, Summary of Discrete Compounding Formulas with Discrete Payments
- - = -
Factor Excel Cash Flow -
Flow Type Notation Formula Command Diagram i
S Compound
I amount = FV(i,N . P . , 0 )
N (F/e i, N )
G Present
i L worth = PV(i, N , F , -0)
E (PIE i, N
E Compound
: Q amount
= u i, N ) = P V ( i , N , A , . 0)
- A
L
Sinking
P fund
A ( M E i. N )
Y
i M AAA AA /
r E
5
I N Present i.
+ illv - 1 I
f
i;
i
T
s
worth
(P/A,i, N )
= .[(I
i ( 1 + i)" I
D E
$ R Capital
i I recovery A = P[
E ( M e i, N ) (1 + ilN - 1
r S
Linear
gradient
"
"r
8
I
Present
worth
+ i)" - iN - 1
I E (P/G,i, N)
Conversion fact01
j T (AIG,i, Rr)
S Geometric
E gradient
R
I Present
E worth
s ,,
(PIA g, i, N )
--.----
, Summary of Formulas
Effective Interest Rate per Payment Period
Discrete compounding i = [ ( I + ~ / ( c K ) ] '- 1
Continuous compounding i erlK - 1 - Recovery Period (Year
where i -effective interest rate per payment period
r =nominal interest rate or APR
C = number of interest periods per payment
period
K = number of payment periods per year
r / K = nominal interest rate per payment period
Market Interest Rate
i - i' + f + i'f
where i = market interest rate
if = inflation-free interest rate
-
,f = general inflation rate
Present Value of Perpetuities
p = market related risk index
r, = market rate of return
Capital Recovery with Return Cost of Debt
CR(i) = ( I - S ) ( A / P ,i, N ) + iS
Book Value
= I - x
11
1'1
D, where id
c,
=
-
cost of debt
the amount of term loan
Straight-Line Depreciation c,, = the amount of bond financing
-
(I - S)
D,? -
N
c,, = total debt = c, t c,,
k, = the before-tax interest rate on the term loan
kh = the before-tax interest rate on the bond
Declining Balance Depreciation
D,, - aI(1 - a)"-'
t,,, = the firm's marginal
-
Weighted-Average Cost of Capital
tax rate
1
where a = declining balance rate. and 0 < a 5
N
Cost of Equity
where k = cost of capital
where i, = cost of equity c,, = total equity capital
rf = risk-free interest rate V = Cd + C,
, Library of Congress Cataloging-in-Publication Data on File
Vice President and Editorial Director, ECS: Marcia J. Horton
Acquisitions Editor: Dorothy Marrero
Vice President and Director of Production and Manufacturing. ESM: David W Riccardi
Executive Managing Editor: Vince O'Brien
Managing Editor: David A. George
Production Editor: Scotr Disanno
Director of Creative Services: Paul Eelfanti
Creative Director: Carole Anson
Art Director and Cover Manager: Maureen Eide
Managing Editor,AV Management and Production: Patricia Bltrns
Art Editor: Xiaohorlg Zhu
Manufacturing Manager: Trudy Pisciotti
Manufacturing Buyer: Lisa McDowell
Marketing Manager: Holly Stark
O 2004 by Pearson Education, Inc.
Upper Saddle River. New Jersey 07458
All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher.
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development. research. and
testing of the theories and programs to determine their effectiveness.The author and publisher make no warranty of any kind. expressed or implied.
with regard to these programs or the documentation contained in this book.The author and publisher shall not be liable in any event for incidental
or consequential damages in connection with, or arising out of. the furnishing, performance. or use of these programs.
Excel is a registered trademark of the Microsoft Coporation. One Microsoft Way. Redmond WA 98052-6399.
ISBN 0-13-030791-2
Pearson Education Ltd., London
Pearson Education Australia Pty. Ltd. Sydney
Pearson Education Singapore, Pte. Ltd.
Pearson Education North Asia Ltd.. Hong Kong
Pearson Education Canada, Inc., Toronto
Pearson Education de Mexico, S.A. de C.V.
Pearson Education-Japan. Tokyo
Pearson Education Malaysia, Pte. Ltd.
Pearson Education, Inc., Upper Saddle River, New Jersey
- - = -
Factor Excel Cash Flow -
Flow Type Notation Formula Command Diagram i
S Compound
I amount = FV(i,N . P . , 0 )
N (F/e i, N )
G Present
i L worth = PV(i, N , F , -0)
E (PIE i, N
E Compound
: Q amount
= u i, N ) = P V ( i , N , A , . 0)
- A
L
Sinking
P fund
A ( M E i. N )
Y
i M AAA AA /
r E
5
I N Present i.
+ illv - 1 I
f
i;
i
T
s
worth
(P/A,i, N )
= .[(I
i ( 1 + i)" I
D E
$ R Capital
i I recovery A = P[
E ( M e i, N ) (1 + ilN - 1
r S
Linear
gradient
"
"r
8
I
Present
worth
+ i)" - iN - 1
I E (P/G,i, N)
Conversion fact01
j T (AIG,i, Rr)
S Geometric
E gradient
R
I Present
E worth
s ,,
(PIA g, i, N )
--.----
, Summary of Formulas
Effective Interest Rate per Payment Period
Discrete compounding i = [ ( I + ~ / ( c K ) ] '- 1
Continuous compounding i erlK - 1 - Recovery Period (Year
where i -effective interest rate per payment period
r =nominal interest rate or APR
C = number of interest periods per payment
period
K = number of payment periods per year
r / K = nominal interest rate per payment period
Market Interest Rate
i - i' + f + i'f
where i = market interest rate
if = inflation-free interest rate
-
,f = general inflation rate
Present Value of Perpetuities
p = market related risk index
r, = market rate of return
Capital Recovery with Return Cost of Debt
CR(i) = ( I - S ) ( A / P ,i, N ) + iS
Book Value
= I - x
11
1'1
D, where id
c,
=
-
cost of debt
the amount of term loan
Straight-Line Depreciation c,, = the amount of bond financing
-
(I - S)
D,? -
N
c,, = total debt = c, t c,,
k, = the before-tax interest rate on the term loan
kh = the before-tax interest rate on the bond
Declining Balance Depreciation
D,, - aI(1 - a)"-'
t,,, = the firm's marginal
-
Weighted-Average Cost of Capital
tax rate
1
where a = declining balance rate. and 0 < a 5
N
Cost of Equity
where k = cost of capital
where i, = cost of equity c,, = total equity capital
rf = risk-free interest rate V = Cd + C,
, Library of Congress Cataloging-in-Publication Data on File
Vice President and Editorial Director, ECS: Marcia J. Horton
Acquisitions Editor: Dorothy Marrero
Vice President and Director of Production and Manufacturing. ESM: David W Riccardi
Executive Managing Editor: Vince O'Brien
Managing Editor: David A. George
Production Editor: Scotr Disanno
Director of Creative Services: Paul Eelfanti
Creative Director: Carole Anson
Art Director and Cover Manager: Maureen Eide
Managing Editor,AV Management and Production: Patricia Bltrns
Art Editor: Xiaohorlg Zhu
Manufacturing Manager: Trudy Pisciotti
Manufacturing Buyer: Lisa McDowell
Marketing Manager: Holly Stark
O 2004 by Pearson Education, Inc.
Upper Saddle River. New Jersey 07458
All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher.
The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development. research. and
testing of the theories and programs to determine their effectiveness.The author and publisher make no warranty of any kind. expressed or implied.
with regard to these programs or the documentation contained in this book.The author and publisher shall not be liable in any event for incidental
or consequential damages in connection with, or arising out of. the furnishing, performance. or use of these programs.
Excel is a registered trademark of the Microsoft Coporation. One Microsoft Way. Redmond WA 98052-6399.
ISBN 0-13-030791-2
Pearson Education Ltd., London
Pearson Education Australia Pty. Ltd. Sydney
Pearson Education Singapore, Pte. Ltd.
Pearson Education North Asia Ltd.. Hong Kong
Pearson Education Canada, Inc., Toronto
Pearson Education de Mexico, S.A. de C.V.
Pearson Education-Japan. Tokyo
Pearson Education Malaysia, Pte. Ltd.
Pearson Education, Inc., Upper Saddle River, New Jersey
