CONTENTS CHAPTER 1 INTEREST RATE MEASUREMENT 1

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1 CONTENTS CHAPTER 1 INTEREST RATE MEASUREMENT Introduction Interest Accumulation and Effective Rates of Interest Effective Rates of Interest Compound Interest Simple Interest Comparison of Compound Interest and Simple Interest Accumulated Amount Function Present Value Canadian Treasury Bills Equation of Value Nominal Rates of Interest Actuarial Notation for Nominal Rates of Interest Effective and Nominal Rates of Discount Effective Annual Rate of Discount Equivalence between Discount and Interest Rates Simple Discount and Valuation of U.S. T-Bills Nominal Annual Rate of Discount The Force of Interest Continuous Investment Growth Investment Growth Based on the Force of Interest Constant Force of Interest Inflation and the Real Rate of Interest Factors Affecting Interest Rates Summary of Definitions and Formulas Notes and References Exercises 57 iii

2 iv CONTENTS CHAPTER 2 VALUATION OF ANNUITIES Level Payment Annuities Accumulated Value of an Annuity Accumulated Value of an Annuity Some Time after the Final Payment Accumulated Value of an Annuity with Non-Level Interest Rates Accumulated Value of an Annuity with a Changing Payment Present Value of an Annuity Present Value of an Annuity Some Time before Payments Begin Present Value of an Annuity with Non-Level Interest Rates Relationship Between a ni and s ni Valuation of Perpetuities Annuity-Immediate and Annuity-Due Level Payment Annuities Some Generalizations Differing Interest and Payment Period m-thly Payable Annuities Continuous Annuities Solving for the Number of Payments in an Annuity (Unknown Time) Solving for the Interest Rate in an Annuity (Unknown Interest) Annuities with Non-Constant Payments Annuities Whose Payments Form a Geometric Progression Differing Payment Period and Geometric Frequency Dividend Discount Model for Valuing a Stock Annuities Whose Payments Form an Arithmetic Progression Increasing Annuities Decreasing Annuities Continuous Annuities with Varying Payments Unknown Interest Rate for Annuities with Varying Payments 134

3 CONTENTS v 2.4 Applications and Illustrations Yield Rates and Reinvestment Rates Depreciation Depreciation Method 1 The Declining Balance Method Depreciation Method 2 The Straight-Line Method Depreciation Method 3 The Sum of Years Digits Method Depreciation Method 4 The Compound Interest Method Capitalized Cost Book Value and Market Value The Sinking Fund Method of Valuation Summary of Definitions and Formulas Notes and References Exercises 155 CHAPTER 3 LOAN REPAYMENT The Amortization Method of Loan Repayment The General Amortization Method The Amortization Schedule Retrospective Form of the Outstanding Balance Prospective Form of the Outstanding Balance Additional Properties of Amortization Non-Level Interest Rate Capitalization of Interest Amortization with Level Payments of Principal Interest Only with Lump Sum Payment at the End Amortization of a Loan with Level Payments Mortgage Loans in Canada Mortgage Loans in the US The Sinking-Fund Method of Loan Repayment Sinking-Fund Method Schedule 208

4 vi CONTENTS 3.4 Applications and Illustrations Makeham s Formula The Merchant s Rule The US Rule Summary of Definitions and Formulas Notes and References Exercises 216 CHAPTER 4 BOND VALUATION Determination of Bond Prices The Price of a Bond on a Coupon Date Bonds Bought or Redeemed at a Premium or Discount Bond Prices between Coupon Dates Book Value of a Bond Finding the Yield Rate for a Bond Amortization of a Bond Applications and Illustrations Callable Bonds: Optional Redemption Dates Serial Bonds and Makeham s Formula Definitions and Formulas Notes and References Exercises 265 CHAPTER 5 MEASURING THE RATE OF RETURN OF AN INVESTMENT Internal Rate of Return Defined and Net Present Value The Internal Rate of Return Defined Uniqueness of the Internal Rate of Return Project Evaluation Using Net Present Value Alternative Methods of Valuing Investment Returns Profitability Index Payback Period Modified Internal Rate of Return (MIRR) Project Return Rate and Project Financing Rate 289

5 CONTENTS vii 5.2 Dollar-Weighted and Time-Weighted Rate of Return Dollar-Weighted Rate of Return Time-Weighted Rate of Return Applications and Illustrations The Portfolio Method and the Investment Year Method Interest Preference Rates for Borrowing and Lending Another Measure for the Yield on a Fund Definitions and Formulas Notes and References Exercises 306 CHAPTER 6 THE TERM STRUCTURE OF INTEREST RATES Spot Rates of Interest The Relationship Between Spot Rates of Interest and Yield to Maturity on Coupon Bonds Forward Rates of Interest Forward Rates of Interest as Deferred Borrowing or Lending Rates Arbitrage with Forward Rates of Interest General Definition of Forward Rates of Interest Applications and Illustrations Arbitrage Forward Rate Agreements The Force of Interest as a Forward Rate At-Par Yield Definitions and Formulas Notes and References Exercises 354

6 viii CONTENTS CHAPTER 7 CASHFLOW DURATION AND IMMUNIZATION Duration of a Set of Cashflows and Bond Duration Duration of a Zero Coupon Bond Duration Applied to Approximate Changes in Present Value of a Series of Cashflows Duration of a Coupon Bond Duration of a Portfolio of Series of Cashflows Duration and Shifts in Term Structure Effective Duration Asset-Liability Matching and Immunization Redington Immunization Full Immunization Applications and Illustrations Duration Based On Changes in a Nominal Annual Yield Rate Compounded Semiannually Duration Based on Changes in the Force of Interest Duration Based on Shifts in Term Structure Shortcomings of Duration as a Measure of Interest Rate Risk A Generalization of Redington Immunization Definitions and Formulas Notes and References Exercises 405 CHAPTER 8 ADDITIONAL TOPICS IN FIXED INCOME INVESTMENTS Fixed Income Investments Certificates of Deposit Money Market Funds Mortgage-Backed Securities (MBS) Collateralized Debt Obligations (CDO) Treasury Inflation Protected Securities (TIPS) and Real Return Bonds Bond Default and Risk Premium Convertible Bonds 422

7 CONTENTS ix 8.2 Interest Rate Swaps A Comparative Advantage Interest Rate Swap Swapping a Floating Rate Loan for a Fixed Rate Loan The Swap Rate Determinants of Interest Rates Government Policy Risk Premium Time Preference Liquidity Definitions and Formulas Notes and References Exercises 437 CHAPTER 9 ADVANCED TOPICS IN EQUITY INVESTMENTS AND FINANCIAL DERIVATIVES The Dividend Discount Model of Stock Valuation Short Sale of Stock in Practice Additional Equity Investments Mutual Funds Stock Indexes and Exchange Traded Funds Over-the-Counter Market Capital Asset Pricing Model Financial Derivatives Defined Forward Contracts Forward Contract Defined Prepaid Forward Price on an Asset Paying No Income Forward Delivery Price Based on an Asset Paying No Income Forward Contract Value Forward Contract on an Asset Paying Specific Dollar Income Forward Contract on an Asset Paying Percentage Dividend Income Synthetic Forward Contract Strategies with Forward Contracts 466

8 x CONTENTS 9.6 Futures Contracts Commodity Swaps Definitions and Formulas Notes and References Exercises 480 CHAPTER 10 OPTIONS Call Options Put Options Equity Linked Payments and Insurance Option Strategies Floors, Caps, and Covered Positions Synthetic Forward Contracts Put-Call Parity More Option Combinations Using Forwards and Options for Hedging and Insurance Option Pricing Models Foreign Currency Exchange Rates Definitions and Formulas Notes and References Exercises 530 ANSWERS TO TEXT EXERCISES 537 BIBLIOGRAPHY 573 INDEX 577

ASC301 A Financial Mathematics 2:00-3:50 pm TR Maxon 104

ASC301 A Financial Mathematics 2:00-3:50 pm TR Maxon 104 Instructor: John Symms Office: Math House 204 Phone: 524-7143 (email preferred) Email: jsymms@carrollu.edu URL: Go to the Courses tab at my.carrollu.edu.