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The Time Value of MoneyPowerPoint Presentation

The Time Value of Money

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### The Time Value of Money

Richard MacMinn

Objectives

- To stress that the time value of money is an integral part of financial decision making.
- To discuss compounding techniques
- To discuss discounting techniques

Richard MacMinn

Future Value

- Suppose you place $100 in a savings account that pays 7.2% interest, compounded annually. How does the account grow?
- fv1 = 100 (1.072)
- fv2 = 100 (1.072)2
- fvT = 100 (1.072)T

Richard MacMinn

Future Value

- The future value of a one dollar stream of savings for n years, i.e., one dollar saved at dates t = 1, 2, . . . , T, is

Richard MacMinn

Future Value

- If a dollar is compounded m times per period then the future value may be expressed as

Richard MacMinn

Future Value

- As m approaches infinity, the factor where e = 2.71828
- Given continuous compounding, the future value of a dollar n periods hence is

Richard MacMinn

Present Value

- A dollar today is worth more than a dollar tomorrow!
- Present value is the inverse of future value.

Richard MacMinn

Present Value

- The present value of a dollar received in one year is
- The present value of a dollar received in T years is

Richard MacMinn

Present Value

- The present value of a stream of one dollar returns received at dates t = 1, 2, . . . , T is

Richard MacMinn

Annuity

- An annuity is a stream of equal dollar returns for a specified number of periods, e.g., pension funds, insurance contracts, sinking funds.
- The value of a T year annuity that pays one dollar per year is

Richard MacMinn

Annuity

- Loans paid off in equal installments over a fixed period are annuities, or equivalently, amortized loans.
- The value L of the of the amortized loan is

Richard MacMinn

Perpetuity

- A perpetuity is an annuity payable indefinitely.
- The present value of an indefinitely long one dollar stream is

Richard MacMinn

Growing Perpetuity

- A growing perpetuity is a perpetuity with a payment that grows at a constant rate g.
- The payment stream may be specified as 1, (1 + g), (1 + g)2, (1 + g)3, . . . , and its value as

Richard MacMinn

Annuity Again

- The present value of an annuity is
- This is the difference between a perpetuity that begins paying at t = 1 and one that begins paying at t = T + 1.

Richard MacMinn

Bond Value

- A bond that pays a level interest stream and then the principal at maturity is a combination of an annuity and a single payment.
- Bonds also typically pay interest semiannually and the bond value B is

Richard MacMinn

Links

- QUICKEN FINANCIAL PLANNER Extensive planning software http://www.quicken.com/
- RETIRE SECUREPrice Waterhouse Cooper's retirement aidhttp://www.pwcglobal.com/
- S&P PERSONAL WEALTH Standard & Poor's asset allocation modelhttp://www.personalwealth.com/

Richard MacMinn

Links

- T. ROWE PRICE Good, simple ''what if'' program http://www.troweprice.com
- VANGUARD Solid online retirement planning http://www.vanguard.com

Richard MacMinn

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