of he lease? Lease Cos ( +.5) Cos $2,774.

8 2-43 Annuiy Shor Cu FV Annuiy Shor Cu 2-44 The sae loery adverises a jackpo prize of $295.7 million, paid in 25 insallmens over 25 years of $.828 million per year, a he end of each year. If ineres raes are 5.9% wha is he rue value of he loery prize? Loery Value ( +.59) Value $52,6, Fuure Value of an Annuiy The fuure value of an asse ha pays a fixed sum each year for a specified number of years. FV of annuiy C ( + r) r Annuiy Shor Cu 2-45 Consan Growh Perpeuiy 2-46 Wha is he fuure value of $2, paid a he end of each of he following 5 years, assuming your invesmen reurns 8% per year? C r g FV 2, $7,332 ( +.8).8 5 g he annual growh rae of he cash flow Consan Growh Perpeuiy 2-47 Consan Growh Perpeuiy 2-48 NOTE: This formula can be used o value a perpeuiy a any poin in ime. C r g C r + g Wha is he presen value of $ billion paid a he end of every year in perpeuiy, assuming a rae of reurn of % and a consan growh rae of 4%?..4 $6.667 billion

9 2-49 Perpeuiies Ineres Quoaions 2-5 A hree-year sream of cash flows ha grows a he rae g is equal o he difference beween wo growing perpeuiies. All ineres raes are always saed on an annual basis. There is no expecion from his rule. Easier o compare raes!, if we agree o pay 2% acual ineres on loan for hree monhs, he ineres is saed as.2x4.8 or 8%. The one monh reasury bill rae is saed as.25% (per annum), he rae per monh is.25/2.46 or.46%. Effecive Ineres Raes 2-5 Effecive Ineres Raes 2-52 Effecive Annual Ineres Rae - Ineres rae ha is annualized using compound ineres. example Given a monhly rae of %, wha is he Effecive Annual Rae (EAR)? Wha is he Annual Percenage Rae (APR)? Annual Percenage Rae - Ineres rae ha is annualized using simple ineres. example Effecive Ineres Raes Given a monhly rae of %, wha is he Effecive Annual Rae (EAR)? Wha is he Annual Percenage Rae (APR)? + EAR (+.) 2 EAR (+.) -.268or 2.68% APR.x 2.2or 2.% EARper monhgiven2.68%: 2 /2 [.268]. x Typical example Ineres raes are saed as simple annual raes (APR) on credi cards for your monhly deb on he card. Amazon.co.uk offers a Masercard wih APR 6.9%. How much do you pay per monh, if you use he credi? How much do you pay in ineres if you use he credi for a whole year? (EAR) 2-54

10 2-55 Web Resources Click o access web sies Inerne connecion required hp://finance.yahoo.com

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