Chapter 5 Introduction to Valuation: The Time Value of Money

Key Concepts and Skills Be able to compute the future value of an investment made today Be able to compute the present value of cash to be received at some future date Be able to compute the return on an investment Be able to compute the number of periods that equates a present value and a future value given an interest rate Be able to use a financial calculator and/or a spreadsheet to solve time value of money problems

Future Value and Compounding Present Value and Discounting Chapter Outline Future Value and Compounding Present Value and Discounting More on Present and Future Values

Time Value of Money Many financial decisions require comparisons of cash payments at different dates Example: 2 investments that require an initial investment of $100 Timing Inv 1 Inv 2 After 1 year $30 $20 After 2 years $30 $20 After 3 years $30 $40 After 4 years $30 $60 If you should choose one of them, which would you choose?

Compounding Future Value: amount to which an investment will grow after earning interest Compounding: the process of accumulating interest in an investment over time to earn more interest Compound interest: Interest earned on both the initial principal and the reinvested interest from prior periods

Time principal Interest 0 $100 $0 1 $100 $10 2 $110 $11 Future Value FV of $100 in 2 years if k=10% Time principal Interest 0 $100 $0 1 $100 $10 2 $110 $11 So $100 today  $121 in 2 years

simple and compounded interest? What is the difference between simple and compounded interest? Compound interest assumes accumulated interest is reinvested (therefore, interest earns interest). Simple interest assumes interest is not reinvested. Interest is earned each period on the original principal only.

Present Value and Discounting Present Value: value today of a future cash flow PV is simply the reverse of future value PV works backward through time, while future value goes forward through time Discounting: finding present value of some future amount

Example 3 different ways to find future value of a single cash flow Find FV of $100 in 2 years @ 10% FV2= 100*(1+10%)2 formula = 100 FVIF2,10% table 100 PV 10 i 2 n FV financial calculator in general FVn= PV (1+i)n PV, FV formulas are based on this equation 4 variables given any 3, you can calculate the 4th

solving for n in how many years will $100 grow to $121 @ i= 10% Formula way: 100*(1+10%)n =121 (1+10%)n =1.21 n ln(1+10%)=ln 1.21 Table way: 100 FVIFn,10% =121 FVIFn,10% =1.21 Refer to FVIF Table. Look down the 10% column to find 1.21. Financial calculator way: 100 PV 10 i 121 FV n

Solving for i At what rate of return will $100 grow to $121 in 2 years Formula way: 100*(1+i)2 =121 (1+i)2 = 1.21 1+i = (1.21)1/2 =1.10 i = 0.10 = 10% Table way: 100 FVIF2,i =121 FVIF2.i =1.21 Refer to FVIF Table. Look across 2 period row to find 1.21. Financial calculator way: 100 PV 2 n 121 FV i