Basic Principles of Valuation

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1 Basic Priciples of Valatio Basic Priciples of Valatio Jes Carste Jackwerth Uiversity of Kostaz 2 Otlie Basic Priciples of Valatio Motivatio Defiitio of the Net Preset Vale he Net Preset Vale a the creatio of vale Discotig Perpetities a aities Compoig Assmptios a comptatio

2 3 Motivatio Basic Priciples of Valatio A great eal : year cash flow Net cash flow is C0 C C2 C Decisios base o et cash flows o ot take opportity costs ito accot 4 Net Preset Vale I Basic Priciples of Valatio Iterest rate is r Net Preset Vale = sm of iscote et cash flows NPV C 0 C C2 r ( 2 C3 ( 3... C ( Net Preset Vale of the great eal at r = 0% is NPV ( 0.) ( 0.)

3 5 Net Preset Vale II Basic Priciples of Valatio Discot rate correspos to the respective opportity cost of capital, i.e. riskless cash flows are iscote with the risk-free rate risky cash flows ee to be iscote with a iterest rate with the same level of risk Net Preset Vale positive et preset vale creates wealth egative et preset vale estroys wealth Preset Vale (more geeral tha NPV) preset vale = sm of iscote et cash flow (ofte excles ivestmets) 6 Basic Priciples of Valatio Net Preset Vale a the Creatio of Vale I he great eal is worth as mch as havig i the bak, as oe ca replicate this cash flow as follows year 0: borrow a cosme borrow a ivest i the project year : bak balace is ( ). = borrow a ivest i the project year 2: bak balace is ( ). = 2.82 receive from the project a pay back loa year 3: bak balace is ( ). = receive from the project a pay back loa 3

4 7 Basic Priciples of Valatio Net Preset Vale a the Creatio of Vale II Assmptios firm is free to borrow a le coterexample: baks have to hol reserves creit iterest = ebit iterest coterexample: persoally, yo ca borrow o a creit car at 25% bt yo le o yor accot at 0% shareholers iterests i the firm are solely fiacial coterexample: Friea Spriger wol ot sell her shares i orer keep cotrol of the pblisher Spriger Verlag shareholers are free to by or sell shares coterexample: I the UK, the state ows a gole share a ths has certai rights, here for istace the right to veto a sale of efese compaies 8 Ftre Vales Basic Priciples of Valatio How mch is worth tomorrow? Borrowig a leig is possible at r = 0%.00 toay = (+0.) i year =.0 i year =. (+0.) i 2 years = (+0.) 2 i 2 years =.2 i 2 years = (+0.) 3 i 3 years =.33 i 3 years a toay = a (+ r ) i years = A i years A is the ftre vale i years of a iveste ow 4

5 9 Preset Vales Basic Priciples of Valatio How mch is, receive i oe year, worth toay? a ( 0.) a a is the Preset Vale of A, receive i years A a ( A a ( he iscot factor is ( Example:, receive i 3 years, is worth toay at r = 0% ( 0.) Perpetity Basic Priciples of Valatio Costat cash flow i perpetity cash flow is P per year, startig i year oe iscot rate is r preset vale is obtaie sig the geometric series year 0 2 PV cash flow 0 P P P P P P / r Example eowig a chair i fiace at the iversity iterest rate is 0% esire cotribtio is 50,000 per year i perpetity he reqire eowmet toay is 50,000 / 0. = 500,000 5

6 Growig Perpetity Basic Priciples of Valatio Growig cash flow i perpetity cash flow is P i year oe growth rate of cash flows per year is g, startig i year two iscot rate is r year 0 2 PV cash flow 0 P P(+g) P(+g) - P / (r - g) Example eowig a chair i fiace at the iversity cotribtios are 50,000 i year oe the cotribtios have to icrease by 5% per year, r is 0% he reqire eowmet toay is 50,000 / ( ) =,000,000 2 Aity I Basic Priciples of Valatio Derivatio of the PV for costat cash flows over years cash flow is P per year, startig i year, lastig years year 0 2 PV cash flow 0 P P P P 0?? replicate cash flows sig two perpetities perpetity 0 P P P P P P / r perpetity P (P / / ( + PV(Aity) = PV(Perpetity ) - PV(Perpetity 2) = P P r r ( P r ( 6

7 3 Aity II Basic Priciples of Valatio he -year aity factor with iterest rate r is r ( Example eowig a chair i fiace at the iversity iscot rate is r = 0% cotribtios are 50,000 per year for 5 years he reqire eowmet is 50, ( 0.) 5 89,539 4 Compo Iterest I Basic Priciples of Valatio Compo iterest is the iterest o the reivestmet of the iterest pai rig the ivestmet perio Ivest 00 for oe year at 8% with aal compoig oe obtais 00 ( 0.08) 08 with semi-aal compoig oe obtais (.04) with qarterly compoig oe obtais (.02) with -times compoig per year oe obtais

8 5 Compo Iterest II Basic Priciples of Valatio Limit as goes to ifiity As the time betwee paymets of iterest (a its reivestmet) becomes smaller, moey i the accot grows a fially coverges Relatio betwee aally compoig a -times per year compoig r 00 e r 0.08 r ( 6 Discot Factors Basic Priciples of Valatio aal compoig at iterest rate r ( -times compoig at iterest rate r r cotios compoig at iterest rate R e R e R 8

9 7 Methos for Comptig the Net Preset Vale Basic Priciples of Valatio Example of a iscot table at r = 0% year total cash flow iscot factor preset vales Calclator ivie cash flow i each year t by ( + t the sm over all perios Spreasheet i Excel comptes PV NPV(r, A2:C2) - 00 ote: C is i cell A2; C 0 = -00 ees to be ae 8 BMA, 9 th eitio: Chapter 3 Qestio 4 BMA, 0 th eitio: Chapter 2 Qestio 4 BMA, th eitio: Chapter 2 Qestio 4 Basic Priciples of Valatio A factory costs 800,000. Yo expect that it will proce a iflow after operatig costs of 70,000 a year for 0 years. If the opportity cost of capital is 4%, what is the et preset vale of the factory? What will the factory be worth at the e of five years? 9

10 9 BMA, 9 th eitio: /a BMA, 0 th eitio: /a BMA, th eitio: /a Basic Priciples of Valatio PV 70, year aity factor at 4% 70, , ,720 NPV PV iitial ivestmet 86,720 PV at e of year five 70,00 5-year aity factor at 4% 70, , ,60 20 BMA, 9 th eitio: Chapter 3 Qestio 22 BMA, 0 th eitio: Chapter 2 Qestio 22 BMA, th eitio: Chapter 2 Qestio 22 Basic Priciples of Valatio I orer to fiace a car with a list price of 0,000, Kagaroo Atos makes the followig offer: Yo pay,000 ow a the 300 a moth for the ext 30 moths. rtle Motors ext oor oes ot offer free creit bt will give yo,000 off the list price. If the rate of iterest is 0% a year, which compay is offerig the better eal? 0

11 2 BMA, 9 th eitio: /a BMA, 0 th eitio: /a BMA, th eitio: /a Basic Priciples of Valatio mothly 2 r (.) PV Kagaroo, aity factor for 30 perios at 0.79% per perio, , ,986 PV rtle 0,000,000 9,000

1 The Power of Compounding

1 The Power of Compounding 1 The Power of Compoudig 1.1 Simple vs Compoud Iterest You deposit $1,000 i a bak that pays 5% iterest each year. At the ed of the year you will have eared $50. The bak seds you a check for $50 dollars.