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Chapter 5

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York University

Economics

ECON 4400

Dr.

Summer

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CHAPTER 5INTRODUCTION TO VALUATION THE TIME VALUE OF MONEYLearning ObjectivesLO1How to determine the future value of an investment made todayLO2How to determine the present value of cash to be received at a future dateLO3How to find the return on an investmentLO4How long it takes for an investment to reach a desired valueAnswers to Concepts Review and Critical Thinking Questions1LO2 The four parts are the present value PV the future value FV the discount rate r and the number of payments or periods t2LO1 2 Compounding refers to the growth of a dollar amount through time via reinvestment of interest earned It is also the process of determining the future value of an investment Discounting is the process of determining the value today of an amount to be received in the future3LO1 2 Future values grow assuming a positive rate of return present values shrink4LO1 2 The future value rises assuming its positive the present value falls5LO2 Its a reflection of the time value of money The Province of Ontario gets to use the 7604 immediately As payment for deferring his own use of that money the investor receives one interest payment of 2396 plus return of the principal amount of 7604 on the maturity date 6LO2 The key considerations would be 1 Is the rate of return implicit in the offer attractive relative to other similar risk investments and 2 How risky is the investment ie how certain are we that we will actually get the 10000 Thus our answer does depend on who is making the promise to repay 7LO2 The Province of Alberta security would have a somewhat higher price because Alberta is a stronger borrower than Ontario as reflected in a AAA credit rating for Alberta and a lower AA credit rating for Ontario 8LO2 The price would be higher because as time passes the price of the security will tend to rise toward 100 This rise is just a reflection of the time value of money As time passes the time until receipt of the 100 grows shorter and the present value rises In 2010 the price will probably be higher for the same reason We cannot be sure however because interest rates could be much higher or Ontarios financial position could deteriorate Either event would tend to depress the securitys price45Solutions to Questions and ProblemsNOTE All end of chapter problems were solved using a spreadsheet Many problems require multiple steps Due to space and readability constraints when these intermediate steps are included in this solutions manual rounding may appear to have occurred However the final answer for each problem is found without rounding during any step in the problemBasic1LO1 The simple interest per year is500008 400So after 10 years you will have 400104000 in interest The total balance will be 5000 40009000With compound interest we use the future value formulatFVPV1 r 10FV50001081079462The difference is 107946290001794622LO1 To find the FV of a lump sum we usetFVPV1r11FV2250110 6419517FV8752108 149993914FV76355117 687764178FV183796107 315795753LO2 To find the PV of a lump sum we usetPVFV1r6PV15451107 10295657PV51557113 219148523PV886073114 435169018PV550164109 1166313246

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