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. 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. 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. 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. 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. Definition -- the frequency that interest is applied to the investment. Examples -- daily, monthly, or annually.

Reinvesting -- How to Earn Interest 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 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 With Non-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 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 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. 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. 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 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 the Interest Rate in Compounding From 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. 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. 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 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) 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? 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 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

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. 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 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