Chapter 4 time value of money

PowerPoint

to accompany

Chapter 4
Time Value Of
Money


Learning Goals:
•

Discuss the role of time value in finance and the basic
patterns of cash flows.

•

Understand present and future value.

•

Describe annuities, and perpetuities.

•

Find future/present values of a stream of cash flows.

•

Understand the effect of frequently compounding
interest.

ã

Determine amortisation parameters.
Copyright â 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


The Role Of Time Value
•

The “time value of money” principle says that all
things being equal, a dollar today is worth more
than a dollar that will be received at some future
date.



Financial values and decisions can be assessed
by considering:
 Future Value
 Present Value

Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


The Role Of Time Value
•

Future cash flows are best depicted through the
use of a timeline:
Cash Flows On
Top

Time On Bottom

Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Compounding & Discounting

Page 147.
Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Useful Calculation Tools


Formulas Formula Sheet.pdf



Financial Tables – Appendix AFinancial
Tables.pdf



Electronic SpreadsheetsAnnuity.xls



Financial Calculators

Page 147.
Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Financial TablesFinancial
Tables.pdf

Page 148.

Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Basic Cash Flow Patterns


Single Amount: One lump sum.



Annuity: Series of cash flows of equal amount,
received at equal time intervals.



Mixed Stream: Series of cash flows that are not
equal or a series of cash flows that are not
received at equal time intervals.

Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Future Value Of A Single
Amount


Future Value: the value of a present amount at a
future date (Go to excel sheet) .



Calculated by applying compound interest over a
specified period of time.



FVn = PV x (1 + i)n [Equation 4.4]
Where:
 FVn = Future value at the end of period n




PV = Present value
i = Annual interest rate
n = Number of periods
Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Future Value Of A Single
Amount


Future Value Interest Factor (FVIF): the multiplier
used to calculate FV at a given discount rate.

•

Written as FVIFi,n

•

FVIFi,n = (1 + i)n [Equation 4.5] Financial
Tables.pdf

•

FVn = PV x FVIFi,n [Equation 4.6]
Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition

Future Value Of A Single
Amount


Example: Jane Farber places $800 in a savings
account paying 6% interest compounded annually.
She wants to know how much money will be in the
account at the end of five years. Formula Sheet.pdf



Formula:
FVn = PV x (1 + i)n
= 800 x (1 + 0.06) 5
= $1,070.58

Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Future Value Of A Single
Amount


Financial Calculator:
i = 6, PV = -800, n = 5
FVn = $1,070.58



Financial Tables: (Using Appendix A-1)
FVn = PV x FVIFi,n
FVn = 800 x 1.338
FVn = $1,070.40
Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Future Value Relationship

Page 153.
Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Present Value Of A Single
Amount


Present Value: the current value of a future amount.



Calculated by discounting cash flows over a
specified period of time.

Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition

Present Value Of A Single
Amount


Present Value Interest Factor (FVIF): the multiplier
used to calculate PV at a given discount rate.

•

Written as PVIFi,nFinancial Tables.pdf

Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Present Value Of A Single
Amount


Example: Pam Valentine wishes to find the
present value of $1,700 that will be received eight
years from now. Pam’s opportunity cost is 8%.



Formula:
PV =

FVn

(1 + i)n
=
1,700
(1 + 0.08) 8
= $918.46

Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Present Value Of A Single
Amount


Financial Calculator:
i = 8, FV = 1,700 , n = 8
PV = $918.46



Financial Tables: (Using Appendix A-3)Financial
Tables.pdf
PV = FVn x PVIFi, n
PV = 1,700 x 0.540
PV = $918.00
Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition

Present Value Relationship

Page 156.
Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Annuities


Annuity: a stream of equal periodic cash flows
over a specified time period.



Two types:
1.

2.



Ordinary Annuity: Cash flow occurs at the end
of each period.
Annuity Due: Cash flow occurs at the
beginning of each period.

Unless otherwise stated, in finance the term
annuity refers to ordinary annuities.
Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –

9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Future Value Of An Ordinary
Annuity


Calculated by summing the future value of all future
cash flows



FVIFAi,n = (1 + i)t–1 [Equation 4.13]Financial Tables.pdf



FVAn = PMT x FVIFAi,n

[Equation 4.14]

Where:
FVAn = Future value of an annuity at the end of
period n
FVIFAi,n = Future value interest factor - annuity
Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition






Present Value Of An Ordinary
Annuity

Calculated by summing the present value of all future
cash flows.Financial Tables.pdf

PVAn = PMT x PVIFAi.n [Equation 4.16]
Where:
PVAn = Present value of an annuity at the end of
period n.
PVIFAi,n = Present value interest factor – annuity.

Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Future Value Of An Annuity
Due


Earns interest for a year more than an ordinary
annuity, as the cash flows occur at the start of the
period.

[Equation 4.17]

Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition

Present Value Of An Annuity
Due


As the first annuity occurs at the beginning of the first
period, the annuity must be discounted back one
less year than for an ordinary annuity.

[Equation 4.18]

Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Perpetuities


An ordinary annuity with an infinite life.



PVIFA i, ∞ = 1
i



[Equation 4.19]

PVA ∞ = PMT x PVIFAi, ∞yrs
Where:
∞ = infinite number of periods

Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition


Mixed Streams


A series of unequal periodic cash flows with no
particular pattern.



Future Value Of A Mixed Stream: Calculated by
adding together the future values of each cash
flow at the specified future dates.



Present Value Of A Mixed Stream: Calculated by
adding together the present values of each future
cash flow.

Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –
9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition