1 Financial Engineeing and Computations Basic Financial Mathematics Dai, Tian-Shy
2 Outline Time Value of Money Annuities Amotization Yields Bonds
3 Time Value of Money PV + n = FV (1 + FV: futue value = PV ( + n PV: pesent value : inteest tate FV 1 n: peiod tems
4 Quotes on Inteest Rates is assumed to be constant in this lectue. Annualized ate.
5 Time Value of Money Peiodic compounding (If inteest is compounded m times pe annum nm FV = PV 1 + m Continuous compounding (3.1 FV = PVe n m 1 1 n lim(1 + = e lim(1 + = lim(1 + = e t t m m m m/ t nm n Simple compounding
6 Common Compounding Methods Annual compounding: m = 1. Semiannual compounding: m = 2. Quately compounding: m = 4. Monthly compounding: m = 12. Weekly compounding: m = 52. Daily compounding: m = 365
7 Two widely used yields Bond equivalent yield (BEY --Annualize yield with semiannual compounding Motgage equivalent yield (MEY --Annualize yield with monthly compounding
8 Equivalent Rate pe Annum Annual linteest ate is 10% compounded d twice pe annum. Each dolla will gow to be one yea fom now. ( 1 + (0.1/ 2 2 = The ate is equivalent to an inteest ate of 10.25% compounded d once pe annum.
9 Convesion between compounding Methods Suppose 1 is the annual ate with continuous compounding. Suppose 2 is the equivalent compounded m times pe annum m Then 1 Theefoe 1 m = e + 1 = ln 1 2 = m m 2 m e 1 m
10 Ae They Really Equivalent? Recall 1 and 2 on the pevious example. They ae based on diffeent cash flow. In what sense ae they equivalent?
11 Annuities Odinay annuity Annuity due Pepetual annuity
12 Odinay annuity An annuity pays out the same C dollas at the end of each yea fo n yeas. With a ate of, the FV at the end of nth yea is n 1 n i (1 1 C (1 + = C + (3.4 i= 0 c c n
13 Geneal annuity If m payments of C dollas each ae eceived pe yea (the geneal annuity, then Eq.(3.4 becomes ( 1 + n m m 1 C m The PV of a geneal annuity is ( 1+ nm i 1 m C 1 + = C i= 1 m m n m (3.6
14 Annuity due Fo the annuity due, cash flow ae eceived at the beginning i of each yea. The FV is n i= 1 C (1 + i (1 + = C n 1 (1 + (35 (3.5 If m payments of C dollas each ae eceived pe yea (the geneal annuity, then Eq.(3.5 becomes C c (1 + m m n m 1 (1 + m n
15 Fomula Odinay annuity PV: 1 (1 + C n Geneal annuity 1 (1 + C m m n m FV: C n ( C nm ( 1+ m m 1 Annuity due 1 (1 + n PV: C (1 + 1 (1 + C m m n m 1 + m (1 + n 1 FV: C (1 + nm (1 + m 1 C 1 + m m
16 Pepetual annuity An annuity that lasts foeve is called a pepetual annuity. We can dive its PV fom Eq.(3.6 by letting n go to infinity: i nm i ( nm m PV = lim C 1+ = lim C = n n i 1 m = This fomula is useful fo valuing pepetual fix- coupon debts. m mc
17 Example: The Golden Model Detemine the intinsic value of a stock. Let the dividend id d gows at a constant t ate Stock pice= Pesent value of the infinite seies of futue dividends. D D(1+g D PV (All ft futue dividends id d = ; g g > Whee D: Expected dividend pe shae one yea fom now. : Requied ate of etun fo equity investo. g: Gowth ate in dividends id d (in pepetuity.
18 In Class Execise: Show that D PV (All futue dividends = ; > g g
21 Example The PV of an annuity of $100 pe annum fo 5 yeas at an annual inteest ate of 6.25%
22 In Class Execise In above example, please use Excel to compute the FV of an annuity of $100 pe annum fo 5 yeas at an annual inteest ate of 6.25%. Veify this esult equal to the futue value of the PV of $
23 Amotization It is a method of epaying a loan though hegula payment of inteest and pincipal. The size of the loan (the oiginal balance is educed by the pincipal pat of each payment. The inteest pat of each payment pays the inteest incued on the emaining i pincipal i lbalance. As the pincipal gets paid down ove the tem of the loan, the inteest pat of the payment diminishes. See next example!
24 Example: Home motgages Conside a 15-yea, $250,000 loan at 8.0% inteest ate, epay pythe inteest 12 pe month. Because PV = 250,000, n = 15, m= 12, and = 0.08 we can get a monthly payment C is $2, C C C $ = (1 + (1 + ( i 1 ( = 1 12 C + = C C i= /12 =
25 (0.08/12 Payment-Inteest We compute it in last page
26 Calculating the Remaining i Pincipal i Right afte the kth payment, the emaining pincipal is the PV of the futue nm-k cash flows, C(1 + m 1 + C(1 + m C(1 + m ( nm k = 1 (1 + C m m nm+ k Time K nm-k Cash flow C C C
27 Yields The tem yield denotes the etun of investment. It has many vaiants. (1 Nominal yield (coupon ate of the bond (2 Cuent yield (3 Discount yield (4 CD-equivalent yield
28 Discount Yield U.S Teasuy bills is said to be issue on a discount basis and is called a discount secuity. When the discount yield is calculated fo shot-tem secuities, a yea is assumed to have 360 days. The discount yield (discount ate is defined as Inteest pa value puchase pice 360 days pa value numbe of days to matuity (3.9 Inteest ate Annualize
29 CD-equivalent yield It also called the money-maket-equivalent yield. It is a simple annualized inteest ate defined as pa value puchase pice 365 days puchase pice numbe of days to matuity (3.10
30 Example 3.4.1: 341 Discount yield If an investo buys a U.S.$10,000, 6-month T-bill fo US$9521 U.S.$ with 182 days emaining to matuity Discount yield= ild =
31 Intenal Rate of Retun (IRR It is the inteest ate which hequates an investment s PV with its pice X. X = C 1 (1 + IRR 1 + C 2 (1 + IRR C n (1 + IRR IRR assumes all cash flows ae einvested at the same ate as the intenal ate of etun. It doesn t conside the einvestment isk. 2 IRR is discount ate fo evey ypeiod n X C 1 C 2 C 3 Cn
32 Evaluating eal investment with IRR Multiple IRR aise when thee is moe than one sign evesal in the cash flow patten, and it is also possible to have no IRR. Evaluating eal investment, IRR ule beaks down when thee ae multiple IRR o no IRR. Additional poblems exist when the tem stuctue of inteest ates is not flat. thee is ambiguity about what the appopiate hudle ate (cost of capital should be.
33 Class Execise Assume that a poject has cash flow as follow espectively, and initial cost is $1000 at date 0,,please calculate the IRR. If cost of capital is 10%, do you think it is a good poject? CF at date IRR ?
34 Class Execise (Excel Multiple IRR
35 Holding Peiod Retun c Reinvest: e P n The FV of investment in n peiod is FV = P ( 1+ y Let the einvestment ates e, the FV of pe cash income is n 1 n 2 C (1 + e + C (1 + e C (1 + e + C Value is given We define HPR (y is n P(1 + y n = C (1 + e n 1 + C (1 + e n C (1 + e + C
36 Methodology fo the HPR(y Calculate the FV and then find the yield that equates it with the P Suppose the einvestment ates has been detemined to be e. Step Peiodic compounding Continuous compounding (1Calculate the futue value (2Find the HPR FV = n t= 1 C (1 + e n t FV = C n e ( e 1 e e 1 y 1 y = ln( = n P FV 1 n P FV
37 Example 3.4.5:HPR A financial instument pomises to pay $1,000 fo the next 3 yeas and sell fo $2,500. If each cash can be put into a bank account that pays an effective ate of 5%. 3 The FV is 1000 ( t= 1 3 t = The HPR is 2500(1 + HPR 3 = HPR = /3 1 =
38 Numeical Methods fo Yield Solve f ( = n t= 1 Ct (1 + t x = 0, fo 1, x is maket pice Recall X = C C 1 1 Let f ( (1 + IRR (1 + IRR = C ( C C 1 n n +... C (1 + IRR (1 + IRR n n (1 + n n X = X 0 The function f( is monotonic in, if C t > 0 fo all t, f(, t, hence a unique solution exists.
39 The Bisection Method Stat with a and b whee a < b and f(a f(b < 0. Then f( must tbe zeo fo some (a, b. If we evaluate f at the midpoint c (a + b / 2 (1 f(a f(c < 0 a<<c (2 f(c f(b < 0 c<<b Afte n steps we will have confined within a Afte n steps, we will have confined within a backet of length (b a / 2 n.
40 Bisection Method Lt Let f ( = C (1 + Solve f(=0 nc - x f( 1 + C ( C (1 + f(a>0,f(b<0 => a<<b Let c=(a+b/2 f(a>0 f(c<0 => a<<c n n X a IRR c b
45 The Newton-Raphson Method Conveges faste than the bisection method. Stat with a fist appoximation X 0 to a oot of f(x = 0. Then f( xk x k 1 x + k (3.15 f ( x k When computing yields, f ( x = t C n t t+ 1 t= 1 (1 + x Recall the bisection method, the X hee is (yield in the bisection method!
46 Figue3.5: Newton-Raphson method f(x k θ f( Xk f ( Xk = tanθ = X X X X = X k+ 1 X k+ 1 = k k k + 1 f( Xk f ( X k f( X f k ( X If f(x k+1 =0, we can obtain X k+1 is yield k k
49 Bond A bond is a contact between the issue (boowe and the bondholde (lende. Bonds usually efe to long-tem debts. Callable bond, convetible bond. Pue discount bonds vs. level-coupon bond
50 Zeo-Coupon Bonds (Pue Discount Bonds The pice of a zeo-coupon bond that pays F dollas in n peiods is F P = ( 1+ whee is the inteest ate pe peiod No coupon is paid befoe bond matue. n Can meet futue obligations without einvestment isk. F (pa value P n peiods
51 Level-Coupon Bonds It pays inteest based on coupon ate and the pa value, which is paid at matuity. F denotes the pa value and C denotes the coupon. P = C ( C ( C (1 + n + F (1 + n
52 Picing of Level-Coupon Bonds P = = whee C (1 + nm i m + C C (1 + m F C (1 + 1 (1 + = C + F (1 + + nm m + i nm = 1 (1 + m (1 + m m (1 + n: time to matuity (in yeas m : numbe of payments pe yea. : annual ate compounded m times pe annum. C = Fc/m whee c is the annual coupon ate. m nm m nm F m nm (3.18 C C C C Pay m times F P Yea 1 Yea 2
53 Yield To Matuity The YTM of a level-coupon l bond dis its IRR when the bond is held to matuity. Fo a 15% BEY, a 10-yea bond with a coupon ate of 10% paid semiannually sells fo P = (1 + 0 (1 + (1 + 2 ( 1+ (0.15 / / = ( 1+ (0.15/ 2 =
54 Yield To Call Fo a callable bond, the yield to states matuity measues es its yield to matuity ty as if wee e not callable. ab The yield to call is the yield to matuity satisfied by Eq(3.18, when n denoting the numbe of emaining coupon payments until the fist call date and F eplaced with call pice. C C F(call pice Pa value P A Company call the bonds Matuity
55 Homewok A company issues a 10-yea bond with a coupon ate of 10%, paid semiannually. The bond is called at pa afte 5 yeas. Find the pice that guaantees a etun of 12% compounded semiannually fo the investo. (You ae able to use Excel to un it.
56 Pice Behavios Bond pice falls as the inteest t ate inceases, and vice vesa. A level-coupon bond sells at a pemium (above its pa value when its coupon ate is above the maket inteest ate. at pa (at its pa value when its coupon ate is equal to the maket inteest ate. at a discount (below its pa value when its coupon ate is below the maket inteest ate.
57 Figue 3.8: Pice/yield elations Pemium bond Pa bond Discount bond
58 Figue 3.9: Pice vs. yield. Plotted is a bond that pays 8% inteest on a pa value of $1,000,compounding annually. The tem is 10 yeas.
59 Day Count Conventions: Actual/Actual The fist actual efes to the actual numbe of days in a month. The second efes to the actual numbe of days in a yea. Example: Fo coupon-beaing Teasuy secuities, the numbe of days between June 17, 1992, and Octobe 1, 1992, is days (June, 31 days (July, 31 days (August, 30 days (Septembe, and 1 day (Octobe.
60 Day Count Conventions:30/360 Each month has 30 days and each yea 360 days. The numbe of days between June 17, 1992, and Octobe 1, 1992, is days (June, 30 days (July, 30 days (August, 30 days (Septembe, and 1 day (Octobe. In geneal, the numbe of days fom date1 to date2 is 360 (y2 y (m2 m1 + (d2 d1 (y y ( ( Whee Date1 (y1,m1, d1 Date (y2,m2, d2
61 Bond pice between two coupon date (FllPi (Full Pice, Dity Pice Pi In eality, the settlement date may fall on any day between two coupon payment dates. C C 100 w 1 2 n Settlement date Numbe of days to the next payment date w = Numbe of days in the coupon peiod Dity Pice= C (1 + ω + C (1 + ω C ( 1+ ω n (1 + ω n + 1
62 Accued Inteest The oiginal bond holde has to shae accued inteest in 1-ω ω peiod - Accued inteest is C ( 1 ω The quoted pice in the U.S./U.K. does not include the accued inteest; it is called the clean pice. Dity pice= Clean pice+ Accued inteest
63 Example Conside a bond with a 10% coupon ate, pa value$100 and paying inteest semiannually, with clean pice The matuity date is Mach 1, 1995, and the settlement date is July 1, The yield to matuity is 3%.
64 Example: solutions Thee ae 60 days between July 1, 1993, and the next coupon date, Septembe 1, The ω= 60/180, C=5,and accued inteest is 5 (1-(60/180 = Dity pice= clean pice = days settle
65 Execise Befoe: A bond selling at pa if the yield to matuity equals the coupon ate. (But it assumed that the settlement date is on a coupon payment tdate. Now suppose the settlement date fo a bond selling at pa (i.e., the quoted pice is equal to the pa value falls between two coupon payment dates. Then its yield to matuity is less than the coupon ate. The shot eason: Exponential gowth is eplaced by linea gowth, hence ovepaying the coupon.
71 Homewok Pogam execise: Calculate the dity and the clean pice fo a bond unde actual/actual and 30/360 day count convesion. Input: Bond matuity date, settlement date, bond yield, and the coupon ate. The bond is assumed to pay coupons semiannually.
Leaning Objectives FI00 Copoate Finance Sping Semeste 2010 D. Isabel Tkatch Assistant Pofesso of Finance Calculate the PV and FV in multi-peiod multi-cf time-value-of-money poblems: Geneal case Pepetuity
YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE Septembe 1999 Quoted Rate Teasuy Bills [Called Banke's Discount Rate] d = [ P 1 - P 1 P 0 ] * 360 [ N ] d = Bankes discount yield P 1 = face
AMB111F Financial Maths Notes Compound Inteest and Depeciation Compound Inteest: Inteest computed on the cuent amount that inceases at egula intevals. Simple inteest: Inteest computed on the oiginal fixed
CONCEPT OF TIME AND VALUE OFMONEY Simple and Compound inteest What is the futue value of shs 10,000 invested today to ean an inteest of 12% pe annum inteest payable fo 10 yeas and is compounded; a. Annually
Valuation of Floating Rate onds 1 Joge uz Lopez us 316: Deivative Secuities his note explains how to value plain vanilla floating ate bonds. he pupose of this note is to link the concepts that you leaned
How Much Should a Fim Boow Chapte 19 Capital Stuctue & Copoate Taxes Financial Risk - Risk to shaeholdes esulting fom the use of debt. Financial Leveage - Incease in the vaiability of shaeholde etuns that
INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem
Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation
MACROECONOMICS 2006 Week 5 Semina Questions Questions fo Review 1. How do consumes save in the two-peiod model? By buying bonds This peiod you save s, next peiod you get s() 2. What is the slope of a consume
Leaig Objectives Chapte 2 Picig of Bods time value of moey Calculate the pice of a bod estimate the expected cash flows detemie the yield to discout Bod pice chages evesely with the yield 2-1 2-2 Leaig
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
Solution to Poblem: Chapte 7 P7-1. P7-2. P7-3. P7-4. Authoized and available hae LG 2; Baic a. Maximum hae available fo ale Authoized hae 2,000,000 Le: Shae outtanding 1,400,000 Available hae 600,000 b.
xam #1 Review Answes 1. Given the following pobability distibution, calculate the expected etun, vaiance and standad deviation fo Secuity J. State Pob (R) 1 0.2 10% 2 0.6 15 3 0.2 20 xpected etun = 0.2*10%
Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the
Retiement Benefit 1 Things to Remembe Complete all of the sections on the Retiement Benefit fom that apply to you equest. If this is an initial equest, and not a change in a cuent distibution, emembe to
. Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate
Investos/Analysts Confeence: Accounting Wokshop Agenda Equity compensation plans New Income Statement impact on guidance Eanings Pe Shae Questions and answes IAC03 / a / 1 1 Equity compensation plans The
9:6.4 INITIAL PUBLIC OFFERINGS 9:6.4 Sample Questions/Requests fo Managing Undewite Candidates Recent IPO Expeience Please povide a list of all completed o withdawn IPOs in which you fim has paticipated
CHAPTR 10 Aggegate Demand I Questions fo Review 1. The Keynesian coss tells us that fiscal policy has a multiplied effect on income. The eason is that accoding to the consumption function, highe income
Loyalty Rewads and Gift Cad Pogams: Basic Actuaial Estimation Techniques Tim A. Gault, ACAS, MAAA, Len Llaguno, FCAS, MAAA and Matin Ménad, FCAS, MAAA Abstact In this pape we establish an actuaial famewok
Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new high-speed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease
9.4 Annuities Objectives 1. Calculate the futue value of an odinay annuity. 2. Pefo calculations egading sinking funds. Soewhee ove the ainbow... skies ae blue,... and the deas that you dae to dea...eally
Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates Cash Flow Financial transactions and investment opportunities are described by cash flows they generate. Cash flow: payment
The Pedictive Powe of Dividend Yields fo Stock Retuns: Risk Picing o Mispicing? Glenn Boyle Depatment of Economics and Finance Univesity of Cantebuy Yanhui Li Depatment of Economics and Finance Univesity
Iteest Fiace Pactice Poblems Iteest is the cost of boowig moey. A iteest ate is the cost stated as a pecet of the amout boowed pe peiod of time, usually oe yea. The pevailig maket ate is composed of: 1.
Money Supply By the Bank of Canada and Inteest Rate Detemination Open Opeations and Monetay Tansmission Mechanism The Cental Bank conducts monetay policy Bank of Canada is Canada's cental bank supevises
9.5 Aotization Objectives 1. Calculate the payent to pay off an aotized loan. 2. Constuct an aotization schedule. 3. Find the pesent value of an annuity. 4. Calculate the unpaid balance on a loan. Congatulations!
Problems and Solutions CHAPTER Problems. Problems on onds Exercise. On /04/0, consider a fixed-coupon bond whose features are the following: face value: $,000 coupon rate: 8% coupon frequency: semiannual
Zero-Coupon Bonds (Pure Discount Bonds) The price of a zero-coupon bond that pays F dollars in n periods is F/(1 + r) n, where r is the interest rate per period. Can meet future obligations without reinvestment
Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
Real Estate Equity Deivatives Geltne Mille 2 nd Edition Chapte 26 Section 26.3 Real Estate Deivatives (Index Retun Swaps) Real Estate Equity Deivatives A deivative is an asset whose value depends completely
Life Insuance Puchasing to Reach a Bequest Ehan Bayakta Depatment of Mathematics, Univesity of Michigan Ann Abo, Michigan, USA, 48109 S. David Pomislow Depatment of Mathematics, Yok Univesity Toonto, Ontaio,
Conveting knowledge Into Pactice Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 2 0 1 0 C o p y i g h t s V l a d i m i R i b a k o v 1 Disclaime and Risk Wanings Tading
Kuwait University College of Business Administration Department of Finance and Financial Institutions Using )Casio FC-200V( for Fundamentals of Financial Management (220) Prepared by: Dalia A. Marafi Version
Bond Pricing - 1 Chapter 11 Several Assumptions: To simplify the analysis, we make the following assumptions. 1. The coupon payments are made every six months. 2. The next coupon payment for the bond is
Aity Deivatios 4/4/ Deivatio of Aity ad Pepetity Fomlae A. Peset Vale of a Aity (Defeed Paymet o Odiay Aity 3 4 We have i the show i the lecte otes ad i ompodi ad Discoti that the peset vale of a set of
Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 firstname.lastname@example.org August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad
A Note on Risky Bond Valuation C. H. Hui Banking Poliy Depatment Hong Kong Monetay Authoity 0th Floo,, Gaden Road, Hong Kong Email: Cho-Hoi_Hui@hkma.gov.hk C. F. Lo Physis Depatment The Chinese Univesity
Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Assistant Pofesso Depatment of Economics, Univesity of Kaachi e-mail: email@example.com and Mohammed Nishat Pofesso and Chaiman,
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,
The Pesonal-Tax Advantages of Equity Richad C. Geen and Buton Hollifield Gaduate School of Industial Administation Canegie Mellon Univesity Decembe 23, 999 Discussions with Piee Collin Dufesne, Bob Dammon,
6 Formulas Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing
FIN 302 Class Notes Chapter 5: Valuing Bonds What is a bond? A long-term debt instrument A contract where a borrower agrees to make interest and principal payments on specific dates Corporate Bond Quotations
Contingent capital with epeated inteconvesion between debt and equity Zhaojun Yang 1, Zhiming Zhao School of Finance and Statistics, Hunan Univesity, Changsha 410079, China Abstact We develop a new type
Risk Sensitive Potfolio Management With Cox-Ingesoll-Ross Inteest Rates: the HJB Equation Tomasz R. Bielecki Depatment of Mathematics, The Notheasten Illinois Univesity 55 Noth St. Louis Avenue, Chicago,
1 Bond Price Arithmetic The purpose of this chapter is: To review the basics of the time value of money. This involves reviewing discounting guaranteed future cash flows at annual, semiannual and continuously
Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194-114 Online ISSN: 213-953 Pint ISSN: 213-8423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics
The impact of migation on the povision of UK public sevices (SRG.10.039.4) Final Repot Decembe 2011 The obustness The obustness of the analysis of the is analysis the esponsibility is the esponsibility
Define What Type of Tade Ae you? Boke Nightmae srs Tend Ride By Vladimi Ribakov Ceato of Pips Caie 20 of June 2010 1 Disclaime and Risk Wanings Tading any financial maket involves isk. The content of this
Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation
JOURNL OF ECONOMICS ND FINNCE EDUCTION Volume 7 Numbe 2 Winte 2008 39 The Supply of Loanable Funds: Comment on the Misconception and Its Implications. Wahhab Khandke and mena Khandke* STRCT Recently Fields-Hat
1. Time Value of Money 3 2. Discouned Cash Flow 35 3. Saisics and Make Reuns 49 4. Pobabiliies 81 5. Key Fomulas 109 Candidae Noe: This is a lenghy Sudy Session ha, along wih Sudy Session 3, you should
Chapter 8 Bond Valuation with a Flat Term Structure 1. Suppose you want to know the price of a 10-year 7% coupon Treasury bond that pays interest annually. a. You have been told that the yield to maturity
Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An
CHAPTER 14: BOND PRICES AND YIELDS PROBLEM SETS 1. The bond callable at 105 should sell at a lower price because the call provision is more valuable to the firm. Therefore, its yield to maturity should
Liquidity and Insuance fo the Unemployed Robet Shime Univesity of Chicago and NBER firstname.lastname@example.org Iván Wening MIT, NBER and UTDT email@example.com Fist Daft: July 15, 2003 This Vesion: Septembe 22, 2005
Fixed Income Instruments III Intro to the Valuation of Debt Securities LOS 64.a Explain the steps in the bond valuation process 1. Estimate the cash flows coupons and return of principal 2. Determine the
CALCULATOR TUTORIAL INTRODUCTION Because most students that use Understanding Healthcare Financial Management will be conducting time value analyses on spreadsheets, most of the text discussion focuses
Interest Rates and Bond Valuation Chapter 6 Key Concepts and Skills Know the important bond features and bond types Understand bond values and why they fluctuate Understand bond ratings and what they mean
The Binomial Distibution A. It would be vey tedious if, evey time we had a slightly diffeent poblem, we had to detemine the pobability distibutions fom scatch. Luckily, thee ae enough similaities between
Chapte 32. A Macoeconomic Theoy of the Open Economy Open Economies An open economy is one that inteacts feely with othe economies aound the wold. slide 0 slide 1 Key Macoeconomic Vaiables in an Open Economy
VISCOSITY OF BIO-DIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use
Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.
UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + = - - -
Univesity of Pisa Ph.D. Pogam in Mathematics fo Economic Decisions Leonado Fibonacci School cotutelle with Institut de Mathématique de Toulouse Ph.D. Dissetation Optimal Capital Stuctue with Endogenous
ISSUE ONE > JUNE 2013 WELCOME TO OUR NEW NEWSLETTER PARTNERS OUTLOOK Welcome to the band new Patnes Outlook newslette. It s had to believe it s June and anothe end of financial yea is aleady ceeping up.
196 Part Interest Rates and Valuing Cash Flows Chapter 6 APPENDIX B The Yield Curve and the Law of One Price Thus far, we have focused on the relationship between the price of an individual bond and its
Cate-Penose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
Application fo Admission GENEVA COLLEGE 3 2 0 0 C o l l e g e A v e n u e, B e a v e F a l l s, P A 1 5 0 1 0 Application Instuctions When to apply You may apply fo admission any time afte you junio yea
I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining
CHAPTER 14: BOND PRICES AND YIELDS 1. a. Effective annual rate on 3-month T-bill: ( 100,000 97,645 )4 1 = 1.02412 4 1 =.10 or 10% b. Effective annual interest rate on coupon bond paying 5% semiannually:
Instuctions to help you complete you enollment fom fo HPHC's Medicae Supplemental Plan Thank you fo applying fo membeship to HPHC s Medicae Supplement plan. Pio to submitting you enollment fom fo pocessing,
Saving and Investing fo Ealy Retiement: A Theoetical Analysis Emmanuel Fahi MIT Stavos Panageas Whaton Fist Vesion: Mach, 23 This Vesion: Januay, 25 E. Fahi: MIT Depatment of Economics, 5 Memoial Dive,
FIN 301 Homework Solution Ch4 Chapter 4: Time Value of Money 1. a. 10,000/(1.10) 10 = 3,855.43 b. 10,000/(1.10) 20 = 1,486.44 c. 10,000/(1.05) 10 = 6,139.13 d. 10,000/(1.05) 20 = 3,768.89 2. a. $100 (1.10)