TIME VALUE OF MONEY

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Financial Management

by ZgMark1 |

CHAPTER 2

TIME VALUE OF MONEY

OVERVIEW

A dollar in the hand today is worth more than a dollar to be received in the future because, if you had it

now, you could invest that dollar and earn interest. Of all the techniques used in finance, none is more

important than the concept of time value of money, also called discounted cash flow (DCF) analysis.

Future value and present value techniques can be applied to a single cash flow (lump sum), ordinary

annuities, annuities due, and uneven cash flow streams. Future and present values can be calculated

using, a regular calculator, a calculator with financial functions, or a spreadsheet program. When

compounding occurs more frequently than once a year, the effective rate of interest is greater than the

quoted rate.

OUTLINE

Time lines are used to help visualize what is happening in time value of money problems. Cash flows are

placed directly below the tick marks, and interest rates are shown directly above the time line; unknown

cash flows are indicated by a symbol for the particular item that is missing. Thus, to find the future value

of $100 after 5 years at 5 percent interest, the following time line can be set up:

Time:05%12345

||||||

Cash flows:-100FV5 = ?

Finding the future value (FV), or compounding, is the process of going from today's values (or present

values) to future amounts (or future values). It can be calculated as

FVn = PV(1 + i)n = PV(FVIFi,n),

where PV = present value, or beginning amount; i = interest rate per year; and n = number of periods

involved in the analysis. FVIFi,n, the Future Value Interest Factor, is a short-hand way of writing the

equation. This equation can be solved in one of three ways: numerically with a regular calculator, with a

financial calculator, or with a spreadsheet program. For calculations, assume the following data that were

presented in the time line above: present value (PV) = $100, interest rate (i) = 5%, and number of years

(n) = 5.

â– To solve numerically, use a regular calculator to find 1 + i = 1.05 raised to the fifth power, which

equals 1.2763. Multiply this figure by PV = $100 to get the final answer of [pic].

â– With a financial calculator, the future value can be found by using the time value of money input

keys, where N = number of periods, I = interest rate per period, PV = present value, PMT = payment,

and FV = future value. By entering N = 5, I = 5, PV = -100, and PMT = 0, and then pressing the FV key,

the answer 127.63 is displayed. â ﾝ‘ Some financial calculators require that all cash flows be designated

as either inflows or outflows, thus an outflow must be entered as a negative number (for example, PV =

-100 instead of PV = 100).

â ﾝ‘ Some calculators require you to press a “Compute” key before pressing the FV key.

â– Spreadsheet programs are ideally suited for solving time value of money problems. The spreadsheet

itself becomes a time line.

| |A |B |C |D |E |F |G | |2 |Time |0 |1 |2 |3 |4 |5 | |3 |Cash flow |-100 | | | | | | |4 |Future value | |105.00 |

110.25 |115.76 |121.55 |127.63 |

â ﾝ‘ Row 4 contains the spreadsheet formula for future value. â ﾝ‘ The Excel formula in Cell G4 is written

as =-$B$3*(1+$B$1)^G2. This gives us flexibility to change the interest rate in Cell B1 to see how the

future value changes with changes in interest rates. â ﾝ‘ An alternative Excel formula in Cell G4 could

have been entered. This is the FV function, and it is =FV(5%,5,0,-100,1). The first argument of this

formula is the interest rate, the second the number of periods, the third the annual payments, the fourth

is the present value, and the fifth indicates that payments are all made at the end rather than the

beginning of each year.

â– Note that small rounding differences will often occur among the various solution methods.

â– In general, you should use the easiest approach.

â– A graph of the compounding process shows how any sum grows over time at various interest rates.

The greater the interest rate, the faster the growth rate.

Finding present values is called discounting, and it is simply the reverse of compounding. In general, the

present value of a cash flow due n years in the future is the amount which, if it were on hand today,

would grow to equal the future amount. By solving for PV in the future value equation, the present value,

or discounting, equation can be developed and written in several forms:

[pic]

â– PVIFi,n, the Present Value Interest Factor, is a short-hand way of writing the equation. â– To solve

for the present value of $127.63 discounted back 5 years at a 5% opportunity cost rate, one can utilize

any of the four solution methods: â ﾝ‘ Numerical solution: Divide $127.63 by 1.05 five times to get PV =

$100. â ﾝ‘ Financial calculator solution: Enter N = 5, I = 5, PMT = 0, and FV = 127.63, and then press

the PV key to get PV = -100. â ﾝ‘ Spreadsheet solution:

| |A |B |C |D |E |F |G | |2 |Time |0 |1 |2 |3 |4 |5 | |3 |Cash flow | |0 |0 |0 |0 |127.63 | |4 |Present value |100 | |

| | | |

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Financial Management by ZgMark1 | CHAPTER 2 TIME VALUE OF MONEY OVERVIEW A dollar in the hand today is worth more than a dollar to be received in the future because, if you had it now, you could invest that dollar and earn interest. Of all the techniques used in finance, none is more important than the concept of time value of money, also called discounted cash flow (DCF) analysis. Future value and present value techniques can be applied to a single cash flow (lump sum), ordinary annuities, annuities due, and uneven cash flow streams. Future and present values can be calculated using, a regular calculator, a calculator with financial functions, or a spreadsheet program. When compounding occurs more frequently than once a year, the effective rate of interest is greater than the quoted rate. OUTLINE Time lines are used to help visualize what is happening in time value of money problems. Cash flows are placed directly below the tick marks, and interest rates are shown directly above the time line; unknown cash flows are indicated by a symbol for the particular item that is missing. Thus, to find the future value of $100 after 5 years at 5 percent interest, the following time line can be set up: Time:05%12345 |||||| Cash flows:-100FV5 = ? Finding the future value (FV), or compounding, is the process of going from today's values (or present values) to future amounts (or future values). It can be calculated as FVn = PV(1 + i)n = PV(FVIFi,n), where PV = present value, or be ...
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