ACCA+P4+Key+Point+Notes+June+2010

ACCA P4 Advanced Financial Management Key Point Notes June 2010

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________________________________________________________________________ Sunil Bhandari – www.IntelligentAccountancyTutorsLtd.co.uk

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Key PointNotes

June 2010

ACCAP4

Advanced Financial Management

Tutor:Sunil Bhandari

Tutor Contact DetailsMobile: 07833 096979E-mail: viawww.IntelligentAccountancyTutorsLtd.co.uk

These notes are not intended to cover the whole syllabus, but target key examinable areas.

Copyright to Intelligent Accountancy Tutors Ltd


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Use of these Key Point Notes

These notes have been written as an aid to assist studentspreparing for the ACCA P4 June 2010. They accrue for thetopics tested in the past exams.

It is of paramount importance that they are used with an upto date Revision Kit (KAPLAN or BPP). A combination ofusing the notes and question practice is the best way toprepare for the forthcoming exams.


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Index

Chapter Number Chapter Name Page NumbersPreliminaries 5-16

Chapter One Cost of Capital 17-26

Chapter Two Capital Structure &Raising Finance

27-35

Chapter Three Dividend policy 37-39

Chapter Four How lenders set theirInterest Rates

41-46

Chapter Five Advanced InvestmentAppraisal

47-57

Chapter Six Adjusted Present Value 59-64

Chapter Seven Modified Internal Rate ofReturn (MIRR)

65-70

Chapter Eight Capital Rationing 71-74

Chapter Nine Foreign Currency Risk 75-84

Chapter Ten Interest Rate Risk 85-96

Chapter Eleven Valuaton ofOptions+Value at Risk

97-112

Chapter Twelve Business Valuations &Mergers &Acquisitions

115-134

Chapter Thirteen Modern ValuationMethods

135-139

Chapter Fourteen Corporate Reconstruction& Reorganisation

141-145

Chapter Fifteen Question 4 & EmergingIssues

147-148


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Exam Formulae and Tables


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Exam Technique

First 15 minutes Read the questions carefully

Recognise the topic being tested

I would recommend that Section B questions are donefirst and then Section A

Next 180 minutes

Attempt the questions in your ranked order.

Stay within your time allocation both on each part ofthe question and on the question itself.

If the written elements are unrelated to thecomputations-try front load as they represent ‘easier’marks.

Try to attempt all parts to all the questions.

If in doubt about how to compute a value-make areasonable estimate and move on.


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General

Numerical Questions

State formula

Show method

Explain as you go

Make assumptions if in doubt

Written Questions Check format – report / essay/ listed points

Headings / subheadings / columnar

Simple short paragraphs-essays and reports

Use ‘numbered’ points for most questions-simplesentence approach.


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Tips

These will be posted on my website sometime in late May2010.


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'What the Current Examiner(Bob Ryan) Has SaidRecently'

Key facts

The Examiner sees this as a “Masters Level” paper. He

expects students to demonstrate expertise, and real

world knowledge / awareness. For example, when

questioned about the Futures question (Q5 D08) he

said that students should be familiar with Open and

Settlement quotes since this is how prices are quoted in

the real world (e.g. on the NYBOT website).

There’s no point question spotting. It is more important

to have worked through past exam questions.

Main problems in the last 3 papers

Weak knowledge of basic F9 topics

Weak integration with other Professional Level papers.

The Examiner expects the students to have a good

knowledge of (for example) P1 and P2 topics.

Lack of contextual understanding. He has suggested

the students should read widely around the subject e.g.

the Financial Times, his own text book “Corporate

Finance and Valuation”.


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The “essay question” (Q4) and written areas in general

were badly done.

Students missing easy marks. Bob Ryan explained that

there are lots of easy marks, but then his “mark ramp”

is quite steep, so only good candidates pick up the

higher level marks. He says this helps to differentiate

between candidates.

Positives

Good standards of English

Good attention to presentation

Good understanding of options and their role


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Chapter One

Cost of Capital

1 Weighted Average Cost of Capital (WACC)

1.1 This is the formula given on your formula sheet.

1.2 Remember that:-

Ke= Cost Of Equity

Kd(1-t) = Cost of Debt

Kd= Yield to maturity on debt

Ve=Market value of the Equity Capital.

Vd= Market Value of the Debt Capital

t= Corporation tax rate


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1.3 The examiner often re-presents the above formula as:-

WACC= Were + Wdrd(1-t)

We= Ve or (1-Wd)Ve+Vd

Wd= Vd or (1-We)Ve+Vd

re=Ke=Cost Of Equity

rd(1-t)=Kd(1-t)=Cost of Debt

Therefore, it’s the same Formula!!

2 Cost of Equity (Ke, re)

2.1 Formulae are given in the exam as:-

This can be simply presented as:-

Ke or re =Rf +βe(Rm-Rf)

This you have to rearrange to:-

re=Do(1+g) +gPo


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This latter formula applies under M&M assumptions with tax.

2.2 Lets clear up the additional symbols to those listed under1.2 above:-

Rf=Risk Free ReturnRm= Return on the Market Portfolioβe=Systematic Risk being faced by the

shareholders.Do=The dividend per share (DPS) today or last paid.g = Constant annual growth rate in dividends.Po =Share price currentlyKei= Cost of equity assuming all equity position.(Rm-Rf)= Equity Risk Premium.

2.3 A common issue is finding the g value. There are severalways that this can be found.

a) Past growth rate is assumed to be future growth rate.

Example

Today is 31st December 2008

31st December DPS2005 $0.242006 $0.272007 $0.292008 $0.32

g= n√ (Do) -1Dn

n=Increments of growthDn=Oldest DPS given


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g= 3√(0.32) -10.24

g= 0.10

b) Gordon’s Growth Model

b=the proportion of profits retained by the business

re= can be the accounting rate of return(ARR) or cost ofequity

Example

If a company has an ARR of 12% and pays out 30% ofprofits as a dividend.re =14%

g= 0.12 x 0.70=0.084

This is a short term growth measure.

g= 0.14 x 0.70=0.098

This is a long term measure


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3 Cost of Debt (Kd(1-t) or rd(1-t))

3.1 Kd or rd is the yield or minimum return for the debtholder.

Kd(1-t) or rd(1-t) is the cost of debt for the company.

3.2 To find the cost of debt we need to look at the type ofdebt finance.

3.3 Bank Loans

Kd(1-t)=Interest % x (1-t)

Example

A company has a 11% Bank Loan .Tax =30%

Kd(1-t)=11x(1-0.30)=7.7%

3.4 Traded Bonds-Perpetual

Kd(1-t)=Ints x (1-t)Po

Remember Po is the market value per block of $100.

Example

9% Bonds trading at $89 t=30%

Kd(1-t)=$9 x(1-030) = 7.1%$89


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3.5 Traded Bonds-Redeemable

Kd(1-t) is an IRR computation based upon

Time $To Po (X) Take two guessesT1-Tn Ints X(1-t) X like 10% and 1%Tn CapitalRepayment

X and do an IRR

Example

7.5% Bond redeemable at par ($100)in 5 years time.Trading at $105. t=30%

Time $ 10% PV 1% PVTo Po (105) 1.0 (105) 1.0 (105)T1-Tn IntsX(1-t)

7.50 X(1-0.30)

3.791 19.90 4.853 25.48

T5 CR 100 0.621 62.10 0.951 95.10(23) 15.58

Kd(1-t)=1 + 15.58 X (10-1)=4.63%(15.58+23)

3.6 Quick assumption that the examiner might indicate isthat

Kd(1-t)=RF X (1-t)

OR

Kd(1-t)=Yield X (1-t)

OR

Kd(1-t)=(Yield or Rf + Credit Risk Premium) x 1-t


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3.7 As can be seen above the market value of debt (Po) isgiven per block of $100.This may have to be computed usingthe Dividend Valuation Model (DVM).

i.e Po=Present Value of all future cash flows discounted atthe yield to maturity.

Example:

$20 m 7% Bond will be redeemed in 3 years at par ($100).Yield to maturity is 5.25%.

NB: Don’t forget that discount factor tables also showformulae at the top of each table.

On the PV Table the formula is

(1+r)-n = 1(1+r)n

Hence the Po=

$7 + $7 + $107(1+0.0525)1 (1+0.0525)2 (1+0.0525)3

=$6.65+$6.32+£91.77

= $104.74

The Vd is

$20m X $104.74= $20.948m$100

i.e Book value of Debt X Po

$100


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4 Degearing/Regearing βeta

4.1 βe must reflect the combination of the systematicbusiness and financial risk being faced by a shareholder.

4.2 We can remove the financial risk element via

βa = Asset Beta, measure of systematic business risk

βd= Debt Beta (Often nil)

Example

βe is 1.95 Vd:Ve 1:4

t= 30% βd=NIL

βa = 4 X 1.954+1(1-0.30)

= 4 X 1.954.7

= 1.66


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Now, if the gearing went Vd: Ve 1:2

1.66 = 2 X βe

2+1(1-0.30)

1.66 = 2 X βe

2.7

1.66 X 2.7 = 2.242

4.3 βasset values may have to be combined before gearingup to find βe

Example

ABC is made up of two divisions.

Division Asset βeta Proportion of theBusiness

Food 0.75 40%Clothes 1.80 60%

The company has Wd=0.32 and t=30%.Rf=5% and theequity risk premium is 9%

Hence,

Combined Asset βeta = (0.75 x40%) + (1.80 X 60%)

= 1.38

βa= Ve X βe

Ve+Vd(1-t)

(Note: Wd =Debt Proportion of the company’s finance)


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1.38= 0.68 X βe

0.68+0.32 (1-0.30)

1.38= 0.68 X βe

0.904

1.38 X 0.904 =1.830.68

Take Ke for the company via CAPM

Ke=Rf+(Rm-Rf) βe

(Note (Rm-Rf) is equity risk premium)

Ke =5+ (9)1.83

= 21.47%


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Chapter Two

Capital Structure AndRaising Finance

1 Introduction

How should the company decide the mix ofequity and debt capital?

2 Practical Issues

If the company uses Debt capital funding it shouldconsider:-

Credit Rating of the company Rate of interest it will pay Market conditions- access to debt capital Forecast Cash Flows-to service and repay the debt. Level of Tangible Assets on which secure the loans. Interest will lead to tax savings i.e Tax Shield Constraints on the level of debt from

a) Articles Of Associationb) Loan Agreements.

Effect upon the company gearing ratio(Wd)

Vd:Ve

Will the debt providers exercise influence over thecompany?

The chance of bankruptcy.


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3 Theories of Optimal Capital Structure

3.1 Common Ground-both major views accept two facts:-

a) Yield<Ke

b) Gearing causes Ke to rise –Financial Risk

3.2 Traditional View (NB Ko=WACC)

Key Points:-

1) Ke rises due to financial risk caused by gearing.2) Kd is initially uneffected by gearing but rises at “high”

gearing levels due to the perception of the possibility ofbankruptcy.

3) Ko-trade off of Ke and Kd. Point X is the optimumgearing level where WACC is lowest.


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4) Once point X is reached via trial and error it must bemaintained.

3.3 MM and Tax

Key points:-

1) Assumptions behind the model:- All debt is risk free Only corporation tax exists Debt is issued to replace Equity All types of debt carry one yield, the risk free

rate Full distribution of profits Perfect Capital Market

2) MM concluded that due to the benefit of the taxshield, companies should maximise the use of debtfinance.

3) Specific Equations can be used under MM +Taxtheory.

Vg=Vu+VDT

Ve+Vd


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WACC= Keu {1-T x Vd}(Ve+Vd)

Only the latter is given on the formulae sheet.

Example

ABC is all equity financed. Its Ve is $500m.It has aKe=12%.

If it raises $150m of Debt Finance and tax is 30%.Yieldis 5%.

Vg=Vu+VDT

Vg=$500m+ ($150m X 30%)

= $545m

Split Vd=$150mVe=$395m

WACC = 12(1-{0.30 X 150})545

= 11.01%

Ke = 12+ (1-0.30) (12-5) 150395

= 12+1.86

= 13.86%


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4 Practical Approached /Views

4.1 Static Trade off Theory

MM +TAX view can be reviewed in the light of the practicalissue that too much gearing leads a company towardsbankruptcy.

A revised equation is:-

Vg=Vu+VDt - (Probability of Financial Distress X Costs of FinanceDistress)

Hence an optimum point exists for gearing where Vg ismaximised.

4.2 Pecking Order Theory

Funds are raised in a practical order-ease of accessingfunds.

Order :- 1) Internal Generated Fund2) Debt3) New Issue of Equity

5 Recent Exam Questions on Raising Debt Finance.

“ ….. raise new capital through a bond issue of $2400million….. would be in the form of 10 year, fixed interestbonds with half being in the Yen and half in the Euromarket”


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Key Point Answer:-

Bond issue attractive way of raising $2400 million. Issue costs will be incurred May not be fully subscribed May need to be underwritten –mitigate some of the

risk. Alternative could be via a syndicated loan Syndicated entails:-

Led by arranging bank. Bring banks together who will provide the loan.

Syndication advantages are:-

Loan sizes are larger than one bank can take on itsown.

Banks may be based in different countries –mixedlending package.

Low transaction costs.

Disadvantages

Forex Risk of foreign loans. Risk of a Bank default Rates may be greater than that on Bond market


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Solution:-

a) Key Point answer

Coupon Rate=5.1% +0.90%=6% 0.90% is credit risk premium is key. If too low,

debt will not be taken. If too high, issued at anattractive premium but costly for the company.

Underwriting agreement would be sensible butcostly.

b) Current Vd

WD=0.25

WD = Vd

Ve+Vd

Ve=$1.2billion


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0.25= Vd

1.2+Vd

0.25(1.2+Vd)=Vd

0.30+0.25 Vd=Vd

0.30=0.75 Vd

Vd=0.30 =$0.4billion0.75

Revised Vd

The existing debt of $0.4 billion ($400 million) carries acoupon and assumed yield of 4%.This is 50bp’s aboveRF%.

However, the new credit rating is 90bp’s above theRF%.Hence yield now be 3.5+0.90=4.4%

Therefore, value of the existing debt (via DVM) will nowbe:-

$4 + $4 + $1041.044 1.0442 1.0443

=$3.83+$3.67+$91.40=$98.90Therefore, existing debt’s new Vd=

$400million x $98.90 =$395.60$100

The new debt will be issued at its market value.

Therefore, Vd=$395.60+$400=$795.60million.


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Current Cost of Debt

rd(1-t) =4% X (1-0.30)= 2.8%

New rd(1-t)would be based on a weighted averageapproach.

{( 400 X 6) +( 395.60 X 4.4)} x (1-0.30)795.60 795.60

=3.64%

Hence increase of 84 bp’s.

c) Advantages and Disadvantages of this mode of financing

Pros Cons

Tax Shield benefit Cost

Lower Co’s WACC Damage to credit rating ofthe company

Secure on the tangible WACC could riseasset(plane) therefore lowering Ve


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Chapter Three

Dividend Policy

1 Introduction

To maximise S/H wealth the Board should establish adividend policy-the payment pattern to the equity investors.

2 Theories

Several theories have been put forward to assist:-

2.1 Residual – If spare cash exists at the end of the year paydividend.

2.2 Pattern – Be consistent with dividend payments. Either

a) Pay the same dividend per share (DPS) each year.b) Maintain the payout ratio (DPS/EPS)c) Maintain the same year-on-year growth rate in

dividends.The latter links into the Po via thedividend valuation model (DVM)

2.3 Irrelevancy (M&M)

In a perfect capital market providing the directors caninvest in projects with a positive NPV no dividendsare required. The Ve will rise and the S/H can sell sharesto create the cash the need(Manufacture Dividends).


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3 Practical Considerations

There are many to consider:

Availability of cash What dividends do S/H want (clientele effect)? Signalling effect –payment of dividends indicates a

healthy company Retaining cash is a key source of finance. Dividend growth should be greater than inflation Tax impact upon S/H Effect the dividend will have on dividend

cover(EPS/DPS) Number of investment opportunities will restrict

dividend payments. Risk-paying now is safer than promising to pay next

year Is the dividend within the company law regulations?

4 Alternatives to Cash Dividends

4.1 Scrip Dividends

4.1.1 The S/H will receive extra shares instead of cash on apro rata basis.

4.1.2 This will allow the S/H to sell extra shares for cash andthe gain will be subject to CGT.

4.1.3 The effect will:-

a) Increase the issued equity capitalb) Dilute EPS and Po valuesc) Create pressure for the board to pay more total

dividends in the future as more shares are in issue


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4.2 Share Buy Back

4.2.1 If the board has “one off” period of excess cash, theycould consider a share buy back.

i.e. Buy back shares at Po and cancel them.

4.2.2 Considerations:-

a) Allowable under company law.b) Increase gearing as Ve may fall.c) Tax implications for the S/H(CGT)d) Reduced number of shares will cut supply for

trading purposes.e) Less dividend pressure on the board in future.f) Criticism-is this the best use of company cash.


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Chapter Four

How lenders set theirinterest rates?

1 Credit Risk

1.1 This is the risk of default by the borrower. Occurs whenthe secured asset value falls below the value of the loan

1.2 Loss to the lender depends upon:-

Probability of default occurring. Part of the debt recovered from the sale of the assets.

1.3 Lenders action re credit risk

Assess via credit assessment agencies (the chance thecompany is unable to pay the interest or principal)

Set credit risk premiums to the borrower.

2 Credit Risk Premium

2.1 Risk Neutral Lender –Example

A company has an asset worth $2m and secured debt of$0.8m.The asset can vary in value by 10%monthly.

Therefore,σa = σm x √ Tσa = 10% x √12months

= 34.64% annually

Therefore, Asset can vary in value by


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34.64% X $2m = $692,800 annually

Hence using the “Z” value concept (how many standarddeviations) from normal distribution table.

$1,200,000 = 1.732$692,800

Therefore, $0.8m lies 1.732 standard deviations below the$2m asset value.

$0.8m $2mLies 1.732 σ σ =$692,800Away from $2m

Checking the normal distribution tables for 1.732(or 1.73)=0.4582.

The ‘chance ‘of the asset not falling below $0.8m is

0.4582+0.50=0.9582

If the company defaults then the bank need to recover thedebt. This depends upon:-

Value of theasset


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Type of Asset Covenants on disposing the asset

If (say) only 75% of the debt can be recovered and LIBOR is6%.What premium above LIBOR should the bank set?

Based on a 1 year period and a discount rate equal toLIBOR, the bank needs a present value to equal $800,000 –value of the loan today.

i.e

$800,000= (PV of the cash recd in 1year not defaulting) +(PV of the cash recd in 1year if default occurs)

i= Interest rate the bank sets (inc the risk premium)

$800,000=

{$800,000 X (1+i) X 0.9582} + {75% X $800,000 X (1+i) X0.0418}1+0.06 1+0.06

“Note: 0.0418=1-0.9582”

800,000=723,170(1+i) +23,660(1+i)

800,000=723,170+23,660+746,830 i

(800,000-723,170-23,660) = 0.0712746,830

i.e 7.12% which is 112 basis points above LIBOR OF 6%.

2.2 Risk Adverse Lender

If the bank were more risk adverse the discount rateabove can be adjusted to value greater than LIBOR.


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In other words the “i” would increase accordingly. (Say) in the above example the bank set a discount

rate of 6.5% and not 6%.LIBOR is still 6%.

$800,000=

{$800,000(1+i) X 0.9582}+ {$800,000 X 75%X(1+i) X 0.0418}1.065 1.065

800,000 = 719,775+23,549+743,324ii = 0.0762

i.e = 7.62%

162 Basis points above LIBOR

3 Problems

Finding asset values Assessing the recoverable amounts on default σ assessment


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Chapter Five

Advanced InvestmentAppraisal

1 Net Present Value of Free Cash Flows (FCF)

1.1 Free Cash Flows(FCF)

The cash is available after expenditure andreinvestment into the business.

Computed two ways:-

1) Incremental cash flow approach

Revenue – Costs – Tax -Capex + Scrap Value - AssetReplacement Spending – Working Capital Injection + Taxsaved on Tax Allowable Depreciation.

2) Adjusting Accounting Profit

Net operating profit (beforeinterest and tax)

X

Plus Depreciation XLess Taxation (X)Operating cash flowLess Investment:

X

Replacement non-currentasset investment(RAI)

(X)

Incremental non-currentasset investment(IAI)

(X)


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Incremental working capitalinvestment(IWCI)

(X)

Free cash flow for thecompany

X used in NPV comps

Debt Interest (X)

Debt Repayments (X)Debt Issues XFCF to equity X used to value equity in

certain business valuationmodels.

1.2 Proforma

Time$’000 T0 T1 T2 T3 T4

Revenue(incInflation)

- X X X -

Costs(incInflation)

- (X) (X) (X) -

Operating Cashflows

- X X X -

Tax @ (1yeardelay)

- - (X) (X) (X)

Capex&ScrapValue

(X) - - X

Tax savings onTAD

- - X X X

Assetreplacementspending

- (X) (X) (X) -

Working Capital (X) (X) (X) X -Free Cash Flows (X) X X X (X)Cost of Capital% 1.0 X X X (X)

PV (X) X X X (X)NPV $XXX


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1.3 Relevant Cash Flows

Incremental –caused by the project Future –still to occur Exclude:-

1) Sunk Costs2) Finance Charges3) Dividends4) Non-Cash flows5) Non-incremental fixed overheads

1.4 Inflation

Include in the cash flows

Money/Nominal CFn=Real CFn X (1+h)n

eg Real CF3=$600= 7%pa

Money CF = $600 X (1+0.07)3

= $735

Include in the cost of capital 3 possibles:-

a) Company WACC is inflation inclusiveb) Risk adjusted WACC is inflation inclusive.c) Use the Formula given.

(1+i) = (1+r) (1+h)

h = inflationr = real cost of capitali = money cost of capital

eg r = 10% h=5%

Chapter 1


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(1+i) = (1+0.10) (1+0.05)

1+i = 1.155

i =0.155 or 15.5%

1.5 Taxation

Using the December 08 paper as benchmark, theexaminer showed taxation as a “2 line approach”.

Timings –could be no delay or 1 year delay

Tax on operating cash flows.

eg Extract from the NPV:-

$’000 T1 T2 T3

OperatingCash Flows

200 300 -

Tax 30%(say1year delay)

- (60) (90)

Tax saved on Tax allowable depreciation /CapitalAllowances.

eg Capex will take place over the first year and be finishedby the end of the year. Cost $6.2m.TAD is 50%.First yearallowance followed by straight line allowances for a furtherthree years. Tax is 30 %( no time delay).

T1 Tax saving =50% X $6.2m X 30%=$930,000

T2-T4 Tax saving=50% X $6.2m X 30%=$310,0003 years


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Another Example

T0=1/Jan/09

T0 CAPEX $1000K

T5 Scrap $200K

TAD is 25% reducing balance and tax is 30% with a oneyear delay.

Extract from the NPV:-

Time

$’000 T0 T1 T2 T3 T4 T5 T6

Capex &Scrap

(1000) - - - - 200 -

T.A.D(w1) - - 75 56.25 42.19 31.64 34.92

(w1)

Timing and Tax Saving $’000T2 1000 X 25% X 30% 75T3 75 X (100%-25%) 56.25T4 56.25 X 75% 42.19T5 42.19 X 75% 31.64T6 Balance figure 34.9230%(1000-200)= 240

NB: Other assumptions are possible –so read the questioncarefully.


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1.6 Working Capital

Think as it is a project bank account.

Invest, Adjust, Close!!!

eg

$’000 T0 T1 T2 T3

WC needed - 100 170 300RelevantCash Flows

(100) (70) (130) 300

These go into the NPV

1.7 Cash flows into Perpetuity.

Eg Project has following cash flows and a cost of capital of10%.

Time

$’000 T0 T1 T2 T3 T4-Tperp

CashFlows

(1000) 200 400 300 350pa

10% 1.0 0.909 .826 .751 1 X 0.7510.10

*

* 1 =discount rate for perpetuity0.10

If applied to a cash flow starting at T4 it discounts back to T3


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Therefore,

1 X 0.751 =7.51 is the effective discount rate.0.10

Take the same example as above and now bring in constantgrowth of 2% from T5 each year in perpetuity.

$’000 T0 T1 T2 T3 T4-Tperp

CashFlows

(1000) 200 400 300 350

10% 1.0 0.909 0.826 0.751 9.388*

* 1 X 0.751r-g

1 X 0.751=9.388(0.10-0.02)

i.e 1 computes the discount factor for a cash flow(r-g) with a constant growth rate pa

2 IRR

2.1 The Internal Rate of Return is the cost of the capital thatgives an NPV of NIL

2.2 Example

NPV @10%=$300KNPV @20%=($160K)


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IRR=

10+ { 300 } X (20-10)(300-(-160)

= 16.52%

2.3 Decision rule with IRR is if

IRR>Cost of Capital –Accept

However IRR has many weaknesses which are overcome byMIRR (see a later chapter)

3 Foreign Investment Appraisal

3.1 Predicting future spot rates via formulae provided:-

S1= F0= Future Spot RateS0= Spot Rate Todayhc = Inflation Rate abroadhb= Inflation Rate homeic = Interest Rate abroadib = Interest Rate Home

3.2 Double Taxation-the golden rule is you must pay thehigher of the two rates.


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3.3 Format-may need to change from earlier in this chapterto accrue for double tax.

Example

Jon inc (USA company) has a project in the UK. Cash flowshave been computed already as:-

Time £’000T0 1,000T3 scrap 100T1 operating flows 500T2 operating flows 600T3 operating flows 400

TAD in the UK is straight line and tax rates are

UK 20%USA 30%

with a one year delay

S0=$1.50/£ and inflation is expected to be

USA=5%pa UK=3%pa

What are the free cash flows ready for discounting?

Solution

Notes:-

USA=Home, UK=ForeignS0=$1.50/£ or £0.67/$Spot Rates via PPP:-


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56

Time £/$S0 0.67S1 0.67 X 1.03 =

1.050.66

S2 0.66 X 1.03 =1.05

0.65

S3 0.65 X 1.03 =1.05

0.63

S4 0.63 X 1.03 =1.05

0.62

£’000 T0 T1 T2 T3 T4

OperatingFlows

- 500 600 400 -

TAD(1000-100)

3

- (300) (300) (300) -

Taxable“Profit”

- 200 300 100 -

Tax@20% - - (40) (60) (20)Add backTAD(notcash flow)

- 300 300 300 -

- 500 560 340 (20)Capex&Scrap (1000) - - 100 -

£’000 (1000) 500 560 440 (20)Spot Rates £0.67 £0.66 £0.65 £0.63 £0.62$’000 (1493) 758 862 698 (32)USA Tax(w1) - - (30) (46) (16)FCF (1493) 758 832 652 (48)


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57

(w1) Example working

T1 Taxable Profit=£200Additional Tax=10% X £200=£20Converted @ T1 spot =£20/£0.66

=$30Paid at T2!!!


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59

Chapter Six

Adjusted Present Value

1 When to use it

1.1 APV is a NPV method to be used when:-

Project is core or non-core activity Specific debt Finance is being use on a project. Subsidised interest exists on the project debt finance.

1.2 APV is still the change in shareholder wealth arising fromthe project.

2 Method

Establish the βasset for the project. Using the βasset in CAPM find Keu(all equity Ke

i) Discount the relevant project cash flows using Keu to

find the base case NPV Establish the yield on the debt. Find PV of the issue costs (possibly post tax) using

yield as a discount rate. Find PV of the tax savings on the interest paid on the

loan finance raised using the yield as a discount rate.


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60

APV

$m

Base case NPV XPV of issue costs (X)PV of tax savings on interest X

APV X

Recent Exam Question


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61

Following steps above:-

a) βa = Ve X βe

Ve+Vd(1-t)

= 7500 X 1.407500+2500(1-0.30)

= 1.14

b) Keu=RF+ (Rm-RF)βa

Keu=5.0+ (3.5)1.14

= 9%Note:-

RF=Gilt Yield =5.40-0.40=5 (Rm-RF)=Equity Risk =Premium =3.5


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62

c) Base Case NPV

$m T0 T1 T2 T3 T4 T5 T6

Revenue - 680 900 900 750 320 -Direct Costs - (408) (540) (540) (450) (192) -Lost Cont’n - (150) (150) - - - -OperatingCashfows

- 122 210 360 300 128 -

Tax at 30 % - - (37) (63) (108) (90) (38)

Capex&Scrap (800) - - - - 40 -Tax Savedon CapitalAllowances

(w)

- - 120 48 29 17 14

FCF (800) 122 293 345 221 95 (24)9% 1.0 .917 .842 .772 .708 .650 .596PV (800) 112 247 266 156 62 (14)

Base Case NPV = $29m

Assumptions:- Indirect costs are not incremental Design costs are sunk therefore ignored.

(w)

Timing and Tax Saving $mT2 800 x 50% x 30% 120T3 400 x 40% x 30% 48T4 48 x (100-40)% 29T5 29 X 60% 17T6 Balance figure 1430%(800-40)= 228


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63

d) Yield on new debt=

5.40+1.80=7.2%

i.e LIBOR + 180BP’s

e) Issue costs payable to has to be 2% of loan +Issue costs

i.e $800 m X 2%=$16.33m0.98

f) PV of tax savings on interest paid:-

Loan inc Issue Costs $816.33mInts Paid in T1-T5 @ 7.2% pa $58.77m paTax saved @30%T2-T6 $17.63m paDiscounted at 7.2%

$17.63m + $17.63m + $ 17.63m + $17.63m + $17.63m1.0722 1.0723 1.0724 1.0725 1.0726

15.34+ 14.31+ 13.34+ 12.45+ 11.62= $67.06m

$m

Base Case NPV 29Issue Costs (16.33)PV of Tax Savings 67.06

$79.73m


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3 Subsidised Loans

3.1 If any part of the loan Finance is at a subsidisedrate, then the APV must include an extra benefit.

3.2 PV of the post tax subsidy discounted at the yield.

i.e

Ints pa not paid less tax not saved all discounted at theyield.


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Chapter Seven

Modified Internal Rate ofReturn (MIRR)

1 NPV vs IRR vs MIRR

1.1 NPV represents the increase in Ve arising from theproject. However, it can be hard to explain the “layman”.

1.2 IRR is the cost of capital that causes the NPV to be nil.It’s decision rule

IRR > Project Cost of Capital Accept

1.3 IRR has weaknesses:-

a) Cannot be used to compare mutually exclusiveprojects.

b) Multiple IRR’s exist

when the cash flow pattern is not standardie Standard Pattern -,+,+,+,+

Non-Standard Pattern -, +, +, +,-

1.4 MIRR is a measure that gives an NPV of nil but will leadto a project decision rule consistent with NPV.


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2 Computing MIRR

2.1 Simple Example

Cost of Capital=10%

2.2 Using The Formula

NPV had been computed at 10%.

Time $ 10% PVT0 (1000) 1.0 (1000)T1 400 0.909 363.6

T2 600 0.826 495.6T3 300 0.751 225.3

84.5

* PV of Return Phase=$1084.50

Formula given

PVR=PV of Return Phase Cash FlowsPVI=PV of Investment Cash flowsre=Cost of Capitaln= Year of the final cash flow

Time $’000T0 (1000)T1 400T2 600T3 300

Return phaseof the project

*


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67

(1/3)

MIRR= {1084.50} (1+0.10)-11000

= 0.1301. i.e 13.01%

Alternative Method:

a) Terminal value of Return Phase cash flows.

Time $’000T1 400 X 1.102= 484T2 600 X 1.10 = 660T3 300 X 1.0 = 300

1444

Therefore, we now have a revised set of cash flows

T0 (1000)T3 1444

MIRR is the discount rate that causes an NPV of nil.

Therefore 1444 - 1000 =NIL(1+MIRR)3

1444 =1000(1+MIRR)3

MIRR = 3√(1444) -11000

0.1303 OR 13.03%


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2.3 More complex Example

Time $,000 10% PV

T0 (700) 1.0 (700)T1 (300) 0.909 (272.7)T2 400 0.826 330.4T3 600 0.751 450.6T4 300 0.683 204.9

NPV 13.2

PVI=972.7PVR =985.9

Therefore,

MIRR= {985.9}¼ (1.10)-1972.7

= 10.37%

Both NPV rule and MIRR rule indicate project is worthwhile.

3 Problems with MIRR

3.1 Both NPV and MIRR assume cash flows from a projectare reinvested at re.This may not be the case.

3.2 MIRR may itself have to be “modified” to accrue ofvariable reinvestment rates.

3.3 Defining the “Investment Phase”. Per Q1 Dec 08 twodefinitions were possible giving slightly differentanswers.

(972.7)

985.9


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71

Chapter Eight

Capital Rationing

1 The Problem

1.1 When there is a lack of sufficient cash to invest in allprojects with a positive NPV

1.2 Cash can be restricted due

a. “Hard” Reasons –external constraint eg Credit Crunch.b. “Soft” Reasons –internal restrictions eg Capex Budget

2 Single Period-Divisible Projects

2.1 Compute the Profitability Index (PI) for each project.

PI= NPVCash outlay in critical period

2.2 Rank the projects based upon the PI

3 Multiperiod-Divisible Projects

3.1 Can only be solved by linear programming

3.2 The examiner has indicated the formulation may betested but not arriving at a solution.


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Example

A company has identified the following independentinvestment projects, all of which are divisible and exhibitconstant returns to scale. No project can be done more thanonce.

Project CashFlows at

time:

0 1 2 3

$000 $000 $000 $000A -10 -20 +10 +20B -10 -10 +30 +6C -5 +2 +2 +2

There is only $20,000 of capital available at T0 and only$5000 at T1, plus the cash inflows from the projectsundertaken at T0.In each time period thereafter, capital isfreely available. The appropriate discount rate is 10%.

Solution

Using the Dividend Formulation Model. (Assuming AFull Distribution Policy)

1) Symbols

Dn=Dividends paid at time n.a,b,c,d = Proportions invested in each project.Z= Objective.

2) Objective

Maximise the PV of dividends.

Z= D0+ D1 + D2 + D3

1.10 1.102 1.103


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3) Constraints

10a +10b+5c+D0=20,00020a+10b+D1=5000+2cD2=10a+30b+2cD3=20a+6b+2cDn≥00≤ a, b, c, ≤1


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Chapter Nine

Foreign Currency Risk1. Translation Exposure

1.1 Risk caused by change in the value of a Forex asset orliability over the longterm.

1.2 Example: ABC plc has a US subsidiary worth $10m.

2007 - at $1.50 £6.67m

2008 - at $1.75 £5.71m

Loss to equity (£0.96m)

Funded by a $10m loan.

2007 - at $1.50 £6.67m

2008 - at $1.75 £5.71m

Gain to equity £0.96m

1.3 Not a cash risk, only due to financial reporting!!!!

2 Transaction Exposure

2.1 Change in the value of the spot rate over the shortterm causing a cash gain or loss.

2.2 Must hedge!!


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3 SPOT Rates

3.1 Rate of exchange at a point in time.

(Bid) (Offer)$1.5000 - $1.5555 / £

£0.6429 - £0.6667 / $(Bid) (Offer)

3.2 Picking the correct rate-Quick Method

If the SPOT Rates are FX/Home Currency

We are RECEIVING FX then

Use the right hand rate

4 Internal Hedges

4.1 Invoice in home currency

All transactions in home currency

Transfer risk to the other party

Monopoly power-over our customers or suppliers

4.2 Foreign currency bank account

Held in the main currencies ($, Euro)

Pool all transactions in same FX

Reciprocal andcross over!!!!!


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4.3 Leading and Lagging

Watcher / predictor of spot rate changes in shortterm(say 3 months)

Leading – accelerate exchange(early)

Lagging – delay the exchange(late as possible)

Used a lot by Importers who have to sell their homecurrency

4.4 Netting

Match all FX transactions in the same FX occurring onthe same day

5 External Hedges

5.1 Forward Market(Lock into a Fixed Rate)

“Fix the rate today that will apply on a set future date”

Technique: -

1. Net the future transactions in same FX and samedate. Ascertain if “buying” or “selling” the £.

2. Forward contract, X months, at Forward Rate“may” have to computed as :-

SPOT + Discount (- Premium)

3. Exchange FX at the forward rate on the futuredate.


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5.2 Money Market Hedge(Rate used is Today’s Spot Rate)

“The exchange will take place today at the known spotrate”.

Technique

Home Abroad

Today’s Spot£ Answer FX

X

£ Answer FX

FX

5.3 Futures(Lock into a rate that will approximately equalToday’s Spot Rate)

The hedge is ‘effectively’ like a spread bet. If thecompany will make a transaction loss by the spot raterising, then the hedge is to ‘effectively bet’ that thisevent will occur on the Futures Market. Hence the losson the Spot Market is offset by the profit on the FuturesMarket.

If a gain is made on the Spot Market then a loss will bemade on the Futures Market.

Hence it is trying to lock the rate at approx today’sSpot Rate.

Today

1+ints home

Future Date

1 + ints foreign


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Technique: -

1. Draw the timeline showing all rates. Best if ratesare presented as value of the currency of thecontracts.

2. Setup – Today

Ascertain the downside(d/s) risk ‘Bet’ on the d/s risk via the futures market. No. of contracts =

Net FX Transaction

Futures Rate

Standard Contract Size (in currency of thecontract)

Work out ticks / contract(normally0.0001/currency)

Deposit the returnable margin

3. Close out – future date£

(a)Transaction – at spot XXX

(b) Futures Profit / Loss(No of contracts x Tick value x Tick Movement) @ SPOT XXX

XXX

NB: Loss on transaction, gain on the future or gainon transaction ,loss on the futures.


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5.4 Options (Bet possible Hedge)

“Right to buy (call) or sell (put) FX at a fixed rate overa set period (American) or on a set date (European)”.

Technique: -

1. Timeline-As for futures

2. Set up today

Ascertain if we need a put or a call option Pick a strike rate from: -

1. Cheapest premium or2. Nearest to spot or3. Best possible rate

No. of contracts

Transaction Number

Strike Rate

Standard Contract Size

Summary

Number of contracts x size x rate.

Compute the premium and convert at spot

3. Close out – Future date

All situations cost = premium paid


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81

No receipt or payment in FX – options lapse

Compare spot with strike rate – choose the bestrate for the business

6. Pros & Cons

Pros ConsForward Market

Fixed Rate, certainty Easy Cheap Tailored

Inflexible/contract Lose out on the upside Must ensure FX receipts

arriveMMH

Convert today Cheap Tailored Flexible

Complicated May not apply for FX

receipt

Futures Effectively fix rate No cost Small gain

Complicated Small loss Need cash for margin No tailoring

Options Best hedge – cover

d/s risk only Flexibility Lots of choice

Complicated No tailoring Expensive


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7. SWAPS

7.1 In forex swap, the parties agree to swap equivalentamounts of currency for a period and then re-swap themat the end of the period at an agreed swap rate.

The swap rate and amount of currency is agreedbetween the parties in advance. Thus it is called a‘fixed rate/fixed rate’ swap.

The main objectives of a forex swap are:

To hedge against forex risk, possibly for a longer periodthan is possible on the forward market.

Access to capital markets, in which it may be impossibleto borrow directly.

Forex swaps are especially useful when dealing withcountries that have exchange controls and /or volatileexchange rates.

7.2 Example- Say the bridge will require an initialinvestment of 100m pesos and is will be sold for 200mpesos in one year’s time.

The currency spot rate is 20 pesos/£, and thegovernment has offered a forex swap at 20 pesos/£. Aplc cannot borrow pesos directly and there is no forwardmarket available.

The estimated spot rate in one year is 40 pesos/£.Thecurrent UK borrowing rate is 10%.

Determine whether A plc should do nothing or hedge itsexposure using the forex swap.


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Solution

£m 0 1Without swapBuy 100m pesos @20 (5.0)

Sell 200m pesos @40 5.0Interest on sterling loan (5x 10%)

(0.5)

(5.0) 4.5

£m 0 1With forex swapBuy 100m pesos @20 (5.0)Swap 100m pesos back@20

5.0

Sell 100m pesos @40 2.5Interest on sterling loan (5x 10%)

(0.5)

(5.0) 7.0

A plc should use a forex swap.

(Key idea: The forex swap is used to hedge foreignexchange risk. We can see that in this basic exercise thatthe swap amount of 100m pesos is protected from anydepreciation, as it is swapped at both the start and end ofthe year at the swap rate of 20, whilst in the spot marketpesos have depreciated from a rate of 20 to 40 pesos perpound.)


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85

Chapter Ten

Interest Rate Risk

1

What are the issues?

We have loan finance We have deposits andinterest rates are set earning a variableat a variable rate on a interest rateregular basis

Cover an interest Cover an interestrate rise rate fall


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2 “FIXING” INSTRUMENTS (Lock in to Fixed Rate)

Forward rate agreements(FRA)

Purchased from a merchant Pros Consthe money markets - easy - contract

-flexible -size (≥ $1m)- cheap

Contract that fixes futureinterest rates for a set period

FRA 3-9 @ 4% pa

Fix start Fix stops 9 months Fixed Rate3months from nowfrom now


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87

Interest rate future

Fixing the interest rate can be achieved by using futures.One of the main markets that is used is the UK LIFFE(London International Financial Futures Exchange).

The hedge is achieved by effectively ‘betting’ on the futuresmarket that its interest rate will change. The bet is alwayson the downside (ie those with loans are betting that rateswill increase). Also, the futures interest rate is derived fromthe market interest rates (LIBOR)

If the downside occurs, the company will have to pay moreon its loans as the market rate has risen, but would havemade a profit on the futures market. If rates go down, loaninterest will fall but a loss will be made on the futuresmarket. In both cases, the effective interest rate is fixed.

Futures are complicated by a number of factors.

Contract sizes

Margins / deposits payable at the start of thehedge

Not perfect hedge .May not look in at the currentrate.


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88

3 “CAPPING” METHODS (Setting a ceiling for the loaninterest rate)

Interest rate guarantee(IRG)

Purchased froma merchant bank fora fee Covers the adverse

of interest ratechanges but at acost!!!

Contract that capsthe future interestrate for a setperiod

IRG 3-9 @ 4% pa

Cap starts in Cap stops 9 Capped rate3 months time months from now


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Interest Rate Option

The future and options market provides a product that cancap interest rates for borrowers like an IRG. The hedge is toeffectively have the ‘right to bet’ on an interest rate increaseas shown on the futures market.

As an example, suppose that today is 30 June and thefollowing data is available on September LIFFE options.

Strike price(SP)%

Interest ratecap

(100 – SP)%

Call optionspremium

%

Put optionspremium

%

93.75 6.25 1.29 0.2394.25 5.75 0.69 0.7794.75 5.25 0.16 1.33

If a company wished to protect itself against an interest rateincrease above, say, 5.75%, it would purchase a put option.A premium of 0.77% would be payable now. If the marketinterest rates started to rise, the company would have topay more interest on its loans. However, interest rates onthe futures market will also rise and should this exceed5.75%, the business will exercise its put option. The cashreceived from this should cover most of the extra interestpaid on the loan.

Contract sizes and a standard length of three monthscomplicate interest rate options.


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90

NB Collars

Create a cap & floor simultaneously Save premium Lose benefit of interest rate drops below the floor

4 SWAPS

4.1 Longterm method of hedging where companies “swap”their interest commitments but no their loans.

4.2 Example

Company A wishes to raise $10m and to pay interest ata floating rate, as it would like to be able to takeadvantage of any fall in interest rates. It can borrow forone year at a fixed rate of 10% or at a floating rate of1% above LIBOR.

Company B also wishes to raise $10m.They would preferto issue fixed rate debt because they want certaintyabout their future interest payments, but can onlyborrow for one year at 13% fixed or LIBOR+2%floatingas it has a lower credit rating than company A.

Calculate the effective swap rate for each company –assume savings are split equally.

4.3 Exam Technique

(1) Table of Interest Rates.

Company Fixed Float WantA 10% LIBOR +1% FLOATB 13% LIBOR +2% FIXED


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91

(2) Interest Difference.

%A (Fixed)+B (Float)

10+LIBOR+2 =LIBOR +12

A(Float)+B (Fixed)LIBOR+1+B =LIBOR+14Difference 2%

(3) SWAP DiagramLIBOR+2

A B

12 (w1)

10 LIBOR+2

(w1) 13-(0.5 x2) =12

(4) Effective Rates

A PAY LIBOR

B PAY 12

Both save 1% and get what they want.

4.4 Problems

Fees payable to intermediaries Default risk by one party.


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Recent Exam Question:


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93

Solution

a) (i) Interest Rate Futures

Use a simple 3 step approach

1) Timeline

1 Jan 1 March 31 March(Now)

LIBOR = 6.00 5.00 or 7.00Mar Futures=6.12 * 5.04 (w2)7.04Basis =0.12 0.04 (w1) 0.04 NIL

* Use settlement values Basis falls toif given (100-93.880) nil at the end

of the quarter

(w1) Basis of 0.12 [12 Basis points] will fall to nil by 31stMarch. On the 1st March one month from three is stillremaining. Hence,

1/3 x 0.12=0.04

(w2) As the Mar Futures at 1 Jan was higher than LIBOR[6.12 vs 6.00] it is assumed to stay higher until expiry.


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94

2) 1st Jan-Set up the Hedge

The company will be exposed to movements on theLIBOR for a period of 4 months from 1st March

Buying futures (or effectively betting on a rise ininterest rates)

Number of contacts:-

£30m X 4 months = 80 contracts£500,000 3 months

3) 1st Mar-Close Out Hedge

LIBOR Falls5.00%

LIBOR Rises7.00%

Company will pay 50 BP’s aboveLIBOR

5.50% 7.50%

£ £Payment of 4 months Interest£30m X 4/12 X Interest Rate

(550,000) (750,000)

Loss on Futures(6.12-5.04) X £12.50 X80

0.01

(108,000)

Profit on Futures(7.04 -6.12) X £12.50 X80

0.01

92,000

Effective Cost of Loan (658,000) (658,000)As a % of £30mi.e £658,000 X 12 X 100%

£30m 4

6.58% 6.58%


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(ii) Options

1) Timeline-as for futures above

2) 1st Jan –Set up the Hedge

As the current LIBOR is at 6.00%, the company will buyMarch put options at 94000(100-6.00) to cap it’sinterest rate.

No of contracts – as above 80

Premium Payable

0.168 X 80c X £500,000 X 3/12100

= £16,800

3) 1st March –Close out Hedge

LIBOR5.00%

LIBOR7.00%

£ £Premium Paid (16,800) (16,800)Interest paid-see Futuresabove

(550,000) (750,000)

Compare Cap vs Mar FuturesInterest Rate6.00% vs 5.04% -6.00% vs 7.04%Therefore, Use the option andreceive(7.04-6.00) X 80 X £12.50

0.01

104,000

Total Cost (566,800) (662,800)Effective Annual% 5.67% 6.63%


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96

As both are equally as likely

(5.67% X 0.50) + (6.65% X 0.50)

= 6.15%

Both methods keep the APR below the treasures target of6.60%

However the options are preferred at 6.15%

b) What did the examiner write to answer this:-


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Chapter Eleven

Valuation of Options+Value at Risk1 Valuation of Options

1.1 An option gives the holder the right, but not theobligation to buy or sell a share at a fixed price on aspecified future date.

Details and terminology: -

(a) Put – right to sell.

(b) Call – right to buy.

(c) Exercise price / strike price – price at which sharescan be bought or sold.

(d) Expiry Date – date on which the option can beexercised (European type option).

Our aim is to find the value of the options on theopen market.


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1.2 Components of Option Value

Intrinsic value and time value

There are 5 main components to the value of an option

(a) Intrinsic value, the difference between

(i) The current price of the asset(Pa)

(ii) The exercise price of the option(Pe)

(b) The time value of the premium, reflecting theuncertainty surrounding the intrinsic valuebetween now and the exercise date. Relevantfactors:

(i) Variability in the daily value of the asset(currency, interest etc)(s)

(ii) Time until expiry of the option (a later expirydate having greater risk)(t)

(iii) Interest rates (since cash flows occur at twodifferent times)(r)


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The Black Scholes Option Pricing Model

1.1 The above five factors have been built into the Black-Scholes formula to find the value at time 0 of aEuropean call option. (c).

All three formulae are given in the tables but you mustknow what the symbols stand for.

Symbols:

Pa=share price

Pe=exercise price option

r =annual (continuously compounded) risk free rate ofreturn

t =time to expiry of option in years

s =share price volatility, the standard deviation of therate of return on shares

e =the exponential constant 2.7183

In =natural logarithm

On Your calculator!!


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100

d1 &d2= Compute to two decimal places.

N(d1)& N(d2)=the cumulative value from the normaldistribution tables for the value d1 or d2.Read thebottom of the tables very carefully.

Example

The current share price of B plc shares=$100The exercise price =$95The risk free rate of interest = 10%pa =0.1The standard deviation of =50% =0.5return on the sharesThe time to expiry =3 months=0.25

1) Find d1 and d2

d1=In (100/95)+(0.10+0.5X0.52)0.250.5√0.25

d1=0.051+0.0560.25

d1=0.43

d2=0.43-0.25=0.18

2) N (d1) =0.50+0.1664=0.6664

N (d2) =0.50+0.0714=0.5714

3) Find e-rt

rt =0.1 X0.25 =0.025

e-0.025=0.975


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101

Hence,

c= (100 x 0.6664)-(95 x 0.5714 x 0.975)

=$13.71

1.3 Put-call parity

Black Scholes’ model will only calculate the value of acall option. The value of a call option, a put option, theexercise price and the share price are related (wherethe put and call have the same strike and exercisedate):

Find the value of the put option

p =$13.71-$100+$95 X 0.975

= $6.34


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2 ‘The Greeks’

There are five indicators of how the option pricechanges according to the different factors in the BlackScholes equation.

2.1

Change In Varying With

Delta δ Option value Underlying assetvalue

Gamma Υ Delta Underlying assetvalue

Theta θ Timepremium

Time

Vega no symbol Option value Volatility

Rho ρ Option value Interest rates

2.2 The Delta Hedge

Delta hedging is used by options traders who havewritten options and wish to calculate how many sharesthey need to hold to hedge their position. If the delta is0.7 they will need to hold 0.7 shares for every optionwritten.

The delta also measures how many shares one optionwill ‘cover’ if used to hedge a holding of shares.


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3 FOREX modified Black-Scholes option pricing model.(Grabbe variant)

3.1 Formulae

where

FO=Forward RateX=Exercise RateR=Domestic interest rate.

3.2 Used for the valuation of Forex options.


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3.3 Example


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106


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107


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108


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109


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110

4 Black and Scholes applied to Investment Appraisal.

4.1 Real options on projects

Delay/Defer the project Switch /redeploy resources Expand/contract the project Option to abandon.

4.2 Recent Exam Questions


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Solution

Pa=PV of the project = ($4m+$24m) =$28mPe=Capex=$24mt=2 yearsr=5% (0.05)s=25 %( 0.25)

1) Find d1&d22

d1=ln (28/24)+(0.05+0.5x0.25)20.25 X √2

= 0.154+0.16250.35

= 0.90

d2= 0.90-0.35=0.55

2) N(d1)=0.50+0.0159=0.8159N(d2)=0.50+0.2088=0.7088

3) e-rt

rt=0.05 x 2=0.10

e-0.10=0.9048

Hence c=

(28 X 0.8159) – (24 X 0.9048 X 0.7088)=$7.45m

Hence “value “of the project is NPV +value to delay

$4m+$7.45m=$11.45m


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5. Value at Risk (VaR)

5.1 VaR is a measure of how the market value of asset or aportfolio of assets is likely to decrease over certain time, theholding period (usually 1 to 10 days), under normalconditions.

5.2 Used by Investment banks to measure the market riskof their portfolios.

5.3 Confidence levels are normally set at 95% or 99%.

Example

A bank has estimated the expected value of its portfolio in 2week time will be $50m.with standard deviation of $4.85m.

At 95%,what is VaR?

45% 50%

$50ms=$4.85m

$ 50m-(1.65 X $4.85m) =$42m

There is a 5% chance that the portfolio will fall below$42m.


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Chapter Twelve

Business Valuations &Mergers &Acquisitions

1 Pre-Acquisition Values

1.1 The aim is to find a range of values for acompany. The answer can be presented:-

a)Ve

b)Po

1.2 Net Asset Valuation

1.2.1 Business is worth just the value of it’s Net Assets.

To establish the net assets:-

Total Assets-(Total Liabilities +Preference Shares)

1.2.2 The Net Asset value equals the Ve and can be basedon:-

a) Book Valuesb) Net Realisable Value(NRV)c) Replacement cost

1.2.3 Useful For:-a) “Seller “ to set minimum value of the company

(NRV)b) Companies with lots of tangible high value

assets.Eg: Property Investment company


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1.2.3 Major Weaknesses are:-

a) Not include non-tangible assetsb) Excludes what all assets generate future:-

i. Dividendsii. Profitsiii. Cash Flows

1.2.4 Dividend Valuation Model

1.3.1 The company is worth the present value of it’s futuredividends discounted at the cost of equity

1.3.2 Ve = Total Do(1+g)(Ke-g)

OR

Po = Do(1+g)(Ke-g)

1.3.3 Take Care:-

Growth may not be constant foreverWhere to we get “g” from?CAPM may be needed to find Ke

Often better for valuing a small shareholding

1.3.4 Finding ga) Past Growth model

eg:Year DPS2006 $0.452007 $0.492008 $0.522009 $0.54


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g= 3√ (0.54)-1(0.45)

g=0.063

b) Gordon Growth Model

g=bre

where b=Profit retention ratiore= ARR or Cost of equity

eg A company has a retained profit ratio of 0.45.It hasan ARR of 12% and re of 14%.

Short term g=0.45 X 0.12=0.054Long term g=0.45 X 0.14=0.063

1.4 Price –Earnings Model

1.4.1 A business is worth a multiple of it’s profits.

1.4.2 Ve=Sustainable PAT X Suitable P/E

Po=Sustainable EPS X Suitable P/E

1.4.3 Sustainable PAT-have to adjust the latest reportedreports for non-reoccurring items (post tax)

1.4.4 Suitable P/E:-

a) Take a proxy Company P/Eb) Adjust to suit the company we are valuing.c) Simple rules

i.Ltd Co’s – deduct 30%off proxy Co P/E


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ii.Non-listed PLC’s-deduct 10% toproxy Co P/E

1.4.5 Concerns are:-

Finding a proxy Co P/E Adjustments are arbitrary Sustainable profits needs forecasting

adjustments.

1.5 Present value of Free Cash Flows

1.5.1 A business is worth the discounted value of thefuture cash flows.

1.5.2 Establish:-

a) Future Cash flows and timescalesb) Cost of capital (WACC or Risk adjusted WACC)

1.5.3 Weaknesses are:-

1.5.4 Example

A company has FCF for equity currently at $400m. Ithas a re of 8.5% and returns 30% of its profits. Ifgrowth is expected in perpetuity what is the Ve?

g =b X re =0.30 X 0.085 = 0.0255


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Ve= FCF0(1+g)(re-g)

= $400m (1.0255) = $6,894m(0.085-0.0255)

1.5.5 Another Example

A company has projected its FCF to equity at:-

T1 $420mT2 $490mT3 $510m

From T4 onwards growth will be at 3 %pa.re=7.92%.Find Ve

Time

$m T1 T2 T3 T4-F.EverFCF 420 490 510 510(1.03)

1/1.0792 1/1.07922 1/1.07923 16.171*PV 389 421 406 8,495

Ve=$9,711m

* 1 X 1 = 16.171(0.0792-0.03) (1.0792)3


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1.6 Intellectual Capital(IC)

1.6.1 There are several methods of valuing IC and /or othernon-tangible assets.

1.6.2 Simple estimate

Ve under DVM or P/E Book value of NetOr PV of CF’s method - Assets

1.6.3 Computed Intangible value (CIV)- to compute thisan industry /proxy return on total assets % must begiven in the question.

Approach:-$ ‘000

1) Last reported profit before tax XLess: Industry of Proxy x Co’s total (X)

Return on assets assets

Value Spread X

2) Take value spread X

Tax @X% (X)

Post tax value spread X

3) Assume post tax value spread will stay constantFrom time 1 to perpetuity.

Value of IC=Post tax value Spread x 1/r

r =Cost of Capital


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4) Value of Equity is

Value of IC + Book value of the Assets

1.6.4 Lev’s knowledge earning method

An alternative method of valuing intangible assetsinvolves isolating the earnings deemed to be related tointangible assets, and capitalising them. However its ismore complex than the CIV model in how itdetermines the return to intangibles and the futuregrowth assumptions made.

In practice, this model does produce results that areclose to the actual traded share price, suggesting thatis a good valuation technique.

However, it is often criticised as over complex giventhat valuations are in the end dependent onnegotiation between the parties.

Method

1) Calculate normalised earnings.

These are taken as a weighted average of:

3-5 years of past earnings (adjusted for anyone-off items)

3-5 years of forecast earnings (based on analystpredictions or sales patterns)

with the forecast earnings being given heavierweight.

Note: In the exam you may simply have to usecurrent earnings as an approximation.


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2) Isolate the earnings driven by intangible assets.

$

Normalised earnings XLessReturn on financial/monetaryassets(Rf X monetary assetsemployed)

(X)

LessReturn on physical /tangibleassets(Average industry returnon tangibles X tangible assetsemployed)

(X)

Earnings driven by intangibleassets

X

Lev identified the expected returns on assets as the:

financial /monetary assets-risk free rate tangible assets-average market return in industries

primarily driven by their investment in tangible assets intangible assets-6% premium on the risk free rate.

Note: Financial assets are cash and other assets thatconvert directly into known amounts of cash. The threebasic categories are cash, marketable securities, andreceivalbles.They are essentially current assets.

3) Capitalise the intangible earnings

Rather than simply assume these earnings will grow inperpetuity as under the CIV model, Lev’s model is moresophisticated .He assumes they will grow as follows:

Five years at the current rate of growth.


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Declining growth year on year for the next fiveyears.

Year eleven onwards-growing at the long termpredicted growth rate.

2 Post Acquisitions Values

Follow a 3 step approach

2.1 PreAcquisition Data

Predator Target

No of Equity shares X Xin Issue

PAT X X

EPS X X

Pre acquisition Po X X

P/E Ratio X X

If the P/E ratio of Predator is greater than targetthen a bootstrap method is possible


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2.2 Post Acquisition value of Predator

a) Using Bootstrap$000

Predator PAT X

Target PAT X

Total PAT X

Total PAT X PREDATOR P/E = Ve*

b) Using Add Together$000

Predator Preacquisition Ve X

Target Preacquisition Ve X

X

PV of Synergy Cash flows X

Ve *

*Divide this by the new number of total issuedshares in Predator to find Post Acquisition Po


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2.3 Assess the Takeover

Predator

Check the KPI’s post acquisition againstpre acquisition:-

a) Po risen?b) EPS risen?

Target

Compute the Bid Premium:-

Per Share $

Value received post acquisition XPer target share

Preacquisition price (X)

X

3 Factors to consider in Mergers and Takeovers

3.1 Assets of shares-most companies buy the victimcompany’s shares rather than transferring theirassets. Both are feasible.

3.2 Synergies-concept of “2+2=5”.Many sources exist:

a) Economies of scale from horizontal combinationsreduces costs and increase profits.

b) Buying suppliers can reduce profit charged onpurchases i.e. cut out the middle man.


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c) Improve badly managed /inefficient businesses.

d) Diversify to stabilise profits and cash flows.

e) Access companies that generate cash(Cash Cow)

f) Use the managerial talent of the victim in amore productive way.

g) Market power may allow consumer priceincreases and more profits.

3.3 Finance-to fund the takeover the predator companyCould use:-

a) Cashb) Sharesc) Loan Stock


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3.4 Regulation of Takeovers

3.5 Defences-The victim company could defend atake-over in several ways:-

a)Appeal to the Competition Commission indicatingthe takeover is anticompetitive.

b)Find an alternative/Friendly buyer (White Knight)


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c)Appeal to the shareholders and manage a defenceshowing that the takeover will not benefit them.

d)Super majority-set up in the Articles requiring ahigh proportion of S/H to agree on takeovers.

e)Poison pill strategy –creation of “tripwires”invoked on a takeover causing the acquirer tospend more money.


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Chapter Thirteen

Modern Valuation Methods1 VALUE BASED MEASURES

1.2 More recent approaches to valuations and performancemeasures have focused on shareholder value. It isaccepted that companies exits to maximise shareholdervalue, yet managers continue to be rewarded based ontraditional accounting measures. The three terms to befamiliar with are:

(a) Economic value added (EVA)

(b) Market value added (MVA)

(c) Shareholder value added (SVA)

Economic Value Added

1.3 EVA = Net operating profit after tax (NOPAT) – imputedinterest charge

EVA shows whether a company is making sufficientprofit to cover its cost of capital. It is a similarapproach to residual income.

1.4 NOPAT is calculated by taking the operating profit frompublished accounts, adding back interest and taking offthe tax paid. It is sometimes referred to as cashearnings before interest but after tax.


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1.5 The imputed interest charge is calculated as the capitalemployed multiplied by the WACC. This represents thereturn on capital required to keep the investors happy.

1.6 A positive EVA indicates that a company is adding valuefor its shareholders. Therefore, if managers’remuneration is linked to EVA, the interests ofmanagers and shareholders should be aligned.

1.7 Disadvantages of EVA include:

Calculations can be complicated and involve manyadjustments to accounting information

EVA is a historic measure

EVA cannot be used to directly compare companiesas it requires an adjustment for their relative sizes

The calculation relies on CAPM for the WACC, whichitself is subject to many restrictive assumptions

1.8 Example

The directors of Old Nick plc wish to establish whetherthey have increased shareholder value in the year toSeptember 20X2. They use the EVA model.

Profit and loss account for year ended 30 September20X2

£mTurnover 150PBT 50Tax 18PAT 32Dividends 10


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Retained earnings 22Additional information:

(a) Included in cost of sales and expenses is £10million of economic depreciation. This is the sameas the depreciation used for tax purposes.

(b) Non-cash expenses amounted to £15 million.

(c) The opening capital employed on the balance sheetwas £108 million.

(d) The pre-tax cost of debt is 10%.

(e) The cost of equity is 15%.

(f) Old Nick plc has an effective tax rate of 35%.

(g) The interest expense in 20X2 was £5 million.

(h) The gearing ratio is 50:50 debt to equity by marketvalue.

Required

Calculate the EVA in the year to September 20X2.


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1.9 Solution

WACC = (50% X 15%) + (50% X 10% X 0.65)

= 10.75% NOPAT:-

£mPAT 32Add: Non – cash Expenses 15

47Add: Post tax ints

(5m X 0.65)3.25

£50.25

EVA = £50.25m – (10.75% X £108m)

= £38.64m

Market Value Added

1.10 MVA is the value added to a business since it wasformed, over and above the money invested in thecompany by shareholders and long term debt holders.

Quick Example

BB Plc2003 Ve = £25m

2004 Ve = £40mRights issue in 2004 = £5m

MVA = £40m - £25m - £5m = £10m


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Shareholder Value Added

1.11 SVA represents the discounted future free cash flowsless the value of the company’s debt. The discountrate will be the company’s WACC.

Quick Example

CC Plc

Free cash flows for T1 on in perpetuity of £1.5m p.a.

WACC = 14%

Vd = £2.5m

SVA = £1.5m x - £2.5m = £8.21m1

0.14


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Chapter Fourteen

Corporate Reconstructionand Reorganisation

1 Causes of Corporate Failure

Corporate failure when a company cannot achieve asatisfactory return on capital over the longer term:

If unchecked, the situation is likely to lead to an abilityof the company to pay its obligations as they becomedue.

The company may still have an excess of assets overliabilities, but if it is unable to convert those assets intocash it will be insolvent.

The issue is more problematic in sectors, or economies,where profitability is not an issue. For example, in theformer Soviet Bloc, the economy simply does notidentify poorly performing companies

For not-for-profit organisations, the issue is usually oneof funding, and failures indicated by the inability toraise sufficient funds to carry out activities effectively.

Although stated in financial terms, the reasons behindsuch failure are rarely financial, but seem to have moreto do with a firm’s ability to adapt to changes in itsenvironment.


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2 Predicting Corporate Failure

2.1 Altman Z-Score Model

The Z score model was first developed by Altman in1968 based on research in the USA into bankruptmanufacturing companies:

Z scores are an attempt to anticipate strategic andfinancial failures by examining company financialstatements.

The Z score is generated by calculating five ratios,which are then multiplied by a predetermined weightingfactor and added together to produce the Z score.

The five ratios, which ,once combined ,were consideredto be the best predictors of failure, are:

Ratio Included to measureX1 Working capital to total

assetsLiquidity

X2 Retained earnings tototal assets

Gearing

X3 Earnings beforeinterest and tax tototal assets

Productivity of thecompany’s assets.

X4 Market value ofequity(includingpreference shares)tototal liabilities

The extent to whichthe equity can declinebefore the liabilitiesexceed the assets andthe company becomesinsolvent

X5 Sales to total assets The ability of thecompany’s assets togenerate revenue.

Z score=1.2 X1 +1.4X2 +3.3X3 +0.6X4 +1.0X5


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2.2 Assessing the risk of failure

The accuracy of prediction of the model. The Z score model was found to be an accurate

predictor of failure for up to two years prior tobankruptcy, but that the accuracy decreases overlonger periods.

What level of Z score indicates different levels oflikelihood of failure? It was found that:

Z score<1.81 indicates that the Company is in dangerand possibly heading towards bankruptcy.

Z score of 3 or above indicates financially sound.

Companies with scores between 1.81 and 2.99 needfurther investigation

2.3 Limitations of corporate failure prediction models

There are number of limitations of the Z score andother similar failure prediction models:

The score estimated is a snapshot-it gives an indicationof the situation at a given point in time but does notdetermine whether the situation is improving ordeteriorating.

Further analysis is needed to fully understand thesituation.

Scores are only good predictors in the short term. Some scoring systems tend to rate companies low-that

is they are likely to classify distressed firms as actuallyfailing.

The Z score was estimated based on manufacturingcompanies. Care needs to be taken when applying it toother types of companies.


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3 Other signs of Corporate Failure

Information in the published accounts, for example:

very large increases in intangible fixed assets a worsening cash and cash equivalents position shown

by the cash flow statement very large contingent liabilities important post balance sheet events Information in the chairman’s report and the director’s

report (include warnings, evasions, changes in thecomposition of the board since last year.

Information in the press (about the industry and thecompany or its competitors).

Information about environmental or external matter.You should have a good idea as to the type ofenvironmental or competitive factors that affect firms.

4 Financial Reconstructions

4.1 Options open to failing companies

a company Voluntary Arrangement (CVA) an administration order

4.2 General principles in devising a scheme

In most cases the company is ailing:

Losses have been incurred with the result that capitaland long term abilities are out of line with the currentvalue of the company’s assets and their earningpotential.

New capital is normally desperately required toregenerate the business, but this will not beforthcoming without a restructuring of the existingcapital and liabilities.


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The general procedure to follow would be:

Write off fictitious assets and the debit balance on profitand loss account. Revalue assets to determine theircurrent value to the business.

Determine whether the company can continue to tradewithout further finance or, if further finance is required,determine the amount required ,in what form(shares,loan stock) and from which persons it is obtainable(typically existing shareholders and financialinstitutions).

Given the size of the write off required and the amountof further finance require, determine a reasonablemanner in spreading the write off(the capital loss)between the various parties that have financed thecompany(shareholders and creditors).

Agree the scheme with the various parties involved.


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Chapter Fifteen

Question 4 and EmergingIssues

1 The Written Question

The Examiner has been consistent on all papers he has setso far. Q4 has been a full written question. There is noindication that this is likely to change in the near future.Common points in past question have been:

Either a two part question of at least two themes withinthe requirements

Ethical Issues

Providing a solution to a Financial or Strategic problem.

2 Preparation

In my view, one way to prepare for this question is to lookback and review what the examiner has set so far and howhe has answered the question.

Go on to the ACCA Global website and read and review thepast answers to ‘Q4’ set by Bob Ryan.


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Documents

ACCA+P4+Key+Point+Notes+June+2010