Transcript Financial Theory - Banks and Markets

Cost of Capital
by Binam Ghimire
1
Learning Objectives
 Concept of cost of capital
 Significance of cost of capital
 Concept debt, preferred and common stock
 Understand stock market
 Dividend Growth Model and Capital Asset Pricing Model
 Compute component costs of different types of capital
 Determine weighted average cost of capital
2
Cost of Capital
Concept:
 Funds from long-term sources of financing
 Compensation
 Different Names:
Required rate of return,
hurdle rate,
opportunity cost,
discount rate
3
Concept:
 Overall cost of capital (Excel File) – pronounced similar
to Quack – W_ _ _
4
Cost of Capital
Basic Assumptions:
 Constant
 Constant
 Constant
 Constant
Business Risk
Financial Risk
Dividend Policy
Tax Rate
5
Cost of Capital
Financing decision:
 Investment Decision
 Capital Structure Decision
 Dividend Policy Decision
6
Capital
Components:
 Debt
+
 Preferred
+
 Common Stock
______________
Total Capital
 The order of capital components (based on their cost)
7
Capital
Components:
Source: Airplane-Pictures.net
 The cost of capital components (is based on degree of
risk)
8
Debt
9
Debt Capital:
Concept
Debt: Bank Loan, Bond, Notes, Debenture
10
Debt Capital:
Concept
A Bond
Source: historycooperative.org
11
Debt Capital
Terminologies:
 Bondholders: Lenders/ Investors
 Bond Issuers: Company raising the money
 Coupon: The fixed interest payment (as a % of face
value – “C”)
 Bond’s face value: principal or par value (“F” or “P”).
Par/ Nominal value of £ 100. The market value is
relative to the nominal value. Say 110% when traded at
£110
 Maturity/ Redemption
 Call Provision
 Sinking Fund Provision
12
Bond:
Types
 Treasury Bond: Government
 Corporate Bond: Companies
 Municipal Bond: State or local government
 Foreign Bond: Foreign government/ companies
13
Bond:
Types
 Pure Discount Bonds
 Level Coupon Bonds
 Consols
14
Bond:
Patterns of Cash Flow
Coupon
Types\Year
1
2
3
4
5
6
Pure Discount Bonds
Payment
F
Level
C
C
C
C
C
C
F+C
Consols
C
C
C
C
C
C
C…
15
Bonds
Types:
 Redeemable
 Irredeemable
 Convertible
 Non-convertible
 Extendable/ Retractable
 Zero coupon/ Strip
 Junk/ high yield/ non investment grade
 Eurobonds
 Inflation linked
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Bond Ratings
 Bond Ratings evaluate the debt issuer to determine
the risk of default
 The leading rating agencies, Standard & Poor's and
Moody's Investors Services
 Moody's ratings, from highest to lowest. Investment
grade: Aaa, Aa1, Aa2, Aa3, A1, A2, A3, Baa1, Baa2,
Baa3. Speculative grade: Ba1, Ba2, Ba3, B1, B2, B3,
Caa1, Caa2, Caa3, Ca, C1
 S&P's ratings. Investment grade: AAA, AA+, AA, AA-,
A+, A, A-, BBB+, BBB, BBB-. Speculative grade: BB+,
BB, BB-, B+, B, B-, CCC+, CCC, CCC-, CC, D
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Preference Share
18
Preference Shares:
Concept/ Characteristics
 Hybrid
 Higher risk than ……………… Capital but Lower than
……………… Capital
 Provided that there are sufficient profits, available,
preference shares will normally be given a fixed rate of
dividend each year and preference dividends will be paid
before ordinary dividends are paid.
 If a business is wound up, preference shareholders may be
given priority over the claims of ordinary shareholders.
 Preference shareholders are not usually given voting
rights, although these may be granted when the
preference dividend is in arrears.
 Similar to Debt as both offer a fixed rate of return. But less
popular why?
19
Preference Shares
: Types (colour the right hand side column)
Cumulative
Allows the business to buy back
the shares from shareholders at
some agreed future date.
Non-Cumulative
The right to receive arrears of
dividends (not given in the past
as a result of there being
insufficient profits)
Participating
No right to receive arrears of
dividends (not given in the past
as a result of there being
insufficient profits)
Redeemable
The right to a further share in
profits available for dividend
(after they have been paid their
fixed rate and after ordinary
shareholders have been awarded
a dividend).
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Ordinary Share
21
Ordinary Shares:
Concept/ Characteristics
 Backbone
 There is no fixed rate of dividend and ordinary
shareholders will receive a dividend only if profits
available for distribution still remain after other investors
(preference shareholders and lenders) have received
their returns in the form of dividend payments or
interests.
 If the business is “wound-up” the ordinary shareholders
will receive any proceeds from asset disposal only after
lenders and creditors, and after preference
shareholders, have received their entitlements.
 On the other hand the potential returns facing ordinary
shareholders are …………………...
22
Ordinary Shares:
Concept/ Characteristics
 Ordinary shareholders exercise control over the
business through their voting rights. This gives them the
power to elect the directors and to remove them from
office.
23
Stocks and the Stock Market:
An IPO
 Initial Public Offering (IPO), also referred to simply
as a "public offering", is when a company issues
common stock or shares to the public for the first time.
24
Stocks and the Stock Market:
An IPO
 In addition, once a company is listed, it will be able to
issue further shares via a rights issue, thereby again
providing itself with capital for expansion without
incurring any debt.
 This regular ability to raise large amounts of capital from
the general market, rather than having to seek and
negotiate with individual investors, is a key incentive for
many companies seeking to list
25
Stocks and the Stock Market:
An IPO
 There is competition amongst stock exchanges for IPO’s.
 In April 2008 Fresnillo, the world's largest producer of silver, listed on the
London Stock Exchange (LSE).
 The company, the first Mexican one to be listed in London, raised some $2
billion, but its initial public offering had broader ramifications. You might
have expected a Mexican company to head straight for Wall Street. That it
did not both shows the success of the LSE's efforts in Latin America and
also highlights the extent to which London now dominates mining finance.
 Four of the five largest mining companies in the world are listed in London.
A decade ago, Toronto might have been their favoured destination, if it
was not New York.
 But compared with Toronto, London has more liquidity, as well as more
analysts, bankers and lawyers specialising in natural resources.
 Fresnillo's boss, Jaime Lomelín, said in the Economist that London's appeal
has grown over New York because of the way it treats taxes, and because
he prefers the LSE's approach to corporate governance.
26
Stocks and the Stock Market:
The FTSE 100
 The FTSE 100 Index is a share index of the 100 most highly
capitalised companies listed on the London Stock Exchange.
 The index began on 3 January 1984 with a base level of 1000; the
highest value reached to date is 6930.2, on 30 December 1999.
 FTSE 100 companies represent about 80% of the market
capitalisation of the whole London Stock Exchange.
 Even though the FTSE All-Share Index is more comprehensive, the
FTSE 100 is by far the most widely used UK stock market indicator.
 The constituents of the index are determined quarterly; the largest
companies in the FTSE 250 Index are promoted if their market
capitalisation would place them in the top 90 firms of the FTSE 100
Index
 As of July 2009 that threshold would be £1.97bn.
27
Stocks and the Stock Market:
The FTSE 100
 As of 23/7/2009 the largest companies in the
FTSE100 are:
NAME
HSBC HDG. (ORD $0.50)
BP
VODAFONE GROUP
GLAXOSMITHKLINE
INDUSTRY
BANKS
OILIN
TELMB
PHRMC
MV( £m)
96338.06
94737.19
60351.02
59848.1
• The FTSE100 is dominated by a small number of sectors:
• Oil Industry = 18.86%
• Banks = 16.23%
• Mining = 11.55%
28
Stocks and the Stock Market:
NASDAQ
 The NASDAQ-100 is a stock market index of 100 of
the largest domestic and international non-financial
companies listed on the NASDAQ stock exchange.
 It is a modified market value-weighted index; the
companies weights in the index are based on their
market capitalization, with certain rules capping the
influence of the largest components.
 It does not contain financial companies, and includes
companies incorporated outside the United States; both
of these factors differentiate this index from the S&P
500 and the Dow Jones Industrial Average.
29
Stocks and the Stock Market:
NASDAQ
 The NASDAQ 100 is also dominated by a small number of
sectors:
 Software = 21.24%
 Telecommunications Equipment = 13.7 5%
 Semiconductors = 10.02
 As of 23/7/2009 the largest companies in the NASDAQ 100 are:
NAME
MICROSOFT
APPLE
CISCO SYSTEMS
ORACLE
INTEL
GOOGLE 'A'
INUSTRY
SOFTW
COMPH
TELEQ
SOFTW
SEMIC
INTNT
MV ($ m)
220712.9
139829.3
123720.9
108907.2
106896.8
103110.4
30
Stocks and the Stock Market:
S&P 500
 Compare this to the S&P 500:
EXXON MOBIL
MICROSOFT
WAL MART STORES
JOHNSON & JOHNSON
PROCTER & GAMBLE
INTERNATIONAL BUS.MCHS.
AT&T
OILIN
SOFTW
BDRET
PHRMC
NDRHP
CMPSV
TELFL
341530.7
220712.9
191596.6
163101.7
159929.6
152713.8
146555.9
31
Stocks and the Stock Market:
Shanghai 180 Index
PETROCHINA 'A'
INDUSTRIAL & COML.BK.OF CHINA 'A'
CHINA PTL.& CHM.'A'
BANK OF CHINA 'A'
CHINA LIFE INSURANCE 'A'
CHINA MERCHANTS BANK 'A'
PING AN INSURANCE (GP.) CO. OF CHINA 'A'
BANK OF COMMS.'A'
CITIC SECURITIES 'A'
OILIN
BANKS
OILIN
BANKS
LFINS
BANKS
LFINS
BANKS
INVSV
MV (Yuan)
2501695
1307513
935554.6
789515.4
690507.6
298298.9
297044.5
261373.4
230541.2
MV( USD)
366248.2
191419.9
136965.2
115585.1
101090.3
43670.97
43487.32
38265.07
33751.24
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Stocks Valuation :
Book Value
 Book value is an accounting concept
 The firm’s book value of equity includes common stock
+ share premium (paid in capital) + retained earning
 Book value per share is simply the amount per share of
common stock to be received if all of the firm’s assets
are sold for their exact book value and all liabilities
(including preference stock) are paid
 Book value per share is computed by dividing total book
value by number of shares outstanding
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Stocks Valuation :
 Balance sheet of ABC Company on 31st December, 2009
is shown in table
 What is the book value of the company and book value
per share?
Liabilities and capital
Current liabilities
Long term debt
Common stock (10,000 shares)
Paid in capital (share premium)
Retained earning
Total
Amount (£ )
100,000
400,000
100,000
200,000
200,000
1,000,000
Assets
Current assets
Fixed assets
Total
Amount (£ )
400,000
600,000
1,000,000
 Liquidation value
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Stocks Valuation :
 Market Value
 Market value of a stock is the current (actual) price at
which the stock is being traded in the market
 Company’s future growth, earnings, earning power, level
of risk etc. are reflected in market price of the security
 Therefore, common stock’s price fluctuates widely
35
Stocks Valuation :
Intrinsic Value
 Intrinsic value: Present value of expected future cash
flows discounted at appropriate required rate of return
 Intrinsic value of a security is theoretical value or fair
value. It is based on future cash flows, future prospects,
future state of the economy and other factors that affect
the valuation of the security or asset
 Intrinsic value of a security is its economic value. In an
efficient market there is no significant difference
between market value and intrinsic value of the security
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Stocks Valuation Concept:
Book, Liquidation, and Market Value
 Which value will be higher for a profitable, and growing
firm? (among book, liquidation and market)
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Cost of Equity
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Cost of Equity:
Methods
 Dividend Growth Model (DGM)
 Capital Asset Pricing Model (CAPM)
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DGM
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DGM
 The most common is the constant growth model
 Assumes that dividend will grow forever at a constant
rate, g, and it is less than required return, ks
 Also known as Gordon Model
 If a firm’s future dividend payments per share are
expected to grow at a constant rate, g, per period
forever then the dividend at any future time period t can
be forecasted as follows:
Dt = D0 (1+g)t
 Example – ABC Co. stock paid a dividend £ 10 per-share
last year, which is expected to grow at a constant rate
of 5 percent forever. What will be the Dividend for next
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year and the year after next?
DGM
 Formula for Price of stock (applies the TVM concept)
D0 (1+ g)
D0 (1 + g)1 D0 (1+ g)2
P0=
+
+ ... +
(1 + ks)1
(1 + ks)2
(1 + ks)
D1
P0 
Ks  g
 Rearranging the above, the formula for Gordon’s model:
D1
Ks   g
P0
 Where D1 = D0(1+g)
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DGM
 Or, Gordon Model =
D0 (1 g)
ks 
g
P0
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DGM:
Example (No Growth)
 ABC Company's common stock is currently trading at
£80 a share.
 The stock paid a dividend of £ 5 a share recently.
 The dividend is not expected to grow.
 What is the cost of ABC stock ?
44
DGM:
Example (With Growth)
 ABC Company's common stock is currently trading at
£80 a share.
 The stock paid a dividend of £ 5 a share recently.
 The dividend is expected to grow by 6%.
 What is the cost of ABC stock ?
45
DGM:
More Examples
 But first two terminologies
Ex Dividend
Cum Dividend
A security which no longer carries the right to the
most recently declared dividend
The payment of a dividend is due in the near future
and investors who buy the share now will receive the
dividend
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DGM:
Example 1
 The ordinary shares of Kewell Ltd are quoted at £5 per
share ex div. A dividend of 40p per share has just been
paid and there is expected to be no growth in dividends.
What is the cost of equity?
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DGM:
Example 2
 The ordinary shares of Gerrard Ltd are quoted at £2 per
share. A dividend of 15p is about to be paid and there is
expected to be no growth in dividends. What is the cost
of equity?
48
DGM:
Example 3
 Alonso Ltd. has a share price of £4 ex div and has
recently paid out a dividend of 20p. Dividends are
expected to grow at an annual rate of 5%. What is the
cost of equity?
49
DGM:
Example 4
 X Ltd. Is planning to pay a dividend of 30p per share.
The share price is £3.50 cum div. Dividends are
expected to grow by 5% per annum. What is the cost of
equity?
50
Estimating Growth
 Two methods, First Method
1
n
 D0 
  1
g  
 Dn 
 Where D0 = Current Dividend (say 2010), Dn = Dividend
n years ago (say 2005)
 The above formula is exactly same to PV in TVM
51
Estimating growth:
Example 5
 Sissoko Ltd paid a dividend of 20p per share 4 years
ago, and the current dividend is 33p. The current share
price is £6 ex div. a) Estimate the rate of growth in
dividends. b) Calculate the cost of equity.
52
Estimating growth:
Example 6
 Mascherano Ltd paid a dividend of 6p per share 8 years
ago, and the current dividend is 11p. The current share
price is £2.58 ex div. Calculate the cost of equity.
53
Estimating growth:
Example 7
 Z Ltd paid a dividend of 10p five year’s ago and the
current dividend is 22p. The current share price is £8
cum div. Calculate the cost of equity.
54
Estimating growth:
Second Method (GGM)
 Gordon’s Growth Model
 Formula
 g = Retention Ratio x Return on retained earnings/
reinvestment
 Or,
g = r x b
 This is also written as
 g = b x re
 Where “re” is return on equity
55
Estimating Growth:
Example 8
 The ordinary shares of Torres Ltd are quoted at £5.00
cum div. A dividend of 40p is just about to be paid.
 The company has an annual accounting rate of return of
12% and each year pays out 30% of its profits after tax
as dividends. Estimate the cost of equity.
56
CAPM
57
CAPM Assumptions
 The CAPM assumes that: Investors rely on two factors in making their
decisions: expected return and variance.
 Investors are rational and risk averse and subscribe
to Markovitz (1958) methods of portfolio
diversification.
 Investors all invest for the same period of time.
 There is a risk free investment, and investors can
borrow and lend any amount at the risk-free rate.
 Capital markets are completely competitive
58
CAPM Terminologies:
Systematic and Unsystematic risk
 In the development of portfolio theory Markowitz (1958)
defined the variance of the rate of return as the
appropriate measure of risk.
 However this can be sub-divided into two general types
of risk: systematic and unsystematic risk.
 William Sharpe (1963) defined systematic risk as the
portion of an assets variability than can be attributed to
a common factor.
 Systematic (or market risk) is the minimum level of risk
59
CAPM Terminologies:
Systematic and Unsystematic risk
 Sharpe (1963) defined the portion of an assets
variability that can be diversified away as unsystematic
(or unique) risk.
60
CAPM Terminologies:
Systematic and Unsystematic risk
 Total Risk: Systematic + Unsystematic
 Systematic Risk: Portfolio Risk or Market Risk
 Unsystematic Risk: Diversifiable Risk or Unique Risk
(AKA idiosyncratic risk)
61
CAPM Terminologies:
Systematic and Unsystematic risk
 Select from the following as cause for Systematic and
Unsystematic Risks :
Inflation
Announcement of a small oil strike by a company
Government Tax Policy
Recession
Decision of management of the company to expand/
contract
Controllable
Uncontrollable
62
CAPM Terminologies:
Systematic and Unsystematic risk
Even a little diversification can
substantially reduce variability.
Unsystematic Risk can be reduced
by diversification
Unique risk
Market risk
63
CAPM Terminologies:
Risk Free Rate and Risk Premium
 Given the historical record (higher return), why would
any investor buy anything other than common stocks?
Answer – Risk
64
Historical record
 See how predictably the Treasury bills behaved
compared to the S&P 500 index of large-cap stocks.
65
Historical record
66
Historical record
67
Historical record
68
Historical record – Average Returns
 One way of condensing this information is to calculate
the historical average return.
 Annual Returns Statistics (1926-1997)
Asset
category
Average
Maximum
Minimum
Large-Cap
Stocks
12.83%
53.12%
-43.76%
U.S. Treasury
Bonds
5.41%
44.44%
-7.55%
U.S. Treasury
Bills
4.10%
15.23%
0.01%
Inflation
3.20%
18.13%
-10.27%
69
The risk free rate and risk premium
 Over this 72-year period the average inflation rate was
3.20% per year, while the average return on treasury
bills was 4.10% per year.
 The treasury bill rate exceeded inflation on average by
0.90% per year whilst the return on the large cap
shares exceed the rate of inflation by 12.83% - 3.20%
= 9.63%.
 The government borrows money by issuing debt
securities, which come in different forms. One such form
is a treasury bill.
70
The risk free rate and risk premium
 Because these have such a short investment life and also because
the government can always raise taxes or print money to pay its
bills (at least in the short run), there is essentially no risk associated
with buying them.
 Thus we call the rate of return on such debt as the risk-free rate.
 The difference between the return on risky assets, such as common
stocks, and the risk free rate is interpreted as the risk premium.
 That’s is the additional return we earn for bearing risk.
 Over the period the average risk premium was 8.73% (for large cap
stocks) and 1.31% for US treasury bonds.
 Risky assets therefore, on average, earn a risk premium.
71
Expected Return on Market:
 From the above we can say that
E(R )  R  Risk Premium
M
f
 Or it is the Risk free rate + the compensation for the
risk inherent in the market portfolio
 Hence for the above illustration, over the period the
average risk premium was 8.73%. So the expected
return from the market was
 4.10% + 8.73% = 12.83%
72
Expected Return on Individual security
(using CAPM):
 Need to understand the b (beta)
73
Expected Return on Individual security
(using CAPM):
 The b is the covariance between the return of a
security and the market return divided by the variance
of the market return.
Covariance (R , R )
β
Variance (R )
i
m
m
 It is a stock’s sensitivity to changes in the value of the
market portfolio
74
Expected Return on Individual security
(using CAPM):
 There is a relationship between risk and return
 Quantify the risk and return to find out the value of the
stock
 Thus, in CAPM, cost of equity is the function of risk-free
rate, market rate of return and beta coefficient. The
equation or model can be expressed as
Ks  R f  β (Rm  R f )
 This is also same as Cost of Equity = Risk Free Rate +
Beta x Risk Premium
75
Expected Return on Individual security
(using CAPM):
 If an investor wants to avoid risk altogether, he must
invest in a portfolio consisting entirely of
………………………. such as ……………………..
76
Expected Return on Individual security
(using CAPM):
 If an investor wants to avoid risk altogether, he must
invest in a portfolio consisting entirely of risk free
securities such as Government Debt
 If the investor holds only an undiversified portfolio of
shares he will suffer unsystematic risk as well as
systematic risk.
 If an investor holds a ‘balanced portfolio’ of all the
stocks and shares on the stock market, he will suffer
risk which is the same as the average systematic risk in
the market.
 Individual shares will have risk characteristics which are
different to this market average.
 Their risk will be determined by the industry sector and
gearing. Some shares will be more risky and some less.77
Expected Return on Individual security
(using CAPM):
 The market portfolio (remember, this is the portfolio of
all the shares in the market weighted by capitalization)
is taken to be the benchmark and is given a β factor of
1.
 All other shares or portfolios will have a β factor greater
or smaller than 1 depending on their systematic risk
which is measured by considering their required returns.
If a share or portfolio has a β factor of 0.5 it will move
in line with the market movements but only half as
much. If the share or portfolio has a β factor of 2, it will
again move in line with the market but twice as much.
78
Expected Return on Individual security
(using CAPM):
 If a stock has the same risk as the whole market
portfolio then, B = ……..
 If asset is less risky than the whole market portfolio
then Beta = ………
 If asset is more risky than the whole market portfolio
then Beta = ……..
79
CAPM:
The Security Market Line (SML)
 Shows the relationship between the return of a equity
and the β of the equity
Expected Return
SML
Rm
Rf
b1
 Higher b means higher risk premium
80
CAPM:
The Security Market Line (SML)
 Suppose Rf is 6 %, Rm is 10% and if b = 1 then
 Return on equity (also, Cost of equity) =
Ks  R f  β (Rm  R f )
= 6% + 1 x (10% - 6%)
= 10%
Now suppose the b is 0.5 then
= 6% + 0.5 x (10% - 6%)
= 8%
Again if b = 2
= 14%
81
CAPM:
The Security Market Line (SML)
 SML then will be
SML
Expected Return
14%
10%
8%
6%
b  0.5
b1
b2
82
CAPM:
Example 9
 The market return is 15%. Kuyt Ltd has a beta of 1.2
and the risk free return is 8%.
 Required:
 What is the cost of capital?
83
CAPM:
Example 10
 Crouch plc
The risk-free rate of return is 8%
The market risk premium is 6%
The beta factor for Crouch plc is 0.8
Required: What would be the expected annual
return?
84
CAPM:
Example 11
 The return required by the shareholders of Y ltd is 15%.
The return on the market portfolio is 12% and the
 Risk free rate is 9%.
 Required:
 a) Calculate the equity risk premium of Y’s shares.
 b) Calculate the ß of Y Ltd.
85
Cost of Debt
86
Concept
 Cost of debt should be lower than the cost of equity. In
addition tax on interest is deductable
 The market value of debt is assumed to be the present
value of its future cash flows
 Debt can be
Irredeemable
Redeemable at Par (Face value)
Redeemable at Discount (lower than Par value)
Redeemable at Premium (higher than Par value)
Interest may be fixed or floating
87
Cost of Irredeemable Debt
 Formula
I (1 t)
Kd (ID) 
P0 (Ex Interest)
88
Cost of Irredeemable Debt
Example 12
 Rafa Ltd.- The 10% irredeemable loan notes of Rafa
Ltd. are quoted at £120 ex int. Corporation tax is
payable at 30%. What is the net of tax cost of debt?
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Cost of Redeemable Debt
 Bond valuation model (trial-and-error or IRR method)
can be used to determine cost of redeemable debt
 Formula for the value of the debt is
n
I
M
NP  

t
n
1  k d 
t 1 1  k d 
 Here NP is net proceed
 We need to find Kd which means cost of redeemable
debt
90
Cost of Redeemable Debt, Example
 Suppose ABC Company has 9 percent coupon bonds on
market with 20 years to maturity. The bonds make
annual payment and currently sell for £ 980. Company
has to pay £ 20 per bond underwriting fee. Assume tax
rate is 40 percent.
 Before-tax cost of debt (kd) can be computed using
bond value equation. But price of the bond is replaced
by net proceed.
 NP = £980 – £ 20 = £ 960
91
Cost of Redeemable Debt, Example
 NP = I × PVIFA kd,n + M × PVIFkd,n
Where
I = Interest, M = Value at Maturity, PVIFA = Present value
Interest Factor Annuity and PVIF = Present value
Interest Factor
 NP = I × PVIFA kd,n + M × PVIFkd,n
 £960 = £90 × PVIFAkd,20 + £1000 × PVIFkd,20
92
Cost of Redeemable Debt, Example
 Let us try 9%
PV = £ 90 × PVIFA9%,20 + £1000 × PVIF9%,20
= £ 90 × 9.1285 + £ 1000 × 0.1784 = £ 999.97
= £ 999.97 > £ 960, So let us try at 10%
 PV = £ 90 × PVIFA10%,20 + £1000 × PVIF10%,20
= £ 90 × 8.5136 + £ 1000 × 0.1486 = £ 914.82
93
Cost of Redeemable Debt, Example
 By Interpolation
PVat LR - PVat T R
Kd (RD)  LR 
x (HR  LR)
PVat LR  PVat HR
999.97- 960
 9% 
x (10% 9%)
999.97 (914.82)
= 9.47%
 Is this our answer? (Nearly there)
Note: If you are working out the interpolation using NPV
(not PV as above) then the interpolation formula
NPVat LR
changes to:
Kd (RD)  LR 
x (HR  LR)
NPVat LR  NPVat HR
94
Cost of Redeemable Debt, Example
 Before-tax cost of debt is 9.47 percent. Hence, after-tax
cost of debt is computed as
9.47 percent (1 - 0.4) = 5.68 percent.
 Let us practice the above in excel – See Excel File
95
Bond Calculation in Excel:
An Example
 In October 2007 Tesco raised $2bn (£990m) of debt in its first
dollar-denominated bond issue.
 The bond issue includes 10-year notes paying 5.5 per cent interest
(US$ 850m) and 30-year notes paying 6.15 per cent interest (US
1150m).
 The proceeds of the debt raising, which was jointly arranged by
Citigroup and JP Morgan Cazenove, would be used for "general
corporate purposes“.
 What does this bond offer?
 the first one pays 5.5/2 = 2.75% every six months until
November 2017 then it pays the coupon and the par value of
$100.
 The observed price of the first bond in Datastream was $ 96.28.
Find the YTM for the first bond
96
Bond Calculation in Excel:
An Example
24/07/2008 Year (24/07/08)
15/11/2008
0.31
15/05/2009
0.81
15/11/2009
1.31
15/05/2010
1.81
15/11/2010
2.31
15/05/2011
2.81
15/11/2011
3.31
15/05/2012
3.81
15/11/2012
4.31
15/05/2013
4.81
15/11/2013
5.31
15/05/2014
5.81
15/11/2014
6.31
15/05/2015
6.81
15/11/2015
7.31
15/05/2016
7.81
15/11/2016
8.31
15/05/2017
8.81
15/11/2017
9.31
YTM:
CF
2.75
2.75
2.75
2.75
2.75
2.75
2.75
2.75
2.75
2.75
2.75
2.75
2.75
2.75
2.75
2.75
2.75
2.75
102.75
Sum=
6.28%
PV
2.70
2.62
2.54
2.46
2.39
2.32
2.25
2.18
2.12
2.05
1.99
1.93
1.87
1.82
1.76
1.71
1.66
1.61
58.30
96.28
97
Cost of a Bank Loan
 Formula
 Kd BL = I(1-t)
 Example - Traore has a loan from the bank at 12% per
annum. Corporation tax is charged at 30%. What is the
cost of debt?
= 8.4%
98
WACC:
Formula
 Two methods
 1. Total cost ÷ Total capital
D
P
E
WACC  x k (1  t)  x k  x k
V
V
V
d
p
 2. Sum of weight x cost
WACC  wd kd (1  t )  wp k p  we ke
99
e
WACC:
Example
 See Excel File
100
Thank You
101