Solutions to Practice Questions (Bonds)

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Solutions to Practice Questions (Bonds)"

Transcription

1 Fuqua Business School Duke University FIN 350 Global Financial Management Solutions to Practice Questions (Bonds). These practice questions are a suplement to the problem sets, and are intended for those of you who want more practice. They are Optional, and are not part of the required material. 2. It is recommended that you look at these problems only after you fully understand how to solve the problem sets, the examples we covered in class, and the ones in the lecture notes. 3. Please note that I have collected these exmples from previous teaching material I have had. As such, while in most cases the notation will match the one used in class, the match is not 00%. 4. Some of these questions are easier than the ones you are expected to know how to solve, while others are above the level of knowledge you are expected to show on quizes and the final. ENJOY!

2 FIN 350 Solutions to Practice Questions 2. Suppose you invest $,000. You will have $2,000 in 0 years with this investment. We want to calulate ˆr so that: $2, 000 = $, 000( + ˆr) 0. Solving for ˆr, we get 2=(+ˆr) 0 (2) 0 =+ˆr.078 = + ˆr ˆr =7.8% Note: A useful rule of thumb is the Rule of 72. It says that for reasonable rates of return, the time it takes to double your money is approximately r% 72. Note that in this problem, 72 0 years r 7.2%. r% 2. The credit card company claims that the annual interest rate is 2.583% = 8.996%. However, with monthly compounding, the effective annual rate is (.0583) 2 =20.74%. The rate of 8.996% corresponds to an annual rate compounded monthly. 3. First, let us solve for the equivalent monthly rate ˆr: ( + ˆr) 2 =.2 ˆr =(.2) /2 =0.9489%. The present value of what you get is therefore given by PV + = 500 +ˆr = ( + ˆr) 2 ( + ˆr) 60 ˆr [ ] ( + ˆr) 60 =22, The present value of what you will have to pay back is given by [ 500 PV = ( + ˆr) 60 +ˆr ] ( + ˆr) ( + ˆr) [ ] = ( + ˆr) 60 ˆr ( + ˆr) 20 =20, Since the present value of the money you will get is larger than that you will have to pay back (PV + >PV ), you should accept the offer. 4. (a) We are interested in calculating Observe that so that C ( + r) n + C ( + r) 2n + C +. ( + r) 3n PV ( + r) n = C ( + r) 2n + C +, ( + r) 3n PV PV ( + r) n = C ( + r) n

3 FIN 350 Solutions to Practice Questions 3 which, after rearranging, yields C ( + r) n. (b) Let PVP t denote the present value of a t-year deferred perpetuity paying $ at the beginning of every year. It can be shown that PVP t = ( + r) t +r = r /r ( + r) t. Also, notice that the perpetuity that we are interested in is simply the sum of a -year deferred perpetuity paying $ at the beginning of every year; a 2-year deferred perpetuity paying $ at the beginning of every year; a 3-year deferred perpetuity paying $ at the beginning of every year; Therefore, PVP + PVP 2 + PVP 3 + = /r + /r +r + /r ( + r) 2 + Observe that PV +r = /r +r + /r ( + r) 2 +, so that PV PV +r = r. After rearranging terms, we find that +r r 2. (c) The equivalent semiannual rate ˆr must solve ( + ˆr) 2 =., which implies ˆr =4.88%. The present value of this perpetuity is therefore given by (.0488) 8 500(.0488) =7, (d) Using the formula on slide I..?? (in lecture notes), we have 00(.) =, (a) For no arbitrage to hold, the price of bond B should be three times the price of bond A. This is simply because the face value of bond B is three times the face value of bond A, and both bonds are year zero coupon bonds. Therefore, to make an arbitrage profit you should sell bond B and buy three units of bond A. The cashflow diagram of this strategy is: position Time 0 Time Buy 3 unites of Bond A Sell Bond B Combined 5 0 Thus, you make an arbitrage profit today of $5.

4 FIN 350 Solutions to Practice Questions 4 (b) If you buy bond A you get a return of approximately %, which is clearly greater than 2%. As such you will borrow from the bank at 2% and buy bond A. More specificaly, you can borrow from the bank = $98.04 dollars and buy unit of bond A for $90. This leaves you with an arbitrage profit of $8.04 today. The arbitrage table is as follows: Position Time 0 Time Borrow From Bank Buy Bond B Combined (a) First, let s find the discount factors for and 2 years: DF, and DF 2. We know that the present value of each of the bonds is given by C DF + C 2 DF 2. This implies that the following two equations for the two bonds: 85.0 = 3DF + 03DF = 0DF + 0DF 2 Solving these two equations for the two unknowns DF anddf 2 yields: DF =0.9, DF 2 =0.8. Therefore, the price of a 2 year zero coupon bond with a face of $00 should be F DF 2 = 00(0.8) = $80. (b) r = DF = 0.9 =0. and r 2 = = =0.2. DF (c) For a zero coupon bond the yield is always equal to the relevant spot rate. Thus, y = r 2 =0.2. (d) The yield to maturity of a two year r%(annual) coupon bond solves the equation Thus for bond A the yield to maturity solves 85. = C +y + C + F ( + y) y A ( + y A ) 2, and for bond B it solves 97 = y B ( + y B ) 2. Solving these two equations either directly or by trial and error gives y A = y B = Comment: In an exam a solution stating that each of the two yields is between 0. and 0.2 would suffice.

5 FIN 350 Solutions to Practice Questions 5 7. (a) The one year zero coupon bond s price satisfies PV A = F DF, which implies that the one year discount factor is DF = PV A F = =0.9. On the other hand, the price of bond B satisfies Pluging in the relevant known values yields PV B = C DF +(C + F ) DF = 0DF + 0DF 2 = 0(0.9) + 0DF 2 = 9 + 0DF 2. Therefore, DF 2 = (02.5 9)/0 = 0.85, which implies that the price of a two year zero coupon bond with face of value of $00 is F DF 2 = 00(0.85) = $85. (b) If the 2 year zero coupon bond is $95 dollars an easy way to make an arbitrage profit is to sell the 2 year zero coupon bond and buy the one year zero coupon bond. This will generate a profit of = $5 dollars today. At the end of the first year you will receive $00, since you are long the one year zero coupon bond. You can use this $00 in order to cover the $00 you need to pay at the end of the second year, as you are short the two year zero coupon bond. (c) If there were no arbitrage opportunities the price of a 2 year zero coupon bond with face value of $00 would have to be F DF 2 = 00(0.85) = $85. This implies that the 2 year zero coupon bond is underpriced relative to a replicating portfolio of a 2 year zero coupon bond, which uses bonds A and B. First find the portfolio that would replicate a 2 year zero coupon bonds using bonds A and B: { 00nA +0n B = 0 0n B = 00 { na = n B = Since the bond is cheaper than the replicating portfolio we buy the bond and sell the replicating portfolio. This implies that we buy the bond, buy units of bond A and sell units of bond B. Notice: The replicating portfolio of the 2 year zero coupon bonds consist of short position of units of bond A and long position units of bond B. Since in the arbitrage strategy we are selling the replicating portfolio we need to put a minus in front of the relevant quantities (i.e, under the arbitrage strategy we buy units of bond A and sell units of bond B). This gives an arbitrage profit of $85 $80 = $5

6 FIN 350 Solutions to Practice Questions 6 at time 0. At time, the replicating portfolio generates a cash (in)flow of At time 2 it generates a cash (in)flow of (00) (0) = $ (0) = $00. This is enough to cover the $00 cash (out)flow which is required in order to pay the person who bought the 2-year zero coupon bond from us. Here is the complete arbitrage table: Strategy C 0 C C 2 Buy 0.09 bonds A Sell 0.9 bonds B Buy 2-year ZCB Total 5 0 0

Coupon Bonds and Zeroes

Coupon Bonds and Zeroes Coupon Bonds and Zeroes Concepts and Buzzwords Coupon bonds Zero-coupon bonds Bond replication No-arbitrage price relationships Zero rates Zeroes STRIPS Dedication Implied zeroes Semi-annual compounding

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

Yield to Maturity Outline and Suggested Reading

Yield to Maturity Outline and Suggested Reading Yield to Maturity Outline Outline and Suggested Reading Yield to maturity on bonds Coupon effects Par rates Buzzwords Internal rate of return, Yield curve Term structure of interest rates Suggested reading

More information

CHAPTER 4. The Time Value of Money. Chapter Synopsis

CHAPTER 4. The Time Value of Money. Chapter Synopsis CHAPTER 4 The Time Value of Money Chapter Synopsis Many financial problems require the valuation of cash flows occurring at different times. However, money received in the future is worth less than money

More information

Ing. Tomáš Rábek, PhD Department of finance

Ing. Tomáš Rábek, PhD Department of finance Ing. Tomáš Rábek, PhD Department of finance For financial managers to have a clear understanding of the time value of money and its impact on stock prices. These concepts are discussed in this lesson,

More information

Chapter 4: Time Value of Money

Chapter 4: Time Value of Money 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)

More information

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. 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

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

Notes for Lecture 3 (February 14)

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

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

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

Global Financial Management

Global Financial Management Global Financial Management Bond Valuation Copyright 999 by Alon Brav, Campbell R. Harvey, Stephen Gray and Ernst Maug. All rights reserved. No part of this lecture may be reproduced without the permission

More information

Finance 350: Problem Set 6 Alternative Solutions

Finance 350: Problem Set 6 Alternative Solutions Finance 350: Problem Set 6 Alternative Solutions Note: Where appropriate, the final answer for each problem is given in bold italics for those not interested in the discussion of the solution. I. Formulas

More information

How to calculate present values

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

More information

FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008

FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 Options These notes consider the way put and call options and the underlying can be combined to create hedges, spreads and combinations. We will consider the

More information

Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams

Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present

More information

Determination of Forward and Futures Prices. Chapter 5

Determination of Forward and Futures Prices. Chapter 5 Determination of Forward and Futures Prices Chapter 5 Fundamentals of Futures and Options Markets, 8th Ed, Ch 5, Copyright John C. Hull 2013 1 Consumption vs Investment Assets Investment assets are assets

More information

1 Introduction to Option Pricing

1 Introduction to Option Pricing ESTM 60202: Financial Mathematics Alex Himonas 03 Lecture Notes 1 October 7, 2009 1 Introduction to Option Pricing We begin by defining the needed finance terms. Stock is a certificate of ownership of

More information

Forward Contracts and Forward Rates

Forward Contracts and Forward Rates Forward Contracts and Forward Rates Outline and Readings Outline Forward Contracts Forward Prices Forward Rates Information in Forward Rates Reading Veronesi, Chapters 5 and 7 Tuckman, Chapters 2 and 16

More information

Institutional Finance 08: Dynamic Arbitrage to Replicate Non-linear Payoffs. Binomial Option Pricing: Basics (Chapter 10 of McDonald)

Institutional Finance 08: Dynamic Arbitrage to Replicate Non-linear Payoffs. Binomial Option Pricing: Basics (Chapter 10 of McDonald) Copyright 2003 Pearson Education, Inc. Slide 08-1 Institutional Finance 08: Dynamic Arbitrage to Replicate Non-linear Payoffs Binomial Option Pricing: Basics (Chapter 10 of McDonald) Originally prepared

More information

5. Time value of money

5. Time value of money 1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned

More information

ACI THE FINANCIAL MARKETS ASSOCIATION

ACI THE FINANCIAL MARKETS ASSOCIATION ACI THE FINANCIAL MARKETS ASSOCIATION EXAMINATION FORMULAE 2009 VERSION page number INTEREST RATE..2 MONEY MARKET..... 3 FORWARD-FORWARDS & FORWARD RATE AGREEMENTS..4 FIXED INCOME.....5 FOREIGN EXCHANGE

More information

Determination of Forward and Futures Prices

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

More information

Topics Covered. Ch. 4 - The Time Value of Money. The Time Value of Money Compounding and Discounting Single Sums

Topics Covered. Ch. 4 - The Time Value of Money. The Time Value of Money Compounding and Discounting Single Sums Ch. 4 - The Time Value of Money Topics Covered Future Values Present Values Multiple Cash Flows Perpetuities and Annuities Effective Annual Interest Rate For now, we will omit the section 4.5 on inflation

More information

FNCE 301, Financial Management H Guy Williams, 2006

FNCE 301, Financial Management H Guy Williams, 2006 REVIEW We ve used the DCF method to find present value. We also know shortcut methods to solve these problems such as perpetuity present value = C/r. These tools allow us to value any cash flow including

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

CALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time

CALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time 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

More information

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

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.

More information

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

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

More information

Topic 3: Time Value of Money And Net Present Value

Topic 3: Time Value of Money And Net Present Value Topic 3: Time Value of Money And Net Present Value Laurent Calvet calvet@hec.fr John Lewis john.lewis04@imperial.ac.uk From Material by Pierre Mella-Barral MBA - Financial Markets - Topic 3 1 2. Present

More information

Chapter 4. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved.

Chapter 4. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved. Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value

More information

Chapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.)

Chapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.) Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value

More information

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES 1. Expectations hypothesis. The yields on long-term bonds are geometric averages of present and expected future short rates. An upward sloping curve is

More information

Manual for SOA Exam FM/CAS Exam 2.

Manual for SOA Exam FM/CAS Exam 2. Manual for SOA Exam FM/CAS Exam 2. Chapter 6. Variable interest rates and portfolio insurance. c 2009. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam FM/CAS Exam

More information

Final Exam Practice Set and Solutions

Final Exam Practice Set and Solutions FIN-469 Investments Analysis Professor Michel A. Robe Final Exam Practice Set and Solutions What to do with this practice set? To help students prepare for the final exam, three practice sets with solutions

More information

1.3.2015 г. D. Dimov. Year Cash flow 1 $3,000 2 $5,000 3 $4,000 4 $3,000 5 $2,000

1.3.2015 г. D. Dimov. Year Cash flow 1 $3,000 2 $5,000 3 $4,000 4 $3,000 5 $2,000 D. Dimov Most financial decisions involve costs and benefits that are spread out over time Time value of money allows comparison of cash flows from different periods Question: You have to choose one of

More information

Lecture 4: Properties of stock options

Lecture 4: Properties of stock options Lecture 4: Properties of stock options Reading: J.C.Hull, Chapter 9 An European call option is an agreement between two parties giving the holder the right to buy a certain asset (e.g. one stock unit)

More information

Chapter 2 Present Value

Chapter 2 Present Value Chapter 2 Present Value Road Map Part A Introduction to finance. Financial decisions and financial markets. Present value. Part B Valuation of assets, given discount rates. Part C Determination of risk-adjusted

More information

Bond Valuation. Capital Budgeting and Corporate Objectives

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

More information

The Time Value of Money

The Time Value of Money The Time Value of Money Future Value - Amount to which an investment will grow after earning interest. Compound Interest - Interest earned on interest. Simple Interest - Interest earned only on the original

More information

Fixed Income: Practice Problems with Solutions

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.

More information

Manual for SOA Exam FM/CAS Exam 2.

Manual for SOA Exam FM/CAS Exam 2. Manual for SOA Exam FM/CAS Exam 2. Chapter 5. Bonds. c 2009. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam FM/CAS Exam 2, Financial Mathematics. Fall 2009 Edition,

More information

Key Concepts and Skills. Chapter Outline. Basic Definitions. Future Values. Future Values: General Formula 1-1. Chapter 4

Key Concepts and Skills. Chapter Outline. Basic Definitions. Future Values. Future Values: General Formula 1-1. Chapter 4 Key Concepts and Skills Chapter 4 Introduction to Valuation: The Time Value of Money Be able to compute the future value of an investment made today Be able to compute the present value of cash to be received

More information

Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS

Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS 4-1 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.

More information

FINANCIAL MATHEMATICS FIXED INCOME

FINANCIAL MATHEMATICS FIXED INCOME FINANCIAL MATHEMATICS FIXED INCOME 1. Converting from Money Market Basis to Bond Basis and vice versa 2 2. Calculating the Effective Interest Rate (Non-annual Payments)... 4 3. Conversion of Annual into

More information

Practice Set #1 and Solutions.

Practice Set #1 and Solutions. Bo Sjö 14-05-03 Practice Set #1 and Solutions. What to do with this practice set? Practice sets are handed out to help students master the material of the course and prepare for the final exam. These sets

More information

Chapter 6. Time Value of Money Concepts. Simple Interest 6-1. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years.

Chapter 6. Time Value of Money Concepts. Simple Interest 6-1. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years. 6-1 Chapter 6 Time Value of Money Concepts 6-2 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received in

More information

Manual for SOA Exam FM/CAS Exam 2.

Manual for SOA Exam FM/CAS Exam 2. Manual for SOA Exam FM/CAS Exam 2. Chapter 7. Derivatives markets. c 2009. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam FM/CAS Exam 2, Financial Mathematics. Fall

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

PowerPoint. to accompany. Chapter 5. Interest Rates

PowerPoint. to accompany. Chapter 5. Interest Rates PowerPoint to accompany Chapter 5 Interest Rates 5.1 Interest Rate Quotes and Adjustments To understand interest rates, it s important to think of interest rates as a price the price of using money. When

More information

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

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

More information

Discounted Cash Flow Valuation

Discounted Cash Flow Valuation Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

More information

We first solve for the present value of the cost per two barrels: (1.065) 2 = 41.033 (1.07) 3 = 55.341. x = 20.9519

We first solve for the present value of the cost per two barrels: (1.065) 2 = 41.033 (1.07) 3 = 55.341. x = 20.9519 Chapter 8 Swaps Question 8.1. We first solve for the present value of the cost per two barrels: $22 1.06 + $23 (1.065) 2 = 41.033. We then obtain the swap price per barrel by solving: which was to be shown.

More information

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES Chapter - The Term Structure of Interest Rates CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future

More information

Investments Analysis

Investments Analysis Investments Analysis Last 2 Lectures: Fixed Income Securities Bond Prices and Yields Term Structure of Interest Rates This Lecture (#7): Fixed Income Securities Term Structure of Interest Rates Interest

More information

Bank: The bank's deposit pays 8 % per year with annual compounding. Bond: The price of the bond is $75. You will receive $100 five years later.

Bank: The bank's deposit pays 8 % per year with annual compounding. Bond: The price of the bond is $75. You will receive $100 five years later. ü 4.4 lternative Discounted Cash Flow Decision Rules ü Three Decision Rules (1) Net Present Value (2) Future Value (3) Internal Rate of Return, IRR ü (3) Internal Rate of Return, IRR Internal Rate of Return

More information

Time Value Conepts & Applications. Prof. Raad Jassim

Time Value Conepts & Applications. Prof. Raad Jassim Time Value Conepts & Applications Prof. Raad Jassim Chapter Outline Introduction to Valuation: The Time Value of Money 1 2 3 4 5 6 7 8 Future Value and Compounding Present Value and Discounting More on

More information

Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued

Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued 6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

More information

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES CHAPTER : THE TERM STRUCTURE OF INTEREST RATES CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future

More information

Mathematics. Rosella Castellano. Rome, University of Tor Vergata

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

More information

Accounting Building Business Skills. Interest. Interest. Paul D. Kimmel. Appendix B: Time Value of Money

Accounting Building Business Skills. Interest. Interest. Paul D. Kimmel. Appendix B: Time Value of Money Accounting Building Business Skills Paul D. Kimmel Appendix B: Time Value of Money PowerPoint presentation by Kate Wynn-Williams University of Otago, Dunedin 2003 John Wiley & Sons Australia, Ltd 1 Interest

More information

Chapter The Time Value of Money

Chapter The Time Value of Money Chapter The Time Value of Money PPT 9-2 Chapter 9 - Outline Time Value of Money Future Value and Present Value Annuities Time-Value-of-Money Formulas Adjusting for Non-Annual Compounding Compound Interest

More information

A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2%

A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2% 1 Exam FM Questions Practice Exam 1 1. Consider the following yield curve: Year Spot Rate 1 5.5% 2 5.0% 3 5.0% 4 4.5% 5 4.0% Find the four year forward rate. A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2% 2.

More information

Test 4 Created: 3:05:28 PM CDT 1. The buyer of a call option has the choice to exercise, but the writer of the call option has: A.

Test 4 Created: 3:05:28 PM CDT 1. The buyer of a call option has the choice to exercise, but the writer of the call option has: A. Test 4 Created: 3:05:28 PM CDT 1. The buyer of a call option has the choice to exercise, but the writer of the call option has: A. The choice to offset with a put option B. The obligation to deliver the

More information

MGT201 Lecture No. 07

MGT201 Lecture No. 07 MGT201 Lecture No. 07 Learning Objectives: After going through this lecture, you would be able to have an understanding of the following concepts. Discounted Cash Flows (DCF Analysis) Annuities Perpetuity

More information

Bond valuation. Present value of a bond = present value of interest payments + present value of maturity value

Bond valuation. Present value of a bond = present value of interest payments + present value of maturity value Bond valuation A reading prepared by Pamela Peterson Drake O U T L I N E 1. Valuation of long-term debt securities 2. Issues 3. Summary 1. Valuation of long-term debt securities Debt securities are obligations

More information

Class Note on Valuing Swaps

Class Note on Valuing Swaps Corporate Finance Professor Gordon Bodnar Class Note on Valuing Swaps A swap is a financial instrument that exchanges one set of cash flows for another set of cash flows of equal expected value. Swaps

More information

CHAPTER 7 INTEREST RATES AND BOND VALUATION

CHAPTER 7 INTEREST RATES AND BOND VALUATION CHAPTER 7 INTEREST RATES AND BOND VALUATION Answers to Concepts Review and Critical Thinking Questions 1. No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Long-term Treasury

More information

You just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy?

You just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy? 1 You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each

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

n(n + 1) 2 1 + 2 + + n = 1 r (iii) infinite geometric series: if r < 1 then 1 + 2r + 3r 2 1 e x = 1 + x + x2 3! + for x < 1 ln(1 + x) = x x2 2 + x3 3

n(n + 1) 2 1 + 2 + + n = 1 r (iii) infinite geometric series: if r < 1 then 1 + 2r + 3r 2 1 e x = 1 + x + x2 3! + for x < 1 ln(1 + x) = x x2 2 + x3 3 ACTS 4308 FORMULA SUMMARY Section 1: Calculus review and effective rates of interest and discount 1 Some useful finite and infinite series: (i) sum of the first n positive integers: (ii) finite geometric

More information

I. Readings and Suggested Practice Problems. II. Risks Associated with Default-Free Bonds

I. Readings and Suggested Practice Problems. II. Risks Associated with Default-Free Bonds Prof. Alex Shapiro Lecture Notes 13 Bond Portfolio Management I. Readings and Suggested Practice Problems II. Risks Associated with Default-Free Bonds III. Duration: Details and Examples IV. Immunization

More information

FIN 3000. Chapter 6. Annuities. Liuren Wu

FIN 3000. Chapter 6. Annuities. Liuren Wu FIN 3000 Chapter 6 Annuities Liuren Wu Overview 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams Learning objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate

More information

9. Time Value of Money 1: Present and Future Value

9. Time Value of Money 1: Present and Future Value 9. Time Value of Money 1: Present and Future Value Introduction The language of finance has unique terms and concepts that are based on mathematics. It is critical that you understand this language, because

More information

Convenient Conventions

Convenient Conventions C: call value. P : put value. X: strike price. S: stock price. D: dividend. Convenient Conventions c 2015 Prof. Yuh-Dauh Lyuu, National Taiwan University Page 168 Payoff, Mathematically Speaking The payoff

More information

Chapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.

Chapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value. Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values

More information

Financial Markets and Valuation - Tutorial 1: SOLUTIONS. Present and Future Values, Annuities and Perpetuities

Financial Markets and Valuation - Tutorial 1: SOLUTIONS. Present and Future Values, Annuities and Perpetuities Financial Markets and Valuation - Tutorial 1: SOLUTIONS Present and Future Values, Annuities and Perpetuities (*) denotes those problems to be covered in detail during the tutorial session (*) Problem

More information

How to Calculate Present Values

How to Calculate Present Values How to Calculate Present Values Michael Frantz, 2010-09-22 Present Value What is the Present Value The Present Value is the value today of tomorrow s cash flows. It is based on the fact that a Euro tomorrow

More information

Debt Instruments Set 2

Debt Instruments Set 2 Debt Instruments Set 2 Backus/October 29, 1998 Bond Arithmetic 0. Overview Zeros and coupon bonds Spot rates and yields Day count conventions Replication and arbitrage Forward rates Yields and returns

More information

BF 6701 : Financial Management Comprehensive Examination Guideline

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

More information

Exercise 6 8. Exercise 6 12 PVA = $5,000 x 4.35526* = $21,776

Exercise 6 8. Exercise 6 12 PVA = $5,000 x 4.35526* = $21,776 CHAPTER 6: EXERCISES Exercise 6 2 1. FV = $10,000 (2.65330 * ) = $26,533 * Future value of $1: n = 20, i = 5% (from Table 1) 2. FV = $10,000 (1.80611 * ) = $18,061 * Future value of $1: n = 20, i = 3%

More information

TIME VALUE OF MONEY PROBLEM #5: ZERO COUPON BOND

TIME VALUE OF MONEY PROBLEM #5: ZERO COUPON BOND TIME VALUE OF MONEY PROBLEM #5: ZERO COUPON BOND Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction This assignment will focus on using the TI - 83 to calculate the price of a Zero

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

Bonds. Describe Bonds. Define Key Words. Created 2007 By Michael Worthington Elizabeth City State University

Bonds. Describe Bonds. Define Key Words. Created 2007 By Michael Worthington Elizabeth City State University Bonds OBJECTIVES Describe bonds Define key words Explain why bond prices fluctuate Compute interest payments Calculate the price of bonds Created 2007 By Michael Worthington Elizabeth City State University

More information

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 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

More information

CHAPTER 6 DISCOUNTED CASH FLOW VALUATION

CHAPTER 6 DISCOUNTED CASH FLOW VALUATION CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and

More information

K 1 < K 2 = P (K 1 ) P (K 2 ) (6) This holds for both American and European Options.

K 1 < K 2 = P (K 1 ) P (K 2 ) (6) This holds for both American and European Options. Slope and Convexity Restrictions and How to implement Arbitrage Opportunities 1 These notes will show how to implement arbitrage opportunities when either the slope or the convexity restriction is violated.

More information

MBA Finance Part-Time Present Value

MBA Finance Part-Time Present Value MBA Finance Part-Time Present Value Professor Hugues Pirotte Spéder Solvay Business School Université Libre de Bruxelles Fall 2002 1 1 Present Value Objectives for this session : 1. Introduce present value

More information

The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)

The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL-738 Calculator Reference is made to the Appendix Tables A-1 to A-4 in the course textbook Investments:

More information

FIN 3710. Final (Practice) Exam 05/23/06

FIN 3710. Final (Practice) Exam 05/23/06 FIN 3710 Investment Analysis Spring 2006 Zicklin School of Business Baruch College Professor Rui Yao FIN 3710 Final (Practice) Exam 05/23/06 NAME: (Please print your name here) PLEDGE: (Sign your name

More information

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

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

More information

Interest Rate and Currency Swaps

Interest Rate and Currency Swaps Interest Rate and Currency Swaps Eiteman et al., Chapter 14 Winter 2004 Bond Basics Consider the following: Zero-Coupon Zero-Coupon One-Year Implied Maturity Bond Yield Bond Price Forward Rate t r 0 (0,t)

More information

Investment, Time, and Present Value

Investment, Time, and Present Value Investment, Time, and Present Value Contents: Introduction Future Value (FV) Present Value (PV) Net Present Value (NPV) Optional: The Capital Asset Pricing Model (CAPM) Introduction Decisions made by a

More information

( ) ( )( ) ( ) 2 ( ) 3. n n = 100 000 1+ 0.10 = 100 000 1.331 = 133100

( ) ( )( ) ( ) 2 ( ) 3. n n = 100 000 1+ 0.10 = 100 000 1.331 = 133100 Mariusz Próchniak Chair of Economics II Warsaw School of Economics CAPITAL BUDGETING Managerial Economics 1 2 1 Future value (FV) r annual interest rate B the amount of money held today Interest is compounded

More information

Practice Set #2 and Solutions.

Practice Set #2 and Solutions. FIN-672 Securities Analysis & Portfolio Management Professor Michel A. Robe Practice Set #2 and Solutions. What to do with this practice set? To help MBA students prepare for the assignment and the exams,

More information

The Time Value of Money

The Time Value of Money The Time Value of Money This handout is an overview of the basic tools and concepts needed for this corporate nance course. Proofs and explanations are given in order to facilitate your understanding and

More information

1 Interest rates, and risk-free investments

1 Interest rates, and risk-free investments Interest rates, and risk-free investments Copyright c 2005 by Karl Sigman. Interest and compounded interest Suppose that you place x 0 ($) in an account that offers a fixed (never to change over time)

More information

CHAPTER 22: FUTURES MARKETS

CHAPTER 22: FUTURES MARKETS CHAPTER 22: FUTURES MARKETS PROBLEM SETS 1. There is little hedging or speculative demand for cement futures, since cement prices are fairly stable and predictable. The trading activity necessary to support

More information

MAT 3788 Lecture 8 Forwards for assets with dividends Currency forwards

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

More information

MODULE: PRINCIPLES OF FINANCE

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

More information