The Time Value of MoneyThe Time Value of Money

Mike Shaffer

April 15th, 2005

FIN 191

Learning ObjectivesLearning 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.

• 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 MoneyTime 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.

• 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 InterestInterest 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.

• 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 EquationFuture Value Equation

• FVn = PV(1 + i)nFV = the future value of the investment

at the end of n yeari = the annual interest (or discount)

ratePV = 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.

• FVn = PV(1 + i)nFV = the future value of the investment

at the end of n yeari = the annual interest (or discount)

ratePV = 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 PeriodCompounding Period

• Definition -- the frequency that interest is applied to the investment .

• Examples -- daily, monthly, or annually.

• Definition -- the frequency that interest is applied to the investment .

• Examples -- daily, monthly, or annually.

Reinvesting -- How to EarnInterest on InterestReinvesting -- 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.

• 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 PeriodsCompound 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.

• 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)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

• 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 CalculatorTime Value With a Financial Calculator

• The TI BAII Plus financial calculator keysN = stores the total number of

paymentsI/Y = stores the interest or

discount ratePV = stores the present valuePMT = stores the dollar amount

of each annuity paymentFV = stores the future valueCPT = is the compute key

• The TI BAII Plus financial calculator keysN = stores the total number of

paymentsI/Y = stores the interest or

discount ratePV = stores the present valuePMT = stores the dollar amount

of each annuity paymentFV = stores the future valueCPT = 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.

• 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.

• REMEMBER -- The tables have a discrepancy due to rounding error; therefore, the calculator is more accurate.

Compounding and the Power of TimeCompounding 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.

• 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 YearsThe Power of Time inCompounding Over 35 Years

$0

$50,000

$100,000

$150,000

$200,000

Selma Patty

$0

$50,000

$100,000

$150,000

$200,000

Selma Patty

• 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.

• 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

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%.

• From 1926-1998 the compound growth rate of stocks was approximately 11.2%, whereas long-term corporate bonds only returned 5.8%.

Present ValuePresent 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.

• 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 EquationPresent 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.

• 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 EquationPresent Value of an Annuity Equation

• PVn = PMT (PVIFAi,n)PVn = the present value, in today’s

dollars, of a future sum of moneyPMT = the payment to be made at

the end of each time periodPVIFAi,n = the present-value

interest factor for an annuity

• PVn = PMT (PVIFAi,n)PVn = the present value, in today’s

dollars, of a future sum of moneyPMT = the payment to be made at

the end of each time periodPVIFAi,n = the present-value

interest factor for an annuity

Present Value of anAnnuity 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.

• 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?

1) PV = PMT (PVIFA i,n)

2) PV = $50,000 (PVIFA 5%, 25)

3) PV = $50,000 (14.094)

4) PV = $704,700

• 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?

1) PV = PMT (PVIFA i,n)

2) PV = $50,000 (PVIFA 5%, 25)

3) PV = $50,000 (14.094)

4) PV = $704,700

Amortized LoansAmortized 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

• 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

SummarySummary

• 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.

• 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

• 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