Lecture 2Valuing InvestmentProf. ZhangUniversity of Texas at AustinMcCombs School of BusinessOutline1Compounding2Discounting3Perpetuities4AnnuitiesFIN 367, Lecture 2Valuing Investment2 / 42
Outline1Compounding2Discounting3Perpetuities4AnnuitiesFIN 367, Lecture 2Valuing Investment2 / 42Motivation•At the most general level, aninvestmentis a claim to a stream ofcash flows.•Both real and financial investments.•In order to choose between different investments, we must thereforefind a way to compare cash flows differing in•Size•Timing•Risk•We will first focus on the size and timing of the cash flows and ignorerisk for now.•Compounding and discounting allow us to compare cash flowsdiffering in size and timing.FIN 367, Lecture 2Valuing Investment3 / 42
Time Value of MoneyIn general, a dollar today is worth more than a dollar in one year. Thedifference in value between money today and money in the future is calledthetime value of money.•Suppose you deposit $100 in a bank account which pays 10%interest, you will have $110 at the end of next year.•When we compare cash flows at different periods of time, we shouldtake the time value of money into consideration.FIN 367, Lecture 2Valuing Investment4 / 42Compounding and Future Value: Illustrative ExampleSuppose you deposit $100 in a bank account which pays 10% interest:•Money in the account after one year:Investment:$100Interest:$10= $100×10%Total:$110= $100(1+10%)•Suppose that the interest is credited to your account once a year. Money inthe account after two years:Investment:$110Interest:$11=$110×10%Total:$121= $100(1 + 10%)2•Money in the account after three years:Investment:$121Interest:$12.1= $121×10%Total:$133.1= $100(1 + 10%)3•Continuing this reasoning, you will have$100(1 + 10%)Tat the end ofTyears.FIN 367, Lecture 2Valuing Investment5 / 42
Compounding and Future Value: General CaseMore generally, suppose you deposit $Cin a bank account which pays an interestrate ofr% per year:•Money in the account after one year:Investment:$CInterest:$C×r%Total:$C(1+r%)•Suppose that the interest is credited to your account once a year. Money inthe account after two years:Investment:$C(1+r%)Interest:$C(1+r%)×r%Total:$C(1 +r%)2•Continuing this reasoning, you will have$C(1 +r%)Tat the end ofTyears.FIN 367, Lecture 2Valuing Investment6 / 42Future Value and Compounding Factor•$C(1 +r%)Tis the future valuein T years of an initial investment of$C that earns r% compounded annually.•(1 +r%)Tis called the T-period compounding factor.FIN 367, Lecture 2Valuing Investment7 / 42
More Frequent Compounding•Suppose you deposit $Cin a bank account which paysr% interest, and thatinterest is credited to your account twicea year:•You can then show that you will have $C(1 +r%2) after 6 months,$C(1 +r%2)2after a year, ..., $C(1 +r%2)2Tafter T years.