[Session 3 & 4]
Dec 2015
Education Course Notes
ACCA P4
Advanced Financial Management
Education Class 2
Patrick Lui
hklui2007@yahoo.com.hk
Prepared by Patrick Lui
P. 59
ACCA
Session 3 and 4
Copyright @ Kaplan Financial 2015
Education Course Notes
[Session 3 & 4]
Chapter 3 Financing Decision
LEARNING OBJECTIVES
1.
2.
3.
4.
5.
Identify and assess the appropriateness of the range of sources of finance available to
an organisation including equity, debt, hybrids, lease finance, venture capital, business
angel finance, private equity, and asset securitisation. Including assessment on the
financial position, financial risk and the value of an organisation.
Assess an organisation’s debt exposure to interest rate changes using the simple
Macaulay duration method.
Discuss the benefits and limitations of duration including the impact of convexity.
Assess the organisation’s exposure to credit risk, including:
(i) Explain the role of, and the risk assessment models used by the principal rating
agencies.
(ii) Estimate the likely credit spread over risk free.
(iii) Estimate the organization’s current cost of debt capital using the appropriate
term structure of interest rates and the credit spread.
Assess the impact of a significant capital investment project upon the reported
financial position and performance of the organization taking into account alternative
financing strategies.
Financing
Decision
Short-term
Debt
Long-term
Debt
Valuation of
Debts &
Preference
Shares
Causes of
Interest Rate
Fluctuations
Other Types of
Financing
Duration
Credit
Risk
Credit Spreads &
Cost of Debt
Effect of
Gearing
Overdrafts
Reasons for
Debt Finance
Term Structure
of Interest Rates
Equity
Finance
Meaning of
Duration
Credit Risk
Aspects
Credit
Spreads
Impact of Gearing
on EPS, EBIT &
ROE
Short-term
Loans
Factors
Influencing
Debt Finance
Yield
Curve
Venture
Capital
Calculation of
Duration
Credit Risk
Measurement
Cost of Debt
Degree of
Financial
Gearing
Yield to
Maturity
Business
Angels
Properties of
Duration
Criteria for
Establishing
Credit Ratings
Impact on Credit
Spreads on
Bond Values
Lease
Finance
Modified
Duration
Credit
Migration
Predicting
Credit Ratings
Asset
Securitisation
Benefits of
Duration
Hybrids
Limitations of
Duration
Trade
Credit
Leasing
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Education Course Notes
[Session 3 & 4]
1.
Short-term Debt
1.1
Overdrafts
1.1.1 Overdrafts are one of the most important sources of short-term finance available to
businesses. They can be arranged relatively quickly, and offer a level of flexibility
with regard to the amount borrowed at any time, whilst interest is only paid when the
account is overdrawn.
1.1.2 The bank will generally charge a commitment fee when a customer is granted an
overdraft facility or an increase in his overdraft facility. This is a fee for granting an
overdraft facility and agreeing to provide the customer with funds if and whenever he
needs them.
1.1.3 When a business customer has an overdraft facility, and the account is always in
overdraft, then it has a solid core (or hard core) overdraft. If the hard core element of
the overdraft appears to be becoming a long-term feature of the business, the bank
might wish, after discussions with the customer, to convert the hard core of the
overdraft into a loan, thus giving formal recognition to its more permanent nature.
Otherwise annual reductions in the hard core of an overdraft would typically be a
requirement of the bank.
1.1.4 Advantages and disadvantages of overdrafts:
Advantages


Disadvantages
Flexibility – The borrowing firm is 
not asked to forecast the precise
amount and duration of its
borrowing at the outset but has the 
flexibility to borrow up to a stated
limited.

Cheapness – Banks usually charge
lower interest rate depending on the
Bank retains the right to
withdraw the facility at short
notice.
Bank usually take a fixed charge
or a floating charge as the security.
Bank may require a personal
guarantee of the directors or
owners of the business.
security offered, creditworthiness
and bargaining position of the
borrower.
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1.2
[Session 3 & 4]
Short-term loans
1.2.1 A term loan is a loan for a fixed amount for a specified period. It is drawn in full at the
beginning of the loan period and repaid at a specified time or in defined instalments.
Term loans are offered with a variety of repayment schedules. Often, the interest and
capital repayments are predetermined.
1.2.2 Advantages for the borrower
(a)
The borrower knows what he will be expected to pay back at regular
intervals and the bank can also predict its future income with more certainty.
(b)
Once the loan is agreed, the term of the loan must be adhered to, provided
that the customer does not fall behind with his payments. It is not repayable on
demand by the bank.
1.3
Trade credit
1.3.1 Trade credit is one of the main sources of short-term finance for a business. Current
assets such as raw materials may be purchased on credit with payment terms normally
varying from between 30 to 90 days. Trade credit therefore represents an interest free
short-term loan.
1.3.2 In a period of high inflation, purchasing via trade credit will be very helpful in
keeping costs down. However, it is important to take into account the loss of
discounts suppliers offer for early payment.
1.3.3 Unacceptable delays in payment will worsen a company’s credit rating and
additional credit may become difficult to obtain.
1.4
Leasing
1.4.1 Rather than buying an asset outright, using either available cash resources or
borrowed funds, a business may lease an asset. Leasing has become a popular source
of finance.
1.4.2 Leasing can be defined as a contract between lessor and lessee for hire of a specific
asset selected from a manufacturer or vendor of such assets by the lessee. The lessor
retains ownership of the asset. The lessee has possession and use of the asset on
payment of specified rentals over a period.
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Education Course Notes
[Session 3 & 4]
2.
Long-term debt
2.1
Long-term finance is used for major investments and is usually more expensive and
less flexible than short-term finance.
2.2
Reasons for seeking debt finance:
(a)
Perhaps the current shareholders will be unwilling to contribute additional
capital.
(b)
Possibly the company does not wish to involve outside shareholders who
will have more onerous requirements than current members;
(c)
2.3
May include lesser cost and easier availability, particularly if the company
has little or no existing debt finance.
(d)
Debt finance provides tax relief on interest payments.
Factors influencing choice of debt finance by a company:
(a)
Availability – Only listed companies will be able to make a public issue of
loan notes on a stock exchange; smaller companies may only be able to obtain
significant amounts of debt finance from their bank.
(b)
(c)
Duration – If loan finance is sought to buy a particular asset to generate
revenues for the business, the length of the loan should match the length of
time that the asset will be generating revenues.
Fixed or floating rate – Expectations of interest rate movements will
determine whether a company chooses to borrow at a fixed or floating rate.
Fixed rate finance may be more expensive, but the business runs the risk of
adverse upward rate movements if it chooses floating rate finance.
(d)
(e)
(f)
Security and covenants – The choice of finance may be determined by the
assets that the business is willing or able to offer as security, also on the
restrictions in covenants that the lenders wish to impose.
Gearing and financial risk – If already too high, not suitable to raise debt
finance.
Target capital structure – A company should seek to minimize its WACC. In
practical terms this can be achieved by having some debt in its capital
structure, since debt is relatively cheaper than equity.
(g)
2.4
Economic expectations – It is more easy to borrow money from bank in good
economic conditions.
Factors to be considered by providers of finance:
(a)
Risk and the ability to meet financial obligations –
Providers of finance will assess the ability of the company to meet its future
financial obligations and the risk of the company. The previous record of the
company can be used as a guide to the ability of its board of directors to
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[Session 3 & 4]
manage its finances in a responsible and effective manner.
(b)
Security – The amount of funds made available to a company will also
depend on the availability of assets to offer as security. If security is not
available or is limited, the company will have to pay a higher rate of interest in
compensation for the higher level of risk.
(c)
Legal restrictions on borrowing – Whether there are any legal restrictions on
the amount of debt that the company can take on, for example in existing debt
contracts (restrictive or negative covenants), or in the company’s articles of
association.
3.
Valuation of debts and preference shares
3.1
Bonds are usually redeemable. They are issued for a term of ten years or more, and
perhaps 25 to 30 years. At the end of this period, they will mature and become
redeemable (at par or possibly at a value above par).
3.2
3.3
Some bonds do not have a redemption date, and are irredeemable or undated.
Undated bonds might be redeemed by a company that wishes to pay off the debt, but
there is no obligation on the company to do so.
Formulae
The formulae for the various types of finance are as follows:
Types of finance
Irredeemable debt without tax
Market value
i
P0 
Kd
Irredeemable debt with tax
P0 
Redeemable debt
Preference shares
i  (1  T )
Kd
MV = PV of future interest and redemption
receipts, discounted at investors’ required
returns
D
P0 
Kp
Where:
P0 = ex-div market value of the debt or share
i = annual interest starting in one year’s time
Kd = company’s cost of debt, expressed as a decimal
Kp = cost of the preference shares
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Education Course Notes
[Session 3 & 4]
Example 1 – Irredeemable debt
A company has issued irredeemable loan notes with a coupon rate of 7%. If the required
return of investors is 4%, what is the current market value of the debt?
Solution:
Market value =
7
 $175
4%
Example 2 – Preference shares
A firm has in issue $100, 12% preference shares. Currently the required return of
preference shareholders is 14%.
What is the value of a preference share?
Solution:
Market value of preference share:
D
$12
P0 

 $85.71
K p 14%
Example 3 – Redeemable debt
A company has issued some 9% debentures, which are now redeemable at par in three
years time. Investors now require a redemption yield of 10%. What will be the current
market value of each $100 of debenture?
Solution:
Year
1
2
3
3
Interest
Interest
Interest
Redemption value
Cash flow ($)
DF at 10%
PV ($)
9
9
9
100
0.909
0.826
0.751
0.751
8.18
7.43
6.76
75.10
97.47
Each $100 of debenture will have a market value of $97.47.
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Education Course Notes
[Session 3 & 4]
Example 4 – Convertible debt
A company has in issue convertible loan notes with a coupon rate of 12%. Each $100 loan
note may be converted into 20 ordinary shares at any time until the date of expiry and any
remaining loan notes will be redeemed at $100.
The loan notes have five years left to run. Investors would normally require a rate of return
of 8% pa on a five-year debt security.
Should investors convert if the current share price is:
(a)
$4.00.
(b)
(c)
$5.00.
$6.00.
Solution:
Value as debt
If the security is not converted it will have the following value to the investor:
DF @ 8%
PV ($)
3.993
0.681
47.916
68.100
Interest $12 per year for 5 years
Redemption $100 in 5-years
116.016
Value as equity
Market price
4.00
5.00
6.00
Value as equity ($)
$80 (i.e. 20 × $4)
$100 (20 × $5)
$120 (20 × $6)
If the market price of equity rises to $6.00 the security should be converted, otherwise it is
worth more as debt. The breakeven conversion price is $5.80 per share ($116/20 shares).
The value of the convertible will therefore be $116, unless the share price rises above
$5.80 at which point it will be the value of the equity received on conversion.
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Education Course Notes
[Session 3 & 4]
4.
The Causes of Interest Rate Fluctuations
4.1
The term structure of interest rates
4.1.1 The term structure of interest rates refers to the way in which the yield on a security
varies according to the term of the borrowing, as shown by the yield curve.
4.1.2 There are several reasons why interest rates differ in different markets and market
segments.
(a)
Risk – Higher risk borrowers must pay higher rates on their borrowing, to
compensate lenders for the greater risk involved.
(b)
The need to make a profit on re-lending – Financial intermediaries make
their profits from re-lending at a higher rate of interest than the cost of their
borrowing.
(c)
The size of the loan – Deposits above a certain amount with a bank or
building society might attract higher rates of interest than smaller deposits.
(d)
Different types of financial asset – Different types of financial asset attract
different rates of interest. This is largely because of the competition for
deposits between different types of financial institution.
(e)
Government policy – The policy on interest rates might be significant too. A
policy of keeping interest rates relatively high might therefore have the effect
of forcing short-term interest rates higher than long-term rates.
(f)
The duration of the lending – The term structure of interest rates refers to
the way in which the yield on a security varies according to the term of the
borrowing, that is the length of time until the debt will be repaid as shown
by the yield curve. Normally, the longer the term of an asset to maturity, the
higher the rate of interest paid on the asset.
4.2
Yield curve (收益率曲線)
4.2.1 The yield curve is an analysis of the relationship between the yields on debt with
different periods to maturity.
4.2.2 A yield curve can have any shape, and can fluctuate up and down for different
maturities.
4.2.3 There are three main types of yield curve shapes: normal, inverted and flat (humped):
(a)
(b)
Normal yield curve – longer maturity bonds have a higher yield compared
with shorter-term bonds due to the risks associated with time.
Inverted yield curve – the short-term yields are higher than the
longer-term yields, which can be a sign of upcoming recession.
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(c)
[Session 3 & 4]
Flat (or humped) yield curve – the shorter- and longer-term yields are
very close to each other, which is also a predictor of an economic transition.
4.2.4 The slope of the yield curve is also seen as important: the greater the slope, the
greater the gap between short- and long-term rates.
4.2.5 The shape of the yield curve at any point in time is the result of the three following
theories acting together:
(a)
Liquidity preference theory (流動性偏好理論)
(b)
(c)
Expectations theory
Market segmentation theory (市場分割理論)
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Education Course Notes
4.2.6
[Session 3 & 4]
Liquidity Preference, Expectations and Market Segmentation Theories
(a)
Liquidity preference theory
Investors have a natural preference for more liquid (shorter maturity)
investments. They will need to be compensated if they are deprived of cash
for a longer period.
Therefore the longer the maturity period, the higher the yield required
leading to an upward sloping curve, assuming that the interest rates were not
expected to fall in the future.
(b)
Expectations theory
This theory states that the shape of the yield curve varies according to
investors' expectations of future interest rates. A curve that rises steeply
from left to right indicates that rates of interest are expected to rise in the
future. There is more demand for short-term securities than long-term
securities since investors' expectation is that they will be able to secure
higher interest rates in the future so there is no point in buying long-term
assets now. The price of short-term assets will be bid up, the price of
long-term assets will fall, so the yields on short-term and long-term assets
will consequently fall and rise.
(c)
Market segmentation theory
The market segmentation theory suggests that there are different players in
the short-term end of the market and the long-term end of the market.
As a result the two ends of the curve may have different shapes, as they
are influenced independently by different factors.
The result is separate yield curves that probably do not meet very smoothly.
This introduces a ‘kink’ to the yield curve presumably determined by
arbitrage between the different markets to gain risk-free return.
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4.2.7
[Session 3 & 4]
Significance of Yield Curves to Financial Managers
Financial managers should inspect the current shape of the yield curve when
deciding on the term of borrowings or deposits, since the curve encapsulates
the market's expectations of future movements in interest rates.
A corporate treasurer might analyse a yield curve to decide for how long to borrow.
For example, suppose a company wants to borrow $20 million for five years and
would prefer to issue bonds at a fixed rate of interest. One option would be to issue
bonds with a five-year maturity. Another option might be to borrow short-term for
one year, say, in the expectation that interest rates will fall, and then issue a
four-year bond. When borrowing large amounts of capital, a small difference in the
interest rate can have a significant effect on profit. For example, if a company
borrowed $20 million, a difference of just 25 basis points (0.25% or one quarter of
one per cent) would mean a difference of $50,000 each year in interest costs. So if
the yield curve indicates that interest rates are expected to fall then short-term
borrowing for a year, followed by a 4-year bond might be the cheapest option.
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4.3
[Session 3 & 4]
Yield to maturity
4.3.1 The yield to maturity (or redemption yield) is the effective yield on a redeemable
bond which allows for the time value of money and is effectively the IRR of the cash
flows.
Example 5 – YTM
A five year unsecured bond with a coupon of 5% per annum, redeemable at par and issued
at a 6% discount to par will have a yield to maturity of 6.47%. This is calculated by
assuming a nominal value of $100 and calculating NPVs at 5% and 7% discount rates.
Year
0
Market value
1–5
Interest
5
Capital payment
Cash
DF
PV
DF
PV
flow ($)
5%
($)
7%
($)
(94)
1.000
(94.00)
1.000
(94.00)
5
4.329
21.64
4.100
20.50
100
0.784
78.40
0.713
71.30
6.04
YTM = 5% 
(2.20)
6.04
 (7%  5%)  6.47%
6.04  2.20
5.
Other Types of Financing
5.1
Equity finance
5.1.1 Equity finance is raised through the sale of ordinary shares to investors, either as a
new issue or a rights issue.
5.1.2 The issue of equity is at the bottom of the pecking order when it comes to raising
funds for investments, not only because of the cost of issue but also because equity
finance is more expensive in terms of required returns.
5.1.3 Equity shareholders are the ultimate bearers of risk as they are at the bottom of the
creditor hierarchy in a liquidation. This means that there is a significant risk that they
will receive nothing at all after all other trade payables’ claims have been met.
5.1.4 As with long-term debt, equity finance will be used for long-term investments.
Companies may choose to raise equity rather than debt finance if:
(a)
their gearing ratios are approaching the maximum allowable
(b)
any further increases in gearing will be perceived as a significant increase in
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[Session 3 & 4]
risk by investors.
5.2
Venture capital
5.2.1 Venture capital is long-term capital that is available for around five years. It is
normally offered by specialist institutions, and is aimed at small and medium-size
businesses that have a fairly high level of risk.
5.2.2 Venture capitalists are prepared to provide capital to such businesses if the expected
returns are commensurate with the level of risk taken. This means that venture
capitalists will only be interested in a business with good profit and growth
prospects. The amount of capital invested will vary according to need and may be
provided in stages, subject to certain key objectives being met.
5.2.3 Venture capitalist may be interested in the following types of business:
(a)
Business start-ups – This can cover a wide range of situations from
businesses that are still at the concept stage through to businesses that are
about to begin operations. In practice it seems that venture capitalists prefer to
invest in start-ups that are fairly well advanced.
(b)
Growth capital – This is designed for businesses that have passed the start-up
phase and are seeking capital for further expansion. It is, therefore, a form of
second-stage funding.
(c)
Management acquisitions – Venture capitalists will often provide capital for
managers that wish to take over an existing business. The managers may be
already employed by the business or they may be outside managers that are
looking for a vehicle for their ambitions. This type of financing has proved to
be extremely popular among venture capitalists in recent years.
(d)
Share purchases – Capital may be provided to help finance the buy out of a
part-owner of a business. This may be provided to someone outside the
business or to the other part-owners.
(e)
Business recoveries – Capital may be provided to help turn round the fortunes
of a business that is currently experiencing difficulties.
(f)
Venture capitalists do not usually look for quick cash returns and are often
content to wait for a cash return on realisation of the investment.
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5.3
[Session 3 & 4]
Business angels
5.3.1 Business angels are wealthy individuals who invest in start-up and growth businesses
in return for an equity stake. These individuals are prepared to take high risks in the
hope of high returns. As a result, business angel finance can be expensive for the
business.
5.3.2 Investments made by business angels can vary but, in the UK, most investments are in
the region of ₤25,000.
5.3.3 Business angels are a very useful tool to fill the gap between venture capital and
debt finance, particularly for start-up businesses.
5.3.4 One of the main advantages of business angels is that they often follow up their initial
investment with later rounds of financing as the business grows. New businesses
benefit from their expertise in the difficult early stages of trying to establish
themselves.
(The article “Being an Angel” in the Technical Articles section of the ACCA website
covers Business Angels in more detail.
http://www.accaglobal.com/content/dam/acca/global/pdf/sa_march09_attrill.pdf)
5.4
Lease finance
5.4.1 There are two types of leases:
(a)
A finance lease exists when the substance of the lease is that the lessee
enjoys substantially all of the risks and rewards of ownership, even though
legal title to the leased asset does not pass from lessor to lessee.
(b)
An operating lease is a rental agreement where several lessees are expected
to use the leased asset and so the lease period is much shorter than the
asset’s useful economic life.
5.4.2 Attractions to lessor – the lessor invests finance by purchasing assets from suppliers
and makes a return out of the lease payments from the lessee. The lessor will get
capital allowances on his purchase of the equipment.
5.4.3 Attractions to lessee under finance lease –
(a)
The lessee may not have enough cash to pay for the asset, and would have
difficulty obtaining a bank loan to buy it. If so the lessee has to rent the asset
to obtain use of it at all.
(b)
(c)
Finance leasing may be cheaper than a bank loan.
The lessee may find the tax relief available advantageous.
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[Session 3 & 4]
5.4.4 Attractions to lessee under operating lease –
(a)
The leased equipment does not have to be shown in the lessee’s published
statement of financial position, and so the lessee’s statement of financial
(b)
position shows no increase in its gearing ratio.
The equipment is leased for a shorter period than its expected useful life. In
the case of high-technology equipment, if the equipment becomes out of date
before the end of its expected life, the lessee does not have to keep on using it.
The lessor will bear the risk of having to sell obsolete equipment
secondhand.
5.5
Asset securitisation
(Jun 12)
5.5.1 Securitisation is the process of converting illiquid assets into marketable
asset-backed securities. These securities are backed by specific assets and are
normally called asset-backed securities (ABS).
5.5.2 The oldest and historically most common type of asset securitization is the
mortgage-backed bond or security (MBS).
5.5.3 Very simplistically, the process is as follows:
(a)
A financial entity can purchase a number of mortgage loans from banks.
(b)
The entity pools the mortgage loans together.
(c)
The entity issues bonds to institutional investors. The money raised from
issuing bonds is used to pay for the mortgage loans.
(d)
The institutional investors now have the right to receive the principal and
interest payments made on the mortgage.
5.5.4 Today, virtually anything that has a cash flow (e.g. a loan, a public works project, or a
receivable balance) is a candidate for securitization.
5.5.5 The tangible benefit from securitisation occurs when the pooled assets are divided
into tranches and tranches are credit rated. The higher rated tranches would
carry less risk and have less return, compared to lower rated tranches. If default
occurs, the income of the lower tranches is reduced first, before the impact of
increasing defaults move to the higher rated tranches. This allows an asset of low
liquidity to be converted into securities which carry higher liquidity.
5.5.6 The main reason for securitizing a cash flow is that if allows companies with a credit
rating of, for example, BB but with AAA-rated cash flows to possibly borrow at AAA
rates. This will lead to greatly reduced interest payments as the difference between
BB rates and AAA rates can be hundreds of basis points.
5.5.7 However, securitization is expensive due to management costs, legal fees and
continuing administration fees.
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5.6
[Session 3 & 4]
Hybrids
5.6.1 Hybrids are means of finance that combine debt and equity. Such securities pay a
fixed or floating rate of return up to a certain date, after which the holder has such
options as converting the securities into the underlying equity.
5.6.2 Examples of hybrids include convertible bonds, debt with attached warrants and
preference shares.
5.6.3 Convertible debt has a number of attractions compared with a bank loan of similar
maturity, as follows:
(a)
Self-liquidating (自行收回)
(i)
(ii)
(iii)
(b)
Lower interest rate
(i)
It will be lower than the interest rate on ordinary debt such as a bank
(ii)
(iii)
(c)
Provided that the conversion terms are pitched correctly and
expected share price growth occurs, conversion will be an attractive
choice for bond holders as it offers more wealth than redemption.
This occurs when the conversion value is greater than the
redemption value, or when the conversion value is greater than the
floor value on the conversion date.
If the debt is converted into ordinary shares, it will not need to be
redeemed. A bank loan of a similar maturity will need to have all of the
capital repaid.
loan because of the value of the option to convert.
The returns on fixed-interest debt will not increase with corporate
profitability, so debt providers will have a limited share of the benefits
from the investment of the funds they have provided.
When debt has been converted, however, bond holders become
shareholders and will potentially have unlimited returns, or at least
returns that are higher than the returns on debt finance.
Increase in debt capacity on conversion
(i)
Gearing increases when convertible debt is issued, but if conversion
occurs, the gearing will fall not only because the debt has been
(ii)
(d)
removed, but will fall even further because equity has replaced the
debt.
The debt capacity of the company will therefore be enhanced by
conversion, compared to redemption of a bank loan of a similar
maturity.
More attractive than ordinary debt
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(i)
It may be possible to issue convertible debt even when ordinary debt
(ii)
such as a bank loan is not attractive to lenders, since the option to
convert offers a little extra that ordinary debt does not.
This is the option to convert in the future, which can be attractive to
optimists, even when the short- and medium-term economic outlook
may be poor.
6.
Duration
6.1
What is duration?
(Jun 11, Pilot 13)
6.1.1 Duration (also known as Macaulay duration) is the weighted average length of time
to the receipt of a bond’s benefits (coupon and redemption value), the weights being
the present value of the benefits involved.
6.1.2 Duration gives each bond an overall risk weighting that allows two bonds to be
compared. In simple terms, it is a composite measure of the risk expressed in years.
6.2
Calculating duration
(Jun 11, Pilot 13, Jun 14)
6.2.1 The steps of calculating duration
Step 1: Add the PV of the cash flows in each time period together.
Step 2: Multiply the PV of cash flows for each time period by the time period and
add together.
Step 3: Divide the result of step 2 by the result of step 1.
Example 6 – Calculating duration
ABC Co. has a bond (Bond X) in issue which has a nominal value of $1,000 and is
redeemable at par.
Bond X is a 6% bond maturing in three years’ time and has a gross redemption yield
(GRY) of 3.5%. The current price of the bond is $1,070.12.
Required:
Calculate the duration of the bond.
Solution:
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Bond X
2
60
0.934
3
1,060
0.902
Total
Cash flow ($)
Discount at 3.5%
1
60
0.966
PV
× by year
57.96
1
56.04
2
956.12
3
1,070.12
57.96
112.08
2,868.36
3,038.40
Duration = 3,038.40 / 1,070.12 = 2.84 years
Note that the total PV of the cash flows from the bond is equal to the current market price,
which is what we expect.
6.3
Properties of duration
6.3.1 The basic features of sensitivity to interest rate risk will all be mirrored in the duration
calculation.
(a)
Longer-dated bonds (or longer time to maturity) will have longer durations.
Consider two bonds that each cost $1,000 and yield 5%. A bond that matures
in one year would more quickly repay its true cost that a bond that matures in
(b)
10 years. As a result, the shorter-maturity bond would have a lower
duration and less price risk. The longer the maturity, the higher the duration.
Lower-coupon bonds will have longer duration. The ultimate low-coupon
bond is a zero-coupon bond where the duration will be the maturity.
A bond’s payment is a key factor in calculating duration. If two identical
bonds pay different coupons, the bond with the higher coupon will pay back
its original cost quicker than the lower-yield bond. The higher the coupon,
the lower the duration.
(c)
Lower yields will give longer durations. In this case, the PV of cash flows in
the future will rise if the yield falls, extending the point of balance, therefore
lengthening the duration.
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6.4
[Session 3 & 4]
Modified duration
(Jun 11, Pilot 13, Jun 14)
6.4.1 Modified duration is a measure of the sensitivity of the price of a bond to a change
in interest rates.
6.4.2 Formula:
Modified duration =
Macaulay duration
1 + GRY
This can be used to determine the proportionate change in bond price for a given
change in yield as follows:
ΔP = – Modified duration × ΔY × P
Where:
ΔP = change in bond price
ΔY = change in yield
P = current market price of the bond
Remember there is an inverse relationship between yield and bond price,
therefore the modified duration figure is expressed as a negative number.
Example 7 – Calculating modified duration
Same information as Example 6.
Required:
Calculate the modified duration of the bond.
Solution:
Bond X
Duration = 3,038.40 / 1,070.12 = 2.84 years
GRY = 3.5%
Modified duration =
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2.84
 2.74
1  3.5%
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If, for example, the yield increased by 0.5%, the change in price can be calculated as
follows:
ΔP = –2.74 × 0.5% × $1,070.12 = –$14.66
6.4.3 Properties of modified duration – as the modified duration is derived from the
Macaulay duration, it shares the same properties.
6.5
(a)
Longer dated bonds will have higher modified durations – that is, bonds
which are due to be redeemed at a later date are more price-sensitive to
changes in interest rates and are therefore more risky.
(b)
Lower coupon bonds will have higher modified durations.
(c)
Lower yields will give higher modified durations.
Benefits of duration:
6.5.1 Benefits:
(a)
(b)
(c)
6.6
Duration allows bonds of different maturities and coupon rates to be
directly compared. This makes decision-making regarding bond finance
easier and more effective.
If a bond portfolio is constructed based on weighted average duration, it is
possible to determine portfolio value changes based on estimated changes
in interest rates.
Managers may be able to modify interest rate risk by changing the
duration of the bond portfolio – for example, by adding shorter maturity
bonds or those with higher coupons (which will reduce duration), or by adding
longer maturity bonds or those with lower coupons (which will increase
duration).
Limitations of duration
(Jun 11, Pilot 13, Jun 14)
6.6.1 The main limitation of duration is that it assumes a linear relationship between
interest rates and price, i.e. it assumes that for a certain percentage change in
interest rates there will be an equal percentage change in price.
6.6.2 However, as interest rates change the bond price is unlikely to change in a linear
fashion. Rather, it will have some kind of convex relationship with interest rates.
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6.6.3 As you can see from the diagram above, the more convex the relationship the more
inaccurate duration is for measuring interest rate sensitivity. Therefore duration
should be treated with caution in your predictions of interest rate/price relationships.
6.6.4 Duration can only be applied to measure the approximate change in a bond price
due to interest changes, only if changes in interest rates do not lead to a change in
the shape of the yield curve. This is because it is an average measure based on the
gross redemption yield (yield to maturity). However, if the shape of the yield curve
changes, duration can no longer be used to assess the change in bond value due
to interest rate changes.
7.
Credit risk
7.1
Credit risk aspects
7.1.1 Credit risk, also referred to as default risk, is the risk undertaken by the lender that
the borrower will default either on interest payments or on the repayment of
principal on the due date, or on both.
7.1.2 Creditors to companies such as corporate bondholders and banks are also exposed to
credit risk. The credit risk of an individual loan or bond is determined by the
following two factors:
(a)
The probability of default – this is the probability that the borrower or
counterparty will default on its contractual obligations to repay its debt.
(b)
The recovery rate – this is the fraction of the face value of an obligation that
can be recovered once the borrower has defaulted. When an company defaults,
bond holders do not necessarily lose their entire investment. Part of the
investment may be recovered depending on the recovery rate.
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7.1.3 The loss given default (LGD) is the difference between the amount of money owed
by the borrower less the amount of money recovered.
For example, a bond has a face value of $100 and the recovery rate is 80%. The loss
given default in this case is:
Loss given default = $100 – $80 = $20
7.1.4 The expected loss (EL) from credit risk shows the amount of money the lender should
expect to lose from the investment in a bond or loan with credit risk.
The expected loss (EL) is the product of the loss given default (LGD) and the
probability of default (PD).
EL = PD × LGD
If the probability of default is, say, 10%, the expected loss from investing in the above
bond is:
EL = 0.1 × $20 = $2
7.2
Credit risk measurement
7.2.1 The oldest and most common approach is to assess the probability of default using
financial and other information on the borrowers and assign a rating that reflects the
expected loss from investing in the particular bond.
7.2.2 This assignment of credit risk ratings is done by credit rating companies such as
Standard & Poor, Moody’s Investor Services or Fitch. The table below shows the
credit rating used by Moody’s and Standard and Poor.
Standard & Poor
Moody’s
AAA
Aaa
Highest quality, lowest default risk
AA
Aa
High quality
A
A
Upper medium grade quality
BBB
Baa
Medium grade quality
BB
Ba
Lower medium grade quality
B
B
Speculative
CCC
Caa
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Description of Category
Poor quality (high default risk)
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CC
Ca
Highly speculative
C
C
Lowest grade quality
7.2.3 Both credit rating agencies estimate default probabilities from the empirical
performance of issued corporate bonds of each category. The table below shows the
probability of default for certain credit categories over different investment horizons.
The probability of default within a year for AAA or AA bonds is practically zero
whereas for a CCC bond is 19.79%. However, although the probability of default for a
AAA company is practically zero over a single year, it becomes 1.40% over a fifteen
year period (this is consistent with the theory that, the longer the time horizon, the
riskier the investment).
7.3
Criteria for establishing credit ratings
(Pilot 13)
7.3.1 The criteria for rating international organizations encompasses the following.
Criteria
Explanation
Country risk
No issuer’s debt will be rated higher than the country of
origin of the issuer (the ‘Sovereign Ceiling’ concept)
Universal/Country
importance
The company’s standing relative to other companies in the
country of domicile and globally (measured in terms of sales,
profits, relationship with government, importance of the
industry to the country, etc.)
Industry risk
The strength of the industry within the country, measured by
the impact of economic forces, cyclical nature of the
industry, demand factors, etc.
Industry position
Issuer’s position in the relevant industry compared with
competitors in terms of operating efficiency.
Management evaluation
The company’s planning, controls, financing policies and
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strategies, overall quality of management and succession,
merger and acquisition performance
achievement in financial results.
and
record
of
Accounting quality
Auditor’s qualifications of the accounts, and accounting
policies for inventory, goodwill, depreciation policies and so
on.
Earnings protection
Earnings power including return on capital, pre-tax and net
profit margins, sources of future earnings growth.
Financial gearing
Long-term debt and total debt in relation to capital, gearing,
nature of assets, off-balance commitments, working capital,
management, etc.
Cash flow adequacy
Relationship of cash flow to gearing and ability to finance all
business cash needs.
Financial flexibility
Evaluation of financing needs, plans and alternatives under
stress (ability to attract capital), banking relationships, debt
covenants.
Question 1
GNT Co is considering an investment in one of two corporate bonds. Both bonds have a par
value of $1,000 and pay coupon interest on an annual basis. The market price of the first
bond is $1,079.68. Its coupon rate is 6% and it is due to be redeemed at par in five years.
The second bond is about to be issued with a coupon rate of 4% and will also be redeemable
at par in five years. Both bonds are expected to have the same gross redemption yields
(yields to maturity). The yield to maturity of a company’s bond is determined by its credit
rating.
GNT Co considers duration of the bond to be a key factor when making decisions on which
bond to invest.
Required:
(a)
(b)
(c)
Estimate the Macaulay duration of the two bonds GNT Co is considering for
investment.
(9 marks)
Discuss how useful duration is as a measure of the sensitivity of a bond price to
changes in interest rates.
(8 marks)
Among the criteria used by credit agencies for establishing a company’s credit
rating are the following: industry risk, earnings protection, financial flexibility
and evaluation of the company’s management.
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Briefly explain each criterion and suggest factors that could be used to assess it.
(8 marks)
(Total 25 marks)
(ACCA P4 Advanced Financial Management Pilot Paper 2013 Q4)
7.4
Credit migration
7.4.1 The credit rating of a borrower may change after a bond is issued. This is referred
to as credit migration.
7.4.2 There is another aspect of credit risk which should be taken into account when
investors are investing in corporate bonds, beyond the probability of default.
7.4.3 A borrower may not default, but due to changing economic conditions or
management actions the borrower may become more or less risky than at the time
the bond was issued and as a result, the bond issuer will be assigned by the credit
agency a different credit rating. This is called credit migration.
7.4.4 The significance of credit migration lies in the fact that the assignment of lower
credit rating will decrease the market value of the corporate bond. This is discussed
in the next section in the context of credit spreads.
8.
Credit Spreads and the Cost of Debt Capital
(Dec 11)
8.1
Credit spreads
8.1.1 The credit spread is the premium required by an investor in a corporate bond to
compensate for the credit risk of the bond.
8.1.2 The yield to a government bond holder is the compensation to the investor for
foregoing consumption today and saving. However, corporate bond holders should
require compensation not only for foregoing consumption, but also for the credit risk
that they are exposed to.
8.1.3 As we discussed in the previous section, this is a function of the probability of default,
the recovery rate and the probability of migration.
8.1.4 Assuming that a government bond such as the one issued by the US or an EU
government is free of credit risk, the yield on a corporate bond will be:
Yield on corporate bond = risk free rate + credit spread
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8.1.5 Since credit spreads reflect the credit risk of a bond, they will be inversely related
to the credit quality of the bond. Low credit quality bonds will be characterized by
large spreads and high credit quality bonds will be characterized by low spreads.
8.1.6 An example of credit spreads by type of bond and maturity is given below.
Reuters Corporate Spreads for Industrials (in basis points)
Example 8 – Yield on corporate bond
The current return on a 10 year government bond is 4.2%. ABC Co, a company rated AA,
has 10 year bonds in issue. Using the credit spread table, calculate the expected yield on
ABC Co.’s bonds.
Solution:
The credit spread on a 10 year AA bond is 52, which means that 0.52% should be added to
the return on the government bond.
Expected yield on ABC Co.’s bonds = 4.2% + 0.52% = 4.72%
Example 9 – Yield on corporate bond
A 15 year government bond has a current yield of 5%. BBC Co., a B rated company, has
equivalent bonds in issue. What is the expected yield on BBC Co.’s bonds?
Solution:
The table does not include credit spreads for 15 year bonds therefore some adjustment is
required to the figures we have available.
The credit spread on a 10 year B rated bond is 350 and a 30 year B rated bond is 450. The
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adjustment can be calculated as follows.
350 
(450  350)
 5  375
(30  10)
This means that 3.75% must be added to the yield on government bonds.
The expected yield on BBC Co.’s bonds = 5% + 3.75% = 8.75%
8.2
The cost of debt capital
8.2.1 The cost debt capital for a company is determined by the following:
(a)
its credit rating
(b)
the maturity of the debt
(c)
(d)
the risk-free rate at the appropriate maturity
the corporate tax rate
Cost of debt capital = (1 – tax rate) × (risk free rate + credit spread)
Example 10 – Cost of debt
Joe Co., a BBB rated company, has 5 year bonds in issue. The current yield on equivalent
government bonds is 3.7% and the current rate of tax is 28%.
Required:
Using the information in the credit spread table above, calculate:
(a)
(b)
the expected yield on Joe Co.’s bonds
Joe Co.’s post tax cost of debt associated with these 5 year bonds
Solution:
(a)
(b)
Expected yield on 5 year bonds = 3.7% + 1.05% = 4.75%
Post-tax cost of debt = (1 – 0.28) × 4.75% = 3.42%
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8.3
[Session 3 & 4]
Impact on credit spreads on bond values
8.3.1 We have already mentioned that credit risk is affected by the probability of migration
of a certain debt or loan to another credit category.
8.3.2 In markets where loans or corporate bonds are traded this migration is reflected in
increased spreads. Using only the probability of default and ignoring the
probability of migration from one category to another may give a misleading
estimate of the risk exposure.
8.3.3 Thus a company that has a very low or even zero probability of default but a high
probability of being downgraded will have its credit risk significantly
underestimated.
8.3.4 To explain how credit migration may impact on bond values consider a bond which is
currently rated as BBB. In a year’s time the bond may still be rated BBB, or it may
have a higher or lower credit rating. The probability of being at the same or a different
rating in a year’s time is reproduced in the table below.
Year-end rating
Probability of migration
AAA
0.02%
AA
0.33%
A
5.95%
BBB
86.93%
BB
5.30%
B
1.17%
CCC
0.12%
Default
0.18%
8.3.5 As we have discussed, each credit category implies a different credit spread which in
turn implies a different cost of debt capital. The table below is an example of the cost
of debt capital for bonds of different credit ratings and different maturities. The cost
of debt capital for a AAA bond with a maturity of one year is 3.6%, whereas the cost
of debt capital for a CCC bond with a maturity of 4 years is 13.52%.
Yields by credit category (%)
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8.3.6 The value of a bond is the present value of the coupons and the redemption value,
discounted using the appropriate cost of debt capital.
Example 11 – Impact of credit spreads on bond values
Suppose the bond has a face value of $100 and pays an annual coupon of 6%. Using the
discount factors from the table above, we calculate the value of the bond at the end of a
year if it remained rated BBB using:
PBBB 
6
6
6
6



 101.53
2
3
1.041 (1.0467)
(1.0525)
(1.0563) 4
If it is upgraded to A, it will be worth $102.64
6
6
6
6
PA 



 102.64
2
3
1.0372 (1.0432)
(1.0493)
(1.0532) 4
If it is downgraded to CCC, it will be worth $77.63
6
6
6
6
PCCC 



 77.63
2
3
1.1505 (1.1502)
(1.1403)
(1.1352) 4
The value of the bond when it defaults will not be zero, as the issuing firm will have some
assets. The available empirical evidence from credit agencies shows that about 51% of the
value of a BBB bond is recovered when the issuing from defaults.
If bondholders expect to recover in case of bankruptcy, the non-recoverable amount is $49
per $100 of face value. The Loss Given Default for a BBB bond will therefore be:
LGD = 0.49 × 100 = $49
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The expected loss for the BBB bond in the example is:
EL = 0.0018 × $49 = $0.0882
The low probability of default reduces the credit risk of a BBB bond despite the fact that it
loses nearly 50% of its value in the case of a default.
8.4
Predicting credit ratings
8.4.1 Credit rating companies use financial ratios and other information in order to arrive at
the credit score of a company.
8.4.2 Many researchers have tried to guess the models that are employed by credit rating
agencies and have estimated models which link the observed credit rating to financial
characteristics of a company.
8.4.3 One of these models is the Kaplan Urwitz model. This model calculates a numerical
value for a company based on certain characteristics which is then used to assign a
credit rating to that company.
8.4.4 If a question on the Kaplan-Urwitz model comes up in an exam, the formula will be
given.
A.
Quoted companies
8.4.5 The Kaplan-Urwitz model for quoted companies is as follows.
Y = 5.67 + 0.011F + 5.13π – 2.36S – 2.85L + 0.007C – 0.87β – 2.90σ
Where:
Y = the score that the model produces
F = the size of a firm measured in total assets
π = net income / total assets
S = debt status (subordinated debt = 1, otherwise = 0)
L = gearing (measured as long term debt / total assets)
C = interest cover (PBIT / interest payment)
β = beta of the company estimated using CAPM
σ = the variance of the residuals from the CAPM regression equation (calculated as

2
  2   m2  , where  m2 is the variance of the market)
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8.4.6 Subordinated debt (次級債務) has no priority claim as it is subordinated to other
debt.
8.4.7 Unsubordinated debt is a loan or security that ranks above other loans or
securities with regard to claims on assets or earnings. Also known as a senior
security. In the case of default, creditors with unsubordinated debt would get paid out
in full before the junior debt holders. Therefore, unsubordinated debt is less risky
than subordinated debt.
8.4.8 The classification of companies into credit rating categories is done in the following
way.
Score (Y)
Rating category
Y > 6.76
AAA
Y > 5.19
AA
Y > 3.28
A
Y > 1.57
BBB
Y>0
BB
Example 12 – Kaplan-Urwitz model for quoted company
The following information is available for Kaplan Inc, a quoted company/
Total assets = $650m
Net income = $250m
Type of debt = unsubordinated
Long term debt (unsubordinated) = $200m
Profit before interest and tax = $500m
Interest payments = $40m
In addition, the following CAPM model was estimated:
RKaplan = 0.045 + 0.800 × market risk premium
Kaplan’s volatility (σ) and the volatility of the market are 22% and 20% respectively.
Required:
What is the predicted credit rating for Kaplan Inc, using the Kaplan Urwitz model?
Solution:
The inputs to the model are as follows.
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F = $650m
π = $250 / $650 = 0.385
S = 0 (unsubordinated debt)
L = $200 / $650 = 0.308
C = $500 / $40 = 12.5 times
β = 0.800
σ=
0.22 2  0.82  0.20 2  0.151
Y = 5.67 + (0.011 × 650) + (5.13 × 0.385) – (2.36 × 0) – (2.85 × 0.308) + (0.007 × 12.5) –
(0.87 × 0.800) – (2.90 × 0.151) = 12.87
The credit rating for Kaplan Inc = AAA
B.
Unquoted companies
8.4.9 The second Kaplan Urwitz model was estimated using data on unquoted companies:
Y = 4.41 + 0.014F + 6.4π – 2.56S – 2.72L + 0.006C – 0.53σ
You will notice that there is no beta factor in the above equation – this is because we
are dealing with unquoted companies.
In this case σ is the standard deviation of earnings. All the other variables remain
the same.
Question 2
Levante Co is a large unlisted company which has identified a new project for which it will
need to increase its long term borrowings from $250 million to $400 million. This amount
will cover a significant proportion of the total cost of the project and the rest of the funds
will come from cash held by the company.
The current $250 million unsubordinated borrowing is in the form of a 4% bond which is
trading at $98.71 per $100 and is due to be redeemed at par in three years. The issued bond
has a credit rating of AA. The new borrowing will also be raised in the form of a traded
bond with a par value of $100 per unit. It is anticipated that the new project will generate
sufficient cash flows to be able to redeem the new bond at $100 par value per unit in five
years. It can be assumed that coupons on both bonds are paid annually.
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Both bonds would be ranked equally for payment in the event of default and the directors
expect that as a result of the new issue, the credit rating for both bonds will fall to A. The
directors are considering the following two alternative options when issuing the new bond:
(i) Issue the new bond at a fixed coupon of 5% but at a premium or discount, whichever
is appropriate to ensure full take up of the bond; or
(ii) Issue the new bond at a coupon rate where the issue price of the new bond will be
$100 per unit and equal to its par value.
The following extracts are provided on the current government bond yield curve and yield
spreads for the sector in which Levante Co operates:
Current Government Bond Yield Curve
Years
1
3.2%
Yield spreads (in basis points)
Bond rating
1 year
AAA
5
AA
16
A
BBB
65
102
2
3.7%
3
4.2%
4
4.8%
5
5.0%
2 years
9
22
3 years
14
30
4 years
19
40
5 years
25
47
76
121
87
142
100
167
112
193
Required:
(a)
(b)
(c)
(d)
Calculate the expected percentage fall in the market value of the existing bond if
Levante Co’s bond credit rating falls from AA to A.
(3 marks)
Advise the directors on the financial implications of choosing each of the two
options when issuingthe new bond. Support the advice with appropriate
calculations.
(8 marks)
Among the criteria used by credit agencies for establishing a company’s credit
rating are the following: industry risk, earnings protection, financial flexibility
and evaluation of the company’s management. Briefly explain each criterion and
suggest factors that could be used to assess it.
(8 marks)
The following information is available for the expected situation after the
proposed bond issue.
Total assets = $1,050m
Monthly net income = $25m
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Annual profit before interest and tax = $450m
Standard deviation of earnings = 8%
Assume the new bond is issued with a 5% coupon.
Use the Kaplan-Urwitz model for unquoted companies to predict whether the
credit rating will be AAA, AA or A.
(6 marks)
Note: The model is Y = 4.41 + 0.014F + 6.4π – 2.56S – 2.72L + 0.006C – 0.53σ
(Amended ACCA P4 Advanced Financial Management December 2011 Q3)
9.
Effect of Alternative Financing Strategies on Financial Reporting
9.1
Impact of gearing on EPS, EBIT and return on equity
(Jun 12)
9.1.1 To appreciate the impact of financial gearing we shall explain and calculate the effects
of changes in EBIT on EPS for a company with differing amounts of debt financing.
Example 13 – Financial gearing on EPS
Assume that a company has the following statement of financial position structure.
Asset
Debt
Equity
Current
Proposed
500
500
500
300
200
The company currently has 100 shares in issue with a price of $5. It is proposing to buy
back 60 shares for a total cost of $300, financing this by issuing debt at a cost of 10%. This
will leave 40 shares in issue.
The EPS for the company when it has no debt = EPS (U) = EBIT / 100
Whereas the EPS for the company under the proposed borrowing = EPS (G) = EBIT / 40
The values of the ungeared EPS for different values of EBIT are shown in the table below:
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P. 93
Copyright @ Kaplan Financial 2015
Education Course Notes
[Session 3 & 4]
Scenario Scenario Scenario Scenario Scenario Scenario Scenario
1
2
3
4
5
6
7
EBIT
0
10
30
50
70
90
110
Interest payments
0
0
0
0
0
0
0
Net income
0
10
30
50
70
90
110
EPS (U)
0
0.1
0.3
0.5
0.7
0.9
1.1
Similarly, the values of the geared EPS for different values of EBIT are shown in the table
below:
Scenario Scenario Scenario Scenario Scenario Scenario Scenario
1
2
3
4
5
6
7
EBIT
0
10
30
50
70
90
110
Interest payments
30
30
30
30
30
30
30
Net income
-30
-20
0
20
40
60
80
-0.75
-0.5
0
0.5
1
1.5
2
EPS (G)
As it can seen from the two tables, the earnings for the geared company are more volatile.
When the values of EPS are plotted against the values of EBIT, this is reflected in the
gradient of the line showing the values of the geared EPS, which will be steeper than the
line plotting showing the values of unleveraged EPS.
The breakeven level of EBIT where the two alternative financing schemes give the same
EPS, i.e. when:
EPS (U) = EPS (G)
EBIT = $50. This can be seem from the fact that:
EBIT  30 EBIT

40
100
Implies EBIT = $50
This breakeven point can be checked as follows:
Original all equity structure = 50 / 100 = $0.50
Revised structure = (50 – 30) / 40 = $0.50
Prepared by Patrick Lui
P. 94
Copyright @ Kaplan Financial 2015
Education Course Notes
[Session 3 & 4]
Above an EBIT of $50, the geared structure gives a higher EPS. In addition, the company’s
ROE will exceed the interest cost of 10%. Below $50, it gives a lower EPS and the ROE is
less than the cost of debt of 10%.
At the breakeven point, the ROE is equal to the interest rate on the debt, i.e.:
ROE = EBIT / 500 = 50 / 500 = 10%
At an EBIT of zero, the original ungeared EPS will also be zero. However, with debt, there
will be a loss per share of -30 / 40 = -$0.75.
Note that, although the EPS and ROE are more volatile for the geared company, the mean
return is higher. This can be demonstrated by calculating the mean returns for the above
two capital structures, assuming that each scenario has an equal likelihood of arising.
Ungeared company
Mean net income for ungeared company =
EPS =
51.43
 $0.5143
100
ROE =
51.43
 10.286%
500
0  10  30  50  70  90  110
 $51.43
7
Geared company
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P. 95
Copyright @ Kaplan Financial 2015
Education Course Notes
[Session 3 & 4]
Mean net income for geared company =
EPS =
21.429
 $0.5357
40
ROE =
21.429
 10.714%
200
9.2
 30  20  0  20  40  60  80
 $21.429
7
Degree of financial gearing
9.2.1 The degree of financial gearing measures the sensitivity of EPS to changes in EBIT.
9.2.2 The degree of financial gearing (DFG) is defined as the change in EPS over the
change in EBIT or
% change in EPS
% change in EBIT
The degree of financial gearing can be calculated from the formula:
EBIT
EBIT – Interest
Example 14 – Degree of financial gearing
For the ungeared company in the Example 13 above, the degree of financial gearing can be
calculated as follows, for a particular value of EBIT, say EBIT = $75. For the ungeared
company, we have:
75
1
75  0
Whereas for the geared company, we have:
75
 1.67
75  30
The degree of gearing confirms our earlier finding that the geared EPS is more sensitive to
changes in EBIT.
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P. 96
Copyright @ Kaplan Financial 2015