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TRANSCRIPT
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ACCA Paper P4
Advanced Financial Management
Class Notes
June 2013
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2 www.studyinteract ive.org
Original version prepared by Ken Preece.
Interactive World Wide Ltd. January 2013.
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system, or transmitted, in any form or by any means, electronic,
mechanical, photocopying, recording or otherwise, without the prior written
permission of Interactive World Wide Ltd.
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Contents PAGE
INTRODUCTION TO THE PAPER 5
FORMULAE & TABLES PROVIDED IN THE EXAMINATION PAPER 7
CHAPTER 1: ISSUES IN CORPORATE GOVERNANCE 13
CHAPTER 2: ADVANCED INVESTMENT APPRAISAL SECTION 1 25
CHAPTER 3: ADVANCED INVESTMENT APPRAISAL SECTION 2 51
CHAPTER 4: COST OF CAPITAL 69
CHAPTER 5: THEORIES OF GEARING 85
CHAPTER 6: CAPITAL ASSET PRICING MODEL 103
CHAPTER 7: ADJUSTED PRESENT VALUE 117
CHAPTER 8: INTERNATIONAL INVESTMENT APPRAISAL 129
CHAPTER 9: VALUATIONS, ACQUISITIONS AND MERGERS SECTION 1 145
CHAPTER 10: VALUATIONS, ACQUISITIONS AND MERGERS SECTION 2 169
CHAPTER 11: VALUATIONS, ACQUISITIONS AND MERGERS SECTION 3 179
CHAPTER 12: CORPORATE RECONSTRUCTION AND REORGANISATION 197
CHAPTER 13: CORPORATE DIVIDEND POLICY 211
CHAPTER 14: MANAGEMENT OF INTERNATIONAL TRADE AND FINANCE 221
CHAPTER 15: HEDGING FOREIGN EXCHANGE RISK 237
CHAPTER 16: HEDGING INTEREST RATE RISK 255
CHAPTER 17: FUTURES 269
CHAPTER 18: OPTIONS 283
CHAPTER 19: SWAPS 317
CHAPTER 20: PRINCIPLES OF ISLAMIC FINANCE 329
ACCA STUDY GUIDE 341
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Introduction to the
paper
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INTRODUCTION TO THE PAPER
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Aim of the paper
The aim of the paper is to apply relevant knowledge, skills and exercise
professional judgement as expected of a senior financial executive or advisor, in
taking or recommending decisions relating to the financial management of an
organisation.
Outline of the syllabus
A. Role and responsibility towards stakeholders
B. Economic environment for multinationals
C. Advanced investment appraisal
D. Acquisitions and mergers
E. Corporate reconstruction and re-organisation
F. Treasury and advanced risk management techniques
G. Emerging issues in finance and financial management
Format of the exam paper
The examination will be a three-hour paper (with the additional 15 minutes reading
and planning time) of 100 marks in total, divided into two sections:
Section A:
Section A will contain a compulsory question, comprising of 50 marks.
Section A will normally cover significant issues relevant to the senior financial
manager or advisor and will be set in the form of a case study or scenario. The
requirements of the section A question are such that candidates will be expected to
show a comprehensive understanding of issues from across the syllabus. The
question will contain a mix of computational and discursive elements. Within this
question candidates will be expected to provide answers in a specified form such as
a short report or board memorandum commensurate with the professional level of
the paper in part or whole of the question.
Section B:
In section B candidates will be asked to answer two from three questions,
comprising of 25 marks each.
Section B questions are designed to provide a more focused test of the syllabus.
Questions will normally contain a mix of computational and discursive elements, but
may also be wholly discursive or evaluative where computations are already
provided.
Candidates will be provided (within the examination paper) with a
formulae sheet as well as present value, annuity and standard normal
distribution tables.
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Formulae & tables
provided in the examination paper
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FORMULAE & TABLES PROVIDED IN THE EXAMINATION PAPER
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Formulae
Modigliani and Miller Proposition 2 (with tax)
ke = kie + (1 T)(k
ie kd)
e
d
V
V
The Capital Asset Pricing Model
E(rj) = Rf + j (E(rm) Rf)
The asset beta formula
a =
+
ede
e
))T-1(VV(
V +
+
dde
d
))T-1(VV(
)T-1(V
The Growth Model
P0 = g) - (r
g) + (1 D
e
0
Gordons growth approximation
g = bre
The weighted average cost of capital
WACC =
+ de
e
VV
V ke +
+ de
d
VV
V kd(1T)
The Fisher formula
(1 + i) = (1 + r) (1 + h)
Purchasing power parity and interest rate parity
S1 = S0 )h(1
)h(1
b
c
+
+ Fo = So
)i(1
)i(1
b
c
+
+
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FORMULAE & TABLES PROVIDED IN THE EXAMINATION PAPER
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Modified Internal Rate of Return
MIRR = n
1
I
R
PV
PV
(1 + re) 1
The Black Scholes Option
Pricing Model
c = Pa N(d1) Pe N(d2) e-rt
Where:
d1 = ts
)t0.5s +(r + )/Pln(P 2ea
and
d2 = d1 ts
The Put Call Parity relationship
p = c Pa + Pe e -rt
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FORMULAE & TABLES PROVIDED IN THE EXAMINATION PAPER
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Present value table
Present value of 1 ie (1 + r)-n
Where r = discount rate
n = number of periods until payment
Discount rate (r)
Periods
(n) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% ________________________________________________________________________________
1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 1 2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 2 3 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751 3 4 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683 4 5 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 5
6 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 6 7 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 7 8 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467 8 9 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 9 10 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386 10
11 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 11 12 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 12 13 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 13 14 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263 14 15 0.861 0.743 0.642 0.555 0.481 0.417 0.362 0.315 0.275 0.239 15 ________________________________________________________________________________
(n) 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% ________________________________________________________________________________
1 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 1 2 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694 2 3 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579 3 4 0.659 0.636 0.613 0.592 0.572 0.552 0.534 0.516 0.499 0.482 4 5 0.593 0.567 0.543 0.519 0.497 0.476 0.456 0.437 0.419 0.402 5
6 0.535 0.507 0.480 0.456 0.432 0.410 0.390 0.370 0.352 0.335 6 7 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279 7 8 0.434 0.404 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233 8 9 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225 0.209 0.194 9 10 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162 10
11 0.317 0.287 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135 11 12 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0.137 0.124 0.112 12 13 0.258 0.229 0.204 0.182 0.163 0.145 0.130 0.116 0.104 0.093 13 14 0.232 0.205 0.181 0.160 0.141 0.125 0.111 0.099 0.088 0.078 14 15 0.209 0.183 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065 15
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FORMULAE & TABLES PROVIDED IN THE EXAMINATION PAPER
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Annuity table
Present value of an annuity of 1 ie r
r) + (1 - 1 -n
Where r = discount rate
n = number of periods
Discount rate (r)
Periods
(n) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% ________________________________________________________________________________
1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 1 2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736 2 3 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487 3 4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 4 5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 5
6 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.355 6 7 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868 7 8 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335 8 9 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759 9 10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145 10
11 10.37 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495 11 12 11.26 10.58 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814 12 13 12.13 11.35 10.63 9.986 9.394 8.853 8.358 7.904 7.487 7.103 13 14 13.00 12.11 11.30 10.56 9.899 9.295 8.745 8.244 7.786 7.367 14 15 13.87 12.85 11.94 11.12 10.38 9.712 9.108 8.559 8.061 7.606 15 ________________________________________________________________________________
(n) 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% ________________________________________________________________________________
1 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 1 2 1.713 1.690 1.668 1.647 1.626 1.605 1.585 1.566 1.547 1.528 2 3 2.444 2.402 2.361 2.322 2.283 2.246 2.210 2.174 2.140 2.106 3 4 3.102 3.037 2.974 2.914 2.855 2.798 2.743 2.690 2.639 2.589 4 5 3.696 3.605 3.517 3.433 3.352 3.274 3.199 3.127 3.058 2.991 5
6 4.231 4.111 3.998 3.889 3.784 3.685 3.589 3.498 3.410 3.326 6 7 4.712 4.564 4.423 4.288 4.160 4.039 3.922 3.812 3.706 3.605 7 8 5.146 4.968 4.799 4.639 4.487 4.344 4.207 4.078 3.954 3.837 8 9 5.537 5.328 5.132 4.946 4.772 4.607 4.451 4.303 4.163 4.031 9 10 5.889 5.650 5.426 5.216 5.019 4.833 4.659 4.494 4.339 4.192 10
11 6.207 5.938 5.687 5.453 5.234 5.029 4.836 4.656 4.486 4.327 11 12 6.492 6.194 5.918 5.660 5.421 5.197 4.988 4.793 4.611 4.439 12 13 6.750 6.424 6.122 5.842 5.583 5.342 5.118 4.910 4.715 4.533 13 14 6.982 6.628 6.302 6.002 5.724 5.468 5.229 5.008 4.802 4.611 14 15 7.191 6.811 6.462 6.142 5.847 5.575 5.324 5.092 4.876 4.675 15
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FORMULAE & TABLES PROVIDED IN THE EXAMINATION PAPER
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Standard normal distribution table
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.1 0.2 0.3 0.4
0.5 0.6 0.7 0.8 0.9
1.0 1.1 1.2 1.3 1.4
1.5 1.6 1.7 1.8 1.9
2.0 2.1 2.2 2.3 2.4
2.5 2.6 2.7 2.8 2.9
3.0
0.0000 0.0398 0.0793 0.1179 0.1554
0.1915 0.2257 0.2580 0.2881 0.3159
0.3413 0.3643 0.3849 0.4032 0.4192
0.4332 0.4452 0.4554 0.4641 0.4713
0.4772 0.4821 0.4861 0.4893 0.4918
0.4938 0.4953 0.4965 0.4974 0.4981
0.4987
0.0040 0.0438 0.0832 0.1217 0.1591
0.1950 0.2291 0.2611 0.2910 0.3186
0.3438 0.3665 0.3869 0.4049 0.4207
0.4345 0.4463 0.4564 0.4649 0.4719
0.4778 0.4826 0.4864 0.4896 0.4920
0.4940 0.4955 0.4966 0.4975 0.4982
0.4987
0.0080 0.0478 0.0871 0.1255 0.1628
0.1985 0.2324 0.2642 0.2939 0.3212
0.3461 0.3686 0.3888 0.4066 0.4222
0.4357 0.4474 0.4573 0.4656 0.4726
0.4783 0.4830 0.4868 0.4898 0.4922
0.4941 0.4956 0.4967 0.4976 0.4982
0.4987
0.0120 0.0517 0.0910 0.1293 0.1664
0.2019 0.2357 0.2673 0.2967 0.3238
0.3485 0.3708 0.3907 0.4082 0.4236
0.4370 0.4484 0.4582 0.4664 0.4732
0.4788 0.4834 0.4871 0.4901 0.4925
0.4943 0.4957 0.4968 0.4977 0.4983
0.4988
0.0160 0.0557 0.0948 0.1331 0.1700
0.2054 0.2389 0.2703 0.2995 0.3264
0.3508 0.3729 0.3925 0.4099 0.4251
0.4382 0.4495 0.4591 0.4671 0.4738
0.4793 0.4838 0.4875 0.4904 0.4927
0.4945 0.4959 0.4969 0.4977 0.4984
0.4988
0.0199 0.0596 0.0987 0.1368 0.1736
0.2088 0.2422 0.2734 0.3023 0.3289
0.3531 0.3749 0.3944 0.4115 0.4265
0.4394 0.4505 0.4599 0.4678 0.4744
0.4798 0.4842 0.4878 0.4906 0.4929
0.4946 0.4960 0.4970 0.4978 0.4984
0.4989
0.0239 0.0636 0.1026 0.1406 0.1772
0.2123 0.2454 0.2764 0.3051 0.3315
0.3554 0.3770 0.3962 0.4131 0.4279
0.4406 0.4515 0.4608 0.4686 0.4750
0.4803 0.4846 0.4881 0.4909 0.4931
0.4948 0.4961 0.4971 0.4979 0.4985
0.4989
0.0279 0.0675 0.1064 0.1443 0.1808
0.2157 0.2486 0.2794 0.3078 0.3340
0.3577 0.3790 0.3980 0.4147 0.4292
0.4418 0.4525 0.4616 0.4693 0.4756
0.4808 0.4850 0.4884 0.4911 0.4932
0.4949 0.4962 0.4972 0.4979 0.4985
0.4989
0.0319 0.0714 0.1103 0.1480 0.1844
0.2190 0.2517 0.2823 0.3106 0.3365
0.3599 0.3810 0.3997 0.4162 0.4306
0.4429 0.4535 0.4625 0.4699 0.4761
0.4812 0.4854 0.4887 0.4913 0.4934
0.4951 0.4963 0.4973 0.4980 0.4986
0.4990
0.0359 0.0753 0.1141 0.1517 0.1879
0.2224 0.2549 0.2852 0.3133 0.3389
0.3621 0.3830 0.4015 0.4177 0.4319
0.4441 0.4545 0.4633 0.4706 0.4767
0.4817 0.4857 0.4890 0.4916 0.4936
0.4952 0.4964 0.4974 0.4981 0.4986
0.4990
This table can be used to calculate N(di), the cumulative normal distribution
functions needed for the Black-Scholes model of option pricing.
If di > 0, add 0.5 to the relevant number above.
If di < 0, subtract the relevant number above from 0.5
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Chapter 1
Issues in corporate governance
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CHAPTER 1 ISSUES IN CORPORATE GOVERNANCE
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CHAPTER CONTENTS
FINANCIAL OBJECTIVES ------------------------------------------------ 15
THE UK CORPORATE GOVERNANCE CODE ----------------------------- 16
CODE OF BEST PRACTICE 16
INTERNATIONAL COMPARISONS OF CORPORATE GOVERNANCE -- 22
UNITED STATES OF AMERICA 22
GERMANY 22
JAPAN 23
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FINANCIAL OBJECTIVES
Advanced Financial Management is concerned with the following key decisions:
- What to invest in (INVESTMENT DECISIONS)
- How to finance the investment (FINANCING DECISIONS)
- The level of dividend distributions (DIVIDEND DECISIONS).
Objectives
Primary objective: to maximise the wealth of shareholders. A positive NPV equates
(in theory) to an increase in shareholder wealth.
Secondary objectives may be e.g. meeting financial targets (say satisfactory
ROCE), meeting productivity targets, establishing brands and quality standards and
effective communication with customers, suppliers, employees.
As an alternative to maximising the wealth of shareholders a company must in
reality consider satisficing objectives for each of the major stakeholders.
Stakeholders (user groups) and their goals
These include:
Shareholders
Directors
Management and employees
Loan creditors
Customers
Suppliers
The government
Environmental pressure groups
The general public
Many of these groups may have conflicting objectives, which need to be reconciled.
Corporate governance
Clearly the executive directors of a listed company are both decision-makers and
major stakeholders. They are therefore open to the accusation of making key
decisions for their own benefit. Following a number of notable financial scandals in
the UK during the late 20th century (e.g the Maxwell affair and the collapse of the
BCCI) the Cadbury Committee was set up to investigate procedures for appropriate
corporate governance.
The Cadbury Code (1992) defined corporate governance as the system by which
companies are directed and controlled. This initial document has been subject to
subsequent amendments by the Greenbury, Hampel and Higgs Reports. The
Financial Services Authority requires listed companies to confirm that they have
complied with the Code provisions or in the event of non-compliance to provide
an explanation of their reasons for departure.
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THE UK CORPORATE GOVERNANCE CODE
Code of best practice
Section A: Leadership
A.1 The Role of the Board
Main Principle: Every company should be headed by an effective board
which is collectively responsible for the long-term success of the company.
The annual report should identify the chairman, the deputy chairman (where there
is one), the chief executive, the senior independent director and the chairmen and
members of the board committees. It should also set out the number of meetings
of the board and its committees and individual attendance by directors.
A.2 Division of Responsibilities
Main Principle: There should be a clear division of responsibilities at the
head of the company between the running of the board and the executive
responsibility for the running of the companys business. No one individual
should have unfettered powers of decision.
The roles of chairman and chief executive should not be exercised by the same
individual. The division of responsibilities between the chairman and chief
executive should be clearly established, set out in writing and agreed by the board.
A.3 The Chairman
Main Principle: The chairman is responsible for leadership of the board and
ensuring its effectiveness on all aspects of its role.
The chairman should on appointment meet the independence criteria set out in B.1
below. A chief executive should not go on to be chairman of the same company.
If, exceptionally, a board decides that a chief executive should become chairman,
the board should consult major shareholders in advance and should set out its
reasons to shareholders at the time of the appointment and in the next annual
report. (Compliance or otherwise with this provision need only be reported for the
year in which the appointment is made).
A.4 Non-executive Directors
Main Principle: As part of their role as members of a unitary board, non-
executive directors should constructively challenge and help develop
proposals on strategy.
The board should appoint one of the independent non-executive directors to be the
senior independent director to provide a sounding board for the chairman and to
serve as an intermediary for the other directors when necessary. The senior
independent director should be available to shareholders if they have concerns
which contact through the normal channels of chairman, chief executive or other
executive directors has failed to resolve or for which such contact is inappropriate.
The chairman should hold meetings with the non-executive directors without the
executives present. Led by the senior independent director, the non-executive
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directors should meet without the chairman present at least annually to appraise
the chairmans performance and on such other occasions as are deemed
appropriate.
Section B: Effectiveness
B.1 The Composition of the Board
Main Principle: The board and its committees should have the appropriate
balance of skills, experience, independence and knowledge of the company
to enable them to discharge their respective duties and responsibilities
effectively.
The board should identify in the annual report each non-executive director it
considers to be independent. The board should determine whether the director is
independent in character and judgement and whether there are relationships or
circumstances which are likely to affect, or could appear to affect, the directors
judgement. The board should state its reasons if it determines that a director is
independent notwithstanding the existence of relationships or circumstances which
may appear relevant to its determination, including if the director:
has been an employee of the company or group within the last five
years;
has, or has had within the last three years, a material business
relationship with the company either directly, or as a partner,
shareholder, director or senior employee of a body that has such a
relationship with the company;
has received or receives additional remuneration from the company
apart from a directors fee, participates in the companys share option or
a performance-related pay scheme, or is a member of the companys
pension scheme;
has close family ties with any of the companys advisers, directors or
senior employees;
holds cross-directorships or has significant links with other directors
through involvement in other companies or bodies;
represents a significant shareholder; or
has served on the board for more than nine years from the date of their
first election.
Except for smaller companies (i.e. those below the FTSE 350 throughout the year
immediately prior to the reporting year), at least half the board, excluding the
chairman, should comprise non-executive directors determined by the board to be
independent. A smaller company should have at least two independent non-
executive directors.
B.2 Appointments to the Board
Main Principle: There should be a formal, rigorous and transparent
procedure for the appointment of new directors to the board.
There should be a nomination committee which should lead the process for board
appointments and make recommendations to the board. A majority of members of
the nomination committee should be independent non-executive directors. The
chairman or an independent non-executive director should chair the committee, but
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the chairman should not chair the nomination committee when it is dealing with the
appointment of a successor to the chairmanship. The nomination committee should
make available its terms of reference, explaining its role and the authority
delegated to it by the board. (This requirement would be met by including the
information on the company website).
B.3 Commitment
Main Principle: All directors should be able to allocate sufficient time to the
company to discharge their responsibilities effectively.
For the appointment of a chairman, the nomination committee should prepare a job
specification, including an assessment of the time commitment expected,
recognising the need for availability in the event of crises. A chairmans other
significant commitments should be disclosed to the board before appointment and
included in the annual report. Changes to such commitments should be reported to
the board as they arise, and their impact explained in the next annual report.
The board should not agree to a full time executive director taking on more than
one non-executive directorship in a FTSE 100 company nor the chairmanship of
such a company.
B.4 Development
Main Principle: All directors should receive induction on joining the board
and should regularly update and refresh their skills and knowledge.
The chairman should ensure that the directors continually update their skills and
the knowledge and familiarity with the company required to fulfil their role both on
the board and on board committees. The company should provide the necessary
resources for developing and updating its directors knowledge and capabilities.
To function effectively, all directors need appropriate knowledge of the company
and access to its operations and staff.
The chairman should ensure that new directors receive a full, formal and tailored
induction on joining the board. As part of this, directors should avail themselves of
opportunities to meet major shareholders.
The chairman should regularly review and agree with each director their training
and development needs.
B.5 Information and Support
Main Principle: The board should be supplied in a timely manner with
information in a form and of a quality appropriate to enable it to discharge
its duties.
B.6 Evaluation
Main Principle: The board should undertake a formal and rigorous annual
evaluation of its own performance and that of its committees and
individual directors.
The board should state in the annual report how performance evaluation of the
board, its committees and its individual directors has been conducted.
Evaluation of the board of FTSE 350 companies should be externally facilitated at
least every three years. A statement should be made available of whether an
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external facilitator has any other connection with the company. (This requirement
would be met by including the information on the company website).
The non-executive directors, led by the senior independent director, should be
responsible for performance evaluation of the chairman, taking into account the
views of executive directors.
B.7 Re-election
Main Principle: All directors should be submitted for re-election at regular
intervals, subject to continued satisfactory performance.
All directors of FTSE 350 companies should be subject to annual election by
shareholders. All other directors should be subject to election by shareholders at
the first annual general meeting (AGM) after their appointment, and to re-election
thereafter at intervals of no more than three years. Non-executive directors who
have served longer than nine years should be subject to annual re-election. The
names of directors submitted for election or re-election should be accompanied by
sufficient biographical details and any other relevant information to enable
shareholders to take an informed decision on their election.
Section C: Accountability
C.1 Financial and Business Reporting
Main Principle: The board should present a balanced and understandable
assessment of the companys position and prospects.
C.2 Risk Management and Internal Control
(The Turnbull Guidance, last updated in October 2005, suggests means of
applying this part of the Code)
Main Principle: The board is responsible for determining the nature and
extent of the significant risks it is willing to take in achieving its strategic
objectives. The board should maintain sound risk management and
internal control systems.
The board should, at least annually, conduct a review of the effectiveness of the
companys risk management and internal control systems and should report to
shareholders that they have done so. The review should cover all material controls,
including financial, operational and compliance controls.
C.3 Audit Committee and Auditors
(The FRC Guidance on Audit Committees - formerly referred to as the Smith
Guidance - suggests means of applying this part of the Code)
Main Principle: The board should establish formal and transparent
arrangements for considering how they should apply the corporate
reporting and risk management and internal control principles and for
maintaining an appropriate relationship with the companys auditor.
The board should establish an audit committee of at least three, or in the case of
smaller companies (i.e. those below the FTSE 350 throughout the year immediately
prior to the reporting year) two, independent non-executive directors. In smaller
companies the company chairman may be a member of, but not chair, the
committee in addition to the independent non-executive directors, provided he or
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she was considered independent on appointment as chairman. The board should
satisfy itself that at least one member of the audit committee has recent and
relevant financial experience.
Section D: Remuneration
D.1 The Level and Components of Remuneration
Main Principle: Levels of remuneration should be sufficient to attract,
retain and motivate directors of the quality required to run the company
successfully, but a company should avoid paying more than is necessary
for this purpose. A significant proportion of executive directors
remuneration should be structured so as to link rewards to corporate and
individual performance.
The performance-related elements of executive directors remuneration should be
stretching and designed to promote the long-term success of the company.
The remuneration committee should judge where to position their company relative
to other companies. But they should use such comparisons with caution, in view of
the risk of an upward ratchet of remuneration levels with no corresponding
improvement in performance.
They should also be sensitive to pay and employment conditions elsewhere in the
group, especially when determining annual salary increases.
In designing schemes of performance-related remuneration for executive directors,
the remuneration committee should follow the provisions of this Code.
Where a company releases an executive director to serve as a non-executive
director elsewhere, the remuneration report (required by UK legislation) should
include a statement as to whether or not the director will retain such earnings and,
if so, what the remuneration is.
D.2 Procedure
Main Principle: There should be a formal and transparent procedure for
developing policy on executive remuneration and for fixing the
remuneration packages of individual directors. No director should be
involved in deciding his or her own remuneration.
The board should establish a remuneration committee of at least three, or in the
case of smaller companies two, independent non-executive directors. In addition
the company chairman may also be a member of, but not chair, the committee if he
or she was considered independent on appointment as chairman. The
remuneration committee should make available its terms of reference, explaining
its role and the authority delegated to it by the board. Where remuneration
consultants are appointed, a statement should be made available of whether they
have any other connection with the company (This requirement would be met by
including the information on the company website).
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Section E: Relations with shareholders
E.1 Dialogue with Shareholders
Main Principle: There should be a dialogue with shareholders based on the
mutual understanding of objectives. The board as a whole has
responsibility for ensuring that a satisfactory dialogue with shareholders
takes place.
The chairman should ensure that the views of shareholders are communicated to
the board as a whole. The chairman should discuss governance and strategy with
major shareholders. Non-executive directors should be offered the opportunity to
attend scheduled meetings with major shareholders and should expect to attend
meetings if requested by major shareholders. The senior independent director
should attend sufficient meetings with a range of major shareholders to listen to
their views in order to help develop a balanced understanding of the issues and
concerns of major shareholders.
E.2 Constructive Use of the AGM
Main Principle: The board should use the AGM to communicate with
investors and to encourage their participation.
At any general meeting, the company should propose a separate resolution on each
substantially separate issue, and should, in particular, propose a resolution at the
AGM relating to the report and accounts. For each resolution, proxy appointment
forms should provide shareholders with the option to direct their proxy to vote
either for or against the resolution or to withhold their vote. The proxy form and
any announcement of the results of a vote should make it clear that a vote
withheld is not a vote in law and will not be counted in the calculation of the
proportion of the votes for and against the resolution.
The company should ensure that all valid proxy appointments received for general
meetings are properly recorded and counted. For each resolution, where a vote has
been taken on a show of hands, the company should ensure that the following
information is given at the meeting and made available as soon as reasonably
practicable on a website which is maintained by or on behalf of the company:
the number of shares in respect of which proxy appointments have been
validly made;
the number of votes for the resolution;
the number of votes against the resolution; and
the number of shares in respect of which the vote was directed to be
withheld.
The chairman should arrange for the chairmen of the audit, remuneration and
nomination committees to be available to answer questions at the AGM and for all
directors to attend.
The company should arrange for the Notice of the AGM and related papers to be
sent to shareholders at least 20 working days before the meeting.
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INTERNATIONAL COMPARISONS OF CORPORATE
GOVERNANCE
The broad principles of corporate governance are similar in the UK, the USA and
Germany, but there are significant differences in how they are applied. Whereas
the UK and Germany have voluntary corporate governance codes, the US system is
based upon legislation within the Sarbanes-Oxley Act.
United States of America
Whereas the UK has historically relied upon a system of self-regulation and
voluntary codes of best practice, the USA corporate governance structure is more
formalised, with legally enforceable controls.
In the US, statutory requirements for publicly-traded companies are set out in the
Sarbanes-Oxley Act. These requirements include the certification of published
financial statements by the CEO and the chief financial officer (CFO), faster public
disclosures by companies, legal protection for whistleblowers, a requirement for an
annual report on internal controls, and requirements relating to the audit
committee, auditor conduct and avoiding improper influence of auditors.
The Act also requires the Securities and Exchange Commission (SEC) and the main
stock exchanges to introduce further rules, relating to matters such as the
disclosure of critical accounting policies, the composition of the Board and the
number of independent directors. The Act has also established an independent
body to oversee the accounting profession, which is known as the Public Company
Accounting Oversight Board. Managers must be careful to comply with regulations
to avoid possible legal action against the company or themselves individually.
Germany
As both the UK and Germany are members of the EU, they must both follow EU
directives on company law. A major difference that exists in the board structure for
companies is that the UK has a unitary board (consisting of both executive and
non-executive directors), whereas German companies have a two-tier board of
directors. The Supervisory Board of non-executives (Aufsichtsrat) has
responsibility for corporate policy and strategy and the Management Board of
executive directors (Vorstand) has responsibility primarily for the day-to-day
operations of the company.
The Supervisory Board typically includes representatives from major banks that
have historically been large providers of long-term finance to German companies
(and are often major shareholders). The Supervisory Board does not have full
access to financial information, is meant to take an unbiased overview of the
company, and is the main body responsible for safeguarding the external
stakeholders interests. The presence on the Supervisory Board of representatives
from banks and employees (trade unions) may introduce perspectives that are not
present in some UK boards. In particular, many members of the Supervisory Board
would not meet the criteria under UK Corporate Governance Code for their
independence.
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Japan
Although there are signs of change in Japanese corporate governance, much of the
system is based upon negotiation or consensual management rather than upon a
legal or even a self-regulatory framework. Banks as well as representatives of
other companies (in their capacity as shareholders) also sit on the Boards of
Directors of Japanese companies.
It is not uncommon for Japanese companies to have cross holdings of shares with
their suppliers, customers and banks etc., all being represented on each others
Board of Directors. There are often three boards of directors: Policy Boards,
responsible for strategy and comprised of directors with no functional responsibility;
Functional Boards, responsible for day to day operations; and largely symbolic
Monocratic Boards. The interests of the company as a whole should dictate the
actions of these boards. This is in contrast to the UK or USA systems where, at
least in theory, the board should act primarily in the best interests of the
shareholders, being the owners of the company.
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Chapter 2
Advanced investment
appraisal section 1
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CHAPTER CONTENTS
INVESTMENT APPRAISAL TECHNIQUES ------------------------------- 27
1. ACCOUNTING RATE OF RETURN 27
2. PAYBACK PERIOD 28
3. DISCOUNTED CASH FLOW 28
INFLATION AND DISCOUNTED CASH FLOW -------------------------- 34
MONEY CASH FLOWS 34
REAL CASH FLOWS 34
RELATIONSHIP BETWEEN MONEY INTEREST RATES AND REAL INTEREST RATES 34
TAXATION AND INVESTMENT APPRAISAL ---------------------------- 36
CAPITAL RATIONING ---------------------------------------------------- 38
WHAT ARE THE 2 TYPES OF CAPITAL RATIONING? 38
CAPITAL RATIONING AND TIME 38
SINGLE PERIOD CAPITAL RATIONING 40
MULTI-PERIOD CAPITAL RATIONING 43
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INVESTMENT APPRAISAL TECHNIQUES
Assumed objective is
Selection of those projects which will maximise the wealth of the owners (or
shareholders) of the enterprise. Involves a consideration of FUTURE events, not
PAST performance.
Accepted techniques are
1. Accounting Rate of Return (alternatively called Return on Investment)
2. Payback Period
3. Discounted Cash Flow, of which there are two major variants:
(a) Net Present Value
(b) Internal Rate of Return (alternatively called Yield).
1. Accounting rate of return
The ARR (or ROI) is a measure of relative project profitability, which expresses:
1. the expected average annual profit (after allowing for depreciation, but
before taxation) emerging from a project
as a percentage of
2. the investment involved. Normally the average investment over the life
of the project is used, but initial investment is sometimes employed.
Advantages
It is relatively easy to understand
The required figures are readily available from accounting data.
The ROI technique is frequently used as an assessment of managements
actual (hindsight) performance.
It gives an indication as to whether available projects are meeting target
returns on capital employed.
Disadvantages
Based on accounting profits not cash flows - the success of an enterprise
depends on its ability to generate cash. The ability to invest depends on
availability of cash.
Ignores the time value of money
It is relative rate of return, thus ignores the size of the project
No set rules (theoretical or practical) for determining the cut-off rate of
return.
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2. Payback period
The Payback Period demonstrates how long an enterprise must expect to wait
before the after-tax cash flows generated by the project allow it to recoup the initial
amount invested. Thus it gives an investor an idea of how long their money will
be at risk; a short payback period is taken to reveal low risk, and a long payback -
high risk.
Advantages
The most tried and tested of all methods
Easy to calculate and understand
An enterprise with limited cash resources is obviously concerned with speed of
return.
Some companies combine DCF techniques with the payback method.
Disadvantages
Does not measure profitability nor increases in shareholders wealth, since it
ignores cash flows expected to arise beyond the payback period.
Ignores the time value of money (but discounted payback sometimes used).
No set rules (theoretical or practical) for determining the minimum acceptable
payback period.
May be difficult to measure the initial amount invested when eg net outlays
arise in both the initial and final years of a project.
3. Discounted cash flow
DCF is a method of capital investment appraisal which takes account of:
1. The overall cash flows arising from projects, and
2. The timing of those cash flows.
Only relevant cash flows are considered (ie those future cash flows which arise as a
result of those projects) and the timing effect is incorporated by means of the
discounting technique.
Both the Accounting Rate of Return and the Payback approaches are surpassed by
the DCF methods. The basic arguments are:
it is better to consider cash rather than profits because cash is how investors
will eventually see their rewards (ie dividends, interest, or the proceeds from
the sale of the shares or debentures).
the timing of the cash flows is important because early cash receipts can be
reinvested to earn interest.
it is important to consider the cash flows arising over the entire life of a
project.
The technique of discounting reduces all future cash flows to current equivalent
values (present values) by allowing for the interest which could have been earned if
the cash had been received immediately.
There are two common techniques, net present value and internal rate of return,
but net terminal value can be used.
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DCF Net present value
The NPV of a project is the net value of a projects cash flows after discounting (ie
allowing for reinvestment) at the companys cost of capital. Projects with a negative
NPV should be rejected.
N.B. Cost of capital is the average required return which is set by the market for
the company in view of the risk associated with its operations.
Provided that:
1. The project under consideration is of average risk for the company, and
2. There is no restriction on access to capital,
a positive NPV provides the best theoretical estimate of the total absolute increase
in wealth which accrues to an enterprise as a result of accepting that project.
However in the short run the use of the NPV rule may not lead to good profits being
reported in the published accounts of the enterprise although in the long term
cash flows and reported profits should move in tandem.
The NPV rule has a sound theoretical basis and is likely to produce investment
decision advice of consistently good quality.
DCF Internal rate of return (economic return/yield)
The IRR (or Economic return) of a project is that discount rate which when applied
to a projects cash flows provides an NPV of zero. The IRR is therefore the expected
earning rate of an investment. If the IRR of a project exceeds the cost of capital
of that enterprise, that project is acceptable.
When considering a single project in isolation IRR will give the same decision as
NPV (ie if the NPV of a project is positive, its IRR will exceed the cost of capital).
However, when choosing between mutually exclusive projects, the two techniques
may conflict and (subject to the provisos set out above) NPV always provides the
correct solution.
Disadvantages of IRR
1. IRR provides a relative (as opposed to an absolute) result, and may give
incorrect decision advice if mutually exclusive projects:
o Are of different size, or
o Have unequal lives.
2. May be multiple IRRs or no IRR
3. Cannot adapt to expected changes in cost of capital during the life of a
project.
4. Makes an inconsistent assumption about the rate at which cash surpluses can
be reinvested; it assumes they are reinvested at whatever the IRR happens to
be. The companys cost of capital is a more appropriate reinvestment rate ie
the assumption underlying NPV.
5. More difficult to calculate than the theoretically more sound NPV approach.
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Example Congo Ltd
Congo Ltd is considering the selection of one of a pair of mutually exclusive
investment projects. Both would involve purchase of machinery with a life of five
years
Project 1 would generate annual cash flows (receipts less payments) of 200,000;
the machinery would cost 556,000 and have a scrap value of 56,000.
Project 2 would generate annual cash flows of 500,000; the machinery would cost
1,616,000 and have a scrap value of 301,000.
Congo uses the straight-line method for providing depreciation.
Its cost of capital is 15 per cent per annum. Assume that annual cash flows arise
on the anniversaries of the initial outlay, that there will be no price changes over
the project lives and that acceptance of one of the projects will not alter the
required amount of working capital.
Requirements:
(i) Calculate for each project
(a) the accounting rate of return (ie the percentage of the average
accounting profit to the average book value of investment) to the nearest 1%.
(b) the net present value
(c) the internal rate of return (Yield or Economic return) to the nearest 1%,
and
(d) the payback period to one decimal place.
Ignore taxation.
(ii) WITHOUT ANY REFERENCE TO THE INCREMENTAL YIELD METHOD, briefly
explain which one of the discounted cash flow techniques used in part (i) of
this question should be used by the management of Congo Ltd, in deciding
whether Project 1 or Project 2 should be undertaken.
Suggested solution to Congo Ltd
(i) Summary of results
Project 1 2
a) Accounting rate of return 33% 25%
b) Net present value (000) 142 210
c) Internal rate of return (Economic return) 25% 20%
d) Payback period (years) 2.8 or 3 3.2 or 4
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Summary of rankings
Better project
a) Accounting rate of return 1
b) Net present value 2
c) Internal rate of return 1
d) Payback period 1
WORKINGS
Project 1 Project 2
(a) Accounting rate of return 000 000
Initial investment 556 1,616
Scrap value (56) (301)
Total depreciation 500 1,315
Annual depreciation 100 263
Cash flows 200 500
Depreciation (see above) (100) (263)
Average accounting profit 100 237
Project 1 Project 2
000 000
Average book value of investment (000)
(556 + 56) 306
(1,616 + 301) 958
Accounting rate of return 33% 25%
(b) Net present value
000 000
Year
0 Initial outlay (556) (1,616)
1 5 Cash flows
200 x 3.352 670
500 x 3.352 1,676
5 Residual value
56 x 0.497 28
301 x 0.497 ___ 150
Net present value (000) 142 210
(c) Internal rate of return (Economic return)
000 000
By trial and error
Try 20%
Initial outlays (556) (1,616)
Cash flows 598 1,495
Residual values _22 _121
NPV (000) 64 NIL
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Try 25%
Initial outlays (556) (1,616)
Cash flows 538 1,345
Residual values __18 __99
NPV (000) NIL (172)
IRR 25% 20%
(d) Payback period
000 000
Annual cash flows 200 500
Initial investment 556 1,616
Payback period in years
If cash flows arose during each year 2.8 3.2
If cash flows arose at year end (as in this
question)
3 4
(ii) Investment Decision
This example illustrates the conflict which will often be found between the two
discounted cash flow appraisal techniques in a ranking decision.
Under the net present value criterion, project 2 is preferred because it has a
higher net present value when the project cash flows are discounted at the
cost of capital. On the other hand project 1 has the higher internal rate of
return.
To decide which method of ranking is correct it is necessary to consider the
assumed objective of the firm, which is to maximise the wealth of the
providers of finance. Both projects earn more than the required rate of return
but project 2 generates larger cash surpluses in excess of the required
amounts than project 1, as can be seen from the net present value
calculations. It is these cash surpluses which improve the wealth of the
owners of the firm.
IRR provides a relative (as opposed to an absolute) result, and may give
incorrect decision advice if mutually exclusive projects are of different size (as
in this instance) or have unequal lives.
IRR makes an inconsistent assumption about the rate at which cash surpluses
can be reinvested; it assumes they are reinvested at whatever the IRR
happens to be. The companys cost of capital is a more appropriate
reinvestment rate i.e. the assumption underlying NPV.
Accordingly PROJECT 2 IS PREFERRED TO PROJECT 1 and this can be justified
by the following argument:
Project 1 is relatively more profitable than project 2, but it is smaller. The
two projects are mutually exclusive, which means that only one of them can
be accepted. It is better for the owners of the company to receive the large
cash surpluses from a large adequately profitable project than to receive the
smaller cash surpluses from a small very profitable project. Taken to
extremes, a return of ten per cent on 1,000 is better than a return of one
thousand per cent on a penny.
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Tutorial Note
This question examines the conflicting rankings sometimes given by the NPV
and IRR technique. You may wish to add a graph to amplify your solution to
part (c).
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INFLATION AND DISCOUNTED CASH FLOW
The mechanics of allowing for inflation are basically easy to handle in DCF
calculations. The real difficulty is one of predicting what the rate will be. At this
point we will discuss the mechanics.
There are two possible techniques:
1. discount money (nominal) cash flows at the money (nominal) discount rate.
2. discount real cash flows at the real discount rate.
Money cash flows
These are the predictions of the actual sums of money which will be received and
paid taking into account predicted inflation levels. The money rate of interest is
the interest rate which is normally quoted and contains an allowance for inflation
(for example, a 20% discount rate may contain an allowance for expected inflation
of 5%).
Real cash flows
These are cash flows expressed in todays prices. A real discount rate is the real
required rate of return after adjusting the money discount rate for the inflation
allowance.
Relationship between money interest rates and real
interest rates
Suppose we can invest money in a bank to earn 7% per annum interest. However,
we expect inflation to be 4% per annum next year. If I invest 1 this must grow to
1.04 to keep pace with inflation. So, if I have 1.07 cash in the bank after one
year, the real interest I have received is 1.07 - 1.04 = 3p. When compared with
the capital required to keep pace with inflation (1.04), this shows a return of
0.03/1.04 = 2.9%.
The formula which relates real and money interest rates is as follows:
1 + r = i1
m1
+
+
or, according to the ACCA Formula Sheet, (1 + i) = (1 + r)(1 + h)
Where r is the real interest rate, m is the money interest rate and i is the rate of
inflation.
Thus 1 + r = 1.07/1.04 in the above example, giving r = 0.029 or 2.9%.
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Suggested solution to AP
Method 1: Compute the real discount rate and discount the real cash flows
1 + r = 1+ m = 1.155 = 1.1
1 + i 1.05
Thus r = 0.1 or 10%
Real cash flow 10% factor Present value
Year
0 (1,500) 1 (1,500)
1 670 1/1.1 609.1
2 500 1/1.12 413.2
3 1,200 1/1.13 901.6
NPV 423.9
Method 2: Compute the money cash flows, using the rate of inflation and discount
at the money discount rate.
Money cash flow 15.5% factor Present value
Year
0 (1,500) 1 (1,500)
1 670 x 1.05 = 703.5 1/1.155 609.1
2 500 x 1.052 = 551.25 1/1.1552 413.2
3 1,200 x 1.053 =1,389.15 1/1.1553 901.6
NPV 423.9
Please note that discount rates have been computed as opposed to looked up in
tables, to ensure that accuracy is obtained for the reconciliation.
Example AP
A project requires an outlay of 1.5m in year 0 and will repay cash flows in real
terms (todays prices) as follows:
Year 000 1 670 2 500 3 1,200
The companys money cost of capital is 15%. Appraise the project if inflation is
estimated to remain at 5% per annum.
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TAXATION AND INVESTMENT APPRAISAL
Example AA plc
AA plc buys a fixed asset for 10,000 at the beginning of an accounting period (1
January 2001) to undertake a two year project.
Net trading revenues at t1 and t2 are 5,000 per annum.
The company sells the fixed asset on the last day of the second year for 6,000.
Corporation tax = 33%. Writing down allowance = 25% reducing balance.
Required:
Calculate the net cashflows for the project.
Suggested solution to AA plc
t0 t1 t2 t3
Net trading revenue 5,000 5,000
Tax at 33% (1,650) (1,650)
Fixed asset (10,000)
Scrap proceeds 6,000
Tax savings on WDAs _____ ____ 825 495
Net cashflow (10,000) 5,000 10,175 (1,155)
WORKING
Tax savings on writing down allowances
Tax relief
at 33%
Timing
t0 Investment in fixed asset 10,000
t1 WDA @ 25% (2,500) 825 t2
7,500
t2 Proceeds (6,000)
Balancing allowance (1,500) 495 t3
Example BB plc
BB plc buys a fixed asset for 10,000 at the end of the previous accounting period
(31 December 2000) to undertake a two year project.
Net trading revenues at t1 and t2 are 5,000 per annum.
The fixed asset has zero scrap value when it is disposed of at the end of year 2.
Corporation tax = 33%. Writing down allowance = 25% reducing balance.
Required:
Calculate the net cashflows for the project.
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Suggested solution to BB plc
t0 t1 t2 t3
Net trading revenue 5,000 5,000
Tax at 33% (1,650) (1,650)
Fixed asset (10,000)
Tax savings on
WDAs
_____ 825 619 1,856
Net cashflow (10,000) 5,825 3,969 206
WORKING
Tax savings on writing down allowances
Tax relief at 3% Timing
t0 Investment in fixed asset 10,000
t0 WDA @ 25% (2,500) 825 t1
7,500
t1 WDA @25% (1,875) 619 t2
5,625
t2 Proceeds ____
Balancing allowance (5,625) 1,856 t3
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CAPITAL RATIONING
Where the finance available for capital expenditure is limited to an amount which
prevents acceptance of all new projects with a positive NPV, the company is said to
experience capital rationing.
What are the 2 types of capital rationing?
They are:
1. Hard capital rationing
This applies when a company is restricted from undertaking all worthwhile
investment opportunities due to external factors over which it has no control.
These factors may include government monetary restrictions and the general
economic and financial climate (eg, a depressed stock market, which precludes a
rights issue of ordinary shares).
2. Soft capital rationing
This applies when a company decides to limit the amount of capital expenditure
which it is prepared to authorise. Segments of divisionalised companies often have
their capital budgets imposed by the main board of directors. A company may
purposely curtail its capital expenditure for a number of reasons eg, it may consider
that it has insufficient depth of management expertise to exploit all available
opportunities without jeopardising the success of both new and ongoing operations.
Capital rationing and time
Capital rationing may exist in a:
1. Single period
This is where available finance is only in short supply during the current period, but
will become freely available in subsequent periods.
Projects may be:
(i) Divisible An entire project or any fraction of that project may be
undertaken. In this event projects may be ranked by means of a
profitability index, which can be calculated by dividing the present value (or
NPV) of each project by the capital outlay required during the period of
restriction.
Projects displaying the highest profitability indices will be preferred. Use of
the profitability index assumes that project returns increase in direct
proportion to the amount invested in each project.
(ii) Indivisible An entire project must be undertaken, since it is impossible to
accept part of a project only. In this event the NPV of all available projects
must be calculated. These projects must then be combined on a trial and
error basis in order to select that combination which provides the highest total
NPV within the constraints of the capital available. This approach will
sometimes result in some funds being unused.
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2. Multi-period
This is where available finance is limited not only during the current period, but also
during subsequent periods.
Projects may be:
(i) Divisible - In this event, linear programming is used to determine the
optimal combination of projects. Two techniques, which both result in
identical project selections can be used ie the objective is to either:
Maximise the total NPV from the investment in available projects, or
Maximise the present value (PV) of cash flows available for dividends.
(ii) Indivisible - In this event, integer programming would be required to
determine the optimal combination of investments.
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Single period capital rationing
Example of single period capital rationing Banden Ltd
Banden Ltd is a highly geared company that wishes to expand its operations. Six
possible capital investments have been identified, but the company only has access
to a total of 620,000. The projects are not divisible and may not be postponed
until a future period. After the projects end, it is unlikely that similar investment
opportunities will occur.
Expected net cash inflows (including salvage value)
Initial Project Year 1 2 3 4 5 outlay
A 70,000 70,000 70,000 70,000 70,000 246,000 B 75,000 87,000 64,000 180,000
C 48,000 48,000 63,000 73,000 175,000 D 62,000 62,000 62,000 62,000 180,000 E 40,000 50,000 60,000 70,000 40,000 180,000 F 35,000 82,000 82,000 150,000
Projects A and E are mutually exclusive. All projects are believed to be of similar
risk to the companys existing capital investments.
Any surplus funds may be invested in the money market to earn a return of 9%
per year. The money market may be assumed to be an efficient market. Bandens
cost of capital is 12% per year.
Required:
(a) Calculate:
(i) The expected net present value;
(ii) The expected profitability index associated with each of the six
projects.
Rank the projects according to both of these investment appraisal
methods and explain briefly why these rankings differ.
(b) Give reasoned advice to Banden Ltd recommending which projects
should be selected.
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Solution to single period capital rationing example Banden Ltd
(a) (i) Calculation of expected Net Present value
Project NPV
A. 70,000 x 3.605 - 246,000 = 6,350
B. 75,000 x 0.893 + 87,000 x 0.797 + 64,000
x 0.712 - 180,000 = 1,882
C. 48,000 x 0.893 + 48,000 x 0.797 + 63,000
x 0.712 + 73,000 x 0.636 - 175,000 = (2,596)
D. 62,000 x 3.037 - 180,000 = 8,294
E. 40,000 x 0.893 + 50,000 x 0.797 + 60,000
x 0.712 + 70,000 x 0.636 + 40,000 x 0.567
- 180,000 = 5,490
F. 35,000 x 0.893 + 82,000 x 0.797 + 82,000
x 0.712 - 150,000 = 4,993
(ii) Calculation of Profitability Index
Present value of cash inflows initial outlay:
Project PI
A. 252,350/246,000 = 1.026
B. 181,882/180,000 = 1.010
C. 172,404/175,000 = 0.985
D. 188,294/180,000 = 1.046
E. 185,490/180,000 = 1.031
F. 154,993/150,000 = 1.033
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Ranking NPV P.I
1 D D
2 A F
3 E E
4 F A
5 B B
6 C C
The rankings differ because NPV is an absolute measure of the benefit from a
project, whilst profitability index is a relative measure, and shows the benefit
per of outlay. Where the initial outlays vary in size the two methods may
give different rankings.
(b) In a capital rationing situation, the projects should be selected which give the
greatest total NPV from the limited outlay available.
A and E are mutually exclusive.
C is not considered as it has a negative NPV.
Total outlay is limited to 620,000.
Possible selections are:
Projects Expected NPV Total NPV Outlay in 000
A, B, D (6,350 + 1,882 + 8,294) 16,526 (246 + 180 + 180) 606
A, B, F (6,350 + 1,882 + 4,993) 13,225 (246 + 180 + 150) 576
A, D, F (6,350 + 8,294 + 4,993) 19,637 (246 + 180 + 150) 576
B, D, E (1,882 + 8,294 + 5,490) 15,666 (180 + 180 + 180) 540
B, D, F (1,882 + 8,294 + 4,993) 15,169 (180 + 180 + 150) 510
B, E, F (1,882 + 5,490 + 4,993) 12,365 (180 + 180 + 150) 510
D, E, F (8,294 + 5,490 + 4,993) 18,777 (180 + 180 + 150) 510
The recommended selection is projects A, D and F
Tutorial note: Neither the NPV nor PI rankings will necessarily be appropriate
because of the sheer size of these indivisible investments. In this particular
instance, because of the similarity in size of the projects, only three can be
undertaken, and the NPV ranking clearly leads to A, D and E. Profitability
index will not work if projects are indivisible or where multiple limiting factors
exist. The PI might lead to the incorrect solution of D, E and F.
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Multi-period capital rationing
Please remember that you are only likely to be asked to set up the
equations for both the linear programming and integer programming
formulations and then to interpret the output. The actual solving of these
equations are computer-based calculations.
Example of multi-period capital rationing using linear
programming Barney Ltd
The management team of Barney Ltd has identified the following independent
investment projects, all of which are divisible.
No project can be delayed or performed on more than one occasion. The projected
cash flows during the life of each project are as follows:
Year 0 Year 1 Year 2 Year 3 Year 4
000 000 000 000 000
Project A (25) (50) 25 50 50 Project B (25) (25) 75 - -
Project C (12.5) 5 5 5 5 Project D - (37.5) (37.5) 50 50 Project E (50) 25 (50) 50 50 Project F (20) (10) 37.5 25 -
The capital available at Year 0 is only 50,000 and only 12,500 is available at
Year 1, together with any cash inflows from the projects undertaken at Year 0.
From Year 2 onwards there is no restriction on the access to capital. The
appropriate cost of capital is 10%.
Required:
Formulate both:
1. The NPV linear programme, and
2. The PV of dividends linear programme.
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Suggested solution to Barney Ltd
NPV formulation
Since the objective is to maximise the total NPV from these projects, it is initially
necessary to calculate the NPV of each project at a discount rate of 10%:
Year 0 Year 1 Year 2 Year 3 Year 4 Total
NPV
Discount factor
(10%) 1.000 0.909 0.826 0.751 0.683
000 000 000 000 000 000
Project A (25) (45.45) 20.65 37.55 34.15 +21.90
Project B (25) (22.73) 61.95 - - +14.22
Project C (12.5) 4.55 4.13 3.75 3.42 +3.35
Project D - (34.09) (30.97) 37.55 34.15 +6.64
Project E (50) 22.73 (41.30) 37.55 34.15 +3.13
Project F (20) (9.09) 30.98 18.77 - +20.66
The combination of projects, which will maximise the total NPV can now be
specified, where:
a = the proportion of Project A to be undertaken
b = the proportion of Project B to be undertaken
c = the proportion of Project C to be undertaken
d = the proportion of Project D to be undertaken
e = the proportion of Project E to be undertaken
f = the proportion of Project F to be undertaken
The objective function, which represents the maximum NPV that can be earned, is:
z = 21.90a + 14.22b + 3.35c + 6.64d + 3.13e + 20.66f
This is subject to the following constraints:
Year 0 : 25a + 25b + 12.5c + 50e + 20f 50
Year 1 : 50a + 25b + 37.5d + 10f 12.5 + 5c + 25e
Furthermore : 0 a, b, c, d, e, f 1
When solved, the linear programme will provide the proportions of each project
which should be undertaken in order to establish the value of z, which represents
the maximum NPV achievable in view of the limitation of available capital.
Notice that the first constraint relates to the limited capital available at Year 0. The
second constraint concerns the capital limitation at Year 1, which is of course eased
by the Project C and E cash inflows, which can also be used to fund investment
needs at that time.
The third constraint shows that each project can only be undertaken once and that
it is impossible to undertake a negative quantity of any project. This non-negative
rule is essential, since if it were excluded a computer model may well establish that
negative quantities of a project could make cash inflows available that would be
included within the solution!!
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PV of dividends formulation
The combination of projects, which will maximise the PV of cash flows available for
dividends must be specified, where:
a = the proportion of Project A to be undertaken
b = the proportion of Project B to be undertaken
c = the proportion of Project C to be undertaken
d = the proportion of Project D to be undertaken
e = the proportion of Project E to be undertaken
f = the proportion of Project F to be undertaken
The objective function will be based upon the premise that:
z = the PV of dividends.
The dividend flows need to be defined for each year up to the point where the
investment with the longest life ceases in this case up to the end of Year 4 ie
d0 = the dividend flow generated at Year 0 by the projects selected
d1 = the dividend flow generated at Year 1 by the projects selected
d2 = the dividend flow generated at Year 2 by the projects selected
d3 = the dividend flow generated at Year 3 by the projects selected
d4 = the dividend flow generated at Year 4 by the projects selected
Therefore the objective function, which represents the present value of the
maximum dividends, discounted at the cost of capital of 10% is:
z = d0 + 1.1
d1 + 2
2
1.1
d +
3
3
1.1
d +
4
4
1.1
d
alternatively
z = d0 + 0.909 d1 + 0.826 d2 + 0.751 d3 + 0.683 d4
This is subject to the following constraints:
Year 0 : 25a + 25b + 12.5c + 50e + 20f + d0 50
Year 1 : 50a + 25b + 37.5d + 10f + d1 12.5 + 5c + 25e
Year 2 : 37.5d + 50e + d2 25a + 75b + 5c + 37.5f
Year 3 : d3 50a + 5c + 50d + 50e + 25f
Year 4 : d4 50a + 5c + 50d + 50e
Furthermore : 0 a, b, c, d, e, f 1
Additionally : d0, d1, d2, d3, d4 0
When solved, the linear programme will provide the proportions of each project
which should be undertaken in order to establish the value of z, which represents
the maximum PV of dividends earned in view of the capital constraints.
With an NPV formulation, we only have constraints for the periods during which
capital rationing exists (in this instance, Years 0 and 1), whereas under the
dividend formulation we have a constraint for every year of potential project cash
flows (in this case, Years 0 to 4).
The available funds are the same as in the NPV formulation (ie available capital
together with cash inflows from the projects); however the dividend flow for each
period must also be included. Furthermore an additional non-negative constraint is
used, since the dividends must be greater than or equal to zero. If this constraint
were excluded, a computer model may specify negative dividend payments, which
make cash inflows available that could be used to finance more projects!!
One advantage of the PV of dividends formulation is that it removes the need to
even calculate the NPV of each investment opportunity, since the discounting
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process is carried out by the linear programme as part of the calculation of the
solution.
Notice the only difference in the value of z in these formulations is as follows:
Under the NPV formulation, z provides the NPV of the project returns,
whereas
Under the PV of dividends formulation, z provides the PV of the project
returns.
Dual values
Dual values (also referred to as shadow prices) reflect the change in the objective
function as a result of having one more or one less unit of scarce resource. In the
context of capital rationing the scarce resource is available cash, so that the dual
price states the change in the objective function if one more unit of currency (eg
1) becomes available or if one less GB pound is invested.
Shadow prices can therefore be used to calculate the impact of raising additional
finance for further investment or the effect of diverting capital away from current
projects into newly discovered investments.
The dual price depends upon which method is used to formulate the linear
programme ie
Under the NPV formulation, it reflects the change in the NPV if 1 more or
1 less is available
Under the PV of dividends formulation, it reflects the change in the PV of
cash available for dividend payments if 1 more or 1 less capital is available.
Dual prices relate only to marginal changes in the availability of capital. Thus,
suppose that a dual value of 1.25 arises under the PV of dividends method, this
means that if an additional 1 of funds became available, the total value of the
objective function would rise by 1.25. It does not necessarily mean that if an
additional 10,000 became available, that the value of the objective function would
increase by (10,000 x 1.25) 12,500.
Shadow prices can therefore be used to test the validity of new investments which
emerge. The cash flows generated by the new project can be compared with the
cash flows lost by diverting funds from existing investments, thereby calculating the
effect of diversion of that finance.
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Example of the use of dual values in linear programming
Bruno Ltd
Bruno Ltd is experiencing capital rationing during both Year 0 and Year 1 in
relation to a number of divisible projects. It has used linear programming to
develop an investment strategy over its three year planning horizon for dividend
payments, using a cost of capital of 10%.
Shadow prices have been calculated under the NPV formulation for the two years
of capital constraints and under the PV of dividends formulation for the three year
planning horizon. The dual prices per 1 of capital available are as follows:
NPV method PV of dividends method
Year 0 0.1 (1 + 0.1) = 1.1
Year 1 0.08 (0.909 + 0.08) = 0.989 Year 2 0 (0.826 + 0) = 0.826
A new investment opportunity has emerged with the following cash flows:
Cash flow
000 Year 0 (75) Year 1 50
Year 2 50
Required:
Appraise the new project using both the NPV dual prices and the PV of
dividend shadow prices.
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Solution to Bruno Ltd
Appraisal using NPV dual values
The NPV of the new investment project is:
Year Cash flow Discount
factor Present value
000 @ 10% 000
0 (75) 1 (75)
1 50 0.909 45.45
2 50 0.826 41.3
NPV 11.75
The net dual value of the new investment project (ie the impact of diverting funds
from the current investment strategy) is:
Year Cash flow Shadow price Opportunity cost
000 000
0 (75) 0.1 (7.5)
1 50 0.08 4
2 50 0 - _
Net dual value (3.5)
Accordingly, the NPV of the current investment strategy would fall by 3,500 if the
new project were accepted. However, Bruno Ltd would benefit from the positive
NPV of that new investment opportunity. Therefore:
000
NPV of new project 11.75
Net dual value (3.5)
Net benefit of undertaking new project 8.25
This indicates that this project is worth further consideration, since if it were
accepted in full (and in doing so does not violate the marginality assumption of dual
values) it would result in the value of the objective function increasing by 8,250.
Appraisal using PV of dividends dual values
The net dual value of the new investment project (ie the impact of diverting funds
from the current investment strategy) is:
Year Cash flow Shadow price Opportunity cost
000 000
0 (75) 1.1 (82.5)
1 50 0.989 49.45
2 50 0.826 41.3
Net dual value (ie net benefit of undertaking new
project) 8.25
The two techniques will always provide the same result, but as can be seen the PV
of dividends dual prices technique is far quicker and simpler to solve.
Again, the project is worth considering; the linear programme should therefore be
reformulated (by including the new project) and then re-solved.
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Solution to Toby Ltd
The problem is to identify that combination of investment projects which will
produce the highest possible total NPV (within the annual funding limitations).
For instance, if Projects C and D were undertaken, they would satisfy the annual
capital constraints, because the combined investment for Year 0 is 12,500, for
Year 1 is 30,000 and for Year 2 is 37,500, whilst achieving a total positive NPV of
25,000.
On the other hand, if Projects A and B were selected, they would also remain within
the annual capital limitations. The combined investment for Year 0 is 40,000, for
Year 1 is 25,000 and for Year 2 is 40,000, whilst achieving a total positive NPV of
47,500. This amount exceeds the NPV earned by the combination of Projects C
and D.
This problem can be solved by an integer programming formulation. The
procedures would be to establish the value of variables YA, YB, YC and YD for each of
the four projects, which maximise the total net present value ie
Maximise: 20,000 YA + 27,500 YB + 15,000 YC + 10,000 YD
Example of multi-period capital rationing using integer
programming Toby Ltd
The management team of Toby Ltd has identified four indivisible projects, which
require funds to be invested over the next few years, as set out below:
Project A Project B Project C Project D
Year 0 17,500 22,500 - 12,500 Year 1 25,000 - 15,000 15,000 Year 2 10,000 30,000 20,000 17,500
The board of directors of that company has approved the following capital
expenditure programme for those same accounting periods:
Year 0 40,000
Year 1 35,000 Year 2 42,500
The four projects are expected to produce the following positive net present
values:
Project A Project B Project C Project D
Project NPV +20,000 +27,500 +15,000 +10,000
Required:
Discuss the approach for calculating the optimum mix of projects.
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Subject to three annual capital investment constraints:
Year 0 : 17,500 YA + 22,500 YB + 0 YC + 12,500 YD 40,000
Year 1 : 25,000 YA + 0 YB + 15,000 YC + 15,000 YD 35,000
Year 2 : 10,000 YA + 30,000 YB + 20,000 YC + 17,500 YD 42,500
The solution to the above problem would result in YA = 1, YB = 1, YC = 0, YD = 0.
In other words, both Project A and Project B would be selected, whilst the other two
projects would be rejected and the positive NPV of the entire investment strategy
would be 47,500.
Notice that the above solution is superior to the combination of YA = 0, YB = 0, YC
= 1, YD = 1, since the combined positive NPV of Project C and Project D is only
25,000, as already stated.
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Chapter 3
Advanced investment
appraisal section 2
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CHAPTER CONTENTS
MODIFIED INTERNAL RATE OF RETURN ------------------------------ 53
CALCULATING THE MIRR 53
FREE CASH FLOW -------------------------------------------------------- 56
DEFINITION OF FREE CASH FLOW 56
FREE CASH FLOW TO EQUITY 57
RISK AND UNCERTAINTY ----------------------------------------------- 61
SENSITIVITY ANALYSIS 61
PROBABILITY AND EXPECTED VALUES 62
MONTE CARLO SIMULATION 62
PROJECT VALUE AT RISK 63
DURATION ---------------------------------------------------------------- 64
THE MACAULAY DURATION METHOD ---------------------------------- 66
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MODIFIED INTERNAL RATE OF RETURN
To assist in remedying some of the deficiencies of IRR, a technique called Modified
Internal Rate of Return (MIRR) has been developed. MIRR has certain advantages
in that it:
Eliminates the possibility of multiple internal rates of return.
Addresses the reinvestment rate issue ie it does not make the assumption
that the companys reinvestment rate is equal to whatever the project IRR
happens to be.
Provides rankings which are consistent with the NPV rule (which is not always
the case with IRR).
Provides a % rate of return for project evaluation. It is claimed that non-
financial managers prefer a % result to a monetary NPV amount, since a %
helps measure the headroom when negotiating with suppliers of funds.
Calculating the MIRR
The MIRR assumes a single outflow at time 0 and a single inflow at the end of the
final year of the project. The procedures are as follows:
Convert all investment phase outlays as a single equivalent payment at time
0. Where necessary, any investment phase outlays arising after time 0 must
be discounted back to time 0 using the companys cost of capital.
All net cash flows generated by the project after the initial investment (ie the
return phase cash flows) are converted to a single net equivalent terminal
receipt at the end of the projects life, assuming a reinvestment rate equal to
the companys cost of capital.
The MIRR can then be calculated employing one of a number of methods, as
illustrated in the following example.
Example Carter plc
Carter plc is considering an investment in a project, which requires an immediate
payment of 15,000, followed by a further investment of 5,400 at the end of the
first year. The subsequent return phase net cash inflows are expected to arise at
the end of the following years:
Net cash inflows
Year
1 6,500 2 7,750 3 5,750 4 4,750
5 3,750
Required:
Calculate the modified internal rate of return of this project assuming a
reinvestment rate equal to the companys cost of capital of 8%.
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Solution to Carter plc
Single equivalent payment discounted to year 0 at an 8% discount rate:
Year
0 15,000
1 (5,400 x 0.926) _5,000
Present Value (PV) of investment phase cash flows 20,000
Single net equivalent receipt at the end of year 5, using an 8% compound rate:
Year 8% compound factors
1 6,500 1.3605 8,843
2 7,750 1.2597 9,763
3 5,750 1.1664 6,707
4 4,750 1.08 5,130
5 3,750 1 3,750
Terminal Value (TV) of return phase cash flows 34,193
The above compound factors are produced with a calculator.
A five year PV factor can now be established ie (20,000 34,193) = 0.585
Using present value tables, this 5 year factor falls between the factors for 11% and
12% ie 0.593 and 0.567. Using linear interpolation:
MIRR = 11% + 0.567) - (0.593
0.585) - 0.593( x (12% - 11%) = 11.3%
Alternatively, the MIRR may be calculated as follows;
MIRR = 000,20
193,34
5 1 = 11.3%
Furthermore, in examples where the PV of return phase net cash flows has already
been calculated, there is yet another formula for computing MIRR (which is given
on the ACCA formulae sheet). This for