Lecture Three Time Value of Money © 2011 John Wiley and Sons

Learning Outcomes Explain what is meant by the “time value of money” Describe the concept of simple interest and the process of compounding Apply your knowledge of future and present value concepts to relevant Business and Personal finance contexts.

Time Value of Money Concepts Important Principle of Finance: “Money has a time value”—money can grow or increase over time and money today is worth less than money received in the future Time Value of Money: Math of finance whereby interest is earned over time by saving or investing money Simple Interest: Interest earned only on the principal of the initial investment

Time Value of Money Concepts (continued) Present Value: Value of an investment or savings amount today or at the present time Future Value: Value of an investment or savings amount at a specified future time Basic Equation: Future value = Present value + (Present value x Interest rate)

Time Value of Money Example: Simple Interest Basic Information: You have $1,000 to save or invest for one year and a bank will pay you 8% for use of your money. What will be the value of your savings after one year? Basic Equation: Future value = Present value + (Present value x Interest rate) Future value = $1,000 + ($1,000 x .08) = $1,000 + $80 = $1,080

Time Value of Money Example: Simple Interest (continued) Alternative Basic Equation: Future value = Present value x (1 + Interest rate) Future value = $1,000 x (1 + .08) = $1,000 x 1.08 = $1,080

Compounding to Determine Future Values Compounding: Arithmetic process whereby an initial value increases at a compound interest rate over time to reach a value in the future Compound Interest: Earning interest on interest in addition to interest on the principal or initial investment

Compounding to Determine Future Values: An Example Basic Information: You plan to invest $1,000 now for two years and a bank will pay you compound interest of 8% per year. What will be the value after two years? Basic Equation for discounting back 2 years: Future value = Present value x [(1 + Interest rate) x (1 + Interest rate)] Future value = $1,000 x (1.08 x 1.08) = $1,000 x 1.1664 = $1,166.40

Discounting to Determine Present Values Discounting: An arithmetic process whereby a future value decreases at a compound interest rate over time to reach a present value Basic Equation: Present value = Future value x {[1/(1 + Interest rate)] x [1/(1 + Interest rate)]}

Discounting to Determine Present Values: An Example Basic Information: A bank agrees to pay you $1,000 after two years when interest rates are compounding at 8% per year. What is the present value of this payment? Basic Equation: Present value = Future value x {[1/(1+ Interest rate)] x [1/(1 + Interest rate)]} Present value = $1,000 x (1/1.08 x 1/1.08) = $1,000 x 0.8573 = $857.30

Formula Four Basic Variables: FV = future value PV = present value r = interest rate n = number of periods Key Concept: Knowing the values for any three of these variables allows solving for the fourth or unknown variable

Compounding or Discounting More Often than Once a Year Basic Equation: FVn = PV(1 + r/m)nxm Where: m = number of compounding periods per year and the other variables are as previously defined Example: What is the future value of a two-year, $1,000, 8% interest loan with semiannual compounding? FVn = $1,000( 1 + 0.08/2)2x2 = $1,000(1.04)4 = $1,000(1.1699) = $1,169.90

Effective Annual Rate (APR) Effective Annual Rate (APR): true interest rate when compounding occurs more frequently than annually EAR Equation: EAR = (1 + r)m - 1 Example: What is the EAR on a credit card loan charges 18% annually with monthly payments? Rate per month = 18%/12 = 1.5% EAR = (1 + 0.015)12 - 1 = 1.1956 - 1 = 19.56%

Bibliography Hiller, D., Clacher, I., Ross, S., Westerfield, R. and Jordan, B. (2011) Fundamentals of Corporate Finance European Edition, 1st edition, McGraw-Hill Education 2011. Hickman, K., Hunter, H. & Byrd, J. W. Foundations of Corporate Finance, West Publishing Company, 1996. Pike, R. , Neale, B. and Linsley, P. (2012) Corporate Finance and Investment, 7th edition, Pearson Education Limited. Pike, R. and Neale, B. (2008) Corporate Finance and Investment, 6th edition, FT Prentice Hall. [Ebook is available]