# Chapter 22 Credit Risk

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Chapter 22 Credit Risk May 22, Suppose a 3-year corporate bond provides a coupon of 7% per year payable semiannually and has a yield of 5% (expressed with semiannual compounding). The yields for all maturities on risk-free bonds is 4% per annum (expressed with semiannual compounding). Assume that defaults can take place every 6 months (immediately before a coupon payment) and the recovery rate is 45%. Estimate the default probabilities assuming (a) that the unconditional default probabilities are the same on each possible default date and (b) that the default probabilities conditional on no earlier default are the same on each possible default date. Solution (a) Assuming that the unconditional default probabilities are the same on each possible default date. The calculation are as follows: 0.5 Q Q 1 Q Q 1.5 Q Q 2 Q Q 2.5 Q Q 3 Q Q Total Q The bond pays a coupon of 3.5 every six months and has a continuously compounded yield of 5% per year. Its market price is The risk-free value of the bond is obtained by discounting the promised cash flows at 4%. It is The total loss from defaults should therefore be equated to = The value of Q implied by the bond price is therefore given by Q = , or Q = The implied probability of default is 1.72% per year. (b) Assuming that the default probabilities conditional on no earlier default are the same on each possible default date.the calculation are as follows: 1

2 0.5 Q Q 1 Q(1-Q) Q(1-Q) 1.5 Q(1-Q) Q(1-Q) 2 2 Q(1-Q) Q(1-Q) Q(1-Q) Q(1-Q) 4 3 Q(1-Q) Q(1-Q) 5 That is 63.68Q+61.14Q(1 Q)+58.64Q(1 Q) Q(1 Q) Q(1 Q) Q(1 Q) 5 = or Q = The implied probability of default is 1.94% per year A company has 1- and 2-year bonds outstanding, each providing a coupon of 8% per year payable annually. The yields on the bonds (expressed with continuous compounding) are 6.0% and 6.6%, respectively. Risk-free rates are 4.5% for all maturities. The recovery rate is 35%. Defaults can take place halfway through each year. Estimate the risk-neutral default rate each year. Solution The yields imply that the price of the 1-year bond is the price of the 2-year bond is % = % ( %) 2 = the price of the similar 1-year risk-free bond is % = the price of the similar 2-year risk-free bond is % ( %) 2 = First we consider the 1-year corporate bond. Table 1 below calculates the expected loss from default in terms of Q on the assumption that defaults can take place halfway through each year, or at time 0.5 years. The expected value of the risk-free bond at time 0.5 years is 108e =

3 Table 1:Calculation of loss from default on a bond in terms of the default probabilities per year, Q. Notional principal=\$ Q Q The expected loss is 67.11Q. Let We obtain a value for Q equal to 2.18% Q = Then we consider the 5-year corporate bond. Table 2 below calculates the expected loss from default in terms of Q on the assumption that defaults can take place halfway through each year, or at times 0.5, 1.5 years. The expected value of the risk-free bond at time 1.5 years is 108e = The expected value of the risk-free bond at time 0.5 years is 8e e = Table 2:Calculation of loss from default on a bond in terms of the default probabilities per year, Q. Notional principal=\$ Q Q 1.5 Q Q Total Q The expected loss is Q. Let We obtain a value for Q equal to 3.00%. Since Q = % % = 3.82% Thus the risk-neutral default rate in the first year is 2.18% and in the second year is 3.82%. 3

4 Explain carefully the distinction between real-world and risk-neutral default probabilities. Which is higher? A bank enters into a credit derivative where it agrees to pay \$100 at the end of 1 year if a certain company s credit rating falls from A to Baa or lower during the year. The 1-year risk-free rate is 5%. Using Table 22.6, estimate a value for the derivative. What assumptions are you making? Do they tend to overstate or understate the value of the derivative. Solution Real world default probabilities are the true probabilities of defaults which can be estimated from historical data. Risk-neutral default probabilities are the probabilities of defaults in a world where all market participants are risk neutral and which can be estimated from bond prices. Risk-neutral default probabilities are higher. This means that returns in the risk-neutral world are lower. From Table 22.6, the probability of a company moving from A to Baa or lower in one year is 5.92%, thus the value of the derivative is e = The approximation in this is that the real-world probability of a downgrade is used. To value the derivative correctly the risk-neutral probability of a downgrade should be used. Since the risk-neutral probability of a default is higher than the real-world probability, it seems likely that the same is true of a downgrade. This means that 5.63 tends to understate the value of the derivative The value of a company s equity is \$4 million and the volatility of its equity is 60%. The debt that will have to be repaid in 2 years is \$15 million. The risk-free interest rate is 6% per annum. Use Merton s model to estimate the expected loss from default, the probability of default, and the recovery rate in the event of default. Explain why Merton s model gives a high recovery rate. (Hint: The Solver function in Excel can be used for this question.) Solution Merton s model is where and In this case, E 0 = V 0 N(d 1 ) De rt N(d 2 ) d 1 = ln V 0/D + (r + σ 2 V /2)T σ V T and d 2 = d 1 σ V T σ E E 0 = N(d 1 )σ V V 0 E 0 = 4, σ E = 60%, r = 0.06, T = 2, D = 15 Using the Solver function in Excel, there are V 0 = , σ V = , d 2 = The market value of the debt is V 0 E 0, or The present value of the promised payment on the debt therefore is 15e =

5 The expected loss from default is And the probability of default is = 1.65% i.e., 15.61%. But there is N( d 2 ) = (1 R) Q = 1.65% Thus the recovery rate is R = = 89.43% The reason the recovery rate is so high is as follows. There is a default if the value of the assets moves from to below 15. A value for the assets significantly below 15 is unlikely. Conditional on a default, the expected value of the assets is not a huge amount below Suppose that a bank has a total of \$10 million of exposures of a certain type. The 1- year probability of default averages 1% and the recovery rate averages 40%. The copula correlation parameter is 0.2. Estimate the 99.5% 1-year credit VaR. Solution In this case, V (0.995, 1) = N ( N 1 (0.01) + 0.2N 1 (0.995)) ) = Showing that the 99.5% worst case default rate is 9.46%. The 1-year 99.5% credit VaR is therefore (1 0.4)or \$0.57 million. 5

### Expected default frequency

KM Model Expected default frequency Expected default frequency (EDF) is a forward-looking measure of actual probability of default. EDF is firm specific. KM model is based on the structural approach to

### ECO 4368 Instructor: Saltuk Ozerturk. Bonds and Their Valuation

ECO 4368 Instructor: Saltuk Ozerturk Bonds and Their Valuation A bond is a long term contract under which a borrower (the issuer) agrees to make payments of interest and principal on speci c dates, to

### Put-Call Parity. chris bemis

Put-Call Parity chris bemis May 22, 2006 Recall that a replicating portfolio of a contingent claim determines the claim s price. This was justified by the no arbitrage principle. Using this idea, we obtain

### The Single Name Corporate CDS Market. Alan White

The Single Name Corporate CDS Market Alan White CDS Structure Single Name DJ Index Products CDS Notional x [ ] bp p.a. Buyer Credit Risk of ABC Seller 125 Equally Weighted Names Buyer Delivery 10MM Principal

### NIKE Case Study Solutions

NIKE Case Study Solutions Professor Corwin This case study includes several problems related to the valuation of Nike. We will work through these problems throughout the course to demonstrate some of the

### 2 Stock Price. Figure S1.1 Profit from long position in Problem 1.13

Problem 1.11. A cattle farmer expects to have 12, pounds of live cattle to sell in three months. The livecattle futures contract on the Chicago Mercantile Exchange is for the delivery of 4, pounds of cattle.

### Notes for Lecture 3 (February 14)

INTEREST RATES: The analysis of interest rates over time is complicated because rates are different for different maturities. Interest rate for borrowing money for the next 5 years is ambiguous, because

### Caput Derivatives: October 30, 2003

Caput Derivatives: October 30, 2003 Exam + Answers Total time: 2 hours and 30 minutes. Note 1: You are allowed to use books, course notes, and a calculator. Question 1. [20 points] Consider an investor

### Chapter 13 The Black-Scholes-Merton Model

Chapter 13 The Black-Scholes-Merton Model March 3, 009 13.1. The Black-Scholes option pricing model assumes that the probability distribution of the stock price in one year(or at any other future time)

### VALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS QUESTIONS See answers below

VALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS QUESTIONS See answers below 1. Determine the value of the following risk-free debt instrument, which promises to make the respective

### Protective Put Strategy Profits

Chapter Part Options and Corporate Finance: Basic Concepts Combinations of Options Options Call Options Put Options Selling Options Reading The Wall Street Journal Combinations of Options Valuing Options

### 1 The Black-Scholes Formula

1 The Black-Scholes Formula In 1973 Fischer Black and Myron Scholes published a formula - the Black-Scholes formula - for computing the theoretical price of a European call option on a stock. Their paper,

### Valuing Stock Options: The Black-Scholes-Merton Model. Chapter 13

Valuing Stock Options: The Black-Scholes-Merton Model Chapter 13 Fundamentals of Futures and Options Markets, 8th Ed, Ch 13, Copyright John C. Hull 2013 1 The Black-Scholes-Merton Random Walk Assumption

### HEC Paris MBA Program. Financial Markets Prof. Laurent E. Calvet Fall 2010 MIDTERM EXAM. 90 minutes Open book

HEC Paris MBA Program Name:... Financial Markets Prof. Laurent E. Calvet Fall 2010 MIDTERM EXAM 90 minutes Open book The exam will be graded out of 100 points. Points for each question are shown in brackets.

### Financial-Institutions Management

Solutions 3 Chapter 11: Credit Risk Loan Pricing and Terms 9. County Bank offers one-year loans with a stated rate of 9 percent but requires a compensating balance of 10 percent. What is the true cost

### UCLA Anderson School of Management Daniel Andrei, Derivative Markets 237D, Winter 2014. MFE Midterm. February 2014. Date:

UCLA Anderson School of Management Daniel Andrei, Derivative Markets 237D, Winter 2014 MFE Midterm February 2014 Date: Your Name: Your Equiz.me email address: Your Signature: 1 This exam is open book,

### 1 Pricing options using the Black Scholes formula

Lecture 9 Pricing options using the Black Scholes formula Exercise. Consider month options with exercise prices of K = 45. The variance of the underlying security is σ 2 = 0.20. The risk free interest

### Notes for Lecture 2 (February 7)

CONTINUOUS COMPOUNDING Invest \$1 for one year at interest rate r. Annual compounding: you get \$(1+r). Semi-annual compounding: you get \$(1 + (r/2)) 2. Continuous compounding: you get \$e r. Invest \$1 for

### FIN 472 Fixed-Income Securities Debt Instruments

FIN 472 Fixed-Income Securities Debt Instruments Professor Robert B.H. Hauswald Kogod School of Business, AU The Most Famous Bond? Bond finance raises the most money fixed income instruments types of bonds

### , plus the present value of the \$1,000 received in 15 years, which is 1, 000(1 + i) 30. Hence the present value of the bond is = 1000 ;

2 Bond Prices A bond is a security which offers semi-annual* interest payments, at a rate r, for a fixed period of time, followed by a return of capital Suppose you purchase a \$,000 utility bond, freshly

### Beyond preferred stock valuation of complex equity and hybrid instruments

Beyond preferred stock valuation of complex equity and hybrid instruments ASA Advanced Business Valuation Conference October 2015 Amanda A. Miller, Ph.D. 4 June 2015 Amanda A. Miller, Ph.D. (amanda.miller@ey.com)

### 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

### t = 1 2 3 1. Calculate the implied interest rates and graph the term structure of interest rates. t = 1 2 3 X t = 100 100 100 t = 1 2 3

MØA 155 PROBLEM SET: Summarizing Exercise 1. Present Value [3] You are given the following prices P t today for receiving risk free payments t periods from now. t = 1 2 3 P t = 0.95 0.9 0.85 1. Calculate

### 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

### Call and Put. Options. American and European Options. Option Terminology. Payoffs of European Options. Different Types of Options

Call and Put Options A call option gives its holder the right to purchase an asset for a specified price, called the strike price, on or before some specified expiration date. A put option gives its holder

### Jorge Cruz Lopez - Bus 316: Derivative Securities. Week 11. The Black-Scholes Model: Hull, Ch. 13.

Week 11 The Black-Scholes Model: Hull, Ch. 13. 1 The Black-Scholes Model Objective: To show how the Black-Scholes formula is derived and how it can be used to value options. 2 The Black-Scholes Model 1.

### Option Valuation. Chapter 21

Option Valuation Chapter 21 Intrinsic and Time Value intrinsic value of in-the-money options = the payoff that could be obtained from the immediate exercise of the option for a call option: stock price

### DETERMINING THE VALUE OF EMPLOYEE STOCK OPTIONS. Report Produced for the Ontario Teachers Pension Plan John Hull and Alan White August 2002

DETERMINING THE VALUE OF EMPLOYEE STOCK OPTIONS 1. Background Report Produced for the Ontario Teachers Pension Plan John Hull and Alan White August 2002 It is now becoming increasingly accepted that companies

### Tutorial: Structural Models of the Firm

Tutorial: Structural Models of the Firm Peter Ritchken Case Western Reserve University February 16, 2015 Peter Ritchken, Case Western Reserve University Tutorial: Structural Models of the Firm 1/61 Tutorial:

### Final Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator

University of Stavanger (UiS) Stavanger Masters Program Final Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator The number in brackets is the weight for each problem. The weights

### For the purposes of this Annex the following definitions shall apply:

XIV. COUNTERPARTY CREDIT RISK 1. Definitions ANNEX III: THE TREATMENT OF COUNTERPARTY CREDIT RISK OF DERIVATIVE INSTRUMENTS, REPURCHASE TRANSACTIONS, SECURITIES OR COMMODITIES LENDING OR BORROWING TRANSACTIONS,

Equity-index-linked swaps Equivalent to portfolios of forward contracts calling for the exchange of cash flows based on two different investment rates: a variable debt rate (e.g. 3-month LIBOR) and the

### Mortgage-Backed Securities. Leah DiMartino Matt Houser Brendan LaCerda Kaity McCoy Brian Seremet Justin Sibears

Mortgage-Backed Securities Leah DiMartino Matt Houser Brendan LaCerda Kaity McCoy Brian Seremet Justin Sibears 1 Introduction Mortgage-backed securities (MBS) are debt obligations that represent claims

### Assumptions: No transaction cost, same rate for borrowing/lending, no default/counterparty risk

Derivatives Why? Allow easier methods to short sell a stock without a broker lending it. Facilitates hedging easily Allows the ability to take long/short position on less available commodities (Rice, Cotton,

### Bonds and Yield to Maturity

Bonds and Yield to Maturity Bonds A bond is a debt instrument requiring the issuer to repay to the lender/investor the amount borrowed (par or face value) plus interest over a specified period of time.

### Solutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material. i = 0.75 1 for six months.

Solutions to Supplementary Questions for HP Chapter 5 and Sections 1 and 2 of the Supplementary Material 1. a) Let P be the recommended retail price of the toy. Then the retailer may purchase the toy at

### Financial Options: Pricing and Hedging

Financial Options: Pricing and Hedging Diagrams Debt Equity Value of Firm s Assets T Value of Firm s Assets T Valuation of distressed debt and equity-linked securities requires an understanding of financial

### Homework Solutions - Lecture 2

Homework Solutions - Lecture 2 1. The value of the S&P 500 index is 1286.12 and the treasury rate is 3.43%. In a typical year, stock repurchases increase the average payout ratio on S&P 500 stocks to over

### Bonds, in the most generic sense, are issued with three essential components.

Page 1 of 5 Bond Basics Often considered to be one of the most conservative of all investments, bonds actually provide benefits to both conservative and more aggressive investors alike. The variety of

### The Tangent or Efficient Portfolio

The Tangent or Efficient Portfolio 1 2 Identifying the Tangent Portfolio Sharpe Ratio: Measures the ratio of reward-to-volatility provided by a portfolio Sharpe Ratio Portfolio Excess Return E[ RP ] r

### Bond Options, Caps and the Black Model

Bond Options, Caps and the Black Model Black formula Recall the Black formula for pricing options on futures: C(F, K, σ, r, T, r) = Fe rt N(d 1 ) Ke rt N(d 2 ) where d 1 = 1 [ σ ln( F T K ) + 1 ] 2 σ2

### 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

### Lecture 12. Options Strategies

Lecture 12. Options Strategies Introduction to Options Strategies Options, Futures, Derivatives 10/15/07 back to start 1 Solutions Problem 6:23: Assume that a bank can borrow or lend money at the same

### Properties of Stock Options. Chapter 10

Properties of Stock Options Chapter 10 1 Notation c : European call option price C : American Call option price p : European put option price P : American Put option price S 0 : Stock price today K : Strike

### Chapter 6. Interest Rates And Bond Valuation. Learning Goals. Learning Goals (cont.)

Chapter 6 Interest Rates And Bond Valuation Learning Goals 1. Describe interest rate fundamentals, the term structure of interest rates, and risk premiums. 2. Review the legal aspects of bond financing

### LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs.

LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs. 1. The minimum rate of return that an investor must receive in order to invest in a project is most likely

### 24. Pricing Fixed Income Derivatives. through Black s Formula. MA6622, Ernesto Mordecki, CityU, HK, 2006. References for this Lecture:

24. Pricing Fixed Income Derivatives through Black s Formula MA6622, Ernesto Mordecki, CityU, HK, 2006. References for this Lecture: John C. Hull, Options, Futures & other Derivatives (Fourth Edition),

### CHAPTER 12 RISK, COST OF CAPITAL, AND CAPITAL BUDGETING

CHAPTER 12 RISK, COST OF CAPITAL, AND CAPITAL BUDGETING Answers to Concepts Review and Critical Thinking Questions 1. No. The cost of capital depends on the risk of the project, not the source of the money.

### CFA Level -2 Derivatives - I

CFA Level -2 Derivatives - I EduPristine www.edupristine.com Agenda Forwards Markets and Contracts Future Markets and Contracts Option Markets and Contracts 1 Forwards Markets and Contracts 2 Pricing and

### Value of Equity and Per Share Value when there are options and warrants outstanding. Aswath Damodaran

Value of Equity and Per Share Value when there are options and warrants outstanding Aswath Damodaran 1 Equity Value and Per Share Value: A Test Assume that you have done an equity valuation of Microsoft.

### Determination of Forward and Futures Prices

Determination of Forward and Futures Prices Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012 Short selling A popular trading (arbitrage) strategy is the shortselling or

### BOND - Security that obligates the issuer to make specified payments to the bondholder.

Bond Valuation BOND - Security that obligates the issuer to make specified payments to the bondholder. COUPON - The interest payments paid to the bondholder. FACE VALUE - Payment at the maturity of the

### Understanding Fixed Income

Understanding Fixed Income 2014 AMP Capital Investors Limited ABN 59 001 777 591 AFSL 232497 Understanding Fixed Income About fixed income at AMP Capital Our global presence helps us deliver outstanding

### BF 6701 : Financial Management Comprehensive Examination Guideline

BF 6701 : Financial Management Comprehensive Examination Guideline 1) There will be 5 essay questions and 5 calculation questions to be completed in 1-hour exam. 2) The topics included in those essay and

### Fixed Income: Practice Problems with Solutions

Fixed Income: Practice Problems with Solutions Directions: Unless otherwise stated, assume semi-annual payment on bonds.. A 6.0 percent bond matures in exactly 8 years and has a par value of 000 dollars.

### On Market-Making and Delta-Hedging

On Market-Making and Delta-Hedging 1 Market Makers 2 Market-Making and Bond-Pricing On Market-Making and Delta-Hedging 1 Market Makers 2 Market-Making and Bond-Pricing What to market makers do? Provide

### Market-Consistent Valuation of the Sponsor Covenant and its use in Risk-Based Capital Assessment. Craig Turnbull FIA

Market-Consistent Valuation of the Sponsor Covenant and its use in Risk-Based Capital Assessment Craig Turnbull FIA Background and Research Objectives 2 Background: DB Pensions and Risk + Aggregate deficits

### MODULE: PRINCIPLES OF FINANCE

Programme: BSc (Hons) Financial Services with Law BSc (Hons) Accounting with Finance BSc (Hons) Banking and International Finance BSc (Hons) Management Cohort: BFSL/13/FT Aug BACF/13/PT Aug BACF/13/FT

### Introduction to Options. Derivatives

Introduction to Options Econ 422: Investment, Capital & Finance University of Washington Summer 2010 August 18, 2010 Derivatives A derivative is a security whose payoff or value depends on (is derived

### LECTURE 10.1 Default risk in Merton s model

LECTURE 10.1 Default risk in Merton s model Adriana Breccia March 12, 2012 1 1 MERTON S MODEL 1.1 Introduction Credit risk is the risk of suffering a financial loss due to the decline in the creditworthiness

### Models of Risk and Return

Models of Risk and Return Aswath Damodaran Aswath Damodaran 1 First Principles Invest in projects that yield a return greater than the minimum acceptable hurdle rate. The hurdle rate should be higher for

### Recoveries on Defaulted Debt

Recoveries on Defaulted Debt Michael B. Gordy Federal Reserve Board May 2008 The opinions expressed here are my own, and do not reflect the views of the Board of Governors or its

### PRACTICE EXAM QUESTIONS ON WACC

Dr. Sudhakar Raju Financial Statements Analysis (FN 6450) PRACTICE EXAM QUESTIONS ON WACC 1. The return shareholders require on their investment in a firm is called the: a. dividend yield. B. cost of equity.

### Exercise 6 Find the annual interest rate if the amount after 6 years is 3 times bigger than the initial investment (3 cases).

Exercise 1 At what rate of simple interest will \$500 accumulate to \$615 in 2.5 years? In how many years will \$500 accumulate to \$630 at 7.8% simple interest? (9,2%,3 1 3 years) Exercise 2 It is known that

### Problem Set 1 Foundations of Financial Markets Instructor: Erin Smith Summer 2011 Due date: Beginning of class, May 31

Problem Set Foundations of Financial Markets Instructor: Erin Smith Summer 20 Due date: Beginning of class, May 3. Suppose the debt holders of a cosmetics firm hold debt with a face value of \$500,000.

### 第 9 讲 : 股 票 期 权 定 价 : B-S 模 型 Valuing Stock Options: The Black-Scholes Model

1 第 9 讲 : 股 票 期 权 定 价 : B-S 模 型 Valuing Stock Options: The Black-Scholes Model Outline 有 关 股 价 的 假 设 The B-S Model 隐 性 波 动 性 Implied Volatility 红 利 与 期 权 定 价 Dividends and Option Pricing 美 式 期 权 定 价 American

### 16. Time dependence in Black Scholes. MA6622, Ernesto Mordecki, CityU, HK, 2006. References for this Lecture:

16. Time dependence in Black Scholes MA6622, Ernesto Mordecki, CityU, HK, 2006. References for this Lecture: Marco Avellaneda and Peter Laurence, Quantitative Modelling of Derivative Securities, Chapman&Hall

### Modeling Correlated Interest Rate, Exchange Rate, and Credit Risk in Fixed Income Portfolios

Modeling Correlated Interest Rate, Exchange Rate, and Credit Risk in Fixed Income Portfolios Theodore M. Barnhill, Jr. and William F. Maxwell* Corresponding Author: William F. Maxwell, Assistant Professor

### How to calculate present values

How to calculate present values Back to the future Chapter 3 Discounted Cash Flow Analysis (Time Value of Money) Discounted Cash Flow (DCF) analysis is the foundation of valuation in corporate finance

### CHAPTER 14: BOND PRICES AND YIELDS

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:

### ON THE VALUATION OF CORPORATE BONDS

ON THE VALUATION OF CORPORATE BONDS by Edwin J. Elton,* Martin J. Gruber,* Deepak Agrawal** and Christopher Mann** * Nomura Professors, New York University ** Doctoral students, New York University 43

### Finance Homework Julian Vu May 28, 2008

Finance Homework Julian Vu May 28, 2008 Assignment: p. 28-29 Problems 1-1 and 1-2 p. 145-147 Questions 4-2, 4-3, and 4-4, and Problems 4-1, 4-2, 4-3, and 4-13 P1-1 A Treasury Bond that matures in 10 years

### Bond Valuation. FINANCE 350 Global Financial Management. Professor Alon Brav Fuqua School of Business Duke University. Bond Valuation: An Overview

Bond Valuation FINANCE 350 Global Financial Management Professor Alon Brav Fuqua School of Business Duke University 1 Bond Valuation: An Overview Bond Markets What are they? How big? How important? Valuation

### Bond Pricing Fundamentals

Bond Pricing Fundamentals Valuation What determines the price of a bond? Contract features: coupon, face value (FV), maturity Risk-free interest rates in the economy (US treasury yield curve) Credit risk

### Vilnius University. Faculty of Mathematics and Informatics. Gintautas Bareikis

Vilnius University Faculty of Mathematics and Informatics Gintautas Bareikis CONTENT Chapter 1. SIMPLE AND COMPOUND INTEREST 1.1 Simple interest......................................................................

### Asymmetry and the Cost of Capital

Asymmetry and the Cost of Capital Javier García Sánchez, IAE Business School Lorenzo Preve, IAE Business School Virginia Sarria Allende, IAE Business School Abstract The expected cost of capital is a crucial

### Time Value of Money. Background

Time Value of Money (Text reference: Chapter 4) Topics Background One period case - single cash flow Multi-period case - single cash flow Multi-period case - compounding periods Multi-period case - multiple

### Chapter 6 APPENDIX B. The Yield Curve and the Law of One Price. Valuing a Coupon Bond with Zero-Coupon Prices

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

### MAT 3788 Lecture 8 Forwards for assets with dividends Currency forwards

MA 3788 Lecture 8 Forwards for assets with dividends Currency forwards Prof. Boyan Kostadinov, City ech of CUNY he Value of a Forward Contract as ime Passes Recall from last time that the forward price

### The Time Value of Money

The following is a review of the Quantitative Methods: Basic Concepts principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: The Time

### Equity Value and Per Share Value: A Test

Equity Value and Per Share Value: A Test Assume that you have done an equity valuation of Microsoft. The total value for equity is estimated to be \$ 400 billion and there are 5 billion shares outstanding.

### 9. Himal Trading has EBIT of Rs 80,000, interest expense of Rs 12,000, and preferred

Set A Fundamentals of Financial Management Model Questions 2072 Program: BBS Time: 3 Hours Part: III F.M.: 100 Code: MGT 215 P.M.: 35 The objective of the model questions is to give an overview of the

### Modeling correlated market and credit risk in fixed income portfolios

Journal of Banking & Finance 26 (2002) 347 374 www.elsevier.com/locate/econbase Modeling correlated market and credit risk in fixed income portfolios Theodore M. Barnhill Jr. a, *, William F. Maxwell b

### 1. If the opportunity cost of capital is 14 percent, what is the net present value of the factory?

MØA 155 - Fall 2011 PROBLEM SET: Hand in 1 Exercise 1. An investor buys a share for \$100 and sells it five years later, at the end of the year, at the price of \$120.23. Each year the stock pays dividends

### A Short Introduction to Credit Default Swaps

A Short Introduction to Credit Default Swaps by Dr. Michail Anthropelos Spring 2010 1. Introduction The credit default swap (CDS) is the most common and widely used member of a large family of securities

### Options on an Asset that Yields Continuous Dividends

Finance 400 A. Penati - G. Pennacchi Options on an Asset that Yields Continuous Dividends I. Risk-Neutral Price Appreciation in the Presence of Dividends Options are often written on what can be interpreted

### CVA: Default Probability ain t matter?

CVA: Default Probability ain t matter? Ignacio Ruiz July 211 Version 1.1 Abstract CVA can be priced using market implied risk-neutral or historical real-world parameters. There is no consensus in the market

### Time Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)

Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for

### Mathematics. Rosella Castellano. Rome, University of Tor Vergata

and Loans Mathematics Rome, University of Tor Vergata and Loans Future Value for Simple Interest Present Value for Simple Interest You deposit E. 1,000, called the principal or present value, into a savings

### Exam 1 Morning Session

91. A high yield bond fund states that through active management, the fund s return has outperformed an index of Treasury securities by 4% on average over the past five years. As a performance benchmark

### Pricing Forwards and Swaps

Chapter 7 Pricing Forwards and Swaps 7. Forwards Throughout this chapter, we will repeatedly use the following property of no-arbitrage: P 0 (αx T +βy T ) = αp 0 (x T )+βp 0 (y T ). Here, P 0 (w T ) is

### 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.

### Bonds, Preferred Stock, and Common Stock

Bonds, Preferred Stock, and Common Stock I. Bonds 1. An investor has a required rate of return of 4% on a 1-year discount bond with a \$100 face value. What is the most the investor would pay for 2. An

### CORPORATE VALUATIONS AND THE MERTON MODEL

UNIVERSITÀ DEGLI STUDI ROMA TRE DIPARTIMENTO DI ECONOMIA CORPORATE VALUATIONS AND THE MERTON MODEL Andrea Gheno Working Paper n 55, 2005 UNIVERSITÀ DEGLI STUDI ROMA TRE DIPARTIMENTO DI ECONOMIA Working

### FLOATING RATE BANK LOANS: A BREAK FROM TRADITION FOR INCOME-SEEKING INVESTORS

FLOATING RATE BANK LOANS: A BREAK FROM TRADITION FOR INCOME-SEEKING INVESTORS With about \$713 billion in assets, the bank loan market is roughly half the size of the high yield market. However, demand

### Bond Valuation. Capital Budgeting and Corporate Objectives

Bond Valuation Capital Budgeting and Corporate Objectives Professor Ron Kaniel Simon School of Business University of Rochester 1 Bond Valuation An Overview Introduction to bonds and bond markets» What

### Take-Home Problem Set

Georgia State University Department of Finance MBA 8622 Fall 2001 MBA 8622: Corporation Finance Take-Home Problem Set Instructors: Lalitha Naveen, N. Daniel, C.Hodges, A. Mettler, R. Morin, M. Shrikhande,

### European Options Pricing Using Monte Carlo Simulation

European Options Pricing Using Monte Carlo Simulation Alexandros Kyrtsos Division of Materials Science and Engineering, Boston University akyrtsos@bu.edu European options can be priced using the analytical