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Financial Management
Instructor: Dr Sam Wylie
Office: Room 146
Tel: 03 9349 8185
Textbook: Hawawini and Viallet
Study schedule
Reading for classes 1.7 & 1.8
All of Chapter 1 of Hawawini and Viallet (HV) Chapter 6: pages 185 to 196 & 215—218 (Appendix 6.1) of HV
To prepare for classes 2.3 & 2.4 Review slides for Class from website
Homework and Casework Download Problem Set 1 from the class website. Complete the
questions and submit them in-class (in hard copy) You may discuss the questions in your syndicate groups, but then each
student must complete their own solution to the questions
Introduction
Finance in Modules 1 and 3 is concerned with two things:
Studying how managers make financial decisions to create value for shareholders (or principal beneficiaries of the organization)
-- The value of different projects that the firm could invest in
-- Value creation for shareholders in choosing between those projects
-- The value of securities that the firm issues to finance projects
-- Value creation for shareholders in choosing its capital structure
Introducing the major components of the financial system
-- Financial instruments: Stocks, bonds, bank loans, options, futures, etc.
-- Financial markets: Stock markets, bond markets, money market, futures markets, forex markets, etc.
-- Financial intermediaries: Commercial banks, investment banks, insurance firms, investment managers
-- The Central Bank and Regulators
Introduction
Hawawini and Viallet start with the question “what is the objective of financial decision making in a firm?”
That is a natural starting point for a text on financial management. We will come directly to this crucial question in Class 1.8.
But this is a first course in finance. So, we want to start with a more general question – “what is the purpose of the financial sector of the economy?”
Basic Financial Needs
Households, firms and governments have 5 fundamental financial needs
1. Transfer value through time
2. Transfer and diversify risk
3. Obtain liquidity
4. Make payments
5. Obtain advice
The financial sector creates value by helping households, firms and governments to meet these basic needs
Basic Financial Needs
Transfer value through time Households, firms and governments each face a mismatch in time
between cashflows in and cashflows out
Households
-- Need to borrow early in their life cycle to buy housing and then save in mid- life for retirement
Firms
-- Need to raise capital for projects early in the life-cycle of the firm, but typically generate a cash surplus as mature companies
-- Need to manage fluctuations in working capital due to seasonality in revenues and costs
Governments
-- Borrow to fund budget deficits during the low point of business cycles – ideally helping to stabilize the economy
-- Borrow to create risk-free debt instruments in the economy
Basic Financial Needs
Transfer or diversify risk Households
-- Transfer risks to insurance companies
-- Absorb the riskiness of the cashflows of firms by buying the securities of firms (stocks and bonds) and holding them in diversified portfolios
Firms
-- Sell risky securities that are claims on the cashflows of the firm
-- Transfer risks through insurance contracts and through derivatives markets (options, futures, swaps markets)
-- Diversify credit risk across customers and business risks across products
Governments
-- Absorb macro financial risks – risks of failure of banks, failure of pension funds, etc.
-- Provide social insurance to households
Basic Financial Needs
Obtain liquidity
There are two types of liquidity
-- Payments liquidity the ability of an asset to be used for immediate payment, or to soon revert to cash for immediate payment
-- Asset liquidity the ability of an asset to be quickly bought or sold at near its fundamental value
Households and firms need to be able to access payments liquidity so that they can make purchases and meet obligations when they become due
Liquidity is valuable and expensive to access -- storing liquidity is expensive because cash, bank deposits and other assets that provide payment liquidity have low returns
The central bank is the ultimate source of liquidity
Basic Financial Needs
Make payments
A payments system is the elemental component of any financial system
The payment system
-- Allows secure transactions between unrelated parties
-- Permits immediate discharge of liabilities
-- Provides a store of value
-- Provides a record of transactions
There are three types of payments systems
-- Retail (Credit cards, debit cards, checks, cash)
-- Wholesale (for business to business payments)
-- Institutional (between major financial intermediaries
Basic Financial Needs
Obtain advice
Households
-- Need financial advice on investment management, retirement strategy, tax management, estate planning, etc.
Firms
-- Need financial advice on: project selection; raising capital; risk management; tax management; pension fund management; liquidity management; etc.
Governments
-- Have departments and other organizations for collecting data and providing financial advice – Treasury and Finance Departments, the Reserve Bank of Australia and major finance industry regulators
Basic Financial Needs
We can understand the different parts of the financial system
Financial instruments -- Stocks, bonds, options, futures, swaps, etc.
Financial markets -- Stock markets, bond markets, futures markets, forex markets, etc.
Financial intermediaries -- Commercial banks, investment banks, insurance firms, investment managers
The Central Bank and Regulators
Payments systems
in terms of the value that they add by helping to meet the basic financial needs of households, firms and governments
Objective in financial decision making
Optimal decision making only makes sense in relation to an objective
What is the objective of financial decision makers (managers) in publically owned corporations?
To maximize shareholder value?
-- What do shareholders care about?
-- Is this an objective that all shareholders agree on?
What about other stakeholders in the firm?
How does the objective of managers change if the firm is “closely held?”
What are the objectives of financial managers in not-for-profit organizations? For governments?
Stakeholders
Shareholders
Management
Tax office
Public debt providers
Private debt providers
Suppliers
Employees
Customers
Corporation
Time value of money
How much are riskfree promises of cashflows in the future worth today?
Capital budgetting example
Example: Imagine that you are deciding whether a particular project can be funded within the firm’s capital budget. The project involves the
building of a new medical equipment maintenance facility.
The up-front cost of the new facility is $1.5 mn The facility will be used for 5 years after which it will be superceded and it will
have a residual value of $200,000 The incremental increase in firm’s cashflows from the facility will be $420,000
per year
C1=$420,000
Time521
C5=$620,000C2=$420,000
NPV? . . .
C0=-$1.5 mn
Capital budgetting example
Should you approve the project? We want to compare the the present value of the cashflows to the current costs To get the present value of the future cashflows
-- Discount each of the future cashflows to the present by multiplying the cashflow by a discount factor
-- Sum up the discounted cashflows to get the present value of the stream of future cashflows
-- What is the discount factor?
0 Time1
Today? V1 = $1
Growth factor = 1+r
Discount factor = 1/1+r
Transferring value
How much is a dollar today worth in the future?
0 Time1
$1 todayValue 1 period
from today?
0 1 1V $1 V 1 r V principal + interest
Example: Interest rate on a bank deposit is 5%
1 period
0 Time1
$1 todayValue 1 period
from today?
1 0
1 0
Example: $200 in a bank deposit at 5%
V V 1 r = 200 1 0.05 = $210
Example: $200 in a bank deposit at 5.25%
Now r = 0.0525
V V 1 r = 200 1 0.0525 = $210.50
2 periods
How much is a dollar today worth 2 periods from now?
0 Time1
$1 today V1 = (1+r)
2
0 1
2 1 0 02
This is compounding of interest. V includes interest on interest
Without this compounding we would have "simple" interest
Example (of compound interest):Int
V $1 V 1 r
V V (1 r) V (1 r)(1 r) = V (1 r)
2 22 0
erest rate on a $400 bank deposit is 7%How much does the deposit grow to in 2 years
V V (1 r) = 400(1 + 0.07) = $457.96
2
Value 2 periods from today?
N periods
How much is a dollar today worth N periods from now?
0 Time1
$1 today V2 = (1+r)2
N
8 88 0
N 0 1 r
In Excel this is =12000*power(1.0416,8)
Example: Interest rate on a $12,000 bank deposit is 4.16% for 8 years
V V (1 r) = 12,000(1 + 0.0416) = $16,626.50
V V
2
Value N periods from today?
N3
Average yields
If the interest rate varies from period to period, then how much is the average yield on the investment
Example: An investment of $200 in a particular investment promises 5.1% in the first period and 14.1% in the second period
0 Time1
$1 today V1 = (1+0.051)
2
V2 = (1+0.051)(1.141) = (1+y)(1+y)
5.1% 14.1%
0 1 22 (1 r )(1 r ) 200(1.051)(1.141) $239.84V V
yy
Average yields
2
2
2
2
2
0.5
0.5
2
Dividing both sides by 200
Taking square root of both sides
Subtract one from both sides
y is the average yield on the investment
V (1 y)
200
V(1 y)
200
V 1 y
200
Su
V 200(1 y)
;
0.5
2200(1 0.051)(1 0.141)bstituting the value of V 1 y
200
y 0.095076 9.51%
Notice that the $200 is irrelevant.
Average yield only depends on the interest rates
Average yields
The yield is the geometric mean of the interest rates in the two periods. It is not the arithmetic mean.
What is the arithmetic mean of the interest rates in the 2 periods?
Answer: (5.1 + 14.1)/2 = 9.6%
Is the geometric mean more, or is it less, than the arithmetic mean?
The geometric mean (average yield) is less than the arithmetic mean
That is always true
Consider the example of starting with $100, then realizeing a return of 100% in the first period and then -50% in the second period.
V0 = $100; V1 = $200; V2 = $100
Arithmetic mean of returns is [100 + (-50)]/2 = 25
Geometric mean (average yield) = 0.5
1 1.00 1 ( 0.50 1 0
Negative returns
Imagine an investment of $1000 in a bond fund that returns 26% in the first period and then -12% in the second period. What is the yield on the investment over the two periods?
0 Time1
$1 today V1
2
V2 = (1+0.26)(1+(-0.12)) = (1+y)(1+y)
26% -12%
yy
0.5
0.5(1 0.26)(1 ( 0.12))y = 1
y = (1.26)(0.88) 1 0.052996 5.30%
In excel =power(1.26*0.88,0.5)-1
3 periods
What is the average yield on an investment in a bond fund that returns:
8.1% in the first period
-3.7% in the second period
-7.7% in the third period?
1 2 3
3
1
3
(1 r )(1 r )(1 r ) (1 y)(1+y)(1+y)
(1 0.081)(1 ( 0.037))(1 ( 0.077)) (1 y)
What is the value of y?
y = (1 0.081)(1 ( 0.037))(1 ( 0.077)) 1
1In excel y =power(1.081*0.963*0.923, ) 1 0.0132 1.32%
3
Compounding intervals
Imagine a bank account that offers an annual percentage rate (APR) of interest of 10%, but half the interest is actually calculated and paid after each 6 month period rather than after 12 months. What is the difference
between the APR and the equivalent annually compounded interest rate?
0 Time1
$1 today V1 = (1+0.05)
y = (1 0.05)(1 0.05) 1 0.1025 10.25%
With interest payments made half yearly the realized annual return
is improved by 0.25%. It is always better to get the
power of compounding working sooner.
2
V2 = (1+0.05)(1+0.05)
5% 5%
Compounding intervals
What if the interest on the account (with 10% APR) were paid monthly instead of yearly?
Effective annual rate = (1+0.10/12)12-1 = 10.47%
In excel: =power(1+(0.10/12),12) - 1
As m approaches infinity and compounding becomes continuous the yield is calculated as
Effective annual rate = (1+0.10/m)m – 1 where m, the number of = em - 1
compounding periods, is large
What if the yield were compounded continuously?
Effective annual rate = e0.10 – 1 = 10.52% In excel: =exp(0.10)-1
Compounding intervals
Consider an investment of $4,000 that is paid an APR of 12.6% and is continuously compounded at that rate for 3 years. How much does the investment grow to in 3 years?
Answer: V3 = 4,000 e(0.126)(3) = $5,837.45 =4000*exp(0.126*3)
Consider an investment of $1,000 that realizes an APR of -12%, continuously compounded for 18 months. How much does the investment shrink to in 18 months?
Answer: Vt = 1,000 e(-0.12)(1.5) = $835.27 =1000*exp(-0.12*1.5)
Transferring value
So far we have discussed transferring value into the future -- how much will a dollar today be worth in the future?
But what we really need to know is – how much is cash that will be received in the future worth today?
We will consider the following problems: Single period discounting Discount factor Multiple period discounting Present value of a stream of future cashflows Present value of a perpetuity Present value of an annuity Present value of a growing perpetuity What happens to these present values when the discount factors
change?
Single period discounting
If you were offered an investment that is certain to pay $1 one year from today. Then what would you be willing to pay for it?
Recall from economics that willingness-to-pay (WTP) depends upon your best alternative. You will not pay more than your best alternative
investment that will also deliver $1 with certainty in one year.
If risk-free bank accounts pay 5% per annum then how much would you have to deposit with the bank today to have $1 in one year?
Your best alternative to $1 in the future is to invest 1/(1+r) today, so you will not pay more than 1/(1+r) for a claim on $1 in one year
1/(1+r) is the one period discount factor DF1
0 $0.9524V (1 0.05) = 1, so the required deposit is (1+0.05)
1
Single period discounting
If the risk-free interest rate is 5% then a promise of $1 with certainty in one year is worth 1/(1.05) = $0.9524 today
The present value of $1 in one period is 1/1+r
0 Time1
Today? V1 = $1
Growth factor = 1+r
Discount factor = 1/1+r
Multi-period discounting
The same logic of discounting future cashflows applies to longer periods
V0 V1
Time
V2=$1
10 2
DF = 1/(1+r) for one period
DF = 1/(1+r) for one period
2
2
2 2
How much is $1 promised, without risk, in 2 periods time worth today
1 1 1DF
1 r 1 r 1 r
$1Present value = $1 . DF
1 r
Example: What is the present value PV of riskfree cashflows of $100 after 1 year, $200 after 2 years, $300 after 3 years if the risk free interest rate
for these periods is 7%?
C1=$100
Time30 2
1 1 2 2 3 3
2 3
2 3
PV = C . DF C DF C DF
1 1 1$100 $200 $300
1 r 1 r 1 r
1 1 1$100 $200 $300
1 0.07 1 0.07 1 0.07
$100(0.9346) $200(0.8734) $300(0.8163) $513.04
1
C3=$300C2=$200
PV?
PV example
Example: Consider the same example a different way. Imagine that we invested $513.04 today at an interest rate of 7% and we withdrew $100
after one period, $200 after 2 periods and $300 after 3 periods, then how much would be left?
C1=$100
Time30 2
0
1
2
3
V $513.04
V 513.04(1 0.07) - 100 = $448.95
V 448.95(1 0.07) 200 $280.37
V 280.37(1 0.07) 300 $0
1
C3=$300C2=$200
PV?
PV example
Time1
Invest C0 today
1 1 2 2 3 3 N N
1
2
0
PV = present value of future cashflows
PV = C .DF C .DF C .DF ... C .DF
DF discount factor for cashflow 1
DF discount factor for cashflow 2
NPV = Net present value of the project
NPV = PV - C
2
C1
N3
C0
CNC3C2
Net Present Value (NPV)
Example: What is the net present value (NPV) of an investment in new managerial accounting software. The software costs $250,000 but is expected to deliver improvements to firm cashflow of $70,000 per year for five years. Assume that the opportunity cost of capital for these types
of low risk projects in the firm is 9%.
C1=$70,000
Time52
0 1 1 2 2 5 5
2 5
i5
i=1
i5
i=1
NPV = C + C . DF C DF ... ... C DF
1 1 1250 70 70 ... 70
1 r 1 r 1 r
1250 70
1 r
1250 70 250 70(3.8996)
1 0.09
$22,275.59 Positive NPV
1
C5=$70,000C2=$70,000
NPV? . . .
C0=-$250,000
Example: In the previous example the NPV was positive. The project adds $22,275.59 of value to firm for its shareholders. Now repeat the calculation with a cost of capital of 12.5%
The NPV is no longer positive with the higher cost of capital – the project will destroy value and should be rejected
C1=$70,000
Time52
0 1 1 2 2 5 5
2 5
i5
i=1
NPV = C + C . DF C DF ... C DF
1 1 1250 70 70 ... 70
1 r 1 r 1 r
1250 70 250 70(3.5606)
1 0.125
$760.22 Negative NPV
1
C5=$70,000C2=$70,000
NPV? . . .
C0=-$250,000
Class 2 Debt Markets
Reading for sessions 2.3 & 2.4
You should have read HV Chapter 1 and HV Chapter 6 pp 185-196, 215-218 by this point
To prepare for classes 2.7 & 2.8 Read HV Chapter 6 pp 196-209 Read HV Chapter 8 all pages Review slides for class from website
Major financial decisions
Major financial choices of the firm can be seen in its balance sheet
Assets Liabilities
Cash
Recievables
Inventory
Short term debt
Payables
Long term debt
Equity
Long term
assets
Capital budgetting – choosing which projects proceed
Capital structure – deciding how to finance the firm’s assets
Operational management
of liquidity and trade credit
Risk management – what risk to retain
and what to transfer
Raising capital – from investors through financial intermediaries
Chief Financial Officer
CFO
Controller
· Cash management· Credit management· Financial accounts· Tax accounts· Management accounts
· Restructuring· Investor relations· Corporate Governance Treasurer
· Capital budgetting· Capital structure· Financial planning· Raising capital· Financial risk management· Pension fund management
Chief Financial Officer
In this course (and Corporate Finance) we are mostly concerned with the functions of the Treasury Department, and especially:
Capital budgetting
The process of determining which of the projects that have been proposed by divisions of the firm should proceed. Ideally, every positive NPV project should proceed, however, firms are usually capital constrained and the approved projects must fit within a budget
Capital structure
Deciding what type of securities should be sold to investors to maximize the value of the cashflows generated by the firm. For instance, the CFO might decide that the firm would be more valuable to shareholders if it had more leverage. The CFO might then issue debt to generate cash and then use all the cash to buy back shares of the firm – hence increasing leverage in the firm for the remaining shareholders
Chief Financial Officer
Financial planning
The process of estimating and managing tthe growth of assets and liabilities of the firm and planning capital expenditure, the raising of capital, return of capital to
investors, and working capital levels, to ensure that the firm has the necessary cash on hand at all times
Raising capital
The process of selling claims on the cashflows of the firm to investors – those claims are bank loans, corporate bonds, equity etc.
Financial risk management
Deciding which financial risks should be retained in the firm and which risks should be transferred out of the firm to investors who can bear the risk at lower cost. For instance, the CFOs of Qantas and VirginBlue must decide whether to hedge the risk that the price of oil will go up, because fuel costs represent 20% of their total costs. Qantas has a policy of hedging fuel risk through the futures market (fixing the price for future delivery) and VirginBlue has a policy of not hedging – retaining the risk of a fuel price rise within the firm
Shareholders control of the firm
Shareholders control the firm (if corporate governance is effective)
They vote for the board and the board appoints the CEO and the senior management team
Why is it that shareholders control the firm, rather than otherstakeholders controlling the firm?
Because shareholders are the residual claimants. All other claims on the revenues of the firm are met before the shareholders’ claim (cash in the form of dividends and stock buy-backs)
The residual claimants would probably get nothing if another stakeholder, with an earlier claim on cashflow, controlled the firm
Objective of financial management
What do shareholders want the CFO to maximize?
Generally, shareholders all agree that they want the share price maximized
What do shareholders do to ensure that the management of the firm acts in the interest of shareholders?
This the same as asking how is corporate governance effected in the firm
Shareholders align the incentives of management with that of shareholders by giving management stock options that become valuable
if the stock price rises
Shareholders also replace CEOs that are not focused on creating shareholder value (increasing the share price)
Determining whether a project adds value
To calculate NPV (project’s addition to shareholder’s wealth) we need to:
Estimate the future cashflows (C1, C2, C3, …)
Determine how much future cashflows are worth today
C1
Time321
C3
C2
C0
4
C4D
Net present value (NPV)
Initial cost (C0) funded by debt
and equity
Present value of cashflows (PV)
Project Cashflows
E
Determining present value of future cashflows
Timet21
Ct
D
Consider one cashflow Ct
E
. . . . . .
t
t tC PV 1 r
t
t t
CPV
1 r
Ct is the present value compounded for t periods
PVt is the future value (Ct) discounted for t periods
But what value of r should we use? That is, what discount rate?
Net Present Value
NPV = PV – C0
= Present value of cashflows - current investment
= (Future cashflows adjusted for the return that investors could have received in other projects of the same risk) - investment
= Total revenues – total costs (including costs of capital)
Note that the returns promised to the providers of debt capital are fixed (bank debt and corporated bonds are fixed income
investments)
So, the surplus from the project (the NPV) flows through to theresidual claimants -- shareholders
Net Present Value (NPV)
If the management of the firm can create a project that has a positive net present value then they have created value for the
shareholders
A project creates value if the revenue generated by the project exceeds the costs of all the inputs to the project, including the capital supplied by investors.
Future revenues are estimated and after subtracting cash costs of: labour; payment to vendors and other costs of goods sold; and general selling expenses, we have the operating cashflows from the project each period. These cashflows are destined for the investors in the project (banks, bondholders, shareholders) and the tax office.
The process of reducing the future cashflows by the appropriate discount factor effectively removes from the cashflows the compensation that the providers of capital expect to receive if they had invested their capital elsewhere (the opportunity cost of capital).
What remains after deducting ALL costs from revenues, including the opportunity cost of capital, is the NPV of the project. This NPV accrues to the residual claimants of the firm – shareholders.
Delaying consideration of risk
In Class 3 (session 2.7 and 2.8) we will consider the practicalities of estimating the cashflows in of a project
The choice of an appropriate discount rate for the projects cashflows will be addressed over several classes in Module 3. For now we will assume that the cashflows we are considering are risk-free, or we will simply state the discount rate without consideration of its origin
So, for project evaluation we need to discuss the estimation of cashflows and choice of appropriate discount rates. However, we already have the tools that we need to start valuing financial investments that promise future cashflows
Debt Markets
What type of securities are used to raise debt capital, and how are those securities valued?
Fixed income contracts
Let us start by explaining what bonds are and then we can explain other fixed income instruments by comparison to bonds
Imagine that you purchased a Corporate bond that had a face value of $1000, a coupon rate of 7% and a maturity of 5 years
The bond is a piece of paper (or a computer record) that contractually binds the issuer to pay you interest payments (the coupons) at
regular intervals and repay the principal ($1000) at maturity (5 years from now) The face value (written on the face of old the bonds) is the amount
repaid at maturity The coupon (clipped from the edge of old bonds) is the regular interest
payment. Government and corporate bonds pay coupons every 6 months
The bond may also contain covenants that stipulate certain actions that the bondholder can or cannot take. For instance,
covenants may prohibit increases in dividends beyond a certain percentage of profits
Fixed income contracts
Bonds are issued by Governments and firms and are bought and sold in the bond market. The bond markets are part of the
broader capital markets which include the equity (stock) markets
Bonds that have maturities of between 1 and 10 years are often called notes
Bills are short term fixed income securities with a maturity of less than one year Bills do not pay interest; instead they are issued at a discount. A bill
that pays $1,000 in 180 days might be sold at $970 Bills are issued by:
-- The Federal Government (Treasury bills)
-- Banks (Banks bills)
-- Corporations (Commercial paper, also called promissory notes) The market for fixed income securities of less than 1 year duration is
called the money market (a part of the capital markets)
Bond example
Consider a Government bond that has
A maturity of 5 years
A face value (FV) of $1,000
A coupon rate of 7% (meaning it pays $70 of coupons per annum, $35 each 6 months)
$35
Time1021
$1035
$35
PV?
$35
. . .
3
$35
9
What is the present value of a stream of income that is $1 at the end of each period forever (never repaying the principal)? That is, what is the value of $1 received each period in perpetuity?
Value of a perpetual bond
C1=$1
Time32
2 3
i
i=1
Example: If the opportunity cost of capital is 8% then the present value $1 received in perpetuity is
1 1 1PV = $1 $1 $1 ...
1 r 1 r 1 r
1 1 1$12.5
1 r r 0.08
1
C3=$1C2=$1
PV? . . .
0
Algebra of valuing a perpetuity
2 3 4
2 3 4
2 3 4
2 3 4
2 3 4
2 3 4
2 3 4
Let Y = 1 + x + x x x ....
(1-x)Y = (1-x) 1 + x + x x x ....
Then, (1-x)Y = 1 + x + x x x ....x
1 + x + x x x ....x x x x ....
1
So, if Y = 1 + x + x x x ....
1Then, (1-x)Y = 1 Y = i
1-x
1 + x + x x x ....
f x < 1
Valuing a perpetuity
2 3 4
2 3
What is the PV of a perpetutity that pays $C each period forever, starting at the end of the first period?
C C C CPV = . . .
1 r 1 r 1 r 1 r
1 1 1 1C
1 r 1 r 1 r 1
4
Note that we are missing the 1 from the previous equation so we must subtract 1
. . .r
1 CPV = C 1
1 r1-
1 r
Example: The PV of a dividend payment of $2.50 received at the e
nd of each year in perpetuity, where the
C $2.50opportunity cost of the investment in the share is 15% PV = $16.67
r 0.15
Value of an annuity
An annuity is a series of constant payments that have a defined termination date in the future. An annuity can be thought of as a perpetuity that is terminated at some date in the future. On that
basis we can calculate the value of an annuity
C
Timet2
2 t
t
1 1 1PV = C ...
1 r 1 r 1 r
C 11
r 1 r
1
CC
PV? . . .
Value of an annuity
We can think of buying an annuity with t payments as buying a perpetuity that starts today and selling a perpetuity that starts in t periods from
today, so that all payments after time t cancel out
C
Timet2
t
CPV of the bought annuity
r
C 1PV of the sold annuity = -
r 1 r
The minus sign is because it is sold rather than bought and the discounting is
to bring the value of the perpetuity that starts at tim
e t back to the present
1
CC
PV? . . .
C CCC
. . .
-C -C-C-C
Value of an annuity
Example: What is the present value of an annuity that pays $25,000 each year for 15 years, with the first payment one year from now? Assume
that there is no risk of non payment, and the riskfree rate is 6%
2 t
2 15
t
15
1 1 1PV = C ...
1 r 1 r 1 r
1 1 125 ...
1 0.06 1 0.06 1 0.06
C 11
r 1 r
25 11 $242,806.20
0.06 1 0.06
Bank loan example
Consider a 30 year home loan for $600,000 with equal monthly repayments and a fixed interest rate of 7.7% APR (annual percentage rate)
What are the monthly repayments on this loan?
We know discounting the 360 monthly cashflows at a discount rate of 7.7% will give a present value of $600,000
We know the discount factor for monthly cashflows is
That allows us to back out the cashflows
The annuity equation tell us the present value of constant stream of cashflows (the 360 payments)
If we knew the value of the loan and the repayments then we could calculate the interest rate
10.077
112
Bank loan example
PV of payments on a 30 year home loan for $600,000 with equal monthly repayments and a fixed interest rate of 7.7% APR
What are the monthly repayments on this loan?
2 360
360
360
C C C600,000 = . . .
0.077 0.077 0.0771+ 1+ 1+12 12 12
0.077600,000
C 1 121 ; C =
0.077 0.0771+12 12 1
10.077
1+12
C = $4,277.76
The borrower
makes 360 monthly repayments of $4,277.76
Bond example
Consider a Government bond that has
A maturity of 7 years
A face value (FV) of $1,000
A coupon rate of 8% (meaning it pays $80 of coupons per annum, $40 each 6 months)
Investors can earn 7.5% per annum on similar bonds
$40
Time1421
$1040
$40
PV?
$40
. . .
3
$40
13
Example
Price of the bond is $1026.85
The bond sells at a premium to its face value because the coupon payments are greater than the yield demanded by investors
If the coupon payments were less than the required yield then the bond would sell at a discount (less than the face value)
You can calculate the price of any straight bond in this way
T
1 1 2 2 T T t tt=1
2 14
Price = CF .DF CF .DF . . . CF .DF CF .DF
$40 $40 $1040Price = . . . $1026.85
0.075 0.075 0.0751 1 12 2 2
Yield to maturity of a bond
The price of the bond depends upon the yield that is demanded by investors
The higher the yield demanded the lower the price of the bond
The lower the yield demanded the higher the price
There is a one-to-one correspondence between price and yield
T
1 1 2 2 T T t tt=1
1 2 T2 T
Price = C .DF C .DF . . . C .DF C .DF
C C CPrice = . . .
1 y 1 y 1 y
Price versus yield
$10,000 corporate bond with 8% coupons paid 6 monthly. A 30 year bond and a 7 year bond are shown
0
200
400
600
800
1000
1200
1400
1600
1800
0 0.05 0.1 0.15 0.2
Yield
Pri
ce
in $
7 year 30 year
Example of calculating bond yield from price
Consider a 5 year corporate bond with $1,000 face value and coupon rate of 9%, with coupons paid bi-annually
The bond is currently selling for $992.85. What yield to maturity are investors demanding
1 2 T
2 T
2 10
C C CPrice = . . .
1 y 1 y 1 y
Coupons are paid twice yearly, but yields are always quoted on an annual basis
$45 $45 $1045 $992.85 = . . .
y y y1 1 12 2 2
Searching for a solution gives y
= 9.1815% or use the IRR function in excel
Yield on fixed income instruments
Components of yield
The average yield to maturity of a fixed income security has three components
Yield = rf + credit spread + liquidity spread
rf is the risk free rate of interest
--The riskfree rate varies according to the length of time to maturity of the bond, as shown in the yield curve
-- The riskfree rate differs across countries
Credit spread compensates the investor for the risk of default by the issuer of the fixed income security
Liquidity spread compensates the bondholder for low asset liquidity (loss of value if the bond must be sold quickly)
Introduction to the yield curve
The yield curve shows the required yield on riskfree fixed income securities of different maturities
A typical yield curve is shown below. This yield curve is the ‘normal shape, but the actual yield curve in Oct 2005 is unusually flat (we will discuss later)
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 2 4 6 8 10 12
Maturity in years
Yie
ld
Class 3 NPV and cashflows
Reading for classes 2.7 & 2.8
You should have read HV Chapters 1, 6 and 8 to this point
To prepare for classes 3.7 & 3.8 Review slides for class from website
Homework and Casework Download Problem Set 2 from the class website. Complete the
questions and submit one solution per syndicate in class on 18 October in-class (in hard copy) Complete the questions in your syndicate groups. Each student in the
syndicate should be able to answer all questions
Typical yield curve
The yield curve is derived from the prices of fixed income securities (bills and bonds) issued by the Australian Government The Reserve Bank of Australia (RBA) directly controls only one point on the yield curve – the far left point – overnight lending between banks
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 2 4 6 8 10 12
Maturity in years
Yie
ld
The RBA controls overnight interest rates
Australian yield curve in October 2005
The Australian yield curve is currently unusual in that it is (slightly) inverted, with long term yields lower than the cash rate (interbank lending rate). Under ‘normal’ circumstances the 10 year yield is 250-275 bp above the cash rate.
0
0.01
0.02
0.03
0.04
0.05
0.06
0 2 4 6 8 10 12
Maturity in years
Yie
ld
Recent RBA and Fed interest rate changes
The last 7 meetings of the Reserve Bank of Australia (RBA) have left interest rates (the Cash rate) unchanged The RBA is the central bank in Australia. The Fed (Federal Reserve
Board of Governors) is the central bank in the US. In any economy, the central bank
-- Acts as banker to the Government and large commercial banks
-- Sets the short term (overnight) interest rates
-- Regulates the banking system
-- Collects and publishes data on the economy
On 21 September The Fed raised the US Fed funds rate from 3.50% to 3.75%
The Fed is concerned about rising inflation pressures in the US and over-heating of the US real estate market and rising inflation. The
Australian economy is currently growing less quickly than the US economy (2% per annum versus 3.5% in the US)
Central bank control of interest rates
At the end of each day banks must settle their books. Some banks have surplus liquidity (cash) and some have a deficit. The rate at
which Australian banks lend each other money over-night is called the Cash rate. The same rate in the US is called the Fed funds rate.
The RBA has a target for the Cash rate which it changes from time to time depending on economic circumstances. In late 2003 it increased
the Cash rate target from 4.75% to 5.00%, and then from 5.00% to 5.25%, and then again from 5.25% to 5.50%. The RBA was then concerned by the rapid growth in the total volume of lending to households for purchase of homes.
If the RBA drains cash from the system (by selling Govt bonds in return for cash) then the price of overnight liquidity (the Cash rate) goes up – supply of liquidity is down so the price (the Cash rate) is up.
The yield on longer term lending (3 year notes for instance) is set by supply and demand in the market. If demand for those notes from investors rises then price rises and yield falls. If supply of notes, from the government or corporations, rises then prices of notes fall which means yields rise.
Fed Funds rate
WSJ 21 September 2005
The Federal Reserve raised interest rates for the 11th consecutive meeting
In response to the Fed move, commercial banks raised their prime lending rate, a benchmark for many short-term business and consumer loans, to 6.75% from 6.5%.
Longer-term lending rates will be little affected, however, as bond markets, where long-term rates are set, had anticipated Tuesday's action and showed little response
The graph is courtesy of the WSJ
Cost of debt – Telstra example
Telstra’s most recent long term debt issue – announced on 23 June 2004
‘Roadshow’ in early July 2004 for long-debt issue
Telstra issued €500 mn in 10 year floating interest rate bonds
Road show targetted at institutional investors in Europe and wasorganized by BNP Paribas, Deutsche Bank and JPMorgan
Road show was conducted by the CFO (John Stanhope) and Treasurer (Cliff Davis)
Telstra’s credit rating: S&P A+ Moody’s A1 Fitch A+
What risks does this borrowing pose for Telstra?
-- Risk of increase in interest rates
-- Exchange rate risk
What will they do about that risk? (Subject of Module 4)
Advice from Telstra’s IBs
How does Telstra’s CFO decide that the Europe is the best place to raise debt capital? Investment banks (IBs) have a crucial role here. A big firm like Telstra (annual revenues of $22bn) will have a strong relationship with several investment banks. The CFO will talk regularly with the IBs about the terms under which Telstra could raise capital.
• Where would Telstra get the lowest cost debt capital (lowest interest rates with least restrictive covenants) – a bank loan syndication? A corporate bond issue?
• What maturity is best – 5 year term loan?, 3 year notes, 5 year notes, 10 year bonds?• What debt market will give the best terms? US, Europe, Japan??
The large investment banks (IBs) are constantly (hour to hour) in touch with the large institutional investors (insurance firms, pension funds, mutual funds, etc) that would buy a Telstra corporate bond issue. Moreover, the global IBs are active in the debt and equity markets around the world. Therefore, they can give Telstra accurate assessments of what terms the markets will give Telstra for its debt. Telstra chose two European IBs (Deutsche and Paribas) to tap into the European debt markets, because those IBs are connected to the largest number of European investors.
The IBs that handle the issue will get about a 1.5% fee for underwriting and distributing the debt issue – about €7.5 mn for the deal. Competition between IBs for these deals is keen. The alternative to this bond issue would have been a large bank loan syndicated across a group of banks.
A A AL L L
Borrowers Bank Lenders
Balance Sheet of Borrower/Bank/Lender
Bank liabilities
Australian banks are a large source of capital for Australian corporations
If banks make loans to corporations (and households), then where do banks get that capital from?
-- Checking accounts and immediate access deposits 16%
-- Term deposits for 30 days, 90 days, 180 days, etc. 24%
-- Certificates of deposit 12%
-- Bonds issued to domestic or foreign investors 14%
-- Loans from other banks 8%
-- Other liabilities 18%
-- Equity of the bank shareholders 8%
0.0
200.0
400.0
600.0
800.0
1000.0
1200.0
Jan-8
9
Jan-9
1
Jan-9
3
Jan-9
5
Jan-9
7
Jan-9
9
Jan-0
1
Jan-0
3
Billio
ns o
f D
ollars
(A
us)
Amt due to Overseas
Non-resident liabilities
Other liabilities
Other borrowings
Bill acceptances
Deposits
Bank liabilties
Banks loans in Australia
Term loans
Finance permanent funding requirements such as fixed assets or underlying build up in net working capital requirements
For a term of more than one year – typically 3-5 years
Repayments are usually in equal periodic installments
Usually based on variables interest rates; such as, cash rate plus 300 bp (3%), or bank prime rate plus 100 bp (1%)
Borrowers pay bank commitment fee for any part of the loan that has not be drawn down yet: 45 – 55 bp for large firms
Term loans are often rolled over, at expiry, after review by the bank, and therefore form a long term part of the firm’s financing
Banks loans in Australia
Term loans (cont.) Terms loans often have substantial restrictive covenants Finance companies make medium term loans in the segment that is too
risky for banks
Revolving credit agreement An agreement to have loans of 90 days that will roll over for a
period of about 3 years Bank retains the option to terminate the lending after any 90 day
period, but the rollover is otherwise pre-arranged for 3 years They sometimes give the borrower the option to convert to a term loan
Banks loans in Australia
Mortgage loans Mortgage over real estate is a common security for loans Borrower is legally prevented (through Titles Office) from disposing of the asset until the debt is repayed Mortgage loan is more expensive to set up but provides excellent
collateral for the bank and therefore lower interest rates for the borrower
Commercial mortgages are typically 15 years or shorter
Short term loans Intended to be self liquidating in one year Often fund seasonal or temporary working capital requirements Interest rates on short term loans are lower than term loans by
25-50 bp
Banks loans in Australia
Syndicated loans Large loans are often shared among a syndicate of banks Especially for large resource project loans (Woodside for Northwest
Shelf) and large M&A deals (Patrick to buy controlling stake in VirginBlue)
A lead bank organizes the syndicate and receives fees of about 150 bp for doing so. Organizing bank syndicates is very like issuing bonds to large investors, so it is often done by the syndicated loan desks of investment banks
Insurance firms and superannuation funds may participate in the syndicate, although this is more common outside Australia
Participating banks can sell their share of the loan at a later stage if they need to
In 2004 there were $62 bn of loan syndication deals – 128 deals with an average size of $500 mn per deal
Bank lending by sector
0.0
200.0
400.0
600.0
800.0
1000.0
1200.0
1400.0
Jan-
89
Jan-
91
Jan-
93
Jan-
95
Jan-
97
Jan-
99
Jan-
01
Jan-
03
Bil
lio
ns
of
Do
llar
s (A
us)
Amount due fromoverseas operations
Non-resident assets
Other assets
Commercial Loans
Personal Loans
Residential Loans
Bills receivable
Notes and coins,and deposits duefrom RBA
Bank assets
Debt levels of firms
The leverage of corporations has been rising since the late 1970s
Reasons for increase: Firms have better instruments for managing risk business risk (derivatives), so they can accept more financial risk (leverage) Higher debt levels help to focus the attention of management
Types of debt in US firms $12 trn -- Equity value of non-financial publically listed US
corporations $2.8 trn -- Accounts payable $3.1 trn -- Corporate bonds $0.9 trn -- Bank debt
Small private firms have more bank debt, few corporate bond issues and less accounts payable
Private versus public capital markets
Private debt markets
-- Bank lending
-- Private placement of bonds
-- Leases
Private equity markets
-- Angel investors / wealthy families
-- Venture capital
Public debt markets
-- Treasury bills / Bank bills / Commercial paper (promissory notes)
-- Treasury bonds / Corporate bonds / Mortgage backed bonds
Public equity markets
-- Initial public offering of stock
-- Seasoned offering of stock
Private markets are more opague and illiquid and consequently the cost of capital is higher in private capital markets
NPV and Cashflows
Is NPV the best rule for choosing projects, and what are the practical considerations in estimating cashflows and using the NPV rule?
Determining whether value is added
To calculate NPV (project’s addition to shareholder’s wealth) we need to:
Estimate the future cashflows (C1, C2, C3, …)
Determine how much future cashflows are worth today
C1
Time321
C3
C2
C0
4
C4D
Net present value (NPV)
Initial cost (C0) funded by debt
and equity
Present value of cashflows (PV)
Project Cashflows
E
Project cashflow to investors
Cashflows to tax office
After-tax cashflows to shareholders and debtholders
Depreciation EBIT
Operating expenses = CoGS+GSE
Revenue
Capital expenditure
Change in working capital (ΔWCR)
CFt = EBITt (1-Taxt) + Dept - ΔWCRt - Capext
Estimating future cashflows
We start with the revenue of the firm
Then subtract operating expenses: Cost of goods sold (CGS) + General selling expenses (GSE) + depreciation
The remaining cashflow is earnings before interest and taxes (EBIT)
Tax is applied to EBIT at the rate of TC (the effective corporate tax rate or the project)
Then non-cash expenses are added back – to reflect the fact that those cashflows remain to be used in the firm or paid out to
investors
Some after-tax cashflows are used retained for growth in the firms assets: Capital expenditure (Capex) on long term assets and
change in net working capital (ΔNWC -- which might be positive or negative)
Estimating future cashflows
The remaining cashflows are paid out to investors. It is this remaining cashflow that is discounted in the capital budgetting process
Important: Note, that in this method we are assuming that cashflows to debtholders are after tax, when in fact they go out of the firm
before corporate tax is applied. To undo this incorrect (but simplifying assumption) we put (1-TC) in front of the required
return to debtholders (rD) in the WACC equation
Weighted average cost of capital
The weighted average cost of capital for the project is:
To estimate the WACC for a project we need estimates of the:
Debt to equity ratio of project
Required return on debt for project
Required return on equity for project
Effective corporate tax rate of the project
E C D
E DWACC = r 1 T r
E+D E+D
Dividend imputation
Most OECD countries have some mechanism to reduce the double taxation of corporate earnings (corporate tax + personal tax on
dividends)
Australia has dividend imputation If you receive 70 cents in dividends That income is grossed up to 1.00 – being the income before corporate
tax Then your personal tax rate is applied
-- 47% in your personal tax
-- 15% in your superannuation
So you owe the government 47 cents (or 15 cents), if the dividend is fully franked then you receive 30 cents credit
So on the 70 cents dividend you pay 17c (or receive a rebate of 15 cents)
Dividend imputation
So the effective corporate tax faced by investors in Australia is closer to zero than to 30%
The effective corporate tax is not actually zero because: When corporations pay tax the franking credits are recorded in franking account But they are not used unless dividends are paid Some firms only pay low dividends (and retain earnings for growth) Some investors cannot use franking credits because they do not pay
Australian income taxes
Firms need to integrate franking credits into overall financial planning
Advantages of NPV over other methods
The NPV method of project selection is superior to other methods
Some firms use pay-back periods in choosing projects – althought this is increasingly uncommon
-- Payback period method ignores riskiness of the project and only considers how soon the project is expected to generate enough
cash to cover the cost of the project
-- Sometimes used as a rule of thumb when many investment decisions must be made quickly with limited information
Advantages of NPV over other methods
Many firms apply IRR hurdle rates to projects of different types
-- This is very close to the NPV method
-- The firm might have a 10% hurdle rate for maintenance/cost reduction projects; 14% hurdle rate for extension of existing
business; and 18% for expansion into a new business line
-- A problem is that the IRR may be non-unique if there are some negative cashflows later in the project (clean up costs for
instance)
-- Moreover, the IRR method does not give us the magnitude of gain from a project, so it does not help to decide between competing
projects when capital is constrained
Estimating future cashflows
Consistency is very important in measuring cashflows
Real cashflows must be discounted at a real rate (inflation adjusted) and nominal cashflows must be discounted at a nominal rate
Cashflows must be measured in the same currency
-- The discount rate must be appropriate to the currency. If revenues are in Euros then they must be discounted at the cost of capital for Euro denominated assets
-- Remember that the alternative to investing in assets that deliver Euro cashflows is to return the cash to investors who could do that for themselves
-- Instead of discounting at a Euro discount rate, the projected Euro cashflows can be converted back to $A using expected future
exchange rates (this approach is equivalent to using a Euro discount rate on Euro cashflows)
Estimating future cashflows
Usually cashflow estimates start with income statement proformas but they must be adjusted to reflect actual cashflows
Add back non cash expenses – especially depreciation
Undo the accrual nature of the income statement to reflect actual cash inflows and disbursements. We are concerned with cashflows
when they actually occur
Sunk costs must be ignored
Those costs have been incurred and cannot be recovered regardless of whether the project goes ahead or not
Sunk cost mining example
Consider a mining firm that owns mining rights and is considering a typical mining project with several phases
When the results of Phase 2 come back, how does the firm include the cost of exploration in the decision about whether to proceed to the production phase?
Geo-physical survey and
data purchase
Cost $5 mn
Phase 1
Exploration drilling
program Cost
$20 mn
Phase 2
Production drilling program and mine
construction
Cost $175 mn
Phase 3
Production phase
Phase 4
Mine shut-down and restoration
Cost $25 mn
Phase 5
NPV and strategy
When we have an estimate of the NPV of the project we need to compare that to what we should expect from strategy
Sustainable advantage
If your project proposal has a large NPV, then you should be able to identify the strategic source of that economic profit
-- Cost leadership
-- Product differentiation
-- Niche market
-- Defined barrier to entry
Capital budgetting and the winner’s curse
Imagine that the Australian Government decides to auction oil leases in the Timor Gap
Your consortia and 12 other others decide to bid for the first set of leases
You must decide an amount to bid that will give you:
-- A profitable project if you win (bid low price)
-- A high probability of winning (bid high price)
Geological, market and financial data are combined and you come up with a bid
The other 12 consortia are undertaking the same process Imagine that each consortia has access to the same data, but in processing that data, some consortia under-estimate the value of the lease and some over-estimate the value of the lease Who will win the auction? How is this related to capital budgetting?
Capital budgetting and the winner’s curse
Winners curse resulting from the project proposal process In auctions where there is difficulty in assessing the objective value of
the item being auctioned, there is a tendency for the winner of the auction to find that they only won the auction because they
over- estimated the value of item more than any other bidder
-- There are many examples of this well known phenomenon
-- Oil exploration leases and the radio spectrum licence auctions are recent examples
-- Experienced bidders will factor in the winners curse effect, and if all bidders mark down their bid to reflect the danger of the winner’s
curse, then its effect disappears
-- The point is that only over-estimates of value of the item survive the auction process
A similar problem can arise in capital budgetting
-- The project may have to survive several levels of project selection within the corporation. The danger is that only projects that overestimate their cashflows or underestimate risk can survive the selection process
Importance of real options
Projects are actively managed during their lives and this introduces options to change the project after it is underway
Those real options can be very valuable
A mining firm has the option to shutdown a mine if the price of the product falls in minerals markets, or if the geological problems turn
adverse
By simply estimating future cashflows and the required discount rate, we are ignoring the possibility of shutting down a project that has
lower than expected cashflows – and therefore stemming losses -- or expanding a project that has higher than expected cashflows
If these options are large, and we ignore them, then the project’s NPV has been under-estimated
The consideration of the real options is crucial in most projects. To consider this we need to understand some options theory, so this
discussion is postponed until Module 4
Class 4 Equity markets
How stocks differ from fixed income securities
Cashflows from stocks are not certain – they are not fixed income securities
Stocks are a claim on the residual cashflows of the firm
Stocks include control rights. The owners of the equity shares in the firm can vote on who will govern the firm (the board of directors)
Taxation of income and capital gains may differ between stocks and fixed income securities (taxation of financial assets is highly
variable across tax jurisdictions)
Equity markets
Why do firms list on the stock market?
To access to cheaper sources of capital in the public capital markets
To increase the asset liquidity of shares in the firm
You improve incentives for management through the issuance of stock options
To improve the perception of the firm by customers, suppliers and other stakeholders
To allow the firms founders to sell down, or at least hedge, their stake in the firm over time
To allow venture capital investors to cash out
Asset classes 1926-2000(US Data)
Risk premium estimates
How stocks are traded
Trading of stocks
The major exchanges ASX, NYSE, Nasdaq, LSE, TSE
Dealers versus brokers
-- Brokers help buyers to find sellers and transact and vice-versa
-- Dealers are principals to the transaction – meaning that they actually own the stocks – buying from sellers (at the bid price) and selling to buyers (at the ask price)
Market orders and limit orders
-- A market order instructs the broker to make the trade (buy or sell) at the best price that the market will currently accept
-- A limit order states that the broker should buy X if the price moves to Y or sell Z if the price moves W. The size of the trade is contingent on future prices
Getting best execution of a trade means getting the best price possible
Upstairs market for block trades (very large sell or buy orders)
Valuation of stocks
Equity analysts are the most important source of stock valuations Analysts use a variety of valuation methods
-- Discounted cashflow models
-- Accounting multiples
-- Fundamental measures -- such as installed base of customers
Sell-side analysts
-- Work for investment banks
-- Follow 15-18 stocks in one industry
-- Provide buy/sell recommendations and forecasts of earnings and future stock prices
-- Provide valuation advice in M&A deals
Buy-side analysts
-- Work for investment management firms
-- Follow larger number of stocks in one or more industries
-- Become portfolio managers if they are successful
Valuing stocks: Dividend growth model
The Dividend Growth Model of stock valuation models a share as a claim on a stream of dividends that grows at a constant rate into
the future
Price = Div1/(r – g)
Div1 = dividend at the end of the first year
r = capitalization rate
g = growth rate of dividends
Example: A stock pays expected dividend of $0.60 (starting one year from now) which is expected to grow at 8% and the appropriate discount (capitalization) rate is 15%
Price = 0.60____ = $8.57 0.15-0.08
Valuing stocks: Dividend growth model
Div1
Time32
1
2 31 1 1 1
1
Present value of a perpetuity with cashflow Div and growth g
Div Div Div Div1 g 1 g 1 gPV = ...
1+r 1+r 1 r 1+r 1 r 1+r 1 r
Divshare price
r-g
r = capitalization rate of dividend cashflo
ws
g = growth rate of dividends
1
Div1(1+g)
PV?
. . .
0
Div1(1+g)2
4
Div1(1+g)3
Valuing a growing perpetuity
2 3 42 3
What is the PV of a growing perpetutity that pays $C each period forever, starting at the end of the first period?
1 1 C CPV = C C C C . . .
1 r 1 r 1 r 1 r
1+g
1 r
1+g 1+g 1+g
C1
1+r
2 31+g 1+g
. . .1 r 1 r
1 CPV =
1 g r-g1-
1 r
C
1+r
Example: The PV of a dividend payment of $2.50, which begins one period from now
and then grows at 5% per period in pe
rpetuity, where the opportunity cost of the
C $2.50investment in the share is 15% PV = $25.00
r-g 0.15 0.05
Valuing stocks: Dividend growth model
What is observable in the dividend growth model?
Price (P) is observable - stocks are traded on the stock market and prices of trades are released in real time
Dividends are observable. Last year’s dividend is known. The expected dividend (expected by stock analysts) are reported
in the financial media
Knowing P and Div1 allows us to deduce (r-g). An estimate of g then gives r, or an estimate of r gives g. Analysts report their
estimates of the growth rate of dividends in large firms
Valuing stocks: Earnings per share
The ultimate determinant of the value of any investment, including shares, is the capacity of the investment to generate earnings – profits for
the owners
Earnings per share (EPS) and the price-earnings ratio (PE ratio) are key metrics of the value of shares
Market capitalization = (number of shares issued) x (price per share)
For example: The market capitalization (market cap) of BHP Billiton = 6.13 billion shares x $21.45 per share = $131 bn (ASX and LSE listing)
PE ratio = market capitalization = price per share net income net income per share
Net income of BHP in 2004/5 was $7.9 bn, so PE ratio = 16.7
Valuing stocks: Earnings per share
Can firms that have the same capitalization rate have different PE ratios?
Two firms can have the same current earnings. But if one firm has larger opportunities for investment in positive NPV projects then that potential will be recognized by the stock market in a higher stock price
The earning to price ratio is smaller, the higher is the present value of growth opportunities
Or equivalently, the price-earnings ratio (PE ratio) is higher, the larger are the growth opportunities of the firm (PVGO)
It is the goal of the management of the firm to indentify and create new positive NPV projects. Here we see how new projects feed into the share price (which is what shareholders care most about)
EPSP = PVGO
r
Valuing stocks
Data from the Australian Financial Review October 2005
16.7128.451.6936.35f21.4621.4518293821.45BHP Billiton
21.327.303.3820f5.925.90552935.91Alumina
15.1155.104.48105f23.4623.456364423.45ANZ Banking Corp
17.774.724.0253f11.4011.39317813.20Adelaide Bank
P/E ratio
EPSDiv yield %
Div per share
SellBuyVol 100s
Last sale
Company name
Interpreting stock data
Volume column shows how many shares were traded
Shares are traded in lots of 100. Less than 100 is called an ‘odd lot’ which costs more to trade
Buy and sell columns show the spread on the stock – difference between the bid price of buyers and the ask price of sellers
Dealers in the stock receive their revenue as the spread between buy and sell prices (the bid-ask spread) times the volume of their trades
Dealers are at danger of trading with informed investors – who buy just before stocks go up or sell before they go down
Dealers (and other traders) are at most danger from more informed investors in small stocks because those stocks have more private information that has not already been revealed; because small
stocks are not under the microscope of professional equity analysts
Consequently, the spread on small stocks are much larger
Growth opportunities
Why does BHP have a low dividend yield?
BHP’s profit rose steeply last year because of the China driven commodity boom (from $4.9 bn in 2003/04 to $7.9 bn in
2004/5)
But dividends per share rose only slightly (from 35.79c to 36.40c)
BHP has substantial growth opportunities, and consequently management wishes to keep a lot of cash in the firm (BHP is
purchased Western Mining Corporation for $9 bn in cash in 2005)
Moreover, firms do not allow their dividends to vary as much as their net income does. A firm will only raise dividends to reflect higher
earnings if the firm believes the new, higher level of earnings is permanent
Firms are very reluctant to decrease dividends and consequently are reluctant to raise dividends unless they can maintain them
Growth opportunities
Why does Alumina have a higher PE ratio than BHP?
Note that in comparing PE ratios across firms, we should only compare apples with apples. That means comparing banks, such as Adelaide and ANZ, or comparing mining companies, such as Alumina and BHP; firms that are expected to have the similar capitalization rates (reflecting similar types of risks)
The higher PE ratio of Alumina indicates that the stock market believes that Alumina has more growth opportunities (per dollar of earnings) than BHP does
Think of the price earnings ratio as the amount that investors are prepared to pay for the firms shares per dollar of earnings. If
they pay more they must be expecting something, and that something is increased earnings in the future from existing growth opportunities
Valuing stocks
Example
If a firm has a Price/earnings (PE) ratio of 16 and a capitalization rate of 12%, then how much is the present value of growth
opportunities as a fraction of the market capitalization of the firm?
0 0
0 0
0
0
EPS PVGOP PVGO r.P EPS
r r
EPS PVGOr 1
P P
1 PVGO0.12 1
16 P
PVGO 11 0.479 47.9%
P 16 0.12
Ownership of stocks
$16.8 trnTotal value of US corporate equities
$0.6 trnOther
$0.1 trnBrokers and dealers
$0.2 trnBank personal trusts
$1.2 trnInsurance companies
$1.3 trnGovernment pension funds
$1.6 trnPrivate pension funds
$1.9 trnRest of the world
$3.6 trnMutual funds
$6.3 trnHouseholds
US corporate equities Source: US Federal Reserve Flow of Funds 20 Sept 2005
Stock dealers and liquidity
Dealers of all kind provide liquidity to their market They offer to buy from sellers (at their bid price) and to sell to buyers
at their ask price To do this they must hold an inventory of the item being traded By allowing their inventory to fluctuate with the random arrival of
buyers (dealer’s inventory down) and sellers (dealer’s inventory up), dealers provide asset liquidity to the market
An item has asset liquidity if it can be sold (liquidated) quickly at a price close to its fundamental value
Your stocks have more asset liquidity than your house Asset liquidity is valuable – other things equal investors do not require
as high an expected return to hold a more liquid asset Equivalently, the market will compensate any agent who can increase
the asset liquidity of an asset by offering to buy into or sell out of their inventory at close to fundamental value
Adverse selection examples: Dealers
Dealer in BHP shares
Consider a dealer in BHP shares who posts a (bid) price for buying shares and a (ask) price for selling BHP shares
These bid and ask prices apply only to relatively small amounts of shares, for higher volumes the dealer demands better terms as
shown
Bid price = $21.45
Ask price = $21.46 Sell 1000 shares $21.46
Sell 5000 more shares $21.51
Sell 10,000 more shares $21.56
Sell 20000 more shares $21.66
Buy 1000 shares $21.45
Buy 5000 more shares $21.40
Buy 10000 more shares $21.35
Buy 20000 more shares $21.25
Adverse selection examples: Dealers
1 million share sale
Imagine that a large portfolio manager like Macquarie, Colonial State or MLC has decided to sell 1 million shares of BHP from the stock
portfolios that it manages for its customers
Without concerning ourselves with details of how shares are traded, the order goes to the market and the price is driven down as the
buyers (dealers and others) in the market demand better terms for more and more buying into their inventories
The dealers are compensated for providing liquidity – standing ready to buy when a large sell order arrives – because they buy at lower
prices as the price pressure of the sell order drives the price down temporarily. After the large sell order has passed through the market, the price returns to the fundamental value level and the dealers slowly sell out of their inventories at a price higher than they paid for the stock
Adverse selection examples: Dealers
But, what if the price does not return to its previous level?
What if some information about a decrease in the fundamental value of the stock had reached the seller before it reached the dealers?
That is, what if there is information asymmetry in the market? Then dealers face an adverse selection problem
When they offer to contract with a pool of potential counter-parties, some of whom have superior information about how the
fundamental value of the stock has changed, the dealer will select from the pool of counter-parties investors who’s average quality is less than that of the pool
To protect themselves from the problem of trading with informed traders, dealers can do one of two things Firstly, increase the spread between the buying price (bid price) and
selling price (ask price). A dealer’s revenue = spread x volume
-- Small stocks have larger trading costs than large stocks because the more the hidden information the higher the dealer’s spread
Adverse selection examples: Dealers
Secondly, become more expert at reducing information asymmetry
-- The better an antique dealer at valuing antiques (reducing information asymmetry with informed buyers or
sellers) the more money the dealer will make
Financial market efficiency
Imagine an event that will affect a stock price:
A mining firm strikes a rich vein of ore
A drug company recieves approval for a new drug
A firm (such as Apple Computers today) reports unexpectedly higher profits
Two firms announce to the stock market an unexpected merger
An unpopular CEO resigns unexpectedly
A firm announces a stock buy-back program, etc., etc.
How soon does that information affect the stock price?
Does the stock price change slowly or does it change immediately?
Does the information get to some market participants before others?
Which are the most efficient markets?
Questions about how fast important information becomes incorporated in stock prices (or any financial asset prices) are questions about the
informational efficiency of the stock market
Financial markets in which information that is important for asset prices is quickly incorporated into the prices are informationally efficient
Definition
A financial market exhibits weak form informational efficiency if all past price information is incorporated into asset prices at all
times
A financial market exhibits semi-strong form informational efficiency if all publicly available information is incorporated into asset prices at
all times
A financial market exhibits strong form informational efficiency if all information is incorporated in asset prices at all times
Can any investors outperform the market?
How do we test whether a market is informationally efficient?
One test is to ask whether any investors can acquire information that allows them to achieve returns on their portfolio that are more than commensurate with the riskiness of their portfolio
Start with the investors’ portfolio returns over a long period of time – say 60 months of observations
Over a large number of months the random component averages out to zero, leaving the risk component and skill
The portfolio return any particular month t is composed of 3 components: the expected
return commensurate with the risk taken in that month; the investor's value added due to
their skill; and a random
p,t t
component that changes from month to month
r Expected return for risk + investor's skill component (random component)
Can any investors outperform the market?
If we find that some investors can add value to their portfolios by researching the market and acquiring information that allows them to buy
underpriced securities and sell over-priced securities, then we have evidence that not all relevant information is already incorporated into prices
The problem with searching for out-performance by investors is that the potential levels of value added by investor’s research is small compared to the volatility of financial asset prices
In portfolio performance measurement, the signal to noise ratio is very low. The signal here is the value added of portfolio managers and the noise is the high volatility of stock returns
Return attributable to portfolio’s exposure to systematic risk
Return attributable to non-systematic
risk of portfolio
Skill component -- Added value of
investor’s research
Do portfolio managers add value?
Tests of market efficiency suggest that financial markets in developed countries are substantially informationally efficient. There is little evidence that the average portfolio manager can undertake research and trading that creates value for their investors
Because portfolio managers charge substantial fees the evidence suggests that in well developed stock markets investors are on average better off
investing in the stock market through passive portfolios rather than through actively managed portfolios
So why do most investors choose active portfolio management (with high fees) rather than passive portfolio management (low fee portfolios that
track a market index)?
Many active investors are confident that they can identify a better than average portfolio manager
The concept of market efficiency is not intuitive
Can markets be perfectly efficient?
Imagine that the stock market was believed to be perfectly informationally efficient, so that all investors believe that research into the value of
financial assets was futile, since all information of importance was already reflected in prices. What would happen? Is such a situation possible?
Passive
Active
Private
Total value of share market grows by 20%. From $1 trn on 30 June 2005 to $1.2 trn on 30 June 2006. Who gets the extra $200 bn?
Transaction costs + management fees
What if all portfolios were actively managed
Imagine now that all investors believed that active management of their portfolios by professional money managers would add value. Then what would be the average return on these portfolios?
Passive
Active
Private
Total value of share market grows by 20%. From $1 trn on 30 June 2005 to $1.2 trn on 30 June 2006. Who gets the extra $200 bn?
Transaction costs + management fees
What happened in the dot-com bubble?
If markets are informationally efficient then what happened during the dot-com bubble?
If prices during that “asset price bubble” did not reflect true value (meaning the market was not efficient at that time), then why not?
Winners curse
Difficulty in shorting the dot-com stocks
In the dot-com era, arbitrage of the mis-pricing of the dot-com stocks required shorting on the real side instead of the financial side
Proprietory trading and hedge funds
Investment banks undertake a large amount of proprietory trading; that is, trading on their own account using their own capital, rather than trading on behalf of clients
Hedge funds also are very heavy traders in financial asset markets
Investment banks and hedge funds make large profits from this trading, but does that imply that markets are inefficient? Or, are they being
compensated for something else?
Usually those investment banks and hedge funds are being compensated for providing liquidity to the market -- standing ready to buy from sellers or sell
to buyers
