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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

The Time Value of Money

Mike Shaffer

April 15th, 2005

FIN 191

learning objectives
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
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 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
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
Compounding Period
  • Definition -- the frequency that interest is applied to the investment .
  • Examples -- daily, monthly, or annually.
reinvesting how to earn interest on interest
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 with non annual periods
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 with non annual periods cont d
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
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
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
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
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 in compounding over 35 years
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 the interest rate in compounding
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
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
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
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 an annuity equation cont d
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
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
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
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
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