Bfc2140 hd weekly summary notes PDF

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INTRODUCTION TO CORPORATE FINANCE AND FINANCIAL MATHEMATICSWHAT IS CORPORATE FINANCEThe Financial Management function is centred around corporate finance, which attempts to find the answers to the following questions: - What investments should the firm take on? o THE INVESTMENT DECISION - How can ca...

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BFF2410 TOPIC 1 INTRODUCTION TO CORPORATE FINANCE AND FINANCIAL MATHEMATICS WHAT IS CORPORATE FINANCE The Financial Management function is centred around corporate finance, which attempts to find the answers to the following questions: •

What investments should the firm take on? o

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How can cash be raised for the required investments? o

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THE INVESTMENT DECISION

THE FINANCE DECISION

How should wealth be redistributed to shareholders? o

THE DIVIDEND DECISION

Corporate Objective •

Primary goal is to maximise the value of the firm, which is same as maximising shareholder wealth.

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Every decision that we make as financial managers needs to come back and answer this question o

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“Have we added value?”

If the answer is “yes” the we should undertake the decision If the answer is “no” then we should not!

It’s all about the CASH •

A firm can generate cash flow by selling goods and services produced by productive assets or generated via human capital

•

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The firm can then opt to; o

1) pay remaining cash (residual cash flow) to the owners (or shareholders); or

o

2) reinvest back into the company for growth.

Accounting profits are not the same as cash flow, leave accounting to the accountants! o

Why? Profit maximisation ignores size; timing and risk associated with receipt of cash

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TIME VALUE OF MONEY (FINANCIAL MATHEMATICS) “ A dollar today is worth more than a dollar tomorrow. ” •

The difference in value between money received today and money received in the future

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Two different cash flows at two different points of time have different values

Some important concepts Stream of cash flows •

A series of cash flows lasting several years

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Cash flow = C

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Negative amounts are outflows

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Positive amounts are inflows

SINGLE SUM OR LUMP SUM CASH FLOWS Simple Interest Simple Interest is determined by multiplying the interest rate by the principal by the number of periods.

Interest = Principal x periods x interest rate Future Value (Compounding Techniques) The total amount due at the end of the investment is called the Future Value (FV) and involves compounding interest.

Interest is received on accumulated interest from previous periods as well as on the principal; that is, interest generates further interest.

FVn = C × (1 + r)n Where •

(C) is the cash flow at date 0,

•

(r) is the appropriate interest rate, and

•

(n) is the number of periods over which the cash is invested.

Future Value Interest Factor FVIF Determination 2

(1 + r)n is also called the future value interest factor •

FVIF is the FV of 1 dollar at r% per annum after n periods

•

Future value is due to the number of periods in which interest can be compounded. The larger the number of periods, the greater the future value.

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Future value also depends critically on the interest rate - the higher the interest rate, the greater the future value

Present value (Discounting Techniques) The use of discounting techniques aids in finding the current dollar amount of a given future value.

The general formula for the present value of a multi period case for a single cash flow can be written as:

where •

(PV) is the cash flow at date n=0,

•

(r) is the appropriate interest rate per period,

•

(n) is the number of periods over which the cash is invested.

Present Value Interest Factor PVIF Determination

1/(1 + r)n is also called the present value interest factor •

PVIF is the PV of 1 dollar at r% per annum after n periods

•

Present value is due to the number of periods in which interest can be discounted. The larger the number of periods, the smaller the present value.

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Present value also depends critically on the assumed interest rate (discount rate) - the higher the interest rate, the smaller the present value.

The Rule of 72 •

If you earn r% per year, your money will double in about 72 /r years.

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For example, if property sales grow at 10% per year, it takes about 7.20 (=72/10) years to double your investment. 3

INTEREST RATES Nominal Interest Rates •

The nominal interest rate (NIR) is known is also known as the annual percentage rate (APR) and is simply the stated, or quoted, rate (e.g., 10% pa compounded annually)

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The NIR is simply equal to the interest rate charged per period multiplied by the number of periods per annum.

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For example, if a bank charges 1% per month on a car loan, the NIR is 1% x 12 = 12%

Compounding Frequency •

So far, compounding frequency has been assumed to be annual. In reality compounding frequency is greater than one in any given period

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m is the frequency of compounding in a period

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r is the stated/quoted annual interest rate, and is commonly called the nominal interest rate.

Compounding Periods Compounding an investment m times a year for n years provides for future value of wealth:

Effective Annual Interest Rates •

The EAR (or effective annual yield) is the true interest rate expressed as if it were compounded once per year:

•

Where o

r = the quoted annual interest rate

o

m = the number of compounding periods in a year.

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Continuous Compounding •

Frequency of compounding (or discounting) within a period of time approaches infinity (i.e., interest is charged so frequently that the time between two periods approaches zero)

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Interest is compounded instantaneously

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Where o

C = the cash flow

o

n = the number of periods

o

r = the one-period interest rate

o

e = 2.71828182846, a constant ( base of natural logarithms – also known as Euler’s constant)

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TOPIC 2 FINANCIAL MATHEMATICS MIXED STREAM (OR MULTIPLE) CASH FLOW PATTERNS Future Value of a Mixed Stream •

The approach to calculating the future value of a known mixed stream involves a two step process and requires value additivity. o

Step One: Calculate the future value of each future amount to be received at a comparable point in time.

o

Step Two: Sum all future values at a comparable point in time together to determine the future value of the known mixed stream

Present Value of a Mixed Stream •

The approach to calculating the present value of a known mixed stream also involves a two step process and once again requires value additivity. o

Step One: Calculate the present value of each future amount to be received at a comparable point in time (usually t=0).

o

Step Two: Sum all present values at a comparable point in time to determine the present value of the known mixed stream.

PERPETUITY •

A perpetual cash flow stream of equal amounts, equally spaced in time.

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In other words, a cash flow pattern where the owner receives a regular (FIXED) payment, at a regular (FIXED) point in time FOREVER!

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The formula values cashflows ONE period BEFORE the first cashflow

ANNUITIES •

An annuity is a cash flow amounts, equally spaced in period of time (i.e. 6 years).

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In other words, a cash flow pattern where the owner receives a regular (FIXED) payment, at a regular (FIXED) point in time for a known (FIXED) period of time.

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ORDINARY ANNUITY (Annuity in arrears) o

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ANNUITY DUE (Annuity in advance) o

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Pays a constant amount at the END of each period for a finite number of periods.

Pays a constant amount at the BEGINNING of each period for a finite number of periods.

IMPORTANT Always assume the annuity is ORDINARY thus If nothing is said about the timing of cash flows. ALWAYS assume the cash flow occurs at the END of the period.

Ordinary Annuity •

The first C occurs at the end of the first time period:

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The time period from the date of valuation to the date of the first C is equal to the time period between each subsequent C

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The time period from the date of valuation to the date of the first C is equal to the time period between each subsequent C

Present Value – Ordinary Annuity Formula

Future Value – Ordinary Annuity Formula

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Annuity Due •

An annuity where the first PMT occurs immediately:

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Also known as an annuity in advance.

Value of an Annuity Due

Applications of Annuities •

Equivalent Annuities o

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Growth Annuities o

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unequal life problem

Cash flows that increase each year at a constant rate

Loan Amortisation o

paying off your mortgage

Ordinary Annuity vs Annuity Due

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Growth Annuity •

A growth annuity is an annuity for which the cash flows increase at a constant rate over time.

Loan Amotisation •

Amortised loan - requires the borrower to repay both the principal and interest over time (usually, the amount paid each period is equal)

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TOPIC 3 VALUATION OF BONDS AND EQUITIES BOND VALUATION What is a Bond? •

The ASX defines a bond as: o

“A tradeable debt security, usually issued by a government or semi-government body to raise money. Holders of the bond have lent money for which they receive a fixed rate of interest over a set period of time. The bond is repaid with interest on the predetermined maturity date. Bonds can be traded on the sharemarket.”

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It makes part of the “right hand side” of the balance sheet o

A = L+ E

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Specifically forms part of debt (liabilities)

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Large companies also commonly issue bonds to raise funds in the market.

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Investors therefore lend their money to the company and receive interest payments (called coupons) until such a point in future where the bond matures and the principle isrepaid.

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There are 2 cash flow streams associated with bonds: o

1. Repayment of principal at maturity (value stated on bond)

o

2. Coupon interest payments throughout the life of the bonds.

As with anything else the price of the bond today is simply the PV of all future cash flows.

Valuation of Bonds and Equities •

The Principle: Intrinsic: Value o

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The value of financial securities = PV of all expected future cashflow

Thus, to value bonds or stocks, we need to o

o

Estimate future cash flows: ▪

Amount (how much) and

▪

Timing (when)

Then discount future cash flows at an appropriate rate: ▪

The rate should be appropriate to the risk associated with the security.

Definition and Features of a Bond •

A bond is a certificate showing that a borrower owes a specified sum (the principal / face value)

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Features and notation: o

Coupon payments (CPN): The stated interest payments. Payment is constant and usually payable every year or half year.

o

Coupon rate: The annual coupon divided by the face value.

o

Face value or par value (FV): The principal amount repayable at the end of the term.

o

Maturity (n): The specified date at which the principal amount is payable.

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o

Required Return on Bond (y): the return demanded by a bondholder for investing in a debt security given it’s level of risk.

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Bond issuer o

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Bond holder o

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Person who issues the bond and must repay the face value at maturity, i.e. the borrower

Person who holds the bond certificate and will receive the face value at maturity

A bond is a tradeable financial instrument o

i.e. a bond can be bought and sold

Cash Flows for a Bond •

•

Notation: o

Coupon (CPN or C)

o

Face Value (FV or F)

o

Time to Maturity (n)

Cash flows of a typical bond

Important to realise That a bond will therefore trade many times in its life AND The price will change very regularly.

Bond Value

Note y here is yield – similar to i. It is really a proxy for the required rate of return to debt holders, the cost of debt.

Pure Discount (Zero Coupon) Bonds •

Information needed for valuing pure discount bonds: o

Time to maturity (n) = Maturity date - today’s date

o

Compounding frequency (m)

o

Face value (FV)

o

Discount rate (y)

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Present value of a pure discount bond at time 0:

Coupon Bonds •

Information needed to value coupon bonds: o

Coupon payment dates and time to maturity (n)

o

Coupon payment (CPN) per period and face value (FV)

o

Discount rate (y)

The Effective Annual Yield Interest rates should always be quoted on an annualised basis. Recall that the effective annual interest rate EAR measures the return of $1 in one year.

Bond Yields •

Yield to maturity is the interest rate that equates a bond’s present value of interest payments and principal repayment with its price. –

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This can be viewed as follows.

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o

“The YTM measures the average rate of return obtained by investors if the bond is purchased now and held until maturity and if there is no default on any of the promised payments.”

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There is an inverse relationship between market interest rates and bond price.

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Why? Because the bond price is a present value and there is always a negative relationship between PV and interestrates.

YTM and Bond Value •

When YTM < coupon, the bond trades at a premium

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When YTM = coupon, the bond trades at par

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When YTM > coupon, the bond trades at a discount

Interest Rate Risk •

Interest rate risk is the risk that arises for bond owners from unexpected changes in interest rates.

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All other things being equal, the greater the time to maturity, the greater the interest rate risk.

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All other things being equal, the lower the coupon rate, the greater the interest rate risk.

Bond Concepts (Summary) 1. Bond prices and market interest rates move in opposite directions 2. When coupon rate = YTM, price = par value. When coupon rate > YTM, price > par value (premium bond) When coupon rate < YTM, price < par value (discount bond) 3. A bond with longer maturity has a higher relative (%) price change than one with shorter maturity when the interest rate (YTM) changes. All other features are identical. 4. A lower coupon bond has a higher relative price change than a higher coupon bond when the YTM changes. All other features are identical.

EQUITY VALUATION Share Valuation •

A share (or equity investment) is simply “part-ownership in a company” and form parts of equity on the balance sheet. o

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A = L+ E

In principle, shares can be valued in exactly the same way as bonds by calculating the PV of all future CFs.

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However, share valuation is more difficult than bond valuation for two reasons: o

Uncertainty of promised cash flows

o

Shares have no maturity

Ordinary Share Valuation •

The value of a share is the present value of all expected cash flows to be received from the share, discounted at a rate of return (R) that reflects the riskiness of those cash flows. 13

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The expected cash flows to be received from a share are all future dividends.

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Dividend growth is an important aspect of share valuation.

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We will consider three cases: o

Zero Growth (or Preference share valuation)

o

Constant Growth

o

Variable Growth

Zero Growth Valuation (preference share valuation) •

Shares have a constant dividend (D) into perpetuity, with no growth in dividends. This implies that: Div = Div0 = Div1 = Div2 = Div3 … …

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The value of a share (P0) is then the same as the value of a perpetuity.

Constant Growth Valuation (DDM) •

Dividends grow at the same rate each time period, g, forever.

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The value of a share (P0) is then the same as the value of a growing perpetuity.

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This is the Dividend Growth Model (an application of a growing perpetuity)

Components of Required Return

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Variable Growth Valuation •

Allows for different growth rates.

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Dividends cannot grow at a rate above the required rate of return indefinitely but can do so for a number of years.

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Dividends will grow at a constant rate at some time in the future.

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TOPIC 4 CAPITAL BUDGETING 1: TECHNIQUES FOR EVALUATION WHAT IS CAPITAL BUDGETING? •

Analysis of potential additions to fixed assets.

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Long-term decisions; involve large expenditures.

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Very important to a firm’s future.

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Capital budgeting involves: o

1. Estimating CFs (inflows & outflows).

o

2. Assessing the riskiness of CFs.

o

3. Determining an appropriate discount rate

o

4. Finding NPV and/orIRR.

o

5. Acceptance of project if NPV > 0 and/or IRR > r (WACC).

Types of Investment Decisions •

INDEPENDENT PROJECTS o

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Projects that, if accepted or rejected, will not affect the cash flows of another project.

MUTUALLY EXCLUSIVE PROJECTS o

Projects that, if accepted, preclude the acceptance of competing projects.

Types of Project Cash Flows •

Conventional CF Project (C) o

A negative CF (initial cost outlay) is followed by a series of positive cash inflows – hence there is one change of signs (-vet to +ve)

•

Nonconventional CF Projec...