FNCE10002
PRINCIPLES OF FINANCE
1: OVERVIEW OF PRINCIPLES OF FINANCE AND INTRODUCTION TO FINANCIAL
MATHS I ......................................................................................................... 2
2: INTRODUCTION TO FINANCIAL MATHS II .................................................... 5
3: VALUATION OF DEBT SECURITIES .............................................................. 10
4: VALUATION OF EQUITY SECURITIES .......................................................... 18
5: MODERN PORTFOLIO THEORY AND ASSET PRICING I ................................. 24
7: MODERN PORTFOLIO THEORY AND ASSET PRICING II ................................ 30
8: CAPITAL BUDGETING I .............................................................................. 38
9: CAPITAL BUDGETING II ............................................................................. 43
10: CAPITAL STRUCTURE AND PAYOUT POLICY I............................................ 48
11: CAPITAL STRUCTURE AND PAYOUT POLICY II........................................... 53
12: INTRODUCTION TO OPTIONS .................................................................. 61
SUBJECT OVERVIEW
Finance is the study of how individuals and businesses acquire, spend and manage financial resources.
INVESTMENT ANALYSIS
Where and How to invest and how to finance these investments.
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Valuation of bonds, equities and derivatives
Modern Portfolio theory
Asset pricing and Market efficiency
CORPORATE FINANCE
Decisions of companies and their management
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Capital budgeting – what investments to make
Capital structure, how to finance these investments
Payout policy – what to pay out to shareholders
1: OVERVIEW OF PRINCIPLES OF FINANCE AND
INTRODUCTION TO FINANCIAL MATHS I
The main goal of firms and managers is to maximise the market value of a company’s
equity. This satisfied shareholders as their share prices increase.
According to Capital Market Efficiency the share price of a company should reflect all
relevant information available to the market at a point in time.
The time value of money is the difference between the value of money today and the
value of money in the future.
We can earn interest to turn a PV cash flow into a higher FV cash flow, or we can pay
interest to exchange a FV cash flow for a PV cash flow.
Simple interest calculates the value of a cash flow based purely on the principal.
Compound Interest calculates the value of a cash flow based on both the principal and
accrued (earned) interest.
In order to compare cash flows we must consider them at the same point in time
We can turn a PV into a FV by compounding it and turn a FV into a PV by discounting it.
The PF & FV depend on the time period, the interest rate and the compounding periods.
The value additivity principle states that the PV[FV] of a series of cash flows is equal to
the sum of the PVs[FVs] of each cash flow
If the NPV is above 0 then we should accept the investment.
THE MAIN GOALS OF FIRMS AND MANAGERS
A company is controlled by a board of directors and managed by senior management and the CEO. The
CFO is responsible for investment, financing and cash management decisions. It is owned by shareholders
and managers should ideally do their best to represent and act upon the desires of shareholders.
The reason why we have managers is to help the firm maximise the market value of their equity. This
means we want to maximise the wealth of the shareholders (owners) by increasing our share price. This is
done by managers who take on profitable investments.
Managers must ensure they balance the needs of both shareholders and other stakeholders such as
customers and employees. By maintaining and pleasing customers then they will be able to continue as an
effective company to boost shareholder returns.
The share price may drop if shareholders are not confident in the future of a company and may rise if the
company seems to be promising. Capital Market Efficiency means that the market prices that we observe
should reflect all relevant information available at a point in time.
THE TIME VALUE OF MONEY AND INTEREST RATES
Basic Valuation Principle:
In finance we consider the costs and benefits of cash flows at different points in time.
Costs are the opportunity cost of the next best action. Benefits are the things derived from taking an action.
The time value of money is the difference between the value of money today and the value of money in
the future. We can convert money in the present into money in the future by lending it to the bank (we
earn interest on it, therefore increasing its value in the future), or exchange money in the future for money
in the present by lending from a bank (we pay interest to the bank, decreasing the value in the future)
E.g. investing $100 in the bank at 2% interest for 1 year
Present Value = $100
Future Value = $100 * (1+0.02) = $102, therefore the future value of $100 in 1 year at 2% is $102
SIMPLE AND COMPOUND INTEREST
Simple Interest – We earn interest only on the principal cash flow, and not on any accrued interest.
E.g. we would earn the 2% interest on the $100, meaning we earn $2 interest each year.
Compound interest – Interest is earned on any principal cash flows and on any accrued interest.
E.g. we would earn the 2% interest on the total balance, therefore we would earn (100*0.02) $2 in
the first year, (102*0.02) $2.04 interest in the second year, (104.04*0.02) $
The future value of a cash flow is calculated based on the principal and interest accrued.
PRESENT AND FUTURE VALUES OF CASH FLOWS
In order to compare cash flows we must consider them at the same point in time. Therefore we can
determine future and present values to allow us to compare possible decisions in terms of one time frame.
Future Value – The value of a cash flow at a specific point in the future.
It is the value at which the Present Value is expected to grow to after n periods using a r% interest rate. We
call this compounding to move cash forward in time
Present Value – the value of a cash flow today
It is the value that would grow to the Future Value if invested at r% for n periods. We call this discounting
to move cash back in time
The interest rate, number of periods and compounding periods will all impact upon the present and future
values of cash.
Cash flows are assumed to occur at the end of the period unless otherwise stated.
PRESENT AND FUTURE VALUES OF A SERIES OF CASH FLOWS
Value additivity principle: The PV[FV] of a series of cash flows is equal to the sum of the
PVs[FVs] of each cash flow.
This means that to find the Net Present Value of an investment we need to take the present value of the
benefits and subtract the present value of the outflows. We may need to discount some of the future cash
flows in order to bring them back to the present.
The typical outflow in a question is the initial investment.
We should accept the investment if the NPV is above 0 because it will lead to an overall increase in
benefits.
2: INTRODUCTION TO FINANCIAL MATHS II
TOTAL GROWTH
COMPOUNDED PERIODIC GROWTH
ORDINARY ANNUITIES
ANNUITIES DUE
GROWING ORDINARY ANNUITIES
ORDINARY PERPETUITIES
DEFERRED PERPETUITIES
GROWING ORDINARY PERPETUITIES
IMPORTANT: Make sure you use cash flows from the right period (e.g. C0 is cash flow now, C1 is CF in 1 year)
CALCULATING UNKNOWN INTEREST RATES AND TIME PERIODS
TOTAL GROWTH OVER A PERIOD
COMPOUNDED ANNUAL GROWTH OVER A
PERIOD (annual rate of return)
ANNUITIES AND PERPETUITIES
Annuities are equal period cash flows that last for n periods
An ordinary annuity has cash flows occurring at the END of each period
An annuity due has cash flows occurring at the BEGINNING of each period
A growing ordinary annuity has cash flows occurring at the END of each period that
GROW at a CONSTANT rate
ANNUITIES
Timing
Cash Flows
Ordinary Annuity
Annuity Due
Growing Ordinary Annuity
End
Beginning
End
Same
Same
Grow over time
Perpetuities are equal periodic cash flows that go on forever
An ordinary perpetuity has cash flows that start NOW
A deferred perpetuity has cash flows that start at some FUTURE date
A growing ordinary perpetuity has cash flows occurring at the END of each period
that GROW at a CONSTANT rate
PERPETUITIES
Timing
Cash Flows
Delay
Ordinary Perpetuity
Deferred Perpetuity
Growing Ordinary Perpetuity
End
End
End
Same
Same
Grow over time
Starts Now
Starts Later
Starts Now
USING NATURAL LOGS TO SOLVE EQUATIONS
ORDINARY ANNUITIES
An ordinary annuity is a series of equal, periodic cash flows that occur at the end of each period and last
for n months. The first cash flow occurs at the end of period 1 and the last cash flow at the end of period n.
ANNUITIES DUE
An annuity due is a series of equal, periodic
cash flows that occur at the beginning of each
period and last for n months. The first cash
flow occurs at the end of period 0 and last cash flow at the end of period n-1
The beginning of period n is the same as the end of period n-1
We calculate an annuity due by calculating it as an ordinary annuity and then compounding it by an extra
period.
GROWING ORDINARY ANNUITIES
A growing ordinary annuity is a series of periodic cash flows that grow at a constant rate and occur at the
end of each period, lasting for n months. The first cash flow occurs at the end of period 1 and the last cash
flow at the end of period n.
ORDINARY PERPETUITIES
An ordinary perpetuity is a series of equal periodic cash flows that go on forever, with cash flows occurring
at the end of each period.
If there is a cash flow at time period 0 then we just add this onto the PV as a cash flow at time period 0 is
already at its present value (since present value = time period 0)
DEFERRED PERPETUITIES
A deferred perpetuity is an equal periodic cash flow that starts at a future date and goes on forever, with
cash flows at the end of each period. The first cash flow occurs at the end of time period n+1 when time
period n is the deferred time of the first payment in the future.
GROWING ORDINARY PERPETUITIES
An growing ordinary perpetuity is a series of periodic cash flows that grow at a constant rate over time
and go on forever, with cash flows occurring at the end of each period. The first cash flow occurs at the
end of period 1. It is the same as a perpetuity except the
GROWING ORDINARY DEFERRED PERPETUITIES
Not in course but may be useful knowledge.
3: VALUATION OF DEBT SECURITIES
Annual loan payments can be calculated through an ordinary annuity as they are a
series of equal cash outflows that occur at the end of every period and continue for n
periods. A loan amortisation schedule helps us to plan out our annual payments.
Effective annual interest rates are used when interest is compounded more than once
per year. The below formula-sheet formula only works for a 1 year time horizon.
Cash flows must be matched with interest rates
1 Monthly cash flows compounding monthly  r/12 = monthly interest rate %
2 6-monthly cash flows compounding monthly
o Find the 6 monthly rate by r/12 x 6
o Use the effective interest formula
Debt Securities/Discount Debt Securities are SHORT TERM securities with no coupons.
Long term debt securities can be coupon-paying or zero-coupon
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Coupon payment $ - periodic payment made to bondholders (CP$ = CR% x FV)
Coupon Rate % - rate of interest paid annually (CR% = CP$ / FV)
Coupon Yield % - compares market value to coupon rate (CY% = CP$/MPrice)
Yield to Maturity (rD) – rate of return if held until maturity and there is no default
IF purchase price = Face Value THEN Coupon rate = Coupon yield = Yield-to-maturity
Short Term (ST) – No Coupon Long term (LT) - Coupon
LT - Zero Coupon
rD can be solved algebraically (zero-coupon) or by using a given range (coupons bond)
Longer term investments are more susceptible to interest rate increases which will
cause prices to fall, and are therefore more risky.
LOAN PAYMENTS
Loan – borrowing money and making repayments to pay off the loan over a fixed period of time.
Fixed Rate loans means we fix the interest rate for 1-3 years and then rates can change after that.
PERIODIC LOAN PAYMENTS (C) are represented by an ordinary annuity because they are a series of equal
cash outflows that occur at the end of every period and last for the number of period the loan exists over.
The loan repayment (C) is composed of two parts:
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The principal we are repaying
The interest being charged on the principal borrowed
The Present Value of a loan is found by discounting the periodic payments (C) to the current period.
Alternatively, we an find the value of the periodic payments (C) by substituting in the PV of the loan, the
interest rate and the number of periods and solving for C.
This works because by discounting the payments we are stripping off the interest being charged on them,
leaving us with the sum of the principal balances.
LOAN AMORTISATION SCHEDULE
The annual payment is the value of C and is therefore the same across all periods
The interest paid is the principal remaining x interest rate
The Principal Repaid is the annual payment – interest paid.
The Principal Remaining is the previous balance of principal remaining – Principal Repaid
EFFECTIVE ANNUAL INTEREST RATES
We may receive cash payments and have our interest compound on terms other than annually. For
example, we may receive monthly cash flows but have them compound on a quarterly interest rate.
In this case we need to calculate the effective interest rate re. re is always higher than the regular interest
rate r unless we are dealing purely on annual terms.
In terms of deciding what interest rate is better across a range of options, you want to receive a higher
effective rate from investments (receive more money as interest) and pay a lower effective rate with
loans (pay less money as interest payments)
ALTERNATIVE FORMULA
I prefer to use this formula as it works for periods other than annually, which is the downfall of the formula
on the formula sheet.
The USA uses 360 rather than 365 (days) when calculating compounding on an annual basis. If we want to
calculate on US terms then we will divide the r rate by 360 instead of 365, however we still put it to the
power of 365 like we do in Australia (just an industry convention)
CONTINUOUS COMPOUNDING
If the compound rate is continuous (ie. infinite compounding per second, therefore infinite compounds per
month/year) then we use the following rule:
DEBT SECURITIES
SHORT TERM DEBT SECURITIES / DISCOUNT DEBT SECURITIES - Treasury BILLS (issued by the
government), Bank BILLS (issues by banks)
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Matures in less than a year (usually 90/180 days)
Face value/Par value is the amount we are paid at maturity which contractually MUST be paid
No ‘interest’ is paid – the return earned on the investment is the difference between what we pay
(lower) and what we receive as face value (higher) (assuming interest rates are positive, price < face
value)
LONG TERM DEBT SECURITIES – Treasury BONDS (commonwealth bonds) and Corporate Bonds
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mature after one year (usually several)
Some have coupon (interest) payments, some do not.
Face value/Par value is the amount we are paid at maturity. It is usually $100 (if no face value has
been given in a question then assume the FV = $100) and contractually MUST be paid. Coupon
payments, if applicable, also must contractually be paid
CHARACTERISTICS OF COUPON-PAYING BONDS
The coupon rate (%) is the rate of interest that the investment pays annually
The coupon payment ($) is the annual payment made to bondholders as ‘interest’ of sorts
Coupon Payment $ = Coupon Rate % x Face Value
Example: $100 FV (default) with 5% coupon rate. Therefore the periodic coupon payment is:
$100 x 0.05 = $5 per period
Yield-to-maturity compares the purchase price to the rate of return. The yield to maturity never changes
throughout the life of the investment (see below for more information)
Coupon yield/Current yield (%) is a measurement that compares the market value of the bond to the
coupon payment. This tells us how large the coupon rates are compared to the face value. The coupon
yield may change throughout the life of the investment if the market price fluctuates.
𝐶𝑜𝑢𝑝𝑜𝑛 𝑌𝑖𝑒𝑙𝑑 =
PRESENT VALUE AND MARKET VALUE
If the present value (as calculated in its respective coupon/non-coupon equation) is the same as the
purchase price (the price in the market)
THEN
the coupon rate, current yield and yield-to-maturity will all be the SAME VALUE.
BASIC VALUATION PRINCIPLE FOR FINANCIAL SECURITIES
The price of a security/investment today is the PV of all the future cash flows, discounted at the rate of
return/discount rate.
For example, if company A is selling bonds for $40 then $40 is the expected present value of all the future
cash flows (coupons) that that bond will pay out to investors.
We discount the future cash flows to their value today which tells us how much we would be willing to pay
today to receive these future cash flows later on (hence this is the price that we will pay in the market
now):
TO ESTIMATE THE MARKET VALUE OF AN INVESTMENT
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Solve for the PV when we are given the estimated value of the future cash flows and the required rate
of return
This method can be used to independently value an investment and decide whether this PV
calculated is the same as/higher than/lower than the actual market price of the and therefore
whether it is correctly/over/under priced.
TO ESTIMATE THE REQUIRED RATE OF RETURN ON AN INVESTMENT
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Solve for the rate of return if we are given the future cash flows and current market price (ie. the PV).
We can use this result to compare the investment to a benchmark return to decide whether to invest
in equally risky investments.
PRICING OF SHORT-TERM DEBT / DISCOUNT DEBT SECURITIES
A pure-discount (short term) security is when only the face value is paid. This means no coupon payments
are made out during the life of the investment and the only return to the investor is the receipt of the face
value at the end of the period.
The market value/price of a discount security with no coupons depends on:
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What the final cash flow is (the face value)
The yield to maturity rD
YIELD TO MATURITY
The yield-to-maturity a type of rate of return. It is the rate earned on an investment that is held until it
matures, assuming no default occurs on the security (ie. all coupons are paid as planned). It is the
maximum return that can be earned by the investment because we assume that no default will occur
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The yield to maturity never changes throughout the life of the investment.
Yield-to-maturity is quoted on an annual basis by default.
Discount securities are short term and mature in less than one year however the yield is on an annual
basis, therefore we use the following equation to determine the rate to discount the race value where
n is the number of days until maturity at any point:
𝑛
× 𝑟 𝑎𝑛𝑛𝑢𝑎𝑙 𝑦𝑖𝑒𝑙𝑑 𝑡𝑜 𝑚𝑎𝑡𝑢𝑟𝑖𝑡𝑦
365
EQUATION FOR THE PV OF A PURE-DISCOUNT SECURITY
RELATIONSHIP BETWEEN THE YIELD TO MATURITY AND THE MARKET PRICE
1. Interest rates fall because of good market conditions. Investors do not need a 4% return now and
are happy with 3.5%
2. Everyone starts to purchase the investment and its price rises
3. The yield to maturity rises back to 4%
4. Poor market conditions result in rising interest rates. We perceive the investment to be riskier than
before and therefore want a higher return. We are not happy with 4% and demand 4.5% now.
5. We sell the securities and the price of the security falls
6. The yield falls back to 4%.
YIELDS FALL, PRICES RISE. YIELDS RISE, PRICES FALL – REPEAT. INVERSE RELATIONSHIP.
PRICING OF ZERO-COUPON AND COUPON PAYING BONDS
COUPON PAYING BONDS
Coupon bonds are long term securities. They typically pay fixed coupons every 6 months and also repay
their face value to the investor at maturity. The two types of cash flows mean there are two components
to calculate:
Ordinary annuity of the equal period coupons from period 1 to period n
A single cash flow at the end of period n – the face value repayment at maturity date n.
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The market price of a bond at time period 0 does not take into consideration the value of the coupon in
the current period. We assume that the coupon was paid yesterday and we are starting our analysis from
today, day 0. This is called the ex-coupon price as it is the price after the current coupon was paid.
Eg. The price at the end of year 3 considering the coupon in year 3 has already been paid:
We already know that the yield-to-maturity is the required rate of return if we hold an investment until
maturity, assuming no defaults occur. We can use the yield to discount back a bond’s future cash flows to
find the market price today. Therefore the yield is called an ‘internal rate of return’.
Bonds are issued at par when the yield to maturity is the same as the coupon rate and therefore the face
value is the same as the price paid.
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If the yield to maturity is higher than the constant coupon rate then the market price will be lower
than the face value of $100
If the yield to maturity is lower than the constant coupon rate then the market price will be higher
than the face value of $100.
Market value of an entire bond issue =
$
× 𝑡𝑜𝑡𝑎𝑙 𝑓𝑎𝑐𝑒 𝑣𝑎𝑙𝑢𝑒𝑠
ZERO-COUPON BONDS
If there are no coupon payments and we only receive the face value at maturity then the Present Value is:
We can find the PV of the potential coupons over a period by subtracting the zero-coupon bond from the
coupon-paying bond. Zero-coupon bonds sell for cheaper than coupon bonds because the PV is lower.
LEVEL OF RISK OF INVESTMENTS
Default risk/credit risk – risk of inability to make coupon payments and/or maturity payments when due.
S&P Global Ratings and Moody’s Investors Service classify bonds according to a rating of their default risk.
Investment grade debt (AAA – BBB) – have a risk similar to banks. They are unlikely to default and you
safely assume you will receive your payments when due,
Speculative Bonds/junk bonds (BB – D) – higher risk and less certainty you will receive back your
payments. This means they have a higher yield to maturity as investors expect a higher return to
offset the higher risk.
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COUPON RATE AND YIELD TO MATURITY
REMINDER: the coupon rate stays the same during the entire life of the investment (ie. it will always pay
4% coupons, meaning coupons for a $100 face value bond will always be $4). However the yield to
maturity can change during the life of the bond depending on the required return demanded on the bonds
at any point in time.
SOLVING FOR THE YIELD TO MATURITY IN EXAMS
For a Coupon Paying Bond
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Will be a multiple choice question
Given a range of possible rD values
Substitute each into the coupon-bond equation
The correct answer will be the one that gives a PV that is above/below/at the face value $100,
depending on what the question asks.
For a Zero Coupon Bond – solve finding the rD by discounting the single face value payment at maturity
RELATIONSHIP BETWEEN COUPON RATES AND YIELD TO MATURITY
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PRICE = FACE VALUE
the bond is selling at par
o rD = Coupon Rate
PRICE > FACE VALUE
the bond is selling at a premium
o rD < coupon rate
PRICE < FACE VALUE
the bond is selling at a discount
o rD > coupon rate
PRICE SENSITIVITY TO INTEREST RATES
The probability of interest rates rising over a longer period of 10 years is higher than the probability of
interest rates rising over a shorter period of 1 year. Rising interest rates will cause the prices of bonds to
fall.
Therefore prices of longer maturity bonds are more sensitive to changes in interest rates, meaning that
investors bear higher interest rate risk with these longer-term bonds because there is a risk of the price
decreasing. The large number of coupon payments in longer maturity bonds also means that they are more
affected by interest rates.
4: VALUATION OF EQUITY SECURITIES
The initial sale of a share from a company to an investor in the primary market is done
through an IPO, and a subsequent sale from investor to investor through the secondary
market is done on an exchange like the ASX.
An Ordinary Share entitles the owner to receive a portion of a company’s earnings,
called dividends. Companies decide on what dividend to pay each period, meaning it
may vary over time or grow/decrease at a set rate.
The price of an ordinary share is the PV of the future dividends discounted at the
required return on equity rE. If dividends are expected to remain constant then g = 0.
Growth rate = Retention rate x Return on new investment
Growth only increases shareholder value when the company reinvests their earnings in
projects with positive NPVs. Otherwise they should pay out more earnings as dividends.
To find the price of a share with variable growth rates:
- Calculate the PV of dividends for each section of growth (ie. calculate the PV for
the first 3 years with 5% growth, next 5 years with 6% growth etc…)
- Discount the PV of all sections back to time period 0 to find all PV0s
- Add all PV0s together to find the PV of all future cash flows (ie. the share price)
Preference shares are shares that have fixed dividends each year (ie. no growth)
The Price/Earnings ratio compares the current market price to the rE. The P/E ratio will
increase when the dividend payout ratio (a) increases, the growth rate (g) increases or
the required return on equity (rE) decreases.
Capital Market Efficiency: market prices should reflect all relevant information available.
ORDINARY SHARES
ORDINARY SHARES AND TRADING
Ordinary shares represent part ownership of a company. Investors purchase shares from a company. The
company receives the price paid and the investor receives the right to receive a portion of the company’s
profits. Earnings are distributed amongst shareholders as ‘dividend’ payments. In America ‘Shares’ are
called ‘Stocks’ (hence the terms ‘Stock market’ used in US media)
Publicly listed companies sell shares to investors in the primary market through an Initial Public Offering
(IPO) where investors purchase directly from the company. Then shareholders are able to trade shares
they have purchased to others through secondary markets such as the Australian Stock Exchange (ASX)
where investors purchase existing shares from other investors.
A positive return on the first day of trading a new share is referred to as under-pricing of an IPO as the
price of the share closed at a higher amount than it was originally traded at.
MARKET VALUATIONS OF ORDINARY SHARES
Price of an ordinary share = PV of expected cash flows from the share, which have been discounted using
the required rate of return. This is the same concept as the value of bonds/bills.
NPV of a share = PV cash inflows (dividends) – PV cash outflows (initial investment price)
Because of Capital Market Efficiency (see below) where shares prices are expected to reflect all available
information, the NPV of a share should be 0 because the PV of the dividends should equal the initial price
paid. When the NPV is not 0 the price of the shares is misvalued and this presents a possible investment
opportunity to purchase (if undervalued) or sell short (if overvalued)
WHAT SHAREHOLDERS RECEIVE FROM THE COMPANY: DIVIDENDS
Some earnings are reinvested in a company and are used to expand operations. Some earnings may be
kept to pay dividends in the future. Other earnings will be paid out in the current period as dividends. As
investors, we are only concerned about the earnings that we will receive – ie. the dividends per period.
Shares provide an infinite stream (if we never sell them) of uncertain dividends (they can change
according to the decisions of managers) to shareholders.
PRICING OF ORDINARY SHARES
Price of an ordinary share = PV of expected cash flows (dividends) from the share, which have been
discounted using the required rate of return.
This is assuming we pay annual dividends (just aggregate the dividends to get to one year)
We don’t include D0 (the dividend in the current year) when we calculate P0 because we want to calculate
the ex-dividend price (price right after the current period dividend, D0, is paid). This is the same concept as
the ex-coupon price used when calculating the price of bonds.
We can also rearrange this formula to solve for the expected rate of return.
GENERAL DIVIDEND DISCOUNT MODEL
To use this method we have to estimate what the value of the dividend will be at the end of the year which
is not usually accurate, therefore analysts make general estimates as to the expected pattern of dividends.
CONSTANT DIVIDEND GROWTH MODEL
This is used to value shares whose dividends grow (or decline) at a constant growth rate (g) forever. If
dividends will remain the same g = 0. If the company doesn’t pay dividends then this model can’t be used
to price their shares.
g
represents:
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the growth rate of dividends
the expected % change in the price of shares over n periods
IS ALL GROWTH PROFITABLE?
Total earnings are made up of earnings paid out as dividends & earnings reinvested back into the business.
A firm can do either of these actions in order to increase the share price to maximise shareholder value:
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Pay earnings to shareholders as dividends (high dividends today, don’t increase over time)
High earnings paid out as dividends means share prices will increase as investors will be willing to pay
more now for higher dividends.
However if there is a lack of reinvestment into the company then future earnings and future
dividends won’t increase because the company isn’t investing in itself and improving its ability to
generate earnings.
Reinvest their earnings to improve performance (low dividends today, increase over time)
High reinvestment in the company means their ability to earn future earnings will increase, meaning
in the future dividends will increase.
However current dividends will need to be lower in order to allow the investment.
Change in Earnings (ie. growth rate) = New Investment x Return on New Investment
e.g. $0.20 per share change in earnings = $1 new investment x 20% return on investment
Reinvesting earnings and lowering dividends will only raise the share price if the new investment is
expected to result in a positive NPV (ie. the P0 is higher than the share price)
VARIABLE DIVIDEND GROWTH MODEL
Companies may have low/high growth initially, followed by normal growth for the rest of their life.
1. Estimate dividends up to the point when growth becomes constant forever.
2. Calculate the PV0 of the dividends during the growth period.
3. Calculate the PV of the dividends after growth becomes normal, then discount this back to time
period 0.
4. Obtain the final P0 by adding together both of the time period 0 present values.
PREFERENCE SHARES
Preference Shares are shares which give their holders preference over ordinary shareholders with regard
to payment of dividends. This means if the company goes into liquidation or their earnings are way below
the expected level the preference shareholders will receive their dividend payments before the ordinary
shareholders will.
Dividends on preference shares are stated upfront and are guaranteed to be fixed over its life.
PRICING OF ORDINARY PREFERENCE SHARES
The price of a plain vanilla preference share is the PV of the perpetuity of constant
dividends (no growth)
EARNINGS, DIVIDENDS AND PRICES
PRICE/EARNINGS RATIO
Price/Earnings Ratio – ratio of the current market price compared to the expected earnings per share.
A high PE ratio coupled with high growth in earnings implies high growth opportunities.
Expected PE ratio – the amount investors are willing to pay now for $1 of future expected earnings
(
)
(
)
Current PE ratio
(
)
(
)
PRICE/EARNINGS RATIO
We can substitute the D with the equation we use to calculate the dividends paid out.
Dividends paid out = dividend payout ratio (a) x total earnings
We can then transform this equation into the expected PE ratio by dividing by E1
The PE ratio will increase when we:
-
Increase the dividend payout ratio
Increase the growth rate
Decrease the required return on equity
All of these factors impact upon each other and don’t act independently.
PRICING GROWTH OPPORTUNITIES
IMPORTANT!
The present value of growth opportunities is the difference between the PV of a constantly growing
dividend growth model and the PV of a no growth model where a = 1 (pays out all earnings as dividends)
INFORMATION AND STOCK PRICES
Capital Market Efficiency is the idea that market prices reflect all relevant information available at a point
in time as investors learn about information and act on this by purchasing/selling investments. The
valuation models used make use of the following information and we can make assumptions about one of
them if we have the other 2:
-
Future dividends
Share price 𝑃
Required Return on Equity 𝑟
TYPES OF INFORMATION REFLECTED IN SHARE PRICES
Past information:
known to everyone, available on the internet for free. All of this
information is assumed to be reflected in prices as all investors should be aware.
Publicly available information:
widely disseminated by analysis and available to anyone curious.
Private information:
known to top management and few investors.
Only information that is now known to investors will change the market conditions. If investors all
expected the Reserve Bank of Australia to lower the cash rate next week then they would react to this
information immediately. When the RBA actually lowers the cash rate next week investors would not react
to this because the information was already known to them.
USEFUL NOTE ON TERMINOLOGY OF r (RETURNS)
r is used to denote return, however there are different required returns for different investments:
rD is required return on debt, used for bonds/bills/loans (CHAPTER 3)
rE is required return on equity, used here for ordinary shares (CHAPTER 4)
rP is required return on equity but just in terms of preference shares. (CHAPTER 4)
The question will give you the relevant required return, however in questions where you need to deal with
all 3 types of returns (when calculating the WACC – later in the course) it is essential to recognise which
return goes with which investment.
5: MODERN PORTFOLIO THEORY AND ASSET PRICING I
Observed/realised return – the change in cash flows divided by the initial investment
Arithmetic – 1 period, no compounding Geometric – per period, compound & reinvest
Fisher Relationship: Real return = includes inflation, Nominal return = excludes inflation
Individual Stocks do not necessarily have a high-risk high-return relationship.
Portfolios do tend to have a high-risk high-return relationship because individual stock
irregularities tend to cancel each other out, leading to an overall underlying trend.
We can use the Probability Distribution Approach to predict outcomes in a market:
Expected Return: weighted average of returns of portfolio
Standard Deviation: weighted average of the risk dispersion in a portfolio and the
covariance between their returns.
Investors are risk averse, meaning they will choose the lowest risk for a set return.
RISK DIVERSIFICATION means getting rid of unsystematic risk by investing in a portfolio
of assets with negative correlations (-1 correlation gives us the minimum risk portfolio)
Covariance: tells us the direction of comovement (+ve = same direction, -ve = opposite)
Correlation: tells us the direction and strength of comovement.
Portfolio Leveraging – increase risk and return of portfolio
- Borrow money at risk free rate
- Invest original and borrowed wealth in risky security
- Use returns of security to repay the borrowed money
Short Selling – increase risk and return of portfolio
- Borrow less risky shares
- Sell them and invest the funds in a riskier investment
o Riskier investment should earn higher returns than less risky investment
- Purchase back the shares at, hopefully, a lower price and return to owner
Portfolio return
Portfolio risk
RISK AND RETURN OF FINANCIAL SECURITIES
MEASURES OF RETURN
Observed/realised return – the change in cash flows divided by the initial investment
Ordinary Shares: Dividend Yield + Percentage price change
Bonds: Coupon Yield + Percentage Price Change
Long term investors can measure returns using the following methods:
Arithmetic Average Return – return from a one-period investment over a time horizon assuming no
compounding. We assume we invest the same $1 at the start of each period and find the average return
for this across T periods. There is no reinvestment of returns.
Geometric Average Return – return per period over the entire time horizon, assuming there is
compounding. There is reinvestment of returns.
MEASURES OF RISK
Risk is measured by the variability in realised returns around the arithmetic average return.
In simple terms, a risky return means the returns are more variable and have a higher variance/standard
deviation (relevant to SD/Var covered in ECON10005 QM1)
FISHER RELATIONSHIP FOR RETURNS
Nominal return r – interest rate that includes impacts of inflation
Real return rr – interest rate that excludes impacts of inflation
If interest rates are low then this approximation works:
A risk-free investment generally has returns that hover close to the interest rate, meaning returns are not
that high. The simplest example of a risk-free investment is a bank account which pays out at around the
interest rate and therefore doesn’t have as high returns as riskier investments such as shares.
HIGH RISK AND HIGH REALISED RETURNS
‘High risk, high return’ means investments that have a higher risk are expected to earn a higher return in
order to compensate and ‘reward’ the investor for taking on riskier investments.
There is NOT a clear ‘high risk high return’ outcome in the returns of INDIVIDUAL SHARES. This is because
company and industry specific factors, which may be unexpected and may vary significantly from year to
year, influence the actual returns of each individual share. Periodic returns may vary a lot between high
and low returns despite a share having a fixed high/low risk and therefore there is not usually a regular
‘high risk high return’ relationship.
However there IS a clear risk-return relationship in the returns on PORTFOLIOS OF SHARES because
individual movements in a large number of investments balance each other out with the extremities and
irregularities cancelling out, leading to overall returns that correlate with the level of risk. The outcome of
the entire portfolio as a whole does tend to reflect the principle of higher risk, higher return.
PROBABILITY DISTRIBUTION APPROACH
Investors can develop theories as to the different states of the market and the probability of and cash
flows associated with each state in order to predict the return of an investment in the market.
RISK AND RETURN MEASURES FOR SECURITIES
Expected Return – the weighted average of the individual outcomes in a distribution of a market.
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑅𝑒𝑡𝑢𝑟𝑛 = (𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑆𝑡𝑎𝑡𝑒 1 × 𝑅𝑒𝑡𝑢𝑟𝑛 𝑓𝑟𝑜𝑚 𝑆𝑡𝑎𝑡𝑒 1) + (𝑃𝑟𝑜𝑏 2 × 𝑅𝑒𝑡𝑢𝑟𝑛 2)+. ..
Variance/SD – measure of the dispersion around the expected return. The higher the dispersion the
greater the risk and uncertainty (and therefore a higher expected return in a portfolio)
INTERPRETING RISK AND RETURN MEASURES FOR SECURITIES
We can make more general interpretations if the returns are continuous and normally distributed. The
downside is that it assumed an unlimited downside loss potential which is unrealistic because we can’t
loose more than we invested on an investment.
The range (in finance) is assumed to be 2 SD above and below the mean, which contains 95% of the
returns.
INVESTOR PREFERENCES
Investors are assumed to be risk averse,
meaning they prefer a lower level of risk for the
same return.
Given a level of risk they will choose the
investment with the highest return.
Alternatively, given a level of return they will
choose the investment with the lowest risk.
PORTFOLIOS AND RISK DIVERSIFICATION
Portfolio risk decreases as the number of diverse securities in the portfolio increases.
-
-
Unsystematic risk (risk associated with individual markets) of each security can be eliminated via
diversification because the ups and downs of each market/industry/company can be balanced out
by investing across many different markets/industries/companies.
Systematic risk (risk across the entire market, such as interest rates), however, can’t be eliminated
via diversification, meaning some risk will always exist when investing. (see lecture 7)
RISK AND RETURN: TWO ASSET PORTFOLIO
Original Wealth is the total amount of their own money that the investor is investing. The entire amount
w% of this original wealth is divided between the two different assets: w1% allocated to asset 1 and w2%
allocated to asset 2.
Expected Return
Variance
COVARIANCE – the level of co-movement between security returns. It tells us only the direction of the
relationship – the size can only be determined if we standardise the result and find the correlation:
CORRELATION – standardised measure of comovement. It shares the same sign as covariance and tells us
about the direction and strength of the relationship.
CORRELATION AND DIVERSIFICATION
Diversifying works when we choose shares that don’t move in the same way shares we already own move.
If we already own ANZ shares then we would not choose to diversify with NAB shares because they have a
high correlation as they are both in the same banking industry and would therefore have relatively similar
stock movements. We would not get any diversification protection out of such an investment.
However if we already owned ANZ then we would get diversification benefits from investing in Telstra (TLS)
because its correlation with ANZ is relatively low because they are in different industries and are therefore
subject to different market conditions. Diversification benefits would arise because Telstra and ANZ don’t
tend to move together so downfalls in one may result in successes from the other, lowering overall
portfolio standard deviation (risk)
SUMMARY OF CORRELATION AND DIVERSIFICATION
Shares with perfectly negative correlation have higher diversification benefits because the shares move in
complete opposite directions all the time, meaning the risk (standard deviation) of the portfolio is lower
than if the shares were perfectly correlated for any value of expected return.
PORTFOLIO LEVERAGING
Investor borrows funds at the risk-free rate of return and invests both the borrowed funds and their
original wealth in a risky security/portfolio. This allows them to invest more than their original wealth and
therefore increase the expected return on their portfolio, however it also increases the SD (risk)
SHORT SELLING
Investor borrows security A (usually shares) from someone else and sells them while expecting the price to
drop in the future. They can use the money they made to invest in their own projects. If the share price
does drop then the investor purchases back the shares at the lower price, returns them to their owner and
benefits from the money to invest they made in the middle by selling high and buying back low.
As we short sell more of stock A the risk increases as we have to make back more funds, however there is
also an increase in expected returns of stock B which we are investing the extra funds in because more is
being invested as we short sell more of A.
7: MODERN PORTFOLIO THEORY AND ASSET PRICING II
Only unsystematic risk can be eliminated through diversification (increase the number
of assets in portfolio = decreases the Standard Deviation at decreasing rate)
The risk (SD) of a portfolio is determined by the covariance between the individual
securities.
𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓 𝑎 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 = 𝜎 =
𝑤ℎ𝑒𝑟𝑒 𝜎
+𝜎
= 𝜌
±
( , )×𝜎
×𝜎
Systematic risk is considered when pricing securities. It is measured by beta 𝜷
Beta 𝜷 measures how sensitive a security’s return is to unexpected movements in
market portfolio returns. When market return changes 1% → change in security return?
∆
𝜷=∆ =
𝜷𝒔𝒆𝒄𝒖𝒓𝒊𝒕𝒚 𝒋 =
𝜷𝒑𝒐𝒓𝒕𝒇𝒐𝒍𝒊𝒐 = 𝑤 𝛽 + 𝑤 𝛽
𝑪𝒐𝒗𝒂𝒓𝒊𝒂𝒏𝒄𝒆(𝑟
𝑉𝑎𝑟(𝑟
𝜷 < 𝟏 lower risk than market
,𝑟
)
)
= 𝜌𝑪𝒐𝒓𝒓𝒆𝒍𝒂𝒕𝒊𝒐𝒏
𝜷 > 𝟏 higher risk m
×
𝜎
𝜎
𝜷 < 𝟎 higher risk m, opposite movement
CAPM is used to find the required rate of return for securities from their systematic risk
𝑺𝑴𝑳 = 𝑬(𝒓𝑨 ) = 𝑟 + 𝛽 𝐸(𝑟 ) − 𝑟
Market risk premium: 𝐸(𝑟 ) − 𝑟
Security risk premium: 𝛽 𝐸(𝑟 ) − 𝑟
CAPM to value ordinary shares and give a $:
- Calculate required return (CAPM 𝑬(𝒓𝑨 )) and expected return (𝑟 , 𝑃 =
)
- Expected return will converge to the required return, adjust 𝑃 accordingly if given
a P already, or use the new return to find the price
The security market line relates the beta 𝛽 to the expected return 𝐸(𝑟). All risky
securities, correctly priced, will lie on SML. Above SML=under priced, under SML=overpr
Sharpe Ratio: return per unit of total risk
Treynor Ratio: return per unit of systematic risk
Jensen’s Alpha: return Portfolio – E(r) CAPM
LIMITS TO DIVERSIFICATION BENEFITS
In large portfolios the SD (risk) is determined by the covariance between the individual securities, not by
the SD of each security.
As the size of a portfolio increases, the total risk (sd) falls but at a declining rate.
Therefore we can never eliminate all risk because the ability to decrease risk will hit a barrier. However an
investor that eliminates all diversifiable risk by diversifying will only incur systematic (non-diversifiable) risk
Systematic risk includes those factors that affect the whole market like interest rates, therefore no matter
what you invest in you will be impacted by changes in these factors (hence why they can’t be eliminated
via diversification)
ℎ𝑖𝑔ℎ𝑒𝑟 𝒔𝒚𝒔𝒕𝒆𝒎𝒂𝒕𝒊𝒄 𝒓𝒊𝒔𝒌 = ℎ𝑖𝑔ℎ𝑒𝑟 𝒓𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝒓𝒂𝒕𝒆 𝒐𝒇 𝒓𝒆𝒕𝒖𝒓𝒏 (𝑏𝑒𝑐𝑎𝑢𝑠𝑒 ℎ𝑖𝑔ℎ𝑒𝑟 𝑆𝐷 = ℎ𝑖𝑔ℎ𝑒𝑟 𝑟𝑖𝑠𝑘)
EXAMPLE: VARIANCE OF A LARGE PORTFOLIO
Assuming: all securities are equally weighted 1/N, SD of each = 10%, correlation between all pairs = 0.6
𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 𝜎 =
𝜎 =
𝜎
+𝜎,
𝑁
.
𝑁−1
𝑁
+ (0.1)(0.1)(0.6)
As N increases, the first term approaches 0 and the second term approaches 𝜎 , as
and sub n value
approaches 1
CAPITAL ASSET PRICING MODEL
The CAPM is a model that can be used to price (find required rate of return) individual securities.
-
We use it to find the required rate of return
We then sub this return into other models to give a $ value using the future cash flows
The CAPM relates required rates of return to the systematic risk, with a higher level of systematic risk
demanding a higher rate of return.
WHY DO WE NOT INCLUDE NON-SYSTEMATIC RISK WHEN CALCULATING THE RETURN?
Investors have the ability to get rid of diversifiable/non-systematic risk through diversifying their portfolio.
Therefore why should we include this risk in our calculation if we know wise investors will never bear it
because they will diversify?
-
Only considering systematic risk and not including non-systematic risk means the overall risk of the
security is lower
The beta we calculate will only consider the systematic risk
We use the CAPM and the calculated beta to calculate a return, and this return will be the return
necessary to offset the level of systematic risk only
This return which is used to price each security will reflect the fact that only systematic risk is being
paid for
ASSUMPTIONS OF CAPM
-
Investors are risk averse and base decisions only on E(X) and SD
Investors all have the same assumptions about volatilities, correlations and expected returns
Returns are jointly normally distributed
Capital markets have no taxes, transaction costs or government interference
Unlimited borrowing and lending at the risk free rate is possible
Investors only hold efficient portfolios of securities (see below)
CALCULATING THE CAPM
Efficient portfolios are combinations of the risk-free security and the market portfolio.
If we add security A to our portfolio:
-
It is held as part of the market portfolio
The covariance of A will tell us how much it contributes to the systematic risk of the portfolio.
𝑬 𝒓𝒋 = 𝑟 + 𝛽 𝐸(𝑟 ) − 𝑟
𝑬𝒙𝒑𝒆𝒄𝒕𝒆𝒅 𝑹𝒆𝒕𝒖𝒓𝒏 𝒐𝒏 𝑨 = 𝑅𝑖𝑠𝑘𝑓𝑟𝑒𝑒 𝑅𝑎𝑡𝑒 + 𝑅𝑖𝑠𝑘 𝑃𝑟𝑒𝑚𝑖𝑢𝑚
𝑬𝒙𝒑𝒆𝒄𝒕𝒆𝒅 𝑹𝒆𝒕𝒖𝒓𝒏 𝑜𝑛 𝐴 = 𝑅𝑖𝑠𝑘𝑓𝑟𝑒𝑒 𝑅𝑎𝑡𝑒 + (𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑅𝑖𝑠𝑘 𝜷 × 𝑀𝑎𝑟𝑘𝑒𝑡 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 $)
𝑬𝒙𝒑 𝑹𝒆𝒕𝒖𝒓𝒏 𝐴 = 𝑅𝑖𝑠𝑘𝑓𝑟𝑒𝑒 𝑅𝑎𝑡𝑒 + 𝐴𝑚𝑜𝑢𝑛𝑡 𝑅𝑖𝑠𝑘 𝛽 × (𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑚𝑎𝑟𝑘𝑒𝑡 − 𝑟𝑖𝑠𝑘𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒)
Risk Premium will increase as both Amount and Price of risk increase:
-
Amount of risk is the covariance 𝜷 of the security with the market portfolio
Market Price of Risk is the return above the risk-free rate that investors earn for investing all your
money in the market portfolio
MARKET RISK PREMIUM IS DIFFERENT TO RISK PREMIUM
Risk Premium (one security) = how much return it should offer due to risk = 𝛽 𝐸(𝑟 ) − 𝑟
Market risk premium = bonus return market portfolio offers in excess of the risk-free rate = 𝐸(𝑟 ) − 𝑟
No beta is used in the market risk premium because we are considering all stocks (therefore 𝛽 = 1)
BETA, SYSTEMATIC RISK AND THE CAPM
Beta 𝜷 measures how sensitive a security’s return is to unexpected movements in market portfolio return
𝜷 tells us the expected change in the return of the security if the market return changes by 1%
1. Calculate change in returns of market portfolio (range = return with strong market – return with
weak market)
2. Calculate change in returns for each security (range = high returns – low returns)
∆
3. 𝜷 for each security = ∆ =
Systematic risk is measured by the beta
𝜷𝒔𝒆𝒄𝒖𝒓𝒊𝒕𝒚 𝒋 =
𝐶𝑜𝑣(𝑟
𝑉𝑎𝑟(𝑟
𝑏𝑒𝑐𝑎𝑢𝑠𝑒 𝜎
,𝑟
)
=
)
𝜎
= 𝜌
𝜷𝒔𝒆𝒄𝒖𝒓𝒊𝒕𝒚 𝒋 =
𝜌
𝜎
×𝜎
×𝜎
,
×𝜎
… 𝑠𝑢𝑏 𝑖𝑛
×𝜎
𝜎
𝜷𝒔𝒆𝒄𝒖𝒓𝒊𝒕𝒚 𝒋 = 𝜌
,
×
𝜎
𝜎
𝜷𝒔𝒆𝒄𝒖𝒓𝒊𝒕𝒚 𝒋 = ℎ𝑜𝑤 𝑡ℎ𝑒 𝑗 𝑐𝑜𝑚𝑜𝑣𝑒𝑠 𝑤𝑖𝑡ℎ 𝑚𝑜𝑣𝑒𝑚𝑒𝑛𝑡𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑚𝑎𝑟𝑘𝑒𝑡 × 𝑡ℎ𝑒 𝑚𝑜𝑣𝑒𝑚𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑟𝑘𝑒𝑡
𝜷 = 𝟏 Security has same risk as market portfolio (𝛽 𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 = 1)
𝜷 = 𝟎 Security has 0 risk
𝜷 < 𝟏 Security has lower risk than the market portfolio
𝜷 > 𝟏 Security has higher risk than the market portfolio
𝜷 < 𝟎 (-ve) Security has risk. Negative betas mean the security moves in the opposite direction to the
market.
SYSTEMATIC RISK AND CORRELATIONS
Betas are not correlations, they tell us about relative movement between securities and the market.
Both of the following diagrams have high correlations with the market, but the relative movement
determines how high/low the beta
is.
We may invest in negative beta
securities because they will insure
us against market downturns as
the security will have positive
returns when the market is in a
downturn.
We are willing to accept a lower
return than the risk-free rate in
exchange for the diversification
benefits.
SECURITY MARKET LINE
𝑬 𝒓𝒋 = 𝑟 + 𝐸(𝑟 ) − 𝑟
𝑟 tells us the y intercept of the SML and 𝐸(𝑟 ) − 𝑟
gives us the slope.
The securities that lie on the Security Market Line are 0 NPV securities.
EXPECTED AND UNEXPECTED INFORMATION
If something is expected then the market reacts to that information at the point in time even if it has not
occurred yet. Markets will not react to an announcement if it was predicted because investors would have
reacted when they predicted the occurrence in order to put themselves in the best expected position.
Uncertainty will cause the market to move, either changing the intercept (𝑟 ) or the gradient (𝐸(𝑟 ) − 𝑟 )
REGRESSION
Betas are estimated using the market model regression
Regression models look at the error terms and minimises the errors around the line to create the best fit.
𝑅 , = 𝛼 + 𝛽 𝑅 , + 𝑒 , , 𝑤ℎ𝑒𝑟𝑒 𝑡 = 1, 2, 3 … 𝑇 𝑎𝑛𝑑 𝑒 = 𝑒𝑟𝑟𝑜𝑟 𝑡𝑒𝑟𝑚𝑠
If we have an equally weighted portfolio then we can determine a portfolio beta
𝜷𝒑 = 𝑤 𝛽 + 𝑤 𝛽
OTHER CAPM PARAMETERS
In addition to beta, we also need to estimate
-
𝒓𝒇 risk-free rate. It is generally the yield to maturity on long-term government bonds because
these investments are almost 0 risk.
𝑬(𝒓𝒎 ) Expected Market Return) or [𝑬(𝒓𝒎 ) − 𝒓𝒇 ] Market Risk Premium
Only applicable in real life – in exam questions these figures will be given
APPLYING THE CAPM
The CAPM is used to estimate the cost of equity capital.
Low beta portfolios are relevant for less risk tolerant investors, and high beta more suitable for high risk.
The following metrics are used to evaluate the performance of portfolios and securities:
SHARPE RATIO
It tells us the expected return per unit of total risk, so a higher ratio indicates better performance.
However we are using the total risk (standard deviation) as a measure of risk, when only systematic risk is
priced in the market.
TREYNOR RATIO
It tells us the expected return per unit of systematic risk, so a higher ratio indicates better performance.
Because we are using 𝛽 now we are only considering systematic risk.
It may give us different outcomes as the recommendations from the Sharpe ratio.
JENSEN’S ALPHA
Alpha for the market portfolio is 0.
The value of A is the maximum amount that you should be willing to pay a managed to manage your
money, otherwise you will be losing money.
CAPM AND SECURITY SELECTION
Security selection involves identifying securities that are currently under/overvalued.
Correctly priced securities will have an NPV of 0 and because of the 0 NPV, will lie on the security market
line. Incorrectly priced securities will not lie on the security market line.
EFFICIENT PORTFOLIOS
RISK RETURN FRONTIER
Efficient Frontier (FF) is the envelope of risk-return frontiers made up of individual securities. It plots the
lowest risk for a given E(r) by combining individual and portfolio securities.
INVESTOR CHOICE WITH A RISK-FREE SECURITY
The capital market line is a tangent to the efficient frontier. It dominates the efficient frontier in all places
and tells us all of the investing combinations with the choice of a risk-free and risky (M) security.
Between the risk-free and risky (M) securities we are using our own money to invest and are splitting it
between the two securities.
If we pass M towards R then we invest both our own money and borrowed money in the market
portfolio.
Investing decision: Invest in the risk-free or risky security
Financing Decision: Invest your own money or use leverage to invest both borrowed and your own money.
THE MARKET PORTFOLIO
M is the value weighted market portfolio which consists of all RISKY securities traded on financial
markets. (equities, debt securities, alternative investments, anything that is traded).
In equilibrium M has to be the market portfolio because eventually, through rising and falling prices and
rising and falling expected returns, all of the risky securities will eventually be traded and will become a
part of the market portfolio.
PROXIES FOR THE MARKET PORTFOLIO
A market index is used as a proxy (representative sample) for the true market portfolio.
A good market index should reflect the entire market and the relative importance of companies in the
market (usually through value weighted)
Value Weighted: Weighted by market capitalisation ($ of shares x # shares)/total market value of market
Price Weighted: Each stock is weighted according to its share price
Equal Weighted: each security is given an equal weight of 1/number of securities
AUSTRALIA:
All Ordinaries Index: value weighted index of the top 500 ASX traded firms (equal weighted also available)
S&P ASX 200/100: value weighted index of top 200 and 100 ASX traded firms (equal weighted available)
USA
Dow Jones Industrial Average: price weighted index of the top 30 firms
S&P 500: value weighted index of top 500 firms in US markets
Wiltshire 5000 Total Market Index: value weighted index of 3700-3800 US firms that have price data
8: CAPITAL BUDGETING I
Methods of project evaluation are used to choose which is the best project to invest in
NPV is the difference between the PV of cash inflows and PV of cash outflows
DECISION: NPV>0, accept. +ve NPV will increase the market value of a company
IRR is max rate of return earned over life based on the cash flows and initial investment.
DECISION: IRR>r, accept. Will give same decision as NPV when cash flows are normal
1. Reverse decision when inflows occur before outflows (reverse of normal)
2. There will be no IRR if the NPV is always +ve/-ve
3. There will be multiple IRRs if cash flows are switching between +ve and -ve
Independent Projects: DECISION: invest in ALL +VE NPV projects
Mutually Exclusive Projects: DECISION: invest in the HIGHEST +VE NPV project
If decision between IRR and NPV is inconsistent → calculate incremental project
Incremental Project: IRR of B-A cash flows, tells us whether we should accept B over A
With resource constraints use profitability index =
Choose the highest Prof. Indexes of independent projects until the budget is 100% full.
Payback period measures the time for the investment to be recovered in cash flows.
DECISION: project/s lowest time within allowed range
Biased against later developing cash flow projects, ignores time value of money.
CAPITAL BUDGETING PROCESS
1.
2.
3.
4.
Generate Investment Proposals
Evaluate and Select best investment proposals
Approve and control of capital expenditures
Reflective audit of investment projects
METHODS OF PROJECT EVALUATION
Net Present Value (NPV): The difference between the PV of cash inflows and PV of cash outflows ($)
Internal Rate of Return (IRR): The discount rate that makes the NPV 0 (%)
Payback Period/Discounted Payback Period: The amount of time an investment takes to return the initial
investment (years)
Accounting Rate of Return:
Return generated from an investment (%)
Profitability Index:
NET PRESENT VALUE
Cash flows are discounted at the required rate of return (risk of the project).
NPV>0 then accept the project, NPV<0 reject the project, NPV≈0 indifferent/marginal project
NPV = PV of cash inflows – PV of cash outflows
An NPV profile is a linear graph of the relationship between NPV and discount rates.
MARKET VALUE OF COMPANY
Positive NPV projects will increase the market value of a company.
1 Calculate the NPV
EG. NPV = $5,163,147
2. Calculate the total firm value before the investment
3 Calculate the total firm value after the investment
4 Calculate the new share price
INTERNAL RATE OF RETURN
The Internal Rate of Return is the rate of return earned by the project over its life based on the expected
cash flows and the initial investment.
This is the maximum return we are able to earn on the project because we are assuming a 100%
reinvestment rate. Therefore any reinvestment return will be lower than this maximum IRR.
THE IRR AND NPV WILL GIVE THE SAME DECISION RULE WHEN THE CASH FLOWS ARE NORMAL -,+
IRR>r accept project (+ve NPV), IRR<r reject project (-ve NPV), IRR≈r indifferent/marginal project
FINDING THE IRR FOR MULTIPLE CASH FLOWS
In exam questions: We are unable to calculate IRR for multiple cash flows, however we can be given a
range of IRRs and will need to prove that the real IRR is within the range.
The correct IRR will result in NPV=0, therefore prove that one IRR gives a +veNPV and the other IRR gives a
-veNPV, therefore the real IRR will give an NPV of 0 between the + and - NPVs
PROBLEM 1 WITH IRR : DELAYED INVESTMENTS
Delayed Investments are cases where cash inflows come before cash outflows.
In this case, IRR stops being the rate of return and instead becomes the rate we are paying for ‘borrowing’
the initial inflow, so the interpretation of IRR changes.
In this case IRR<r, accept- the decision is reversed
PROBLEM 2 WITH IRR: NO IRRS
When the NPV of a project remains positive/negative across all discount rates there will be NO IRR because
we solve IRR by setting NPV to 0.
Here we have to use the NPV method to decide whether to invest or not
PROBLEM 3 WITH IRR: MULTIPLE IRRS
When the NPV equals 0 at multiple discount rates then there will be multiple IRRs which we can’t solve for.
The number of cash flow sign changes tells us the maximum number of IRRs (0 < # IRR < #sign changes)
We should use the NPV method
COMPARING IRR AND NPV METHODS
INDEPENDENT PROJECTS
Independent projects are projects that are accepted/rejected only on the basis of whether they are good
investments, independent of whether we accept/reject other projects.
Decision rule for independent projects: Invest in ALL POSITIVE NPV projects
MUTUALLY EXCLUSIVE PROJECTS
Mutually Exclusive projects are projects where choosing one project rules out the others as choices.
Decision rule for mutually exclusive projects: accept the HIGHEST NPV (if this NPV is positive)
INCONSISTENCY WITH IRR DECISIONS
IRR will give us the same value, independent of what the discount rate is.
However the NPV considers the discount rate, meaning its value will change as the discount rate changes.
Therefore, when choosing mutually exclusive investments a ‘high IRR’ decision rule may clash with a ‘high
NPV’ decision when comparing across multiple discount rates.
We can use incremental projects to make the decisions from both investments match.
INCREMENTAL PROJECTS
Finding the difference between the cash flows of the two projects gives us the incremental project, or
project B-A (A-B)
The NPV of the incremental project B-A will tell us whether B is worth investing in over project A (IRR>r) or
whether we would be better off investing in A instead (IRR<r)
(note: if you do A-B then the signs of the cash flows switch, it becomes a delayed investment and the
decision rule flips, giving a consistent outcome to above)
PROBLEMS WITH THE IRR
-
The incremental IRR may not exist
There may be multiple incremental IRRS
Even if IRR>r, it doesn’t meant that the NPV is positive and we should invest.
r may change over time so we may not know which one needs to be compared to the IRR
PROJECTS WITH RESOURCE CONSTRAINTS
If there are binding resource constraints (money, production, time) then we can’t choose ALL independent
projects, only those that fit within the constraints.
Decision: use the profitability index to order the investments and choose the higher PIs until the budget is
filled.
𝑃𝑟𝑜𝑓𝑖𝑡𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝐼𝑛𝑑𝑒𝑥 =
𝑁𝑃𝑉
𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑟𝑒𝑠𝑜𝑢𝑟𝑐𝑒 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑 𝑏𝑦 𝑝𝑟𝑜𝑗𝑒𝑐𝑡
The limitation of the PI is that there can only be one resource constraint
Choose the highest PIs that fill up the entire budget.
PAYBACK PERIOD
Payback period is the time it takes for the initial cash outlay on a project to be recovered from the net
cash flows. Decision Rule: accept the project/s with the lowest time within the acceptable time frame.
PROBLEMS WITH THE PAYBACK PERIOD
-
Fails to consider cash flows after the amount has been earned back
Biased against projects that have later cash flows and longer development (e.g. mining)
Ignores the time value of money (unless we use the discounted payback period method)
Its main use is if we have to pick a project to finish quickly to minimise our risk of not making a return.
9: CAPITAL BUDGETING II
A number of issues exist when estimating cash flows for choosing projects
TIMING OF CASH FLOWS: predict short-term cash flows, then assume perpetual g rate
- PV known CF, value of single CF at end of known period > PV perpetual CF, add all
FINANCING CHARGES: not included in CF analysis, included in the discount rate
TYPES OF COSTS: incremental (change from the project) included, sunk not included
CHANGE NET WORKING CAPITAL: ∆𝑵𝑾𝑪 = 𝑵𝑾𝑪
− 𝑵𝑾𝑪
CORPORATE INCOME TAXES: 𝐴𝑓𝑡𝑒𝑟 𝑇𝑎𝑥 = 𝐵𝑒𝑓𝑜𝑟𝑒 𝑇𝑎𝑥 × 0.7
DEPRECIATION TAX SHIELD CASH FLOW: 𝑇𝑎𝑥 𝑆ℎ𝑖𝑒𝑙𝑑 = 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝐸𝑥𝑝𝑒𝑛𝑠𝑒 × 0.3
TAX ON ASSET DISPOSAL: 𝑇𝑎𝑥 𝑝𝑎𝑖𝑑 = 𝐺𝑎𝑖𝑛 × 0.3
FREE CASH FLOWS:
𝑇𝑎𝑥 𝑠𝑎𝑣𝑒𝑑 = 𝐿𝑜𝑠𝑠 × 0.3
(𝑅𝑒𝑣𝑒𝑛𝑢𝑒 − 𝑂𝑝 𝐶𝑜𝑠𝑡𝑠 − 𝐷𝑒𝑝 𝑛) × 0.7 + 𝐷𝑒𝑝 𝑛
(𝑅𝑒𝑣𝑒𝑛𝑢𝑒 − 𝑂𝑝 𝑐𝑜𝑠𝑡𝑠) × 0.7 + (𝐷𝑒𝑝 𝑛) × 0.3
Initial/future investment outlays, changes in NWC, after tax salvage value
INFLATION 𝐹𝑖𝑠ℎ𝑒𝑟 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠ℎ𝑖𝑝: (1 + 𝒏𝒐𝒎𝒊𝒏𝒂𝒍 (𝒊𝒏𝒇)) = (1 + 𝒓𝒆𝒂𝒍 (𝒏𝒐 𝒊𝒏𝒇))(1 + 𝒊𝒏𝒇𝒍𝒂𝒕𝒊𝒐𝒏)
AFTER TAX: multiply each CF by 0.7
AFTER INFLATION: multiply each CF by (1 + 𝒊𝒏𝒇𝒍𝒂𝒕𝒊𝒐𝒏)
PROJECTS WITH DIFFERENT LIVES: only compare NPV across same life
Low Com Mult: Repeat projects until they have the same life, calculate NPV at end
Perpetuity: 𝑵𝑷𝑽
EAV: 𝑬𝑨𝑽 =
= 𝑁𝑃𝑉 ×
×
(
(
)
)
, where 𝑁𝑃𝑉 is NPV from one cycle
→ 𝑵𝑷𝑽 =
(
𝑬𝑨𝑽
)
WACC is required rate of return on investments of similar risk to the company.
Can’t be used if it alters business risk or financial risk.
𝐷
𝐸
𝑃
+𝑟 +𝑟
𝑉
𝑉
𝑉
𝐷
𝐸
𝑃
= 𝑟 (𝟏 − 𝒕𝑪 ) + 𝑟 + 𝑟
𝑉
𝑉
𝑉
𝑊𝐴𝐶𝐶/𝑟 = 𝑟
𝐴𝐹𝑇𝐸𝑅 𝑇𝐴𝑋 𝑟
ISSUES IN CASH FLOW ESTIMATIONS
TIMING OF CASH FLOWS
Some cash flows don’t actually occur at the end of the year but we assume they do.
It may be hard to forecast potential cash flows over a long time therefore we can forecast them over the
next couple of years and then assume they grow at a constant rate forever.
-
Calculate PV of the known cash flows
ie. Next 5 years
-
Calculate the value of the cash flow for the next period
𝐶𝐹 = 𝐶𝐹 (1 + 𝑔)
-
Calculate the PV of the ordinary perpetuity of the infinite cash flows
𝑃𝑉 =
-
Combine them together to find the PV of all cash flows
(
) ….
+
(
)
FINANCING CHARGES
We evaluate a project independent of the cash flows to finance it
The discount rate (require rate of return) already considers the financing charges so we are already
considering it in our calculations, therefore including the cash flows again in calculations would be double
counting their impact.
TYPES OF COSTS
Only costs that change as a result of the project are considered
-
Incremental Cash Flows: cash flows that change (increase or decrease) as a result of undertaking
the project. They are relevant when evaluating a project
Sunk Costs: Occurred in the past, won’t be impacted by the acceptable/rejection of the project and
therefore are irrelevant when evaluating a project
Fixed Overhead Costs: they are relevant only when they change with the decision to take the
project
NET WORKING CAPITAL
𝑁𝑒𝑡 𝑊𝑜𝑟𝑘𝑖𝑛𝑔 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 = 𝑪𝑨𝑺𝑯 + 𝑖𝑛𝑣𝑒𝑛𝑡𝑜𝑟𝑦 + 𝑎𝑐𝑐𝑜𝑢𝑛𝑡𝑠 𝑟𝑒𝑐𝑒𝑖𝑣𝑎𝑏𝑙𝑒 − 𝑎𝑐𝑐𝑜𝑢𝑛𝑡𝑠 𝑝𝑎𝑦𝑎𝑏𝑙𝑒
𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒕𝒉𝒆 𝑵𝑾𝑪 = ∆𝑵𝑾𝑪 = 𝑵𝑾𝑪
-
− 𝑵𝑾𝑪
Increase NWC by choosing the project = cash outflows, an incremental cost
Decrease NWC by choosing the project = cash inflow
TAX AND 3 TYPES OF TAX EFFECTS:
CORPORATE INCOME TAXES
After Tax Cash Flow is the cash outflow from incremental costs, as well as the tax paid on the profit.
𝐴𝑓𝑡𝑒𝑟 𝑡𝑎𝑥 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 = 𝐵𝑒𝑓𝑜𝑟𝑒 𝑡𝑎𝑥 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 × (1 − 𝑡 ), where 𝑡 = 30%
DEPRECIATION TAX SHIELD/SAVING
Depreciation = not a cash flow = not included in net cash flows
However depreciation reduces profits, meaning we pay lower taxes and therefore have a saving in a cash
outflow. This decrease in taxes paid is the depreciation tax shield.
𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑡𝑎𝑥 𝑠ℎ𝑖𝑒𝑙𝑑 = 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 × 𝑡
TAXES PAID ON DISPOSAL OF ASSETS
𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 = 𝑎𝑐𝑞𝑢𝑖𝑠𝑖𝑡𝑖𝑜𝑛 𝑐𝑜𝑠𝑡 − 𝑎𝑐𝑐 𝑑𝑒𝑝 𝑛 and 𝐺𝑎𝑖𝑛(𝑙𝑜𝑠𝑠) = 𝑑𝑖𝑠𝑝𝑜𝑠𝑎𝑙 𝑣𝑎𝑢𝑒 − 𝑏𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒
𝑇𝑎𝑥𝑒𝑠 𝑝𝑎𝑦𝑎𝑏𝑙𝑒 𝑜𝑛 𝐺𝑎𝑖𝑛 = 𝐺𝑎𝑖𝑛 𝑜𝑛 𝑠𝑎𝑙𝑒 × 𝑡
𝑇𝑎𝑥 𝑠𝑎𝑣𝑖𝑛𝑔 𝑜𝑛 𝐿𝑜𝑠𝑠 = 𝐿𝑜𝑠𝑠 𝑜𝑛 𝑠𝑎𝑙𝑒 × 𝑡
𝑵𝒆𝒕 𝒂𝒇𝒕𝒆𝒓 𝒕𝒂𝒙 𝒔𝒄𝒓𝒂𝒑 𝒗𝒂𝒍𝒖𝒆 = 𝑑𝑖𝑠𝑝𝑜𝑠𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 − 𝑡𝑎𝑥 𝑠ℎ𝑖𝑒𝑙𝑑 𝑜𝑟 + 𝑡𝑎𝑥 𝑠𝑎𝑣𝑖𝑛𝑔
TAX AND TAX EFFECTS: INCREMENTAL NET AFTER TAX CASH FLOWS (FREE CF)
𝐹𝑟𝑒𝑒 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤𝑠 = (𝑅𝑒𝑣𝑒𝑛𝑢𝑒 − 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝐶𝑜𝑠𝑡𝑠 − 𝐷𝑒𝑝 𝑛) × 0.7 + 𝐷𝑒𝑝′𝑛
𝐹𝑟𝑒𝑒 𝐶𝑎𝑠ℎ 𝐹𝑙𝑜𝑤𝑠 = (𝑅𝑒𝑣𝑒𝑛𝑢𝑒 − 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝐶𝑜𝑠𝑡𝑠) × 0.7 + 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 × 0.3
Also consider:
-
Initial and future investment outlays
Changes in net working capital
After tax salvage value
INFLATION AND CAPITAL BUDGETING
𝒓 = Nominal Cash Flows include impact of inflation -> use the nominal discount rate (higher)
𝐹𝑖𝑠ℎ𝑒𝑟 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠ℎ𝑖𝑝: (1 + 𝒓) = (1 + 𝒓𝒓 )(1 + 𝒊)
𝒓𝒓 = Real Cash Flows don’t include the impact of inflation -> use the real discount rate (lower)
𝐹𝑖𝑠ℎ𝑒𝑟 𝑅𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠ℎ𝑖𝑝: (1 + 𝒓𝒓 ) =
1+𝒓
(1 + 𝒊)
Where 𝒊 = 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝑝𝑒𝑟 𝑎𝑛𝑛𝑢𝑚
Real cash flows discounted using nominal discount rate -> discounting too much, and vice versa
CALCULATING NPV AFTER TAXES and INFLATION
𝑁𝑃𝑉 = −300000 +
220000 220000 + 25000
+
1.05
1.05
Considering INFLATION means we need to use the NOMINAL r rate and multiply each cash flow by the
INFLATION RATE
𝒊 = 𝟑%
𝐹𝑖𝑠ℎ𝑒𝑟 𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛𝑠ℎ𝑖𝑝: (1 + 𝒓) = (1.05)(1.03), 𝑵𝒐𝒎𝒊𝒏𝒂𝒍 𝑹𝒂𝒕𝒆 = 8.15%
𝑁𝑃𝑉 = −𝑧 +
𝑥 × 𝟏. 𝟎𝟑 (𝑥 + 𝑦) × 𝟏. 𝟎𝟑𝟐
+
𝟏. 𝟎𝟖𝟏𝟓
𝟏. 𝟎𝟖𝟏𝟓
Considering TAXES means we need to multiple each cash inflow by 0.7 to find the amount retained
𝑁𝑃𝑉 = −𝑧 +
𝑥 × 1.03 × 𝟎. 𝟕 (𝑥 + 𝑦) × 1.03 × 𝟎. 𝟕
+
1.0815
1.0815
PROJECTS WITH DIFFERENT LIVES
When comparing NPVs across mutually exclusive projects we have to make sure the life of each project is
the same.
Constant Chain of Replacement: assume all projects can repeatedly be invested in until we achieve a
common life. It can be applied using two methods
LOWEST COMMON MULTIPLE METHOD
Invest in each project multiple times until we reach the lowest common multiple life between the projects.
If project A has a 5-year life and Project B has a 3 year life then the lowest common multiple is 15 years
-
Repeat A 3 times
Repeat B 5 times
Then calculate the NPV of A and of B after the same time frame (15 years)
PERPETUITY METHOD
We assume both projects are invested in for an infinite amount of time.
1. Calculate the NPV at time period 0 assuming we invest just once 𝑁𝑃𝑉
2. Calculate the infinite NPV using the following formula: 𝑵𝑷𝑽 = 𝑁𝑃𝑉 × (
(
)
)
EQUIVALENT ANNUITY VALUE (EAV)
The EAV will give us the cash flow we will ‘receive’ each year if we continue the projects infinitely
1. Calculate the NPV at time period 0 𝑁𝑃𝑉
2. Convert the NPV to an Equivalent Annuity Series
𝑬𝑨𝑽 =
𝑁𝑃𝑉
1
1
×
1
−
𝑟
(1 + 𝑟)
3. Find the Net Present Value of the perpetual cash flows
𝑵𝑷𝑽 =
𝑬𝑨𝑽
𝑟
WEIGHTED AVERAGE COST OF CAPITAL
The WACC is the required rate of return needed to earn on investments of similar risk to the company. It
is used to obtain the market value of the company. It considers the weighting of debt or equity used to
finance an investment. The WACC uses market values, not book values, because market values are
unbiased valuations.
VALUING THE FINANCING COMPONENTS
DEBT (BONDS): Market price = number of bonds x market price. Required Rate of Return = yield to
maturity rD

YTM, not the coupon rate, because no default risk and we assume not trading at par (CR ≠ YTM)
ORDINARY SHARES: Market price = number of shares x market price. Required Rate of Return = rE

Calculate rE using the CAPM or a dividend growth model
PREFERENCE SHARES: Market price = number of shares x market value. Required Rate of Return = rP

𝑟 =
, 𝑤ℎ𝑒𝑟𝑒 𝐷 𝑖𝑠 𝑡ℎ𝑒 𝑝𝑒𝑟𝑝𝑒𝑡𝑢𝑎𝑙 𝑠𝑎𝑚𝑒 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑝𝑎𝑖𝑑 𝑒𝑣𝑒𝑟𝑦 𝑦𝑒𝑎𝑟
The WACC has to lie between the cost of debt (cheapest) and the cost of equity (most expensive)
TAXES AND THE COST OF CAPITAL
Classical Tax system: Interest on debt is tax deductable. There are no tax breaks on dividend income.
Implication Tax system: Interest on debt is tax deductable. We get tax breaks on dividend income that the
company has already paid tax on. WE USE THIS IN AUS
THE ONLY IMPACT ON WACC WILL BE THAT DEBT WILL BE CONVERTED TO AN AFTER-TAX BASIS
The after tax WACC includes the tax impact on debt. It will be lower than the before-tax WACC
𝑪
LIMITATIONS ON USING THE COST OF CAPITAL
WACC cannot be used if it alters business risk or financial risk
-
Business Risk: if the project is outside the normal range of activities for the business
 E.g. Coffee shop starting to sell cars, supermarket starting to rent out space for events
Financial Risk: If the project alters the capital structure of the company then the WACC will no
longer reflect the new debt/equity mix.
If the WACC can’t be used then look at pure project companies where the entire business is the project we
are looking at. We can use their information to get a project-specific discount rate.
10: CAPITAL STRUCTURE AND PAYOUT POLICY I
The two risks faced by companies are
- Business risk – regular operations, faced by all companies that employ equity
- Financial risk – using debt, faced by leveraged companies that employ debt/equity
o Increases risk of variability of returns = increases returns to shareholders
Assume: markets competitive, no corporate taxes, CFs perpetual (easy), 100% div pay
𝑉𝑼𝒏𝒍𝒆𝒗𝒆𝒓𝒆𝒅 =
𝐸𝐵𝐼
𝐸𝐵𝐼 − 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑜𝑛 𝑑𝑒𝑏𝑡 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑜𝑛 𝑑𝑒𝑏𝑡
≫ 𝑉𝑳𝒆𝒗𝒆𝒓𝒆𝒅 =
+
𝑟 𝑜𝑟 𝑟
𝑟𝐸
𝑟𝐷
MM1: firm value is not affected by the choice of capital structure:
If cash flows from assets are the same 𝑉𝑼𝒏𝒍𝒆𝒗𝒆𝒓𝒂𝒈𝒆𝒅 = 𝑉𝑳𝒆𝒗𝒆𝒓𝒂𝒈𝒆𝒅 = 𝐸 (
.)
No arbitrage: no additional money, no additional risk = no additional return
Is arbitrage: same cash flows but 𝑉 ≠ 𝑉 , make additional returns
Homemade leverage: replicate leveraged firm by borrowings x% of debt and investing in
x% of unleveraged firm’s equity
Inc debt = increase EPS = Increase return on equity for shareholders
If shareholders can use homemade leverage they won’t value L higher than UL firm
MM2: cost of equity increases as debt-to-equity ratio increases
Debt shouldn’t impact on 𝑟 , however debt increases equity systematic risk 𝛽 so
shareholders require a higher 𝑟
𝑟 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑑 = 𝑟 𝑈𝑛𝑙𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑑 + 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑓𝑟𝑜𝑚 𝐷𝐸 𝑟𝑎𝑡𝑖𝑜
𝑟 = 𝑟 + (𝑟 − 𝑟 ) ×
𝐷
𝐸
MM WITH CORPORATE TAXES
No corporate taxes = market values the same = no optimal capital structure
Adding in Corporate taxes changes this assumption of no optimum:
- Tax deduction on interest paid on debt = tax break reduces taxes paid
- Optimal capital structure is as much debt as possible
- Value added to leveraged firm value = PV of interest tax shield
𝑷𝑽(𝑻𝒂𝒙 𝒔𝒉𝒊𝒆𝒍𝒅) =
𝑡 (𝐷 × 𝑟 )
𝐷×𝑟
𝑝𝑒𝑟𝑝𝑒𝑡. 𝑑𝑒𝑏𝑡 𝑶𝑹
𝑟
𝑟
1−
1
(1 + 𝑟 )
𝑽𝒂𝒍𝒖𝒆 𝒐𝒇 𝒍𝒆𝒗𝒆𝒓𝒂𝒈𝒆𝒅 𝒇𝒊𝒓𝒎 = 𝑉 = 𝑉 + 𝑃𝑉(𝑇𝑎𝑥 𝑠ℎ𝑖𝑒𝑙𝑑)
𝑚𝑎𝑡𝑢𝑟𝑖𝑛𝑔 𝑑𝑒𝑏𝑡
FINANCIAL LEVERAGE
The two risks faced by companies are:
BUSINESS (OPERATIONAL RISK) – variability of cash flows associated with the nature of the
firm’s operations
- Risk faced by all companies that employ equity (ie. every single company)
FINANCIAL RISK – risk associated with using debt as a source of funding operations
- Risk faced only by companies that take on debt in addition to equity
- Measured as the variability of earnings per share or return on equity over time
EFFECTS OF INTRODUCING LEVERAGE
Financial Leverage introduces additional financial risk by financing some of the operations of the company
using debt.
-
Expected rate of return on equity increases (increase in return)
Variability of returns to shareholders increases (increase in risk)
It is measured using the debt to equity
or debt to assets ratio
MODIGLIANI AND MILLER (MM) ANALYSIS
This model is based on unrealistic assumptions about capital markets
-
-
Market prices are competitive and no one influences them
No corporate taxes, personal taxes, transaction costs or issuing costs, and therefore:
 𝑬𝒂𝒓𝒏𝒊𝒏𝒈𝒔 𝒕𝒐 𝑺𝒉𝒂𝒓𝒆𝒉𝒐𝒍𝒅𝒆𝒓𝒔 = 𝑬𝑩𝑰𝑻 = 𝑬𝑨𝑻 = 𝑬𝑩𝑰
 𝒓𝟎 𝑾𝑨𝑪𝑪 = 𝒓𝑬 𝑪𝒐𝒔𝒕 𝒐𝒇 𝑬𝒒𝒖𝒊𝒕𝒚
Firms use fixed investment policies - investing decision isn’t influenced by their financial decision
No costs associated with liquidation
We also assume the following about the company to find their value (ie. PV of future cash flows)
-
All cash flows from operations are perpetual

-
We can get the PV of the cash flow through 𝑃𝑉 =
All earnings are paid out as dividends
If these perfect market conditions are met then the value of a firm isn’t affected by their capital structure,
however when we deviate from them (in the real world) we see that there is an impact on firm value
VALUE OF UNLEVERED FIRM
𝑉
=
=
= 𝐸 𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦
VALUE OF LEVERED FIRM
𝑉
= 𝐸𝑞𝑢𝑖𝑡𝑦
+ 𝐷𝑒𝑏𝑡
The value of the firm is the PV of each of the cash flows (EBI and Interest) which is simple to find since both
are assumed to be perpetual cash flows
MM PROPOSITION 1: FIRM VALUE
Firm value is NOT affected by the choice of CAPITAL STRUCTURE
In perfect capital markets the value of a firm is the market value of total cash flows generated by assets.
However changing the capital structure will change the way net income/earnings is divided between
debtholders and shareholders.
𝑉
=𝑉
= 𝐸 𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦 if cash flows from assets are same
We assume there is no arbitrage allowed so the firms with the same cash flows, regardless of capital
structure, will have the same market values.
-
No risk-free arbitrage: Don’t use own money, don’t take additional risk -> return = 0
Risk-free arbitrage: Don’t use own money, don’t take additional risk -> return ≠ 0 (make profits)
 Buy low and sell high, or sell high and buy back low
 Occurs when there are the same cash flows but 𝑉 ≠ 𝑉
 This will drive the market values to become the same in equilibrium as investors discover it
MM AND CAPITAL STRUCTURE CHANGES
By utilising debt we can increase the earnings per share and the return on equity for shareholders.
However if shareholders can achieve the same outcome that the firm has themselves then they will not
value the leveraged firm higher than the unleveraged firm.
Shareholders can use homemade leverage by borrowing using their personal account and using the debt
to purchase an equivalent value of shares.
SHAREHOLDERS WILL NOT VALUE THE LEVERAGED FIRM DIFFERENT THAN THE UNLEVERAGED FIRM IF
THEY CAN USE HOMEMADE LEVERAGE.
LENDING FUNDS TO UNDO HOMEMADE LEVERAGE
We can undo company leverage by doing the opposite of borrowing, which is lending funds.
MM PROPOSITION 2: COST OF EQUITY
The cost of equity of a leveraged firm will increase in direct proportion to its debt-to-equity ratio
𝑪𝒐𝒔𝒕 𝒐𝒇 𝑬𝒒𝒖𝒊𝒕𝒚 𝑜𝑓 𝐿𝑒𝑣. = 𝒄𝒐𝒔𝒕 𝒐𝒇 𝒄𝒂𝒑𝒊𝒕𝒂𝒍 (𝑒𝑞𝑢𝑖𝑡𝑦)𝑜𝑓 𝑈𝑛𝑙𝑒𝑣. +𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑓𝑟𝑜𝑚 𝐷𝐸 𝑟𝑎𝑡𝑖𝑜
𝑟 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑑 = 𝑟 𝑈𝑛𝑙𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑑 + 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑓𝑟𝑜𝑚 𝐷𝐸 𝑟𝑎𝑡𝑖𝑜
-
𝑟 remains unchanged because the risk and betas of the assets do not change
𝑟 remains unchanged because the risk-free rate is assumed to be constant
The increase in 𝑟 depends on the change in the D/E ratio
𝑬
𝑶
𝑶
𝑫
Proposition 1 states that the level of debt shouldn’t impact on market value yet shareholders would
receive higher returns under more debt?
Need to consider the link between systematic risk 𝜷 and the debt/equity ratio.
-
As we increase leverage the beta of equity rises
Shareholders are compensated for the higher risk through higher returns on equity
𝜷𝑬 = 𝜷𝑶 + (𝜷𝑶 − 𝜷𝑫 ) ×
𝑫
𝑬
MM and MARKET IMPERFECTIONS
The MM analysis assumes away capital market imperfections. Transaction costs, different costs of
borrowing and changing cost of debt don’t really impact on the analysis if they are included or excluded.
However agency costs, corporate/personal taxes and bankruptcy costs all change how the MM analysis
works and will have a large impact on calculations if included. These things exist in the real world,
therefore the MM assumptions and conclusions don’t apply in the real world.
MM and CORPORATE TAXES
We will now see what happens when we include corporate taxes in the analysis.
Where there are no company taxes there is no optimal capital structure as the market value will be the
same.
When we introduce company taxes there is a tax advantage to having debt in the capital structure and the
optimal capital structure therefore becomes having as much debt as possible.
Under the Classical Tax system (not used in Australia):
-
Interest on debt is a tax-deductable expense (leverage increases, firm value will increase)
Increases after-tax net cash flows where all cash flows are paid out as dividends
PV OF TAX SHIELD WITH PERPETUAL DEBT
The PV of the interest tax shield represents the total value added to the leveraged firm’s value
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑜𝑛 𝑑𝑒𝑏𝑡 = 𝐷 × 𝑟
𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑡𝑎𝑥 𝑠ℎ𝑖𝑒𝑙𝑑 = 𝑡 (𝐷 × 𝑟 )
𝑃𝑉 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑡𝑎𝑥 𝑠ℎ𝑖𝑒𝑙𝑑 =
𝑡 (𝐷 × 𝑟 )
𝑟
𝑃𝑉 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑡𝑎𝑥 𝑠ℎ𝑖𝑒𝑙𝑑 𝑤𝑖𝑡ℎ 𝒑𝒆𝒓𝒑𝒆𝒕𝒖𝒂𝒍 𝒅𝒆𝒃𝒕 = 𝒕𝑪 × 𝑫 (𝑡𝑎𝑥 𝑟𝑎𝑡𝑒 × 𝑚𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑑𝑒𝑏𝑡)
𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑙𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑑 𝑓𝑖𝑟𝑚 = 𝑉 = 𝑉 + 𝑃𝑉(𝑇𝑎𝑥 𝑠ℎ𝑖𝑒𝑙𝑑)
= 𝑉 +
𝑡 (𝐷 × 𝑟 )
𝑟
= 𝑉 + (𝑡 × 𝐷) 𝑂𝑁𝐿𝑌 𝐹𝑂𝑅 𝑃𝐸𝑅𝑃𝐸𝑇𝑈𝐴𝐿 𝐷𝐸𝐵𝑇
This would lead us to imply that the optimal capital structure is 100% debt as we get the maximum tax
breaks the more we increase debt. This would involve turning all shareholders into bondholders and
paying them tax-deductable interest rather than dividends.
However this doesn’t take into consideration other costs like personal taxes, bankruptcy and agency costs.
PV OF TAX SHIELD WITH MATURING DEBT
The tax shield can still be used when we don’t have perpetual debt but instead debt that matures, however
we need to calculate the tax shield separately.
𝑃𝑉 𝑜𝑓 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑡𝑎𝑥 𝑠ℎ𝑖𝑒𝑙𝑑 =
𝐷×𝑟
𝑟
1−
1
(1 + 𝑟 )
11: CAPITAL STRUCTURE AND PAYOUT POLICY II
Corporate taxes and perpetual debt: 𝑉 = 𝑉 + 𝑃𝑉(𝑇𝑎𝑥 𝑠ℎ𝑖𝑒𝑙𝑑)
+ Personal Taxes 𝑉 = 𝑉 + 𝐺 , where Net Gains from Leverage include 𝒕𝒄 , 𝒕𝒑𝒔 , 𝒕𝒑𝒅
+ D, B , A costs 𝑉 = 𝑉 + 𝑃𝑉(𝑇𝑎𝑥 𝑆ℎ𝑖𝑒𝑙𝑑) − 𝑃𝑉(𝐵𝑎𝑛𝑘𝑟. & 𝐴𝑔𝑒𝑛𝑐𝑦 𝐶𝑜𝑠𝑡𝑠)
Trade off between benefits of debt finance and costs of financial distress means that
there is an optimal capital structure at a balanced level of Bankrup. & Agency costs
Fin. distress, bankruptcy & agency costs = capital structure does impact on firm value:
Direct distress: accounting fees
Indirect distress: lost customers/sales
Mgmt aligned with Shareholders, want to transfer bondholder wealth to them but can’t:
- Dilution of claims: debt covt. so mgmt can’t make new debt senior
- Dividend payout: debt covt. so mgmt can’t pay out dividends with borrowed funds
- Excessive risk: financial distress = take on risky/-ve NPV – bondholders receive no
reward for risky behaviour so they prevent or charge higher interest rates on debt
- Debt overhand/underinvestment: not take on low risk projects
NATCF Payout: Retain (new project/cash reserve) Pay Out (repurchase shares/dividends)
Dividend policy: trade-off between retaining profit and paying out dividends
Dividend policy doesn’t affect shareholder wealth if markets are perfect with no taxes
Dividend policy does affect shareholder wealth with taxes and other imperfections
Classical: dividends taxed twice (1 − 𝑡 )(1 − 𝑡 ) – optimal is no dividends
Imputation: div income taxed once (marginal rate) – shareholder clientele formed:
- High marginal tax rates = low/no dividends (taxed on diff), like share repurchases
- Low marginal tax rates = prefer high dividends, get tax break on div income
Optimal dividend policy is to pay dividends to exhaust all available franking credits
Factors affecting dividend policy:
- Taxes (with taxes the policy does affect shareholder wealth)
- Dividend signalling hypothesis, dividends raised w. long-term increase in earnings
- Dividends followed through will support agency relationship between
M&M WITH CORPORATE AND PERSONAL TAXES
𝑉 = 𝑉 + 𝑃𝑉(𝑇𝑎𝑥 𝑠ℎ𝑖𝑒𝑙𝑑)
𝑉 = 𝑉 + 𝒕𝑪 𝐷 – value of leveraged firm with corporate taxes and perpetual debt
With just company taxes the optimal capita structure is to have as much debt as possible in the capital
structure.
However other market imperfections are missing from the analysis.
PERSONAL TAXES AND COMPANY TAXES ON EQUITY AND DEBT INCOME
𝑉 = 𝑉 + 𝐺 , where 𝐺 are the net general gains from leverage.
𝑮𝑳 = 𝐷 1 −
(1 − 𝑡
)(1 − 𝑡
(1 − 𝑡
.
)
.
)
𝒕𝒄 = 𝒕𝒑𝒔 = 𝒕𝒑𝒅 = 𝟎
-
𝑉 =𝑉
No benefits from issuing debt under 0 taxes (Principal 1)
𝒕𝒑𝒔 = 𝒕𝒑𝒅 or 𝒕𝒑𝒔 = 𝒕𝒑𝒅 = 𝟎
-
𝑉 = 𝑉 + 𝒕𝑪 𝐷
Benefits from debt are the tax shield on perpetual debt
𝒕𝒑𝒔 =
-
(𝒕𝒑𝒅 𝒕𝒄)
(
𝒕𝒄 )
𝑮𝑳 = 0
𝑉 =𝑉
No benefits from issuing debt if we have all Australian investors and have fully franked dividends.
Benefits for company (interest on debt is tax deductable) are wiped out by the benefits to
Shareholders (being paid fully franked dividends to all investors within Australia)
OTHER MARKET IMPERFECTIONS
Other non-tax factors that cause firm value to depend on capital structure are
-
Financial distress: Company may be in breach of debt obligations which may/may not lead to
bankruptcy.
Bankruptcy costs: firm fails to make interest or principal payments on debt and defaults.
Agency costs: costs from potential conflicts between parties in a contractual relationship.
 Managers and shareholders are aligned and may conflict with bond holders.
BANKRUPTCY AND CAPITAL STRUCTURE
Direct costs of financial distress/bankruptcy: fees and costs with lawyers, accountants, advisors
-
Typically 3-4% of the pre-bankruptcy market value of assets.
Reduces the value of assets that investors will eventually receive
Indirect costs of financial distress/bankruptcy: cost associated with stakeholders losing confidence in the
company and acting in ways that disrupt their market value
-
Loss of customers, suppliers, employees
Quick sales of assets at lower than market value
They are typically much larger than direct costs.
AGENCY COSTS AND CAPITAL STRUCTURE
If management makes decisions that aren’t in the best interests of bond holders then there will be a
wealth transfer from bond holders to shareholders
Both share and bond holders will bear agency costs
-
If a company goes bankrupt then the bond holders bear the losses as they get claims on what is left
However they demand a higher rate of return and the shareholders pay this cost because they will
receive a lower portion of the earnings once bond holders are paid.
Bondholders therefore will prevent the firm from making decision that will shift wealth away from them by
setting debt covenants.
DILUTION OF CLAIMS
A debt covenant will be applied by current bondholders so that new debt a company issues can’t be made
senior to their existing debt
-
This means that old debt taken out first has to be repaid before new debt
DIVIDEND PAYOUT
A firm can take out debt and use the funds to pay dividends to shareholders, which is a wealth transfer
from bondholders to shareholders.
A debt covenant can therefore be imposed to prevent firms from using debt to pay dividends.
EXCESSIVE RISK TAKING AND ASSET SUBSTITUTION
Firms in financial distress may want to take on very risky investments to have a small chance of generating
massive returns.
-
The bond holders will be paid the normal interest rate – no increased return on their risk
The shareholders would receive the benefits of the successful investment – increased return
Therefore the bond holders may prevent companies from taking on risky investments, or may require a
higher interest rate to be paid so the increased risk is compensated for the excess return.
DEBT OVERHANG AND UNDERINVESTMENT
Firms in financial distress may also not want to take on low risk investments because the benefits of a low
risk investment go to bond holders instead of shareholders.
Rejecting these +ve NPV projects with low risk will transfer wealth from debt holders to shareholders.
THE OPTIMAL CAPITAL STRUCTURE
Including the benefits and costs of debt and the other market imperfection costs:
𝑉 = 𝑉 + 𝑃𝑉(𝑇𝑎𝑥 𝑆ℎ𝑖𝑒𝑙𝑑) − 𝑃𝑉(𝐵𝑎𝑛𝑘𝑟𝑢𝑝𝑡𝑐𝑦 𝑎𝑛𝑑 𝐴𝑔𝑒𝑛𝑐𝑦 𝐶𝑜𝑠𝑡𝑠)
Where 𝑃𝑉(𝑇𝑎𝑥 𝑆ℎ𝑖𝑒𝑙𝑑) is:
-
Benefits from company taxes
Net of costs of personal taxes on the individual level
There is a trade off between:
-
benefits of debt finance – want to increase debt as much as possible to increase firm value
costs of financial distress – find a balance to get the optimal D/E ratio to maximise firm value
USES FOR NET AFTER-TAX CASH FLOWS (FREE CASH FLOWS)
RETAIN: invest in new projects or increase cash reserves
PAY OUT: repurchase shares of pay dividends
TYPES OF PAY OUT POLICIES
Special Dividend: One-off dividend payment, usually much larger than its regular dividend. It is made when
a firm has excess cash sitting around and they don’t have any investments to put it in.
Share Split (share dividend): Dividend paid as shares rather than cash, for everyone share you have you
receive another X shares. The share price after the split decreases.
(opposite to a Reverse Split: a company turns multiple shares into one share, increasing the price)
Share Repurchases/Buybacks:
On market repurchases are when the firm buys back shares from investors and removes them from
the market. This increases the value of shares as each is now worth more.
Off-market repurchases are purchasing back from smaller scale shareholders who only hold a few
shares in order to reduce the number of unique shareholders and reduce communication costs.
Liquidating dividend: returning capital to shareholders from business operations that are being
discontinued.
Dividend reinvestment plan: company will reinvest your cash dividends back into shares, sometimes with
a discount on the market price when reinvesting.
FEATURES OF DIVIDENDS
Dividend declaration: the date a dividend is announced.
Ex-dividend date: 1-2 days before record date, shareholders who purchase shares after this date won’t
receive the announced dividend.
-
The share price will drop by around the $ value of the dividend on this date
Record date: the date on which shareholders on the books will be certified to receive the dividend.
Payment Date: date dividend is paid
TYPES OF DIVIDEND PAYOUT POLICIES
Pure Residual Dividend Policy: pay out earnings the firm doesn’t need to reinvest
-
Unstable dividend and dividend payout ratio
Not usually followed
Smoothed/Fixed dividend policy: a proportion of target earnings paid out as dividends
-
Dividends should be the difference between LONG TERM earnings and capital expenditures
Constant payout dividend policy: pay out a constant ratio of earnings as dividends
-
Unstable dividends paid out, but a stable dividend payout rate
Low regular dividend and extra dividend policy: lower than usual regular dividends, then special dividends
MM AND THE DIVIDEND IRRELEVANCE THEORY
Dividend policy is concerned with how earnings are split up between dividends and retained earnings.
The main idea of the theory is that shareholder wealth is only determined by the earnings generated from
the firm’s assets: dividend policy doesn’t affect shareholder wealth and shareholders have no preference
The main assumptions are
-
Capital markets are perfect
Firm can issue and sell new shares when needed
There are no personal taxes
Capital Structure Given: Firms are all equity financed
Capital Investment Plan Given: Firm has set investment plan not impacted by changes in dividends
Dividend policy is a trade-off between:
-
Retaining earnings (no cash leaves firm)
Paying out earnings as dividends, then issuing new shares to replace dividends paid out
(cash being paid out and then collected again)
Both of these strategies will lead to:
-
No change in the value of the firm
No change in the wealth of old shareholders
 Market Value will fall by the same amount of cash that is paid out as dividends.
PROOF OF NO CHANGE IN VALUE AND WEALTH – ONE PERIOD MODEL
Sources of funds
𝑋 = 𝑐𝑎𝑠ℎ 𝑓𝑟𝑜𝑚 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑠
𝑚𝑃 = 𝐶𝑎𝑠ℎ 𝑓𝑟𝑜𝑚 𝑛𝑒𝑤 𝑠ℎ𝑎𝑟𝑒𝑠 𝑖𝑠𝑠𝑢𝑒𝑠 (𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑛𝑒𝑤 𝑠ℎ𝑎𝑟𝑒𝑠 = 𝑚)
Uses of funds
𝑛𝐷 = 𝐶𝑎𝑠ℎ 𝑓𝑜𝑟 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑝𝑎𝑖𝑑 (𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒𝑠 = 𝑛)
𝐼 = 𝑐𝑎𝑠ℎ 𝑓𝑜𝑟 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑠
The sources of funds and uses of funds must be equal, therefore:
𝑋 + 𝑚𝑃 = 𝑛𝐷 + 𝐼 OR
𝑚𝑃 = 𝑛𝐷 + 𝐼 − 𝑋
𝑚 𝑛𝑒𝑤 𝑠ℎ𝑎𝑟𝑒𝑠 × 𝑠ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒 = [𝑛𝑢𝑚 𝑠ℎ𝑎𝑟𝑒𝑠 × 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠] + 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡𝑠 − 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑐𝑎𝑠ℎ
𝑚 will tell us how many more shares we need to issue to cover all uses of funds (after received op. cash)
The one-period price of shares is
Therefore firm value
0
𝐷1 +𝑃1
1+𝑟𝐸
= 𝑛𝑢𝑚 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 × 𝑃0
Because 𝑛𝐷 is paid out as dividends the firm sells m new shares at price P1 each
(
𝑉 =
)
𝑛𝐷 + (𝑛 + 𝑚)𝑃 − (𝑛𝐷 + 𝐼 − 𝑋)
1+𝑟
𝑉 =
(𝑛 + 𝑚)𝑃 − 𝐼 + 𝑋)
1+𝑟
Dividends 𝑛𝐷 do not appear in the final equation, therefore we can deduce dividend policy is irrelevant
to firm value.
WHEN DIVIDEND POLICY MATTERS
Dividend income and capital gains are taxed differently, meaning shareholders may prefer other
alternatives over dividend payments.
DIVIDEND POLICY IN A CLASSICAL TAX SYSTEM
One dollar of earnings is taxes first at the company tax rate and then at the personal tax rate – TWICE!
𝑎𝑚𝑜𝑢𝑛𝑡 𝑠ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑒𝑟 𝑟𝑒𝑡𝑎𝑖𝑛𝑠 𝑓𝑟𝑜𝑚 $1 𝑜𝑓 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠: (1 − 𝑡 )(1 − 𝑡 )
Capital gains are taxed at a lower rate than dividends.
Shareholders will pay lower taxes on share repurchases because they involve realisation of capital gains,
whereas dividends are treated as ordinary income.
Therefore the optimal dividend policy in a classical tax system is to pay no dividends.
DIVIDEND POLICY IN AN IMPUTATION TAX SYSTEM
Earnings distributed as ‘franked’ dividends are taxed once at the shareholder’s personal tax rate. Capital
gains are taxed at half of the personal tax rate.
The difference between the dividend tax rate and the capital gains tax rate will determine how
shareholder clienteles are formed depending on dividend/reinvestment preferences:
-
Shareholders who have high marginal tax rates -> prefer low/no dividends and instead share
repurchases
Shareholders who have low marginal tax rates -> prefer high dividends that are fully franked
If all shares were held by Aus. residents and their marginal tax rates were less than the company tax rate
then the optimal dividend policy is to pay dividends to exhaust all of the available franking credits.
-
Foreign investors don’t get the tax credits
Shareholders who have marginal tax rates above 30% will have a preference for firms to pay no
dividend because they will be taxed at the difference between the tax rates
 45% personal, 30% firm = pay 15% taxes extra on dividends
 15% personal, 30% firm = refund 15% taxes from dividends
Companies shouldn’t be worried about their payout policy because they will attract shareholders who
prefer the policy that they use (like how Telstra attracts retirees with low marginal tax rates because of
their high dividend payouts)
DIVIDEND POLICY and OTHER NON-TAX FACTORS
RETAIN CASH AND NOT PAY DIVIDENDS
-
Cover potential future cash flows shortages and boost the working capital ratio
Hedge against possible future financial distress
Fund future growth
PAY OUT CASH AS DIVIDENDS
-
Avoid inefficient use of cash like paying management too much
Provide credible signs to the market
DIVIDEND SIGNALLING HYPOTHESIS
Dividend changes reflect managers’ view about a firm’s future earnings prospects.
Raise dividend: if management predicts a long-term increase in the expected level of future earnings
-
Positive signal to shareholders that management expects they can afford higher dividends in the
foreseeable future
Negative signal if they think they are lacking other investment opportunities and are not growing
Cut dividend or eliminate dividend: Only as a last resort.
-
Negative signal as it may signal management has given up hope that earnings will rebound in the
near future and need to retain the dividend cash.
DOES DIVIDEND POLICY MATTER?
Market imperfections drive managers to do what the market wants
-
Taxes: When shareholder clienteles exist then dividend policy isn’t as important
Dividends contain signalling elements about what managers expect future earnings to be
Dividends paid lower the agency costs between management and shareholders
 Market discipline, as management has to pay dividends that they announce they will pay
12: INTRODUCTION TO OPTIONS
Forward, futures and swap contracts are obligations to trade agreed shares
Option contracts give the holder the option to buy/sell the underlying shares (x100)
X = exercise price, agreed price at which to trade, determines when to exercise contract
Call options: 𝑆 > 𝑋 exercise
Put options: 𝑆 < 𝑋 exercise
In the money: it is profitable for the buyer to exercise the option at the current price
For buyers: profitable where the graph has a slope
For sellers: profitable where the graph has a flat slope
Speculative selling: we have expectations about the direction of the share price so we
purchase options rather than the underlying share
- Think price will rise:
- Think prise will fall:
Purchase call options
Purchase put options
Buy shares for X (less) if $ rise
Sell shares for X (more) if $ fall
Hedging: We already own/sold underlying shares, want to reduce exposure via options
Hedge will be the difference between the shares and the put/call option (sum of profits)
- Own shares, think $ fall: Purchase put options
- Sold short, think $ rise: Purchase call options
Sell shares for X (more) if $ fall
Buy shares for X (less) if $ rise
Synthetic positions: mirror the return of shares via buying/selling puts and calls
- Buy Call, Sell Put
- Buy Put, Sell Call
synthetic purchase of shares
synthetic selling short
Option premium = Intrinsic Value (𝐶𝑎𝑙𝑙[𝑆 − 𝑋] 𝑃𝑢𝑡[𝑋 − 𝑆 ])-Time Value
Time value: approach expiration date, time value -> 0
OVERVIEW OF DERIVATIVES MARKETS
Derivative Contract: value is derived from an underlying product (shares, interest rates, currency)
-
Forwards contracts: obligation to buy/sell at agreed price at agreed date
Futures Contracts: a forward contract in standard form with no negotiation
Swap Contracts: obligation to exchange one cash flow stream for another
Option Contracts: holder of the contract has the right, but not the obligation, to buy/sell the
instrument at agreed price at agreed date
Derivative markets are made up of different parties:
-
Arbitragers: look for mispricing and trade over small periods of time
Speculators: are interested in whether prices will rise/fall but have no vested interest in the nature
of the underlying security
Hedgers: have vested interest in the underlying security and want to use derivates to hedge their
exposure to the market.
OPTIONS MARKET
An options contract gives the holder
-
the right to buy/sell the underlying security (100 units per contract)
at or before the expiration rate
at a pre-specified exercise/strike price (the agreed price if the option is exercised)
EXERCISE PRICE X: we always exercise the option if the 𝑆 > 𝑋 (𝑐𝑎𝑙𝑙) or 𝑆 < 𝑋 (𝑝𝑢𝑡), therefore it tells us
at what share price we will exercise the option.
The holder has an option whether to exercise or not. However the seller has an obligation to sell/buy if
the holder decides to exercise the option.
A call option is an option to buy the underlying shares
A put option is an option to sell the underlying shares
American Options: can be exercised at any time up until the expiration date – more valuable and common
European Options: can be exercised only on the expiration date
PAYOFF AND PROFIT ON CALL OPTIONS
FOR THE BUYER
They have the option to buy shares, therefore they want the agreed strike price to be higher than the
current share price so the seller has to purchase the shares for them.
T: value at expiration
t: value at current period of time
Payoff on a call option buyer
𝑴𝒂𝒙(𝑺𝑻 − 𝑿, 𝟎)
Net profit on a call option buyer
𝑴𝒂𝒙(𝑺𝑻 − 𝑿, 𝟎) − 𝑪 (per share)
Share price at expiration = $12, Strike Price = $10
12 − 10 > 0, therefore 𝑴𝒂𝒙(𝑺𝑻 − 𝑿, 𝟎) = 𝑺𝑻 − 𝑿 as we would exercise the option
The seller would have to buy the shares for $12 but we only pay $10 for them.
Share price at expiration = $20, Strike Price = $30
20 − 30 ≤ 0, therefore 𝑴𝒂𝒙(𝑺𝑻 − 𝑿, 𝟎) = 𝟎 and we would not exercise the option because we
would be paying $30 for shares worth $20
The payoff can never be negative (below 0) because in those cases we will not exercise the option
However the profit can be negative when we subtract the price we paid for the call option
FOR THE SELLER
The inverse of above because it is a zero sum game (a set profit has to be split between the parties)
Payoff on a call option seller
−𝑴𝒂𝒙(𝑺𝑻 − 𝑿, 𝟎)
Net profit on a call option seller
−[𝑴𝒂𝒙(𝑺𝑻 − 𝑿, 𝟎) − 𝑪] (per share)
PAYOFF AND PROFIT ON PUT OPTIONS
FOR THE BUYER
This is the right to choose whether to sell the underlying shares at the exercise price.
Payoff on a put option buyer
𝑴𝒂𝒙(𝑿 − 𝑺𝑻 , 𝟎)
Net profit on a put option buyer
𝑴𝒂𝒙(𝑿 − 𝑺𝑻 , 𝟎) − 𝑷 (per share)
𝑿 − 𝑺𝑻 > 𝟎 then 𝑀𝑎𝑥(𝑋 − 𝑆 , 0) = 𝑿 − 𝑺𝑻
𝑿 − 𝑺𝑻 ≤ 𝟎 then 𝑀𝑎𝑥(𝑋 − 𝑆 , 0) = 𝟎
FOR THE SELLER
Payoff on a put option seller
−𝑴𝒂𝒙(𝑿 − 𝑺𝑻 , 𝟎)
Net profit on a put option buyer
[𝑴𝒂𝒙(𝑿−𝑺𝑻 Net profit on a put option seller
−[𝑴𝒂𝒙(𝑿 − 𝑺𝑻 , 𝟎) − 𝑷] (per share)
MONEYNESS OF CALL AND PUT OPTIONS
What the share price is relative to the exercise price at a point in time (t or T)
At the money
𝑆ℎ𝑎𝑟𝑒 𝑃𝑟𝑖𝑐𝑒 𝑺𝑻 = 𝐸𝑥𝑒𝑟𝑐𝑖𝑠𝑒 𝑃𝑟𝑖𝑐𝑒 𝑿
In the money: When it is profitable for the buyer to exercise the option at the current price
Call Option: 𝑆ℎ𝑎𝑟𝑒 𝑃𝑟𝑖𝑐𝑒 𝑺𝑻 > 𝐸𝑥𝑒𝑟𝑐𝑖𝑠𝑒 𝑃𝑟𝑖𝑐𝑒 𝑿
𝑺𝑻 − 𝑿 > 𝟎
Put Option: 𝑆ℎ𝑎𝑟𝑒 𝑃𝑟𝑖𝑐𝑒 𝑺𝑻 < 𝐸𝑥𝑒𝑟𝑐𝑖𝑠𝑒 𝑃𝑟𝑖𝑐𝑒 𝑿
𝑿 − 𝑺𝑻 > 𝟎
Out of the money: When it is not profitable for the buyer to exercise the option at the current price
Call Option: 𝑆ℎ𝑎𝑟𝑒 𝑃𝑟𝑖𝑐𝑒 𝑺𝑻 < 𝐸𝑥𝑒𝑟𝑐𝑖𝑠𝑒 𝑃𝑟𝑖𝑐𝑒 𝑿
𝑺𝑻 − 𝑿 < 𝟎
Put Option: 𝑆ℎ𝑎𝑟𝑒 𝑃𝑟𝑖𝑐𝑒 𝑺𝑻 > 𝐸𝑥𝑒𝑟𝑐𝑖𝑠𝑒 𝑃𝑟𝑖𝑐𝑒 𝑿
𝑿 − 𝑺𝑻 < 𝟎
Deep: when the difference between 𝑺𝑻 and 𝑿 is large
Breakeven price: Share Price 𝑺𝑻 where the profit to the buyer and to the seller is 0
Call Option: 𝑺𝑻 = 𝑋 + 𝐶
Put Option: 𝑺𝑻 = 𝑋 + 𝑃
SPECULATIVE POSITION: CONFIDENT PRICES WILL RISE (BULLISH) BUT
WANT TO MINIMISE DOWNSIDE RISK
BUYER PERSPECTIVE
They buyer thinks that the share price will go up, in which case they will make their profits
(However they want to protect themselves against the possibility that prices will go down)
SELLER PERSPECTIVE
They have to respond to what the buyer chooses to do with the option.
They will make profits if the buyer decides not to exercise.
The seller expects that the share price is going to fall (because then they will keep the premium)
HEDGING WITH OPTIONS
Before we did speculative purchasing where we had expectations for the rise/fall of share prices.
Hedging is when we have existing exposure to the underlying shares which we now work to reduce.
Ie. We own the shares already or we have sold shares short and we want to protect ourselves against loss.
HEDGING AGAINST FALLS IN SHARE PRICES
To hedge exposure we need to purchase a put option so we have the option to sell the shares for a
specified price.
HEDGING AGAINST RISES IN SHARE PRICES
To hedge our exposure to rises in price we need to purchase a call option so we have the option to buy
the shares back at a specified price
PUT CALL PARITY AND SYNTHETIC POSITIONS
Synthetic positions reflect the underlying shares of the company without purchasing the actual shares. We
can use it if short selling/purchasing is expensive or isn’t allowed in a market.
FACTORS AFFECTING EQUITY OPTION PRICES
The price of the underlying share, exercise price and time to expiration determine the price of an option.
Option Premium (price) = Intrinsic value (IV) + time value (TV)
Intrinsic Value: value by which the option is within the money
Call option
Put Option
𝐼𝑛𝑡𝑟𝑖𝑛𝑠𝑖𝑐 𝑉𝑎𝑙𝑢𝑒 = 𝑆 − 𝑋
𝐼𝑛𝑡𝑟𝑖𝑛𝑠𝑖𝑐 𝑉𝑎𝑙𝑢𝑒 = 𝑋 − 𝑆
The lowest intrinsic value is 0 (ie. can’t be negative value)
Time Value: total option premium - intrinsic value
As we approach the expiration date the time value of the option will approach 0 and on the expiration
date the time value is 0.
AN INCREASE IN:
Current Price S
Exercise Price X
Time to expiration T
Volatility of prices 𝝈
Risk-free interest rate 𝒓𝒇
AS A BUYER, RESULTS IN THE VALUE OF A…
CALL OPTION
PUT OPTION
Increasing
Decreasing
Decreasing
Increasing
Increasing
Increasing
Increasing
Increasing
Increasing
Decreasing
Expected dividends 𝑫
Decreasing
Increasing