The time value of money
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The Time Value of Money. 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. Future Value.

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The Time Value of Money

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The time value of money

The Time Value of Money

Richard MacMinn


Objectives

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

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 value1

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 value2

Future Value

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

Richard MacMinn


Future value3

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

Present Value

  • A dollar today is worth more than a dollar tomorrow!

  • Present value is the inverse of future value.

Richard MacMinn


Present value1

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 value2

Present Value

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

Richard MacMinn


Annuity

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


Annuity1

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

Perpetuity

  • A perpetuity is an annuity payable indefinitely.

  • The present value of an indefinitely long one dollar stream is

Richard MacMinn


Growing perpetuity

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

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

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

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


Links1

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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