Basic Financial Mathematics

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Basic Financial Mathematics"

Transcription

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

19 Pesent value Computed by Excel PV(ate, npe, pmt, fv, type Rate: 各 期 的 利 率 Npe: 年 金 的 總 付 款 期 數 Pmt : 各 期 所 應 給 付 ( 或 所 能 取 得 的 固 定 金 額 Fv : 最 後 一 次 付 款 完 成 後, 所 能 獲 得 的 現 金 餘 額 Type 0=> 期 末 支 付 1=> 期 初 支 付

20 Computed by Excel Futue value FV (ate, npe, pmt, pv, type Rate: 各 期 的 利 率 Npe: 年 金 的 總 付 款 期 數 Pmt : 指 分 期 付 款 Pv : 指 現 值 或 一 系 列 未 來 付 款 的 目 前 總 額 Type 0=> 期 末 支 付 1=> 期 初 支 付

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

41 C++: 使 用 while 建 構 二 分 法 float Low=0, High=1; 輸 入 每 期 報 酬 c, 期 數 n, 期 初 投 入 x 令 Middle =(High+Low/2; 找 出 R 落 在 (Low, Middle 或 (Middle,High while(high-low>= false tue 程 式 碼 : float c,x,discount; float Low=0, High=1; int n; scanf("%f",&c; scanf("%f",&x; scanf("%d",&n; while(high-low>= { } pintf("yield ate=%f",high;

42 用 Bisection method 縮 小 根 的 範 圍 已 知 f ( = c (1 + f(<0 >R f(>0 <R 1 + c (1 + 令 Middle=(High+Low/2 將 根 的 範 圍 從 (Low,High 縮 減 到 (Low,Middle (Middle,High c (1 + + c ( c (1 + 用 計 算 債 券 的 公 式 計 算 n } 縮 小 根 的 範 圍 c (1 + n float Middle=(Low+High/2; float Value=0; fo(int i=1;i<=n;i=i+1 { Discount=1; fo(int j=1;j<=i;j++ { x Discount=Discount/(1+Middle } Value=Value+Discount*c; } Value=Value-x; if(value>0 { Low=Middle;} else {High=Middle;}

43 計 算 計 算 IRR ( 完 整 程 式 碼 用 while 控 制 根 的 範 圍 1 2 c (1 + + c ( c (1 + 計 算 (1+ i 縮 小 根 的 範 圍 n float c,x,discount; float Low=0 0, High=1; int n; scanf("%f",&c; scanf("%f",&x; scanf("%d",&n; while(high-low>= { float Middle=(Low+High/2; float Value=0; fo(int i=1;i<=n;i=i+1 { Discount=1; fo(int j=1;j<=i;j++ { Discount=Discount/(1+Middle; Discount/(1+Middle; } Value=Value+Discount*c; } Vl Value=Value-x; Vl if(value>0 { Low=Middle;} else {High=Middle;} } pintf("yield ate=%f",high;

44 第 三 章 第 十 題 Homewok

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

47 Computed by Excel Yield 的 計 算 RATE( npe, pmt,,p pv, fv, type Npe: 年 金 的 總 付 款 期 數 Pmt : 各 期 所 應 給 付 ( 或 所 能 取 得 的 固 定 金 額 Pv : 期 初 付 款 金 額 Fv : 最 後 一 次 付 款 完 成 後, 所 獲 得 的 現 金 餘 額 ( 年 金 終 值 Type 0=> 期 末 支 付 1=> 期 初 支 付

48 Example YTM=2.83% 83%*2=5.66%

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.

66 C++: fo 控 制 結 構 透 過 fo 的 結 構, 程 式 的 片 段 可 重 複 執 行 固 定 次 數 fo(int j=1;j<5;j=j+1 { j=1; pintf(" %d-th Execution\n",j; } 檢 視 :Bond Value poject 當 區 塊 中 只 有 一 行 敘 述 時, 左 右 括 弧 可 省 略 tue j<5 pintf(" %d-th Execution\n",j; j=j+1; Exit false

67 C++: 計 算 債 券 價 格 考 慮 債 券 價 格 的 計 算 假 定 單 期 利 率 為 每 一 期 支 付 coupon c, 共 付 n 期 到 期 日 還 本 100 元 100 c n 債 券 價 格 P = c ( c ( c (1 + n (1 + n

68 i=1 程 式 想 法 i<=n false 列 印 價 格 tue 計 算 第 i 期 payoff 的 現 值 value=value+ value+ 第 i 期 的 現 值 i=i+1 int n; float c,, Value=0,Discount; scanf("%d",&n; scanf("%f",&c; scanf("%f",&; fo(int i=1;i<=n;i=i+1 { } pintf("bondvalue=%f",value;

69 計 算 第 i 次 payoff 的 現 值 i<n 現 值 = i=n 現 值 = 用 fo 計 算 (1 + i c ( 1+ n ( c (1+ 計 算 i (1+ i 考 慮 最 後 一 期 本 金 折 現 計 算 第 i 次 payoff 的 現 值 Discount=1; fo(int j=1;j<=i;j++ { Discount=Discount/(1+; } Value=Value+Discount*c; if(i==n { Value=Value+Discount*100; }

70 完 整 程 式 碼 ( 包 含 巢 狀 結 構 #include <stdio.h> void main( { int n; float c,, Value=0,Discount; scanf("%d",&n; scanf("%f",&c; scanf("%f",&; fo(int i=1;i<=n;i=i+1 { Discount=1; fo(int j=1;j<=i;j++ { Discount=Discount/(1+; } Value=Value+Discount*c; if(i==n { Value=Value+Discount*100; } } pintf("bondvalue=%f",value; } 第 i 次 payoff 的 現 值 Value 為 前 i 次 payoff 現 值

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.

FI3300 Corporate Finance

FI3300 Corporate Finance 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

More information

YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE

YIELD TO MATURITY ACCRUED INTEREST QUOTED PRICE INVOICE PRICE 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

More information

AMB111F Financial Maths Notes

AMB111F Financial Maths Notes 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

More information

CONCEPT OF TIME AND VALUE OFMONEY. Simple and Compound interest

CONCEPT OF TIME AND VALUE OFMONEY. Simple and Compound interest 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

More information

Valuation of Floating Rate Bonds 1

Valuation of Floating Rate Bonds 1 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

More information

How Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes

How Much Should a Firm Borrow. Effect of tax shields. Capital Structure Theory. Capital Structure & Corporate Taxes 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

More information

The Time Value of Money

The Time Value of Money he ime Value of Money Inteest Rates and Futue Value Inteest ates ae a facto in the valuation of vitually all financial instuments. While all money maket ates () ae quoted on an annual basis (PR nnual Pecentage

More information

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS

INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS 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

More information

Introduction to Stock Valuation. Background

Introduction to Stock Valuation. Background Intoduction to Stock Valuation (Text efeence: Chapte 5 (Sections 5.4-5.9)) Topics backgound dividend discount models paamete estimation gowth oppotunities pice-eanings atios some final points AFM 271 -

More information

Chapter 3 Savings, Present Value and Ricardian Equivalence

Chapter 3 Savings, Present Value and Ricardian Equivalence 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,

More information

BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR. John R. Graham Adapted from S. Viswanathan FUQUA SCHOOL OF BUSINESS

BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR. John R. Graham Adapted from S. Viswanathan FUQUA SCHOOL OF BUSINESS BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR John R. Gaham Adapted fom S. Viswanathan FUQUA SCHOOL OF BUSINESS DUKE UNIVERSITY 1 In this lectue we conside the effect of govenment

More information

Continuous Compounding and Annualization

Continuous Compounding and Annualization 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

More information

Ilona V. Tregub, ScD., Professor

Ilona V. Tregub, ScD., Professor 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

More information

Questions for Review. By buying bonds This period you save s, next period you get s(1+r)

Questions for Review. By buying bonds This period you save s, next period you get s(1+r) 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

More information

Learning Objectives. Chapter 2 Pricing of Bonds. Future Value (FV)

Learning Objectives. Chapter 2 Pricing of Bonds. Future Value (FV) 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

More information

GESTÃO FINANCEIRA II PROBLEM SET 1 - SOLUTIONS

GESTÃO FINANCEIRA II PROBLEM SET 1 - SOLUTIONS GESTÃO FINANCEIRA II PROBLEM SET 1 - SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER 2010-2011 Chapte 1 The Copoation 1-13. What is the diffeence

More information

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.

est using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years. 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,

More information

Solutions to Problems: Chapter 7

Solutions to Problems: Chapter 7 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.

More information

Exam #1 Review Answers

Exam #1 Review Answers 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%

More information

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION

STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts

More information

The LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.

The LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero. 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

More information

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request.

Things to Remember. r Complete all of the sections on the Retirement Benefit Options form that apply to your request. 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

More information

Definitions and terminology

Definitions and terminology I love the Case & Fai textbook but it is out of date with how monetay policy woks today. Please use this handout to supplement the chapte on monetay policy. The textbook assumes that the Fedeal Reseve

More information

Firstmark Credit Union Commercial Loan Department

Firstmark Credit Union Commercial Loan Department Fistmak Cedit Union Commecial Loan Depatment Thank you fo consideing Fistmak Cedit Union as a tusted souce to meet the needs of you business. Fistmak Cedit Union offes a wide aay of business loans and

More information

4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero digit to

4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first non-zero digit 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

More information

The Capital Asset Pricing Model. Chapter 9

The Capital Asset Pricing Model. Chapter 9 The Capital Asset Picing odel Chapte 9 Capital Asset Picing odel CAP centepiece of moden finance gives the elationship that should be obseved between isk and etun of an asset it allows fo the evaluation

More information

Equity compensation plans New Income Statement impact on guidance Earnings Per Share Questions and answers

Equity compensation plans New Income Statement impact on guidance Earnings Per Share Questions and answers 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

More information

Personal Saving Rate (S Households /Y) SAVING AND INVESTMENT. Federal Surplus or Deficit (-) Total Private Saving Rate (S Private /Y) 12/18/2009

Personal Saving Rate (S Households /Y) SAVING AND INVESTMENT. Federal Surplus or Deficit (-) Total Private Saving Rate (S Private /Y) 12/18/2009 1 Pesonal Saving Rate (S Households /Y) 2 SAVING AND INVESTMENT 16.0 14.0 12.0 10.0 80 8.0 6.0 4.0 2.0 0.0-2.0-4.0 1959 1961 1967 1969 1975 1977 1983 1985 1991 1993 1999 2001 2007 2009 Pivate Saving Rate

More information

CHAPTER 10 Aggregate Demand I

CHAPTER 10 Aggregate Demand I 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

More information

Problem Set # 9 Solutions

Problem Set # 9 Solutions 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

More information

SUGGESTED SOLUTIONS. 21404 Strategic Financial Management. CA Professional (Strategic Level II) Examination June 2014

SUGGESTED SOLUTIONS. 21404 Strategic Financial Management. CA Professional (Strategic Level II) Examination June 2014 SUGGESTED SOLUTIONS 21404 Stategic Financial Management CA Pofessional (Stategic Level II) Examination June 2014 THE INSTITUTE OF CHARTERED ACCOUNTANTS OF SRI LANKA All Rights Reseved Answe No. 01 (a)

More information

9:6.4 Sample Questions/Requests for Managing Underwriter Candidates

9:6.4 Sample Questions/Requests for Managing Underwriter Candidates 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

More information

International Monetary Economics Note 1

International Monetary Economics Note 1 36-632 Intenational Monetay Economics Note Let me biefly ecap on the dynamics of cuent accounts in small open economies. Conside the poblem of a epesentative consume in a county that is pefectly integated

More information

Ignorance is not bliss when it comes to knowing credit score

Ignorance is not bliss when it comes to knowing credit score NET GAIN Scoing points fo you financial futue AS SEEN IN USA TODAY SEPTEMBER 28, 2004 Ignoance is not bliss when it comes to knowing cedit scoe By Sanda Block USA TODAY Fom Alabama comes eassuing news

More information

Loyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques

Loyalty Rewards and Gift Card Programs: Basic Actuarial Estimation Techniques 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

More information

9.4 Annuities. Objectives. 1. Calculate the future value of an ordinary annuity. 2. Perform calculations regarding sinking funds.

9.4 Annuities. Objectives. 1. Calculate the future value of an ordinary annuity. 2. Perform calculations regarding sinking funds. 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

More information

The Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing?

The Predictive Power of Dividend Yields for Stock Returns: Risk Pricing or Mispricing? 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

More information

Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates

Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates 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

More information

Understanding Financial Management: A Practical Guide Guideline Answers to the Concept Check Questions

Understanding Financial Management: A Practical Guide Guideline Answers to the Concept Check Questions Udestadig Fiacial Maagemet: A Pactical Guide Guidelie Aswes to the Cocept Check Questios Chapte 4 The Time Value of Moey Cocept Check 4.. What is the meaig of the tems isk-etu tadeoff ad time value of

More information

Capital Asset Pricing Model (CAPM) at Work

Capital Asset Pricing Model (CAPM) at Work Capital Asset Picing Model (CAPM) at Wok Some o the Intuition behind CAPM Applications o CAPM Estimation and Testing o CAPM Intuition behind Equilibium Suppose you obseved the ollowing chaacteistics o

More information

Financial Planning and Risk-return profiles

Financial Planning and Risk-return profiles Financial Planning and Risk-etun pofiles Stefan Gaf, Alexande Kling und Jochen Russ Pepint Seies: 2010-16 Fakultät fü Mathematik und Witschaftswissenschaften UNIERSITÄT ULM Financial Planning and Risk-etun

More information

Finance Practice Problems

Finance Practice Problems 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.

More information

CFAspace. CFA Level I. Provided by APF. Academy of Professional Finance 专业金融学院. Corporate Finance Part 1 CFA Lecturer: Travis Cui

CFAspace. CFA Level I. Provided by APF. Academy of Professional Finance 专业金融学院. Corporate Finance Part 1 CFA Lecturer: Travis Cui Povided by APF Academy of Pofessional Finance 专业金融学院 Copoate Finance Pat 1 CFA Lectue: Tavis Cui CFAspace CFA Level I Copoate Finance: 1. 8%, 20 questions, not difficult 2. Close to eal business 3. Little

More information

Controlling the Money Supply: Bond Purchases in the Open Market

Controlling the Money Supply: Bond Purchases in the Open Market 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

More information

Compound Interest Doubling Time Rule: Extensions and Examples from Antiquities

Compound Interest Doubling Time Rule: Extensions and Examples from Antiquities Communications in Mathematical Finance, vol. 5, no. 2, 2016, 1-11 ISSN: 2241-1968 (pint), 2241 195X (online) Scienpess Ltd, 2016 Compound Inteest Doubling Time Rule: Extensions and Examples fom Antiquities

More information

Chapter 11: Aggregate Demand II, Applying the IS-LM Model Th LM t

Chapter 11: Aggregate Demand II, Applying the IS-LM Model Th LM t Equilibium in the - model The cuve epesents equilibium in the goods maket. Chapte :, Applying the - Model Th t C ( T) I( ) G The cuve epesents money maket equilibium. M L(, ) The intesection detemines

More information

9.5 Amortization. Objectives

9.5 Amortization. Objectives 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!

More information

Zero-Coupon Bonds (Pure Discount Bonds)

Zero-Coupon Bonds (Pure Discount Bonds) 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

More information

Prepared by: Dalia A. Marafi Version 2.0

Prepared by: Dalia A. Marafi Version 2.0 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

More information

Agenda. Exchange Rates, Business Cycles, and Macroeconomic Policy in the Open Economy, Part 2. The supply of and demand for the dollar

Agenda. Exchange Rates, Business Cycles, and Macroeconomic Policy in the Open Economy, Part 2. The supply of and demand for the dollar Agenda Exchange Rates, Business Cycles, and Macoeconomic Policy in the Open Economy, Pat 2 How Exchange Rates ae Detemined (again) The IS-LM Model fo an Open Economy Macoeconomic Policy in an Open Economy

More information

Problems and Solutions

Problems and Solutions 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

More information

Power and Sample Size Calculations for the 2-Sample Z-Statistic

Power and Sample Size Calculations for the 2-Sample Z-Statistic Powe and Sample Size Calculations fo the -Sample Z-Statistic James H. Steige ovembe 4, 004 Topics fo this Module. Reviewing Results fo the -Sample Z (a) Powe and Sample Size in Tems of a oncentality Paamete.

More information

Life Insurance Purchasing to Reach a Bequest. Erhan Bayraktar Department of Mathematics, University of Michigan Ann Arbor, Michigan, USA, 48109

Life Insurance Purchasing to Reach a Bequest. Erhan Bayraktar Department of Mathematics, University of Michigan Ann Arbor, Michigan, USA, 48109 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,

More information

Coordinate Systems L. M. Kalnins, March 2009

Coordinate Systems L. M. Kalnins, March 2009 Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean

More information

Japan s trading losses reach JPY20 trillion

Japan s trading losses reach JPY20 trillion IEEJ: Mach 2014. All Rights Reseved. Japan s tading losses each JPY20 tillion Enegy accounts fo moe than half of the tading losses YANAGISAWA Akia Senio Economist Enegy Demand, Supply and Foecast Goup

More information

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 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

More information

Converting knowledge Into Practice

Converting knowledge Into Practice 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

More information

In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature.

In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. Radians At school we usually lean to measue an angle in degees. Howeve, thee ae othe ways of measuing an angle. One that we ae going to have a look at hee is measuing angles in units called adians. In

More information

Some text, some maths and going loopy. This is a fun chapter as we get to start real programming!

Some text, some maths and going loopy. This is a fun chapter as we get to start real programming! Chapte Two Some text, some maths and going loopy In this Chapte you ae going to: Lean how to do some moe with text. Get Python to do some maths fo you. Lean about how loops wok. Lean lots of useful opeatos.

More information

EAS Groundwater Hydrology Lecture 13: Well Hydraulics 2 Dr. Pengfei Zhang

EAS Groundwater Hydrology Lecture 13: Well Hydraulics 2 Dr. Pengfei Zhang EAS 44600 Goundwate Hydology Lectue 3: Well Hydaulics D. Pengfei Zhang Detemining Aquife Paametes fom Time-Dawdown Data In the past lectue we discussed how to calculate dawdown if we know the hydologic

More information

In the lecture on double integrals over non-rectangular domains we used to demonstrate the basic idea

In the lecture on double integrals over non-rectangular domains we used to demonstrate the basic idea Double Integals in Pola Coodinates In the lectue on double integals ove non-ectangula domains we used to demonstate the basic idea with gaphics and animations the following: Howeve this paticula example

More information

Economics 326: Input Demands. Ethan Kaplan

Economics 326: Input Demands. Ethan Kaplan Economics 326: Input Demands Ethan Kaplan Octobe 24, 202 Outline. Tems 2. Input Demands Tems Labo Poductivity: Output pe unit of labo. Y (K; L) L What is the labo poductivity of the US? Output is ouhgly

More information

LINES AND TANGENTS IN POLAR COORDINATES

LINES AND TANGENTS IN POLAR COORDINATES LINES AND TANGENTS IN POLAR COORDINATES ROGER ALEXANDER DEPARTMENT OF MATHEMATICS 1. Pola-coodinate equations fo lines A pola coodinate system in the plane is detemined by a point P, called the pole, and

More information

1.4 Phase Line and Bifurcation Diag

1.4 Phase Line and Bifurcation Diag Dynamical Systems: Pat 2 2 Bifucation Theoy In pactical applications that involve diffeential equations it vey often happens that the diffeential equation contains paametes and the value of these paametes

More information

Derivation of Annuity and Perpetuity Formulae. A. Present Value of an Annuity (Deferred Payment or Ordinary Annuity)

Derivation of Annuity and Perpetuity Formulae. A. Present Value of an Annuity (Deferred Payment or Ordinary Annuity) 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

More information

Real Estate Equity Derivatives

Real Estate Equity Derivatives 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

More information

Chapter 11. Bond Pricing - 1. Bond Valuation: Part I. Several Assumptions: To simplify the analysis, we make the following assumptions.

Chapter 11. Bond Pricing - 1. Bond Valuation: Part I. Several Assumptions: To simplify the analysis, we make the following assumptions. 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

More information

Financing Terms in the EOQ Model

Financing Terms in the EOQ Model Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad

More information

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project

Spirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project 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.

More information

A Note on Risky Bond Valuation

A Note on Risky Bond Valuation 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

More information

The Personal-Tax Advantages of Equity

The Personal-Tax Advantages of Equity 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,

More information

Chapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1

Chapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1 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

More information

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing

Questions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing 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

More information

mv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2 " 2 = GM . Combining the results we get !

mv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2  2 = GM . Combining the results we get ! Chapte. he net foce on the satellite is F = G Mm and this plays the ole of the centipetal foce on the satellite i.e. mv mv. Equating the two gives = G Mm i.e. v = G M. Fo cicula motion we have that v =!

More information

Contingent Convertible Bonds and Capital Structure Decisions

Contingent Convertible Bonds and Capital Structure Decisions Contingent Convetible Bonds and Capital Stuctue Decisions Bois Albul Dwight M. Jaffee Alexei Tchistyi Apil 25, 2010 Abstact This pape povides a fomal model of contingent convetible bonds CCBs, a new instument

More information

Trading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract

Trading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Assistant Pofesso Depatment of Economics, Univesity of Kaachi e-mail: khalidku@yahoo.com and Mohammed Nishat Pofesso and Chaiman,

More information

Chapter 5: Valuing Bonds

Chapter 5: Valuing Bonds 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

More information

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM

AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM 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,

More information

Discounted Cash Flow Valuation

Discounted Cash Flow Valuation 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

More information

I = Prt. = P(1+i) n. A = Pe rt

I = Prt. = P(1+i) n. A = Pe rt 11 Chapte 6 Matheatcs of Fnance We wll look at the atheatcs of fnance. 6.1 Sple and Copound Inteest We wll look at two ways nteest calculated on oney. If pncpal pesent value) aount P nvested at nteest

More information

The Supply of Loanable Funds: A Comment on the Misconception and Its Implications

The Supply of Loanable Funds: A Comment on the Misconception and Its Implications 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

More information

Bond Price Arithmetic

Bond Price Arithmetic 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

More information

Discussion Papers in Economics

Discussion Papers in Economics Discussion Papes in Economics No. No. 003/0 000/6 Dynamics About of Debt Output and Gowth, the Option Consumption to Extend Debt and Physical Matuity Capital in Two-Secto Models of Endogenous Gowth by

More information

Yield Measures, Spot Rates & Forward Rates

Yield Measures, Spot Rates & Forward Rates Fixed Income Yield Measures, Spot Rates & Forward Rates Reading - 57 www.proschoolonline.com/ 1 Sources of Return Coupon interest payment: Periodic coupon interest is paid on the par value of the bond

More information

Risk Sensitive Portfolio Management With Cox-Ingersoll-Ross Interest Rates: the HJB Equation

Risk Sensitive Portfolio Management With Cox-Ingersoll-Ross Interest Rates: the HJB Equation 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,

More information

Contingent capital with repeated interconversion between debt and equity

Contingent capital with repeated interconversion between debt and equity 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

More information

CHAPTER 14: BOND PRICES AND YIELDS

CHAPTER 14: BOND PRICES AND YIELDS 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

More information

The transport performance evaluation system building of logistics enterprises

The transport performance evaluation system building of logistics enterprises 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

More information

Economics 212 Microeconomic Theory I Final Exam. June Faculty of Arts and Sciences Queen s University Answer Key

Economics 212 Microeconomic Theory I Final Exam. June Faculty of Arts and Sciences Queen s University Answer Key Instuctions Economics 1 Micoeconomic Theoy I Final Exam June 008 Faculty of Ats and Sciences ueen s Univesity Anse Key The exam is thee hous in length. The exam consists of to sections: Section A has five

More information

Define What Type of Trader Are you?

Define What Type of Trader Are you? 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

More information

Universal Cycles. Yu She. Wirral Grammar School for Girls. Department of Mathematical Sciences. University of Liverpool

Universal Cycles. Yu She. Wirral Grammar School for Girls. Department of Mathematical Sciences. University of Liverpool Univesal Cycles 2011 Yu She Wial Gamma School fo Gils Depatment of Mathematical Sciences Univesity of Livepool Supeviso: Pofesso P. J. Giblin Contents 1 Intoduction 2 2 De Buijn sequences and Euleian Gaphs

More information

The impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011

The impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011 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

More information

Interest Rates and Bond Valuation

Interest Rates and Bond Valuation 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

More information

Finding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26

Finding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26 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.

More information

Deflection of Electrons by Electric and Magnetic Fields

Deflection of Electrons by Electric and Magnetic Fields 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

More information

Chapter 8. Step 2: Find prices of the bonds today: n i PV FV PMT Result Coupon = 4% 29.5 5? 100 4 84.74 Zero coupon 29.5 5? 100 0 23.

Chapter 8. Step 2: Find prices of the bonds today: n i PV FV PMT Result Coupon = 4% 29.5 5? 100 4 84.74 Zero coupon 29.5 5? 100 0 23. 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

More information

Section 5-3 Angles and Their Measure

Section 5-3 Angles and Their Measure 5 5 TRIGONOMETRIC FUNCTIONS Section 5- Angles and Thei Measue Angles Degees and Radian Measue Fom Degees to Radians and Vice Vesa In this section, we intoduce the idea of angle and two measues of angles,

More information

Algebra and Trig. I. A point is a location or position that has no size or dimension.

Algebra and Trig. I. A point is a location or position that has no size or dimension. Algeba and Tig. I 4.1 Angles and Radian Measues A Point A A B Line AB AB A point is a location o position that has no size o dimension. A line extends indefinitely in both diections and contains an infinite

More information

UNITED KINGDOM DEBT MANAGEMENT OFFICE

UNITED KINGDOM DEBT MANAGEMENT OFFICE United Kingdom Debt Management Office Eatcheap Cout Philpot Lane London EC3M 8UD UNITED KINGDOM DEBT MANAGEMENT OFFICE Fomulae fo Calculating Gilt Pice fom Yield t edition: 8 June 998 nd edition: 5 Januay

More information

Click Here to Buy the Tutorial

Click Here to Buy the Tutorial FIN 534 Week 4 Quiz 3 (Str) Click Here to Buy the Tutorial http://www.tutorialoutlet.com/fin-534/fin-534-week-4-quiz-3- str/ For more course tutorials visit www.tutorialoutlet.com Which of the following

More information