The Time Value of Money

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The Time Value of Money Mike Shaffer April 15 th , 2005 FIN 191 Learning Objectives Understand the concept of the time value of money. Be able to determine the time value of money: Present Value. Future Value. Present Value of an Annuity. Future Value of an Annuity. Time Value of Money

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### The Time Value of Money

Mike Shaffer

April 15th, 2005

FIN 191

Learning Objectives
• Understand the concept of the time value of money.
• Be able to determine the time value of money:
• Present Value.
• Future Value.
• Present Value of an Annuity.
• Future Value of an Annuity.
Time Value of Money
• A dollar received today is worth more than a dollar received in the future.
• The sooner your money can earn interest, the faster the interest can earn more interest.
Interest and Compound Interest
• Interest -- is the return you receive for investing your money.
• Compound interest -- is the interest that your investment earns on the interest that your investment previously earned.
Future Value Equation
• FVn = PV(1 + i)n
• FV = the future value of the investment at the end of n year
• i = the annual interest (or discount) rate
• PV = the present value, in today’s dollars, of a sum of money
• This equation is used to determine the value of an investment at some point in the future.
Compounding Period
• Definition -- the frequency that interest is applied to the investment .
• Examples -- daily, monthly, or annually.
Reinvesting -- How to EarnInterest on Interest
• Future-value interest factor (FVIFi,n) is a value used as a multiplier to calculate an amount’s future value, and substitutes for the (1 + i)n part of the equation.
Compound Interest WithNon-annual Periods
• The length of the compounding period and the effective annual interest rate are inversely related;
• therefore, the shorter the compounding period, the quicker the investment grows.
Compound Interest WithNon-annual Periods (cont’d)
• Effective annual interest rate =

amount of annual interest earned

amount of money invested

• Examples -- daily, weekly, monthly, and semi-annually
Time Value With a Financial Calculator
• The TI BAII Plus financial calculator keys
• N = stores the total number of payments
• I/Y = stores the interest or discount rate
• PV = stores the present value
• PMT = stores the dollar amount of each annuity payment
• FV = stores the future value
• CPT = is the compute key
Time Value With a Financial Calculator (cont’d)
• Step 1 -- input the values of the known variables.
• Step 2 -- calculate the value of the remaining unknown variable.
• Note: be sure to set your calculator to “end of year” and “one payment per year” modes unless otherwise directed.
• Be sure the number or periods is correct.
Tables Vs. Calculator
• REMEMBER -- The tables have a discrepancy due to rounding error; therefore, the calculator is more accurate.
Compounding and the Power of Time
• In the long run, money saved now is much more valuable than money saved later.
• Don’t ignore the bottom line, but also consider the average annual return.
The Power of Time inCompounding Over 35 Years
• Selma contributed \$2,000 per year in years 1 – 10, or 10 years.
• Patty contributed \$2,000 per year in years 11 – 35, or 25 years.
• Both earned 8% average annual return.
The Importance of theInterest Rate in Compounding
• From 1926-1998 the compound growth rate of stocks was approximately 11.2%, whereas long-term corporate bonds only returned 5.8%.
Present Value
• Is also know as the discount rate, or the interest rate used to bring future dollars back to the present.
• Present-value interest factor (PVIFi,n) is a value used to calculate the present value of a given amount.
Present Value Equation
• PV = FVn (PVIFi,n)
• PV = the present value of a sum of payments
• FVn = the future value of the investment at the end of n years
• PVIFi,n = the present value interest factor
• This equation is used to determine today’s value of some future sum of money.
Present Value of an Annuity Equation
• PVn = PMT (PVIFAi,n)
• PVn = the present value, in today’s dollars, of a future sum of money
• PMT = the payment to be made at the end of each time period
• PVIFAi,n = the present-value interest factor for an annuity
Present Value of anAnnuity Equation (cont’d)
• This equation is used to determine the present value of a future stream of payments, such as your pension fund or insurance benefits.
Calculating Present Value of an Annuity: Now or Wait?
• What is the present value of the 25 annual payments of \$50,000 offered to the soon-to-be ex-wife, assuming a 5% discount rate?
• PV = PMT (PVIFA i,n)
• PV = \$50,000 (PVIFA 5%, 25)
• PV = \$50,000 (14.094)
• PV = \$704,700
Amortized Loans
• Definition -- loans that are repaid in equal periodic installments
• With an amortized loan, the interest payment declines as your outstanding principal declines; therefore, with each payment you will be paying an increasing amount towards the principal of the loan.
• Examples -- car loans or home mortgages
Summary
• Future value – the value, in the future, of a current investment.
• Present value – today’s value of an investment received in the future.
• Annuity– a periodic series of equal payments for a specific length of time.
Summary (cont’d)
• Future value of an annuity – the value, in the future, of a current stream of investments.
• Present value of an annuity – today’s value of a stream of investments received in the future.
• Amortized loans – loans paid in equal periodic installments for a specific length of time