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## The 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