Learning Objectives. Learning Objectives. Learning Objectives. Principles Used in this Chapter. Simple Interest. Principle 2:

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1 Learning Objectives Chapter 5 The Time Value of Money Explain the mechanics of compounding, which is how money grows over a time when it is invested. Be able to move money through time using time value of money tables, financial calculators, and spreadsheets. Discuss the relationship between compounding and bringing money back to present. Learning Objectives Define an ordinary annuity and calculate its compound or future value. Differentiate between an ordinary annuity and an annuity due and determine the future and present value of an annuity due. Determine the future or present value of a sum when there are non-annual compounding periods. Learning Objectives Determine the present value of an uneven stream of payments Determine the present value of a perpetuity. Explain how the international setting complicates the time value of money. Principle 2: Principles Used in this Chapter The Time Value of Money A Dollar Received Today Is Worth More Than a Dollar Received in The Future. Simple Interest Interest is earned on principal. $1 invested at 6% per year 1 st year interest is $6. 2 nd year interest is $6. 3 rd year interest is $6. Total interest earned: $18. 1

2 Compound Interest When interest paid on an investment during the first period is added to the principal; then, during the second period, interest is earned on the new sum. Compound Interest Interest is earned on previously earned interest $1 invested at 6% with annual compounding 1 st year interest is $6. Principal is $16. 2 nd year interest is $6.36 Principal is $ rd year interest is $6.74 Principal is $ Total interest earned: $ The amount a sum will grow in a certain number of years when compounded at a specific rate. 1 = (1 + i) Where 1 = the future of the investment at the end of one year i= the annual interest (or discount) rate = the present value, or original amount invested at the beginning of the first year What will an investment be worth in 2 years? $1 invested at 6% 2 = (1+i) 2 = $1 (1+.6) 2 = $1 (1.6) 2 = $ can be increased by: Increasing number of years of compounding Increasing the interest or discount rate 2

3 What is the future value of $5 invested at 8% for 7 years? (Assume annual compounding) n = (1+i) 7 = $857 Using Calculators Using any four inputs you will find the 5th. Set to P/YR = 1 and ED mode. IPUTS 1 I/YR Using Spreadsheets???? Present Value The current value of a future payment = n {1/(1+i) n } Where n = the future of the investment at the end of n years n= number of years until payment is received i= the interest rate = the present value of the future sum of money Present Value What will be the present value of $5 to be received 1 years from today if the discount rate is 6%? = $5 {1/(1+.6) 1 } = $5 (1/1.791) = $5 (.558) = $279 Present Value Using Calculators Using any four inputs you will find the 5th. Set to P/YR = 1 and ED mode. IPUTS I/YR

4 Annuity Compound Annuity Series of equal dollar payments for a specified number of years. Ordinary annuity payments occur at the end of each period Depositing or investing an equal sum of money at the end of each year for a certain number of years and allowing it to grow. Compound Annuity 5 = $5 (1+.6) 4 + $5 (1+.6) 3 +$5(1+.6) 2 + $5 (1+.6) + $5 = $5 (1.262) + $5 (1.191) + $5 (1.124) + $5 (1.9) + $5 Illustration of a 5yr $5 Annuity Compounded at 6% 6% = $ $ $ $53. + $5 = $2,818.5 of an Annuity Using Calculators Using any four inputs you will find the 5th. Set to P/YR = 1 and ED mode. IPUTS I/YR , Present Value of an Annuity Pensions, insurance obligations, and interest received from bonds are all annuities. These items all have a present value. Calculate the present value of an annuity using the present value of annuity table. 4

5 Annuities Due Amortized Loans Ordinary annuities in which all payments have been shifted forward by one time period. Loans paid off in equal installments over time Typically Home Mortgages Auto Loans Payments and Annuities If you want to finance a new machinery with a purchase price of $6, at an interest rate of 15% over 4 years, what will your payments be? Using Calculators Using any four inputs you will find the 5th. Set to P/YR = 1 and ED mode. IPUTS I/YR 4 6, 15-2,11.59 Amortization of a Loan Amortization Schedule Reducing the balance of a loan via annuity payments is called amortizing. Yr. 1 Annuity $2,11.58 Interest $9. Principal $1,21.58 Balance $4, A typical amortization schedule looks at payment, interest, principal payment and balance. 2 3 $2,11.58 $2, , , , , $2, ,

6 Compounding Interest with on-annual periods If using the tables, divide the percentage by the number of compounding periods in a year, and multiply the time periods by the number of compounding periods in a year. Example: 8% a year, with semiannual compounding for 5 years. Input 8% / 2 = 4% as interest Input = 5*2 = 1 as number of periods Perpetuity An annuity that continues forever is called perpetuity The present value of a perpetuity is = PP/i = present value of the perpetuity PP = constant dollar amount provided by the of perpetuity i = annuity interest (or discount rate) The Multinational Firm Principle 1 The Risk Return Tradeoff We Won t Take on Additional Risk Unless We Expect to Be Compensated with Additional Return The discount rate is reflected in the rate of inflation. Inflation rate outside US difficult to predict Inflation rate in Argentina in 1989 was 4,924%, in 199 dropped to 1,344%, and in 1991 it was only 84%. 6