finance notes

FINS1613 Business Finance Semester 2 2009

Version 1.0.0

12th

October 2009

Business Finance Semester 2 2009 2

Contents

Page 3 Basic Concepts

Page 7 Introduction to Financial Mathematics

Page 10 The Valuation of a Firms Securities

Page 14 Capital Budgeting

Page 18 Capital Budgeting Applications Part 1

Page 23 Capital Budgeting Applications Part 2

Page 26 Risk and Return

Page 29 The Capital Asset Pricing Model

Page 32 Cost of Capital and Raising Capital

Page 38 Capital Structure

Page 42 Dividend Policy

Note: This course has prerequisites and, as such, these notes are written

assuming that you have sound knowledge from those prerequisite courses.

Basic Concepts


Basic Concepts

Background

Before we delve into the harder components of business finance, it is imperative that we

learn the basics first.

Types of Business Forms

If you have previously studied Business Studies for the HSC, you can skip this section.

Businesses are usually formed based on a set structure. The most common of these are:

Sole Proprietorships

This is where the business is owned by a single person. It is very simple, fast to

establish and generally has very minimal government regulations. The owner gets to keep

all the profits himself so there is incentive to work harder.

The downside is that it has unlimited liability (where if the business goes bankrupt,

everything the owner owns can be taken by creditors). There is also difficulty in raising large

sums of money as you are a single person. Since the business profits are also the owners

profits, there is no distinct line between personal income and business income. The

business will only generally last as long as the owner is alive or wants to run it.

Partnerships

This is generally the same as a sole proprietorship except that there is more than

one owner. It generally has the same advantages and disadvantages as a sole proprietorship

does.

Corporations

A corporation is a legal entity. That is, it is treated like a person. In this sense,

there is limited liability for the owners as the creditors will only be able to extend as far as

the entity itself is (ie. Just the business). It differs from the two forms above in that the

owners are generally not the people who are running the business; the managers are.

It is advantageous in that it is much easier to raise funds than other forms; and

ownership can be transferred easily and, as such, has an unlimited life. Its disadvantages

are that there are many processes that must be completed to form a corporation and these

take a lot of time and money. The earnings of the corporation are also liable to corporate tax.

It is possible that some businesses may be a hybrid of a selection of the above. Generally, a

business will pick a structure that suits their needs and has the most advantages for them.

Financial Management Decisions

Decisions relating to financial management can be split into two broad categories. These are:

The Investment Decision

This is the decision is also sometimes known as capital budgeting. This is the

decision that is made on how to move effectively use raised funds to generate revenue for

the firm. This could be a decision on which project to take etc.

Basic Concepts


The Financing Decision

This is the decision about how to structure the firms capital (Capital Structure) such as how

much debt and equity they should be using to fund long-term investments. This also includes

working capital management which is the decision for the short-term to ensure the firm has

enough liquidity to use in daily operations.

The Goal of Financial Management

The goal of financial management is ultimately to maximise the value of the firm to

shareholders. That is: increasing shareholder value.

Shareholders of a business generally want an increase in value through:

Increases in capital gains (share price increase)

Dividend payments

Since both of these are generally related to the performance of a firms shares, the goal of

financial management is sometimes shortened to, maximising the firms share price.

A firm may have intermediate goals while they are trying to achieve shareholder value

maximisation. This may include, but is not limited to:

Employee Safety

Ethics (Corporate Governance)

Environmental Issues

Local and/or International Society

The Agency Problem

If you have previously studied ACCT2522, you can skip this section.

The Agency Problem is the problem associated with the division of ownership and

management in corporations. The corporation is meant to be maximising shareholder value but

management may run the company to maximise their own benefits instead of the owners. This

problem does not exist in business forms such as the sole proprietor or the partnership because the

owner is the manager in these forms.

This problem creates agency costs which are the costs associated with managers acting in

ways which do not maximise shareholder value. These costs can be either direct or indirect. Direct

costs are costs associated with monitoring and setting contracts with managers while indirect costs

arise when value maximising investments are rejected by managers.

The agency problem can be addressed to a certain extent with internal mechanisms such as:

Utilising a Board of Directors that consists of both executive (managers from within the

business with good knowledge of business workings) and non-executive members (people

from the outside who do not have very good knowledge of the business but bring in a third

party perspective to decisions).

Basic Concepts


Shareholder meetings. These can be grounds for a proxy fight where shareholders vote to

get rid of current management and replace them with new people if they do not like how

they are currently handling the corporation.

Compensating management with share options instead of bonuses. This means that

management is getting compensated based on the value of the firms shares meaning that

managers will take options to maximise shareholder value.

Setting up Corporate Governance.

Some external mechanisms are:

The threat of hostile takeover. Firms that perform poorly in terms of maximising

shareholder value are usually very attractive takeover targets. When a takeover does

happen, management is usually fired and as such, it is in the managers best interest to keep

shareholder value up to prevent this from occurring.

Corporate Governance

If you have previously studied ACCT1511, you can skip this section.

You can also read the Page 37 of ACCT1511 Course Notes for more information.

Corporate Governance is defined as the framework of rules, relationships, systems and

processes within and by which authority is exercised and controlled in corporations, by the ASX.

The objective of corporate governance is to:

Create value through innovation, development and different values for different companies.

Provide accountability and control systems so we know who is responsible for the firm, to

whom, in what ways, how and why they are there.

The Board of Directors is a part of corporate governance and acts as the mediator between

the shareholders and management, usually because management considers what is best for them,

and not what is best for the shareholders. The Board of Directors acts to protect the interests of

shareholders by exerting a controlling force inside the corporation.

More Agency Problems

From the above, we note the agency problem exists between the managers and the owners.

However, there are also agency problems between any entity that has a financial interest in the firm

such as debtholders, employees, customers, suppliers and even the government.

As such, debtholders usually place controls over loans (called loan covenants) which limit

something the things the company can do in favour of the debtholder. These can be in the form of:

Limit on total debt level allowed

Restrictions on dividends

Required level of debt-to-equity

Failure by the corporation to adhere to these covenants can trigger the debtholder to

immediately ask for full repayment.

Basic Concepts


Primary and Secondary Markets

If you have previously studied FINS1612, you can skip this section.

The primary market is the market for which the original sale of financial securities occurs.

You can think of this as the first hand market, such as when you buy a brand new item from a

store. These are usually either public offerings (sale to the public) or private placements (sale to few

select buyers).

The secondary market is where issued financial securities are traded again. Think of this as

the second hand market where youre simply buying again from people who have previously

bought it from a shop.

Introduction to Financial Mathematics



Background

Finance is all about the numbers. Hence, we need to know how to be able to get these

numbers to be able to provide an accurate analysis for things such as capital budgeting.

The Time Value of Money

A dollar today is worth less than a dollar tomorrow. This is the fundamental principle of

the time value of money. This holds because you can take that dollar you have today, deposit it in a

bank, gain interest on that dollar and it will be worth more tomorrow, even if it is by a few cents.

Example:

I have $100 today and invest it in a one year term deposit at 8% p.a. In one years time, I

would have $108. However, if I had not invested it, I would still have $100.

Some definitions we need to know:

Present Value (PV)

This is the value of the money you have today. ($100 in the above example)

Future Value (FV)

This is the value of the money you have at a specified future date. ($108 in the above

example)

Interest Rate (r)

This is the rate at which the money is invested in. (8% in the above example)

Thus we can see that our initial investment will grow at the rate of (1+r). Thus we can imply:

FV = PV(1+r)

Taking our last example FV = 100(1+0.08) = 108

Multi-Period Investments

Our previous example only took into account one period. If we are to take into account

multiple periods, we need to distinguish between simple interest and compound interest.

Simple interest only gives interest based on the principle. However, compound interest gives

interest based on the principle plus all interest received to date on that investment.

Example:

Following on from the previous example, simple interest would only give interest based on

the principle. That is, over 3 years, we would get: 100(1 + 0.08 x 3) = $124. However with compound

interest, in 3 years we would get: 100(1 + 0.08)3 = $125.97.

The formula for Simple Interest is: FV = PV (1 + r x t)

The formula for Compound Interest is: FV = PV (1 + r)t



From the example, we can see how compound interest will always give more return than

simple interest as it calculates interest based on principle plus previous interest. The difference

between simple interest and compound interest, holding everything else constant, will grow bigger

as periods increase.

Present and Future Value of T Multi-Period Investments

In the following, C is the cash flow, r is the interest rate and t is the time period. Also, the

following are:

, = 1 + 1

, = 1 1 +

Multi-Period investments include:

Annuities

Continual cash flows occur at the end of each time period.

= , = , Annuities Due

Continual cash flows occur at the beginning of each time period.

To find these, simply take the appropriate annuity formula and multiply by (1+r).

Deferred Annuities

A delayed annuity where the first cash flow occurs at k periods later.

= ,1 + Perpetuities

A annuity that is expected to last forever (i.e. No maturity date)

= Where C1 is the first cash flow and g is the rate at which

Growing Perpetuities

A perpetuity that has cash flows which grow at a constant rate.

= Where C1 is the first cash flow and g is the rate at which the cash flows grow at.

Uneven Cash Flow Investments

Where cash flows are not the same each period.

To calculate this, we have to individually take each cash flow and discount it back to the

present or future.

Compounding Periods

Not all investments compound yearly. They could compound semi-annually, quarterly,

monthly, weekly, daily and even continuously. To change the interest rate, we simply divide it by the

number of payments per year. i.e. We divide by 12 if it is compounded monthly. We must also

remember to multiply the time period (t) by the number of compounding periods per year.



To compare rates that have different compounding periods to each other, we can convert

them to effective annual rates. What this does is convert the said interest rate to a rate which, when

compounded yearly, gives the same figure as the other.

This is done with the following formula:

= !1 + "#$ 1

Example:

We have a rate which is 9% p.a. which is compounded monthly. To find the effective annual

rate: = %1 + 0.0912 *

+ 1 = 9.38% This means that we can either:

Compound monthly at 9% p.a.

Compound yearly at 9.38% p.a.

And we would get the same result in the end.

The Valuation of a Firms Securities



Background

A firm is valued by looking at both:

The present value of cash flows generated by the firms productive assets (such as plant,

equipment etc.)

The present value of the sum of cash flows generated by the firms securities.

Knowing that the assets must equal the liabilities plus equities, we can infer that:

V = D + E

Where:

V is the present value of cash flows generated by the firm.

D is the present value of cash flows generated by debt securities.

E is the present value of cash flows generated by equity securities.

Debt vs. Equity

Firms have a choice of using debt and/or equity financing. The majority of firms will use both

types but most will have different levels of both debt and equity. This is usually based on the firms

needs and wants because both debt and equity have their advantages and disadvantages.

Debt Equity

Do not gain ownership of the firm Gain ownership of the firm

Do not gain voting rights in the firm Gain voting rights in the firm

Interest is tax deductible Dividends are not tax-deductible

Must repay interest and principal amounts Dividends do not have to be paid

First claim if the firm goes bankrupt Residual claim if the firm goes bankrupt

Bonds

Bonds are debt instruments that are issued for periods greater than one year. Those that are

issued for periods of less than one year are known as commercial bills.

Bonds have a face value and coupon rate. The principle is generally repaid at maturity date

while coupons are paid semi-annually at the coupon rate. The coupon rate can be a:

Fixed-coupon

The coupon rate is fixed for the entire term of the bond.

Floating rate

The coupon rate is adjusted according to the market interest rate periodically.

Zero-coupon

There are no coupons paid. However, these are usually sold at discount to the face value of

the bond so that some interest is still made.



The coupon payment is the par value multiplied by the coupon rate (annually). Since it is

usually paid semi-annually, the effective yearly rate is usually slightly higher than what is stated.

Extra Features of a Bond

A bond also includes a trust deed which is a contract between the issuer and holder

detailing everything about the bond such as amount of bonds, covenants (if any), call provisions and

sinking fun provisions.

Call provisions allow the issuer to repurchase bonds at any date prior to maturity. Since the

holder will generally lose out on the remaining coupon payments, issuers will generally pay an

amount higher than the face value to compensate for this. If the call option is deferred, it is not

allowed to be exercised before a certain date.

Bonds can also have a sinking fund provision. A sinking fund provision is where a certain

amount/percent of the bonds principle is also retired (i.e. repaid) each year. While this is less risky

because the principle is repaid along the way until maturity and not all at maturity, the coupon

amounts get smaller and smaller as the principle decreases.

Valuating a Bond

Looking at the structure of a bond, we can see it has two major components:

The face value

The coupon payments

The face value can be discounted back to the present to find its present value. The coupon

payments can be treated as if it were an annuity since we get paid at set periods and at set amounts.

When we discount this annuity and add it to the present value of the face value, we can determine

the bonds current value. By doing this, we can find out how much the bond is worth now.

For a zero-coupon bond, this is made easier as we can eliminate the entire coupon annuity

calculation since there are no coupons to begin with.

Bonds can be classified as:

Par bonds (FV = Bond Value)

Discount bonds (FV > Bond Value)

Premium bonds (FV < Bond Value)

Interest Rate Risk

Fluctuating interest rates are a risk for investors. This risk increases as the time to maturity

increases and the value of coupons decreases. This is the cause of two effects known as:

Reinvestment Effect

The reinvestment effect is concerned with the time to maturity. If you had two identical

bonds but the only difference was that one was a 10 year bond and the other was a 1 year

bond, would it be better to invest in one single 10 year bond now (and thus lock in the



interest rate) or invest in 1 year bonds each year (and thus have a different rate each year).

We must note that the interest rate may rise or decline each year so the 1 year bonds would

be better if they rose, but would not be if they declined. This is a choice and risk that the

investor has to make.

Price Effect

The price effect is concerned about the fact that a bonds value will change in terms of yield

as a result of changed in the interest rate. A rising interest rate means the value of the bond

will drop. This risk is greatly magnified the longer the term of the bond is and the lower the

coupon rate is.

The Term Structure of Interest Rates

The relationship between interest rates and time to maturity is known as the term structure

of interest rates and is graphically represented by the yield curve.

However, this general curve would only be correct if we looked at securities which had no

default risk and if inflation did not exist. To compensate for these, we have the:

Inflation Premium

This is the extra increase in interest rates as a result of future expectations of a rising

inflation. The higher the expectation for an increase, the larger the premium is.

Interest Rate Risk Premium

This is the extra increase in interest rates as a result of default risk. The higher the risk of

defaulting is, the higher the premium must be to compensate for this. Usually this increases

as time to maturity increases as the risk of default increases.

Liquidity Premium

There may also be a premium as a result of cash being locked up in an investment. Usually,

this will increase the longer the time to maturity is as cash is locked up for longer.

Shares

Shares are equity instruments that give the holder ownership rights of the firm in question.

Shares can either be:

Ordinary Shares

Ownership of these gives voting rights and residual claim in event the firm goes bankrupt.

Preference Shares

These do not give voting rights to the owner but they do have preferential rights to any

dividends. The dividend, however, can be omitted.

The market value of a share is how much the market believes that the company is worth.

Dividends are payments that are made to shareholders and can be in the form of either cash or

more shares. The dividend growth rate is the rate at which dividends are expected to increases each

year. In most cases, dividends do not grow at constant rates.

We will eventually find that the price of a share is essentially just the present value of all

expected future dividends from the firm.



Dividend Valuation Models

There are different dividend models based on how dividends are expected to grow. These

are:

Constant Dividend

This is where the firm pays a consistent dividend, such as 10c each year. To calculate the

present value of this, we simply use the perpetuity formula (dividend divided by return rate)

as we see this constant dividend as one without maturity.

Constant Dividend Growth

This assumes that the firm will pay a dividend that grows at a certain amount each year,

such as 1%. To calculate this, we use the formula: PV = Dt+1 / (R - g). Where g is the rate at

which dividends grow.

Inconsistent Dividend Growth

This assumes that dividends will be inconsistent for a few years before it becomes consistent

for the remainder. To calculate this, we simply find the present value of the inconsistent

cash flows and the present value of the constant period afterwards. This means using both

the above models together.

Estimating g, the Growth Rate

Most companies will not disclose information such as dividend growth rate. As such, we

must come with ways of estimating them. One approach is to take the firms:

Earnings per share (EPS)

Dividends per share (DPS)

Return on equity (ROE)

From this, we can see from EPS, exactly how much goes into DPS. The difference between

EPS and DPS is how much the company retains in its coffers as retained profit. We assume that this is

reinvested at the companys ROE which would turn into EPS growth. Adding this EPS growth back

onto EPS and repeating the cycle, we can estimate how much the growth rate of dividends will be.

Simply in a formula:

G = (1 payout ratio) x ROE

The payout ratio is the ratio of funds that are dividends. i.e. A firm that has an EPS of 100c

and has a DPS of 50c, the payout ratio is 50/100 which is .

Capital Budgeting


Capital Budgeting

Background

Capital budgeting is also known as the investment decision. That is, finding out which

projects the company should undertake. This section introduces a range of tools to use to help

decide which project is the most ideal for a company.

The Capital Budgeting Process

Capital budgeting is important to a business because it is a large initial outlay of capital to

gain long-term benefits. This means that there is a huge potential for failure and thus, a proper

process must be used. It is as follows:

1. Generate Project Proposals

2. Screen Projects

3. Evaluation

4. Implementation and Control

5. Post-Implementation Audit

For this course, we mostly focus on the evaluation part of the process.

Types of Projects

Projects can generally be classified into four categories, these being:

Replacement

These projects are done to replace things that are already running in the business, such as

worn out/old machinery, re-training staff etc.

Expansion

These projects are done to expand the business such as going into new markets or

expanding on existing products and markets.

Safety and Environmental

These projects are undertaken to ensure compliance with government regulation. These

projects will not always provide positive cash flows for the firm, but they still must be

undertaken to ensure compliance.

Other

These are other projects that do not fit into the above three. For these, we analyse using the

best techniques for that specific project.

Independent and Mutually Exclusive Projects

Independent projects are projects that, when accepted or rejected, will have absolutely no

impact on any other project under consideration. However, mutually exclusive projects are projects

that, when accepted or rejected, can have impacts on other projects. Most of this is due to resource

limitations and capital rationing. This is because the company does not have enough resources or

budget to do all projects respectively, so taking one project means another must be rejected. Such

Capital Budgeting


as if we only have one piece of land, we cannot run two projects if each must use the entirety of that

piece of land.

Contingent projects are those that are dependent on the acceptance or rejection of another

project. They can be further classed as complementary or substitute projects.

Complementary projects are those where the acceptance of another project would further

increase cash flows in the originally accepted project. If a project is to be undertaken only if another

is accepted, this is known as a purely complementary project.

Substitute projects are the opposite of complementary projects in that accepting one

project would impair on the cash flows of another project.

Evaluation

Evaluation is done by:

1) Forecasting predicted cash flows from the project.

2) Determining the level of risk of cash flows.

3) Applying evaluation methods.

In this course, we generally look at applying evaluation methods and assume the cash flows

predicted and the risk level are appropriate.

Accounting Rate of Return

This method uses accounting book values to find out the return on invested physical capital

such as machinery. To use this method we find the average net profit of the firm (after depreciation

and tax) over the life of the project. We also need to find the average book value of capital (after

depreciation) over the life of the project. We then apply the following formula:

AAR = Average Net Income / Average Invested Capital

The decision to accept or not depends if the projects are independent or mutually exclusive.

The decision rule for independent projects is to accept projects with an AAR which is larger than the

target set by the company. For mutually exclusive projects, the rule is to select the project with the

higher ARR.

The advantage of using ARR is that data can be easily obtained by looking through the

financial statements of the company. It is also very easy to calculate once you have the data and it

also takes into account income over the entire life of the project.

The disadvantage is that accounting numbers are generally not overly reflective of real cash

flows because they are done on an accrual basis. This method also ignores the time value of money

in that it assumes cash flows later are worth the same as cash flows now. The benchmark value is

also very arbitrary as it can be set to any value.

Capital Budgeting


Payback Rule

The payback rule simply looks at how long it takes for the investment to return the invested

capital back into the company. To use this method, we simply cumulatively add up cash flows from

the beginning until the figure equals or is greater than the initial invested amount. If it breaks even

in the middle of a year, we assume the flow of cash flows is spaced evenly throughout the year so

that we can find exactly when during that year that we will break even.

Example:

We have an initial investment in a project of $100,000. The cash flows in each year

afterwards are $50,000, $30,000, $30,000, $20,000 and $20,000.

Adding these figures slowly, we get $50,000 then $80,000 then $110,000. We can see that

we breach $100,000 somewhere between year 1 and 2. To accurately find when we can divide as

follows:

($100,000 - $80,000) / ($110,000 - $80,000) = $20,000 / $30,000 = 2/3.

This means we break-even at 2/3rds of the way through year 2, meaning the payback period

is 2.67 years.

For independent projects, we accept any project that is below a target maximum payback

period. For mutually exclusive projects, we choose the one with the shortest payback period.

The advantages of the payback method are that it is simple to use, interpret and has a clear

decision rule.

The disadvantages are an arbitrary payback period benchmark since it can be set to

anything with no real reason. It also ignores all cash flows after the payback period is done, so it is

bias towards projects that regain capital back earlier.

Discounted Payback

This method is an extension of the payback method and attempts to eliminate one of its

disadvantages; that it does not take into account the time value of money. This method is exactly

the same as the previous except that we discount all the cash flows before adding them.

It has the same advantages and disadvantages as the payback method except that it no

longer has the disadvantage that it now does take into account the time value of money.

Net Present Value

The Net Present Value (NPV) Method is a method of simply summing up all of a projects

forecasted discounted cash flows.

For independent projects, we accept the project if its NPV is positive. For mutually exclusive

projects, we choose the one with the highest NPV.

Capital Budgeting


The advantages to NPV are that it has a simple and clear decision rule that is not arbitrary (it

is set and cannot be changed). It can also incorporate risk with a higher discount rate and with this,

takes into account the time value of money. It also takes into account all cash flows generated

throughout the life of the project and correctly ranks projects based on its ability to maximise

shareholder wealth.

The disadvantages are that cash flows are forecasted, so there is a level of risk involved

there. It is also difficult to choose an appropriate discount rate to use. Managers that have no

knowledge of finance also find it hard to grasp the concept of discounting cash flows.

Profitability Index

This method is similar to NPV except that it ranks projects in relative terms. This is so it isnt

biased towards projects with large cash flows. We simply take the NPV and divide it by the initial

outlay to find the profitability index.

For independent projects, we accept if it is higher than 1. For mutually exclusive projects, we

select the one with the highest index.

This is very similar to NPV and usually leads to the same conclusion as if we used NPV.

Capital Budgeting Applications Part 1



Background

So far, we have looked at a few tools we can use to evaluate projects. In this section, we

introduce another two. These are the Internal Rate of Return (IRR) and the Modified Internal Rate of

Return (MIRR).

The Internal Rate of Return

The Internal Rate of Return (IRR) is closely related to the NPV in that the IRR is the discount

rate which, when used to find the NPV of a project, would cause the NPV to equal zero. That is, it is

the projects expected rate of return.

The decision rule for IRR is to accept if the IRR is larger than the hurdle rate (the required

rate of return on the project) for independent projects. This is for an investment project only. For a

financing project, we would need to reverse this decision rule so that we accept the project if the IRR

is lower than the hurdle rate. For mutually exclusive projects, we simply take the project with the

highest IRR.

The formula for calculating IRR is exactly the same as NPV. All we do is set NPV to equal zero.

The equation can only be solved by either using a financial calculator, a spreadsheet or by trial and

error.

The advantage to IRR is that it is very closely related to NPV, normally leading to identical

conclusions. The added bonus is that an interest rate is very intuitive to any manager, unlike NPV.

The disadvantage of IRR is that its hard to find by hand. However, with the advent of

computers, this disadvantage has disappeared in almost all situations. The more pressing problem is

that it assumes interest rates will stay fixed and that cash flows returned back at the beginning of

the project can be reinvested somewhere else at the same rate, which in some cases, is ridiculous to

even contemplate. Sometimes, you can also end up with two IRRs which confuse people.

Multiple Internal Rates of Return

Multiple IRRs result from projects that have both positive and negative future cash flows.

These are considered non-conventional because conventional projects have an initial negative cash

flow followed by a series of positive inflows.

The best way to go about solving this issue is to plot an IRR diagram. By plotting this diagram,

we will be able to see regions where the IRR is positive. Only in these regions should we accept the

project. In all other cases, we should reject the project.

However, in such cases with non-conventional cash flows, we should simply revert to using

NPV as it provides a more reliable result compared to IRR in such a situation.



Comparing IRR and NPV

The NPV of a project at different discount rates can be graphed. When graphed, the value at

which the NPV curve reaches zero NPV is the point where the projects IRR is.

The Crossover rate is the discount rate at which both Project A and Project Bs NPVs are

equal. In the case of mutually exclusive projects, we would take Project B at any discount rate under

the crossover rate and we would take Project A for any discount rate above the crossover rate.

In this situation, if you computed the IRR to find the project with the highest IRR, you would

find that Project A has the higher IRR. However, if you were undertaking this project at a rate which

is lower than the crossover rate, you would be undertaking the wrong project because at rates lower

than the crossover rate, Project B prevails. Thus, it is better to calculate NPV in these situations at

your desired rate of return to confirm your IRR result.

IRR and the Scale and Time Problems

With mutually exclusive projects, the IRR can usually lead to incorrect results and is usually

skewed towards projects on a lower scale and projects that recoup most of their cash flows in early

periods.

To rectify this problem, we need to find the incremental cash flows and then, find the

incremental cash flows NPV and IRR. This means we take the cash flows of the larger project and

deduct the cash flows of the smaller project.

By doing this, if we find that the NPV and IRR are positive for the incremental cash flows, we

should accept the project if it is a scaling problem. We would find that the IRR of the incremental

cash flows is actually the crossover rate of both projects. In this case, we follow our previous rule

and accept the better project based on whether it is above or below the crossover rate.



The Modified Internal Rate of Return

The Modified Internal Rate of Return (MIRR) is similar to the IRR except that it assumes that

cash flows are not reinvested at the IRR rate but instead, at normal discount rates. The MIRR will

also not generate more than one result.

The MIRR works by finding the discount rate at which the present value of a projects costs

equals the present value of the projects terminal value. As such, we can deduce that the formula is:

/ = % 01233*$ 1

Here, TV is the terminal value which means the future value of all cash inflows of the project.

The decision rule is to accept the project if the MIRR is larger than the hurdle rate for

independent projects and to choose the project with the highest MIRR with mutually exclusive

projects.

The advantages to MIRR are that is it similar to IRR but does not generate multiple rates in

the event of non-conventional cash flows. It also assumes that the cash flows are reinvested at the

discount rate, not the IRR rate.

The disadvantage of MIRR is that the calculation is more complicated than other capital

budgeting evaluation tools. It also does not account for different project life spans. When comparing

projects, to ensure that the period is the same, the project with the smaller life span has its missing

years filled with cash flows of zero to compensate.

Forecasting Cash Flows

The majority of capital budgeting evaluation tools require cash flow forecasting. The only

one that does not require this is the AAR. This means that forecasting cash flows is a very large part

of evaluation and is also very crucial to the evaluation as it relies on these forecasted cash flows.

In reality, forecasting cash flows is not as easy as it sounds as there are many factors that

must be taken into account.

When looking at cash flows, we only consider:

Free cash flows

Incremental cash flows only

The timing of cash flows

Inflation

Tax

Free Cash Flow

Free cash flow is the actual cash flow from a project that is available for distribution to other

parties (such as shareholders, debtholders etc.) after all necessary expenses have been deducted

from it. This differs from accounting cash flows as it is not based on the accrual system.



Free cash flow can be determined by:

EBIT + Depreciation Taxes Capital Expenditures Change in net operating working capital

In here, we:

Include the cost of fixed assets

Include non-cash expenses

These provide a tax shield and should be included.

Includes changes in net operating working capital

Found by taking current assets and deducting current liabilities from it.

Ignore financing expenses

The cost of financing is already accounted for in the cost of capital and does not need to be

counted again.

Incremental Cash Flows

Incremental cash flows are cash flows that result from undertaking a project. A relevant

cash flow is one that only results when a project is accepted. All other cash flows are irrelevant and

should be discarded. To this end, we:

Include opportunity costs

These are costs that result from undertaking the project. The assets dedicated to this project

could have otherwise been used on other projects.

Ignore sunk costs

Sunk costs are unavoidable and should be ignored. They will be incurred or have been

incurred regardless of whether the project has been accepted or rejected.

Consider side effects

We need to consider side effects of taking a project. Such as introducing a new product may

degrade the sales of an existing product the company already sells. Such side effects need to

be included.

Need to be aware of allocated overhead costs

Timing of Cash Flows

It is important to note the timing of cash flows so that they can be properly discounted. If we

do not, then we are basically ignoring the time value of money and would skew the result of

evaluation.

Inflation

Inflation is the general downward trend of the purchasing power of money. To account for

inflation, we must discount actual or nominal cash flows using the nominal rate of return. The Fisher

effect can be used to convert nominal rates to real interest rates and vice-versa. The equation is:

(1+rn) = (1+rr)(1+p)

rn is the nominal rate, rr is the real rate and p is the inflation rate.



Tax

Tax is an outflow of cash and needs to be deducted from operating cash flows to find a

firms free cash flows. Three taxes which are relevant to us are:

Goods and Services Tax (GST) Usually 10%

Corporate Income Tax Usually 30%

Capital Gains Tax Varies

GST can generally be disregarded as firms gain GST from selling their products which they

then give to the government. The only exception is in the finance industry as GST cannot be levied

on financial products. Thus, financial firms need to include a GST component in cash payments for

external transactions.

Corporate Income Tax is paid on assessable income (income minus any deductions).

Depreciation, although it is a non-cash expense, must be taken into account as they provide a tax

shield for the company. As always, after-tax cash flows should be discounted at the required rate of

return. For consistency, we should apply the same rate of return for tax and cash flows.

Note that we also get a tax shield or a liability when we sell assets at any price other than its

carrying value.

Capital Gains Tax is paid on any changes in the real value of an asset when it is sold. A real

increase only occurs if the value of the asset rises more than inflation. We treat this as a normal cash

outflow.




Background

The previous sections looked at different tools we can use to evaluate projects. In this

section, we look at more minute details dealing with cash flows.

Forecasting Cash Flows

The cash flows that are forecasted by a company are usually split into three broad categories.

These are:

Initial Investment Outlay

These are cash flows that occur at time zero.

Operating Cash Flows & Net Working Capital

These are cash flows that occur between time zero and the end of the project.

Terminal Cash Flows

These are cash flows that occur at the end of the project such as selling off assets the project

used etc.

By taking into account these three types of cash flows, we can work out net annual cash

flows to use in calculations such as with NPV analysis.

Evaluating a Project with Forecasted Cash Flow

When we look at forecasted cash flows, our first step is usually to sort out what costs are

what. Any assets we buy at the beginning of the project are generally initial investment outlays etc.

Our first step in the entire analysis is thus, to work out the initial outlay. Most importantly,

remember to take into account the required net working capital in year zero as well.

The next step is to work out the operating cash flows and net working capital required

throughout the life of the project. Remember to take into account depreciation and any other

requirements the business has.

The final step is to work out the terminal cash flows. These cash flows are those that result

at the very end of the project such as when we sell off assets used in the project and that we no

longer have a need for. When selling off assets, remember to also calculate the tax saving or liability

that may result when we sell the asset at a different price to its book value. It can also include any

net working capital that was unused.

We can then use these forecasted, and grouped, cash flows in evaluating projects and thus,

select the best project to undertake.

Projects with Unequal Lives

When we have two projects with unequal lives, we cannot compare them properly as the

evaluation results will be skewed. To fix this issue, we can look at two different methods.



The two methods are:

The Equivalent Horizon Approach

With this approach, we assume that we can start the project again with the same

resources/cash flows after it has ended. As such, we can stack these projects end on end

until they both have a common life span. For example: If we had a project with a 3 year life

and a 4 year life, we would expand this out so that the lifetime is 12 years by doing the 3 year

project 4 times and the 4 year project 3 times.

The Equivalent Annuity Approach

In this method, we take the cash flows of the entire project and split them out evenly over

the lifespan of the project. In this way, we can see how much of a return the project gets in

each period (we compare each period now). In this approach, we would select the one with

the higher approach.

Qualitative Factors

One should not only look at quantitative factors that we get from our analysis. There are

qualitative factors that may cause a company to take a project with a lower return such as:

Environmental issues

Government Legislation

Social Consequences

Staff

Corporate Image

Other than this, a firm should also investigate where it gets its positive NPV. It may be

because the firm has a comparative (or competitive) advantage in the market or because the firm

made an error in forecasting cash flows. In any case, a positive NPV should always be double

checked to ensure its authenticity.

A firm should see if such comparative advantages in the market are sustainable in the future

if it impacts on the project. When does the patent run out? When will competitors react? We have

to ask such questions when considering how much cash flow our comparative advantage can give.

To avoid errors in forecasting cash flows, we should use risk analysis and real options

analysis.

Project Risk Analysis

The more risky a project is, the more uncertain the cash flows that the project generates is.

Risk can thus, be incorporated into a project by using a higher discount rate that has been adjusted

to include risk.

Another method is to apply techniques to analyse the sensitivity of the projects NPV to

changes in assumptions in the project (such as assumptions in inflation, taxes etc.) The three

techniques that can be used to do this are the sensitivity analysis, scenario analysis and the

simulation analysis.



The sensitivity analysis measures the impact that the change of one variable has on NPV.

This is done by simply recalculating NPV after changing one variable. However, this technique is

often limited because most underlying variables in NPV analysis are interrelated with each other.

The scenario analysis is similar to the sensitivity analysis except that it alters more than one

variable at a time. We usually do three different scenarios which are the worst case, base case and

best case. This gives an idea of the overall risk of the project.

The simulation analysis is normally done by a computer. The computer selects random

variables and randomly changes them based on assumptions given. This process is repeated many

times and the NPV is calculated each time. From these calculated NPVs, we can find their statistical

means, standard deviation and also the probability of getting a negative NPV.

Note that we should not incorporate risk into the discount rate while doing these analyses.

This is because the whole point of it is to find risk, and if it is already incorporated into it, we are

effectively double counting risk.

Real Options Analysis

NPV analysis does not take into account that managers of a company can change the project

based on the fact if a project is going well or not. Managers could expand the project further if its

doing well or just scrap the entire project if it is failing. A firm could also wait to start a project

instead of starting it right away if there is any reason where waiting would be better than starting

immediately.

These real options can be put onto a tree diagram and be used to physically view different

situations. The probability of each outcome is used in the NPV calculation so that the NPV takes into

account the risk of that particular circumstance occurring. The expected NPV is simply the NPV

generated through that circumstance multiplied by the probability rate.

Risk and Return


Risk and Return

Background

Risk is tied to return in that the larger the amount of risk, the higher the required return is.

In this section, we look at the relationships between risk and return.

Returns on Investment

A return on investment is the profit that is expected to be made when an investment is

made. The return on investment can be measured by:

Dollar Returns

The dollar return is simply the profit made on the investment. That is, we find the amount

received from the investment and deduct the amount invested. Usually when we use this

method, we need to also look at the scale and the length of the project.

Rate of Return

The rate of return is found by simply taking the dollar return and dividing it by the amount

invested. This expresses the dollar return as a percentage which can help us since we do not

need to worry about the scale of the project as much.

Risk and Return

As mentioned, risk and return are related in that the return on investment must be sufficient

enough that the investor is willing to take the risk associated with the investment.

Risk is defined as the probability that actual results will differ from expected results. Risk is

usually measured by using probability. This is usually done by making a payoff matrix. It allows us to

calculate the expected rate of return.

To find the expected rate of return, we simply multiply the estimated rate of return in that

scenario with its probability. We repeat this with all other scenarios and then add them up to get the

expected rate of return.

Example:

Company A wants to invest in Company B. It has done some research and reached the

following conclusion:

There is a 20% chance of a recession occurring and the rate of return would be 3%.

There is a 50% chance of the economy staying the same and the rate of return would be 12%.

There is a 30% chance of a boom occurring and the rate of return would be 20%.

The expected rate of return would thus be:

(0.2)(0.3) + (0.5)(0.12) + (0.3)(0.2) = 0.18

This means the company should expect an 18% p.a. return on investment from Company B.

Risk and Return


Risks

Standalone risk can be measured by using the standard deviation. The standard deviation

tells us how far a distribution of values moved from its expected value (average). To find the

standard deviation, we need to know the expected value and the other values in the distribution.

The standard deviation itself is just the square root of the variance. Thus, to find variance,

we:

Take the expected value and minus from it a value, square the result and multiply it by the

associated probability if there is any.

Repeat the above step for all other values.

Sum all the values together.

To get the standard deviation, simply square root the result from the above steps.

The larger the standard deviation is, the more risky an investment is because it is a measure

of how varied the returns can be. Remember that risk is the chance that the actual differs from the

expected. Thus the larger the variation is, the larger the risk.

If, by chance, the standard variations of two projects are the same, we can calculate the

coefficient of variation to help decide between the two. The coefficient of variation is calculated by

taking the standard deviation and dividing it by the expected return of that project.

The lower the coefficient of variation, the lower the risk is.

Realised Return

The realised rate of return is how much the investment actually makes. This will always be

different from the expected rate of return unless you have invested in risk free assets.

We can use historical realised rates of return to predict future expected rates of return. We

do this by finding the standard deviation like we did before but instead, we base this on the previous

realised rates of return.

However, after summing all the values together as we do in finding the standard deviation,

we need to also divide the summed value by the number of observations minus one before we

square root it. That is, if we have 5 values, we divide the summed values by 4 instead.

Portfolio Returns

Usually, an investor holds more than one stock. This means the portfolios expected return

will be different from each stock. To find this, we must first find the weight each stock has on the

portfolio. This is found by dividing the value of the stock by the total value of the portfolio. We then

multiply this by the expected return of that stock. Repeat this step for all other stocks and sum them

together to get the portfolio return.

The portfolios standard deviation is:

45+ + 4+5++ + 244+6+55+

Risk and Return


Risk Aversion

Some investors do not like taking on a lot of risk. These investors are known as risk adverse

investors. Risk adverse investors will not take on risky investments unless there is a higher expected

return. This is known as the risk premium; the extra amount of return required because the

investment is risky.

More formally, the risk premium is known as the extra return required over the risk-free

rate of return.

Correlation between Stocks

The level of correlation between two stocks can be found by finding the covariance with the

following formula:

Covariance = 12 1 2

Where 12 is the correlation between the two stocks. Rearranging this formula, we find that

the correlation is equal to the covariance divided by the standard deviations of both stocks.

To find the correlation, we find:

The return on investment of one security during the same time interval.

Deduct the mean return on investment of that security.

Repeat the above two steps with the other security and multiply the two results.

Repeat the above three steps with all the other time intervals.

Sum all the results and divide by the number of observations minus one.

The result we get is the covariance. The covariance measures the amount of association

between the two stocks. That is, how similar they are.

The covariance result we get is always between -1 and 1. A positive result means that both

stocks will move in the same direction while a negative result means the stocks will move in opposite

directions.

In reality, most stocks are positively correlated.

Diversifiable Risk and Market Risk

Risk can be divided into two major components, these being:

Diversifiable Risk

This is risk that can be diversified away by investing in many stocks. Generally, these are risks

of each individual investment.

Market Risk

This is risk that cannot be diversified away as it affects in entire market. This can be risk such

as the state of the economy and the price of oil.

The Capital Asset Pricing Model



Background

The Capital Asset Pricing Model (CAPM) is an extension to better understand risk. It

theorises the relationship between market risk and the expected return on an investment.

The Systematic Risk Principle

The systematic risk principle states that because unsystematic risk (diversifiable risk) can be

diversified away, a well diversified portfolio will have only systematic risk (market risk).

Thus, the expected return on an investment only depends on that assets market risk. This

means that an investor will only be rewarded for taking investments with diversification. The

investor will not be rewarded for taking on firm-specific risk since it can be diversified away.

Risk Premium and Risk

In general, a well diversified investor will only expect a risk premium to be available for

systematic risks. There would be no risk premium for unsystematic risk as it can be diversified away

instead.

Systematic risk is generally less than unsystematic risk and, as a result, the risk premium for

systematic risk is generally lower. The diversified investor usually has to accept a lower return.

Beta

Beta is the measure of systematic risk. It shows the correlation between movements in the

market and movements in the stock. A beta of:

1 means that the stock will move exactly the same as the market does.

Above 1 means the stock will move more than the market does.

Less than 1 means the stock will move less than the market does.

The average stock has a beta of 1. This is because the stock market indices are a formulated

using all or selected stocks in the market. Beta can be calculated by taking the standalone risk,

dividing it by the risk of the market and then multiplying by the correlation coefficient.

The beta of a portfolio is simply the weighted average of all the betas of the stocks in that

portfolio.


The Capital Asset Pricing Model (CAPM) is a theory that tries to explain the relationship

between beta and the expected return on an asset. This is mostly done by using the Security Market

Line (SML) which is a graphical representation of the CAPM. This is a line on a graph that depicts the

level of risk premium for an asset can be estimated by taking the stocks beta and multiplying it by

the market risk premium.



The Security Market Line

The Security Market Line (SML) as mentioned above, states that the level of risk premium

for an asset can be estimated by taking the stocks beta and multiplying it by the risk premium.

Mathematically:

k = kRF + x RPM

Where: k is the required return on the asset, kRF is the risk free asset, is the beta for the

asset and RPM is the market risk premium.

A companys position on the line is thus, vulnerable to being changed based on the above

factors such as change in the companys beta and changes in risk aversion. The companys beta can

be changed by changing their capital structure or through changes in industry and competition.

However, we must note that inflation and interest rates also play a role in shaping a companys

position on the SML.

Inflation and the Security Market Line

As mentioned above, inflation

impacts on the SML. Inflation decreases

purchasing power and therefore, causes an

increase in the risk-free rate. An increase in

the risk-free rate means that there will also

be an increase in the rate of return.

Simply, the line shifts upwards on

the SML diagram (from the green line to the

red line). The line shifts upward by the

expected level of inflation.

Risk Aversion and the Security Market Line

When the level of risk aversion

increases, the slope of the SML becomes

steeper. This is because as people become

more risk adverse, they will require a higher

rate of return the more risky the asset is.

On the SML diagram, the curve

simply becomes steeper (from the green

line to the red line). The risk free rate level

stays the same however.

Capital Asset Pricing Model Uses

The CAPM allows us to easily:

Benchmark portfolio performance



Identify under or overvalued assets

Estimate the cost of capital which can then be used in other analysis (such as NPV)

However good the CAPM is though, it has its disadvantages:

Heavy reliance on estimation from historical figures for inputs.

Beta estimation issues. The beta may not always be constant and stable.

It is a model that looks into the future using past data.

The CAPM also assumes that there is a positive relationship between returns and beta and

that beta is the only thing that explains returns. In reality, there could be a variety of other factors

that could influence the expected return on an asset.

Cost of Capital and Raising Capital



Background

Previously, we have looked at ways of spending capital and how to most efficiently do so. In

this section, we look at the cost of capital of an asset and raising the necessary capital to fund it.

Cost of Capital

The cost of capital is the amount of capital that the entity has to spend to invest in an asset.

Contrary to popular belief, the cost of capital is dependent on how the capital is going to be used. It

does not depend on where we get the capital from.

Capital can be gained from:

Equity

Hybrids

Debt

Estimating the Cost of Capital

The cost of capital can be estimated by using the weighted average cost of capital (WACC).

This is the weighted average of the rate of returns required by investors who have invested in the

securities that the firm has issued. The WACC formula is as follows:

7 = %8 :: + * + %;

: + * Where: RE is the cost of equity, RD is the cost of debt, E is the market value of equity

financing and D is the value of debt financing.

Example:

If a firm has $2,000 of equity which costs 10% per year and $5,000 of debt which costs 8%

per year, the firms WACC would be:

7 = %0.08 5,0002,000 + 5,000* + %0.1 2,000

2,000 + 5,000* = =. =>?@ This means that the average cost of capital is 8.57% p.a.

The Cost of Debt

The cost of debt is the rate of return which is required by the firms creditors. Note that this

is not necessarily the prevailing interest rate as debt securities can be issued at a discount which

affects the rate of return. This can be found by:

Finding the Yield-to-Maturity on outstanding bonds

Finding bond yield and then adding risk premium



Looking at financial statements

The first method of finding the cost of debt is more preferable to the other two methods if it

is feasible. The financial statements are only moderately accurate because they use past data.

Estimating the Yield-to-Maturity on Outstanding Bonds

This method is found by simply utilising our bond formula that we learnt previously. Recall:

AB"C DE = 1 1 + + 1 + The cost of debt here is actually the discount rate used (r). So by determining r, we can

estimate the yield-to-maturity on outstanding bonds. However, the value of the bond can be hard to

determine as corporate bonds are not usually frequently traded amongst investors.

Estimating Bond Yield and Adding Risk Premium

This method is very simply in that it finds the risk-free bond yield by simply looking at

government bonds with the same maturity. These are concluded to be risk-free as the government

can never default. We then add a few percentage points based on the firm to allow for a risk

premium. This level depends on how risky the firm is. It is only really useful for large corporations

who have very stable debt levels.

Estimating by looking at the Financial Statements

This method is done by finding the net interest (interest paid minus any interest received)

and dividing it by the carrying value of all debt in the financial statements minus any cash.

Note that this approach assumes that the debt we hold is at market value and that we

would be holding it forever (i.e. perpetuity). Thus it will be skewed if the debt we hold is not at the

current market value.

The Cost of Equity

The cost of equity is the minimum rate of return required by the firms owners. This can be

found by using either the dividend growth model or the CAPM.

Estimating with the Dividend Growth Model

Since we can easily find the market price of a firms shares on the share market, we can

simply use the following formula to find the discount rate.

= :F + Where D1 is the dividend in the first year, P0 is the current price of the shares and g is the

dividend growth rate. The dividend growth rate is estimated by using historical growth rates and/or

analytical forecasts.



This analysis is easy; however, not all companies always pay out dividends. To date,

Microsoft has not paid a single dividend in the entire entitys life. Many companies also never pay

dividends. Even if a company does pay dividends, it may not always be constant or constantly

growing which further serves to weaken this method. It is also very sensitive to the growth rate and

it does not adjust for risk.

Estimating with the CAPM

To estimate with the CAPM, we use the following formula:

; = G + H;[; G] Where E(RE) is the required return on equity, RF is the risk-free rate, E is the equity beta and

E(RE-RF) is the required return on the market above the risk-free rate.

Its strength lies in the fact that it can adjust for risk and applies to all stocks since it does not

need to use dividends as a measurement. Its weakness is that it uses historical data and the beta

estimates may be incorrect.

Estimating the Risk Premium

While we have estimated the cost of equity or capital, we also need to estimate the risk

premium. This can be found by looking at:

Historical values for returns on the stock market. This assumes that realised returns will

equal expected returns and is thus, not very reliable in times of economic instability.

Current stock prices and forecasts. This is done by using a formula which is very similar to

the dividend growth model:

= :F + Where: r is the equity cost of capital, D1 is the forecasted dividend next year, P0 is the

current price of the stock and g is the expected growth rate of the stock.

Note that this method assumes that the forecasts are accurate. If not, they will lead to

deviations.

Issuing New Shares

Instead of digging into the firms retained earnings (its equity stash), the firm can issue new

shares. This is preferable when equity funding is required but there are not enough retained

earnings.

Issuing new shares can either be done using:

Initial Public Offerings (IPOs)

Seasoned Equity Offerings (SEOs)

Rights Issues

Private Placements



Each of these is aimed at different shareholders but all of them have the same goal, to raise

equity by issuing shares.

Issuing shares, however, is a very complicated procedure and a lot of the equity raised is

actually used to cover the costs of the complicated procedure. An investment bank is usually hired to

do the work for the company wanting to issue new shares. These costs need to be taken into

account and usually include:

Management fees

Administrative fees

Portions of management salaries

Underpricing

Underwriting fees (if applicable)

The formula used here is the same as the constant dividend growth model except that the

price per share also includes flotation costs (i.e. 1-F where F is the flotation cost in terms of a

percentage).

The Consistency Principle

Inflation and taxes should be treated consistently. This means nominal cash flows should

always equal the nominal rate while real cash flows should also equal the real rate. The same tax

bracket should be applied to every aspect to ensure that it is consistent.

Taxes

Taxes impact on almost every aspect of finance. Under the classical tax system, taxes are

paid on all aspects on income. This means the shareholder is taxed on the dividend itself and taxed

again as it is a part of personal income. Effectively, this means dividends are double taxed.

However, under an imputation tax system, any tax the firm has made on behalf of the

shareholder can be used by the shareholder as franking credits. This means the shareholder only has

to pay the difference and not the entire tax sum. It effectively eliminates double taxation.

Incorporating Tax into the Weighted Average Cost of Capital

How we incorporate tax into the WACC is entirely dependent on whether we are using a

classical system or an imputation system.

Under a classical system the appropriate before-tax WACC is:

7 = 8 % :[: + ]* + %;[1 01]* %

[: + ]*

Where: TC is the corporate tax rate of the firm.

If we want to find the after-tax WACC, we simply multiply through by 1-TC. You can simply

memorise the above formula and multiply it through by 1-TC to save memorising the following:



7 = 8 [1 01] % :[: + ]* + ; %

[: + ]* Under an imputation system, the appropriate before-tax WACC is:

7 = 8 % :[: + ]* + K;1 01[1 L]M %

[: + ]*

Where: L is the franking credits the shareholders use. The after-tax WACC is the same except that we multiply through by (1-T*C). This is the

effective tax rate after interest to yield corporate tax is paid.

Capital Budgeting with the Weighted Average Cost of Capital

The WACC itself is a measure of the average cost of capital for the firm as a whole. Therefore,

when we use the WACC in new investments, we assume that this new investment is similar to what

the firm has and is currently undertaking; most importantly, in terms of risk. The WACC can only be

used for projects that have the same typical beta that other projects in the firm have, otherwise it is

unusable.

Thus, instead of using the WACC, we use the Project Cost of Capital instead. This is first

done by looking at project risk.

Project Risk

Project risk can be defined in three ways:

Standalone Risk

This is the risk of the project in isolation. It is not affected in anyway by any of the firms

other undertakings. This risk will usually not alter the firms beta coefficient.

Corporate Risk

This is the risk that the project has to the firm itself. It is possible that this investment

actually lowers risk due to diversification.

Market Risk

This is the risk to a well diversified investor in the market. This is measured by seeing how

much of an impact the project will have on the firms beta coefficient. It is, however, the

most difficult to estimate.

After we have evaluated the projects risk level, we can use one of two methods.

Subjective Approach

This is where risk is split into levels (such as high, medium, low etc.) and an appropriate pre-

determined discount rate is applied to it. While this method may not be very accurate, it is very

quick to determine.



Security Market Line Approach

This method takes the SML equation and states that the required rate of return on the

project is equal to:

G + HNO + G Where Rf is the risk free rate, RM is the market return and A is the projects beta. The

problem here lies in how to find the projects beta. We can find it by either using the Pure Play

Method or the Accounting Beta Method.

The Pure Play Method

This method is done by simply looking at other companies that are very similar to the firm in

question. We then estimate the equity betas of those companies and find the average beta. We can

then use this beta in the above formula to find the projects cost of capital.

This method is very useful if the project is not similar to other projects the firm is

undertaking but is only really useful for large projects. Suitable firms to compare to may also be hard

to find.

The Accounting Beta Method

In this method, the beta is estimated by regressing the firms accounting return against a

large number of other firms.

Capital Structure


Capital Structure

Background

The capital structure of a company is the proportion of debt, equity and hybrids used to

comprise the firms financing on investments. Every firm has their own optimal capital structure

and a targeted capital structure by management. Note that the targeted capital structure does not

necessarily have to be the optimal one.

Questions

When looking at a firms optimal capital structure, we have to ask ourselves many questions

including:

How much should the firm borrow?

How much should it raise through shares?

How much equity should be raised internally or externally?

Should the firm seek loans directly from investors or through intermediaries?

Should the firm underwrite a share issue?

These questions can be answered by looking at some capital structure theories.

The Financial Leverage Effect

The financial leverage effect basically states that as companies increasingly finance assets

with debt, shareholders face greater levels of financial risk. Financial risk is the risk associated with

financing and financing with debt carries higher risk than financing with equity. We will discuss this

in the theories to follow.

The Modigliani and Miller Theory (M&M Theory)

The Modigliani and Miller Theory is split into two. One is where there is a perfect capital

market and the other is where there is an imperfect capital market. It assumes that:

There are no taxes or transaction costs

Information is freely available

There are no bankruptcy costs

Firms all have the same business risk but different gearing ratios

Fixed investment policies

All cash flows and projects are perpetual.

There are no capital constraints (unlimited borrowing/lending at same rate for everyone)

No agency conflicts

No asymmetric information (i.e. no signals)

The theory proposes that, the firm is valued based on its expected earnings applied at a risk

level of an all equity firm. The use of homemade leverage proves this idea because an investor can

always change their leverage on a personal level to lower risk.

Capital Structure


Another proposition the theory makes is that the WACC is independent of the firms capital

structure. This means no matter how much or little debt the company has, WACC will not change.

Thus our formula is very simple. The value of a leveraged (VL) and unleveraged (VU) firm is

the same.

P = Q M&M Theory with Taxes

We now relax the assumption that there is no tax. The M&M theory thus proposes that firm

value increases as debt increases because debt provides a tax shield. Interest is tax deductible and as

such, reduces the amount of tax the firm pays compared with equity financing. The present value of

the tax shield is the amount of debt multiplied by the corporate tax rate. This is true because we

assume that all cash flows are perpetual (as stated above).

With tax, the expected return on equity will increase as more debt is added to the firm.

However, the rate of increase is lowered due to the presence of tax.

In this theory, the optimal capital structure is one that has 100% debt. This is because the

more debt there is, the larger the tax shield is. Note that this theory uses a classical tax system. If the

imputation system is applied, the advantage is lessened.

Thus our formula now incorporates the tax shield from debt denoted by TCD.

P = Q + 01: Static (Trade-Off) Theory

The Static (Trade-Off) Theory follows on from M&M Theory with taxes except that it now

relaxes another assumption, that there are no bankruptcy costs. The reason why a 100% debt firm

was the most optimal before was because there were no bankruptcy costs.

As the firms level of debt rises, bankruptcy costs increase as risk increases. Bankruptcy costs

are costs that arise from financial distress within the firm. There could be loan covenants placed on

the firm which will not allow anymore debt as lenders could see the firm as highly risky. As such,

managers will tend to not have too much debt as it could detrimentally affect the business.

The optimal structure here is one that balances the tax shield benefit from debt and

bankruptcy costs. This means the firm should try to keep debt at a level where for each extra dollar

of debt, tax shield savings equals bankruptcy costs. It should not increase debt to a point where for

each extra dollar of debt, bankruptcy costs are greater than tax shield savings it generates.

Thus our formula now incorporates the present value of bankruptcy costs as denoted by

PVBC.

P = Q + 01: R1

Capital Structure


Free Cash Flow Theory

The Free Cash Flow Theory, yet again, relaxes another assumption. This time, we assume

there are agency costs. Agency costs exist because managers and shareholders have a conflict of

interest. A well diversified investor usually only has a very small part of their portfolio in the firm

while managers have their entire portfolios at stake on the firm. As such, managers may be too risk-

averse or, on the contrast, may over invest.

Debt financing reduces the agency costs associated with equity. This is because shareholders

like debt more than equity. However, debt financing increases the agency costs associated with debt

holders. This is because the cost of acquiring and maintaining debt increases.

Thus our formula now becomes:

P = Q + 01: R1 + N1S N1T Signalling Theory

The Signalling Theory drops another assumption. Different people know different things and

thus, there is information asymmetry; unlike M&M theory where information is freely available.

In reality, management obviously knows more information than any investor on the market.

There is information that they would also not tell anyone else such as possible new plans and trade

secrets. Anyone that does trade on this knowledge is an insider trader and is subject to prosecution.

As such, investors in the market look for signals when management acquires new debt or

equity. When debt is acquired, it gives a positive signal that the firm is confident about its future

prospects. This is because to acquire debt, a firm knows it can finance that debt and repay it within

that period of time.

If a firm issues equity, it signals that the firm is taking advantage of overpriced equity to

benefit existing shareholders. This is because equity is more sensitive to mispricing than debt is. It

also signals to investors that the firm is not confident enough to raise debt finance and thus, possibly

has bad prospects.

With such possible signals, management always need to consider what signal they would be

sending to the market by raising either debt or equity. It has been shown that this is a great

influence on the type of finance that managers raise.

Pecking Order Theory

Pecking Order Theory notes that managers are far more inclined to use internal financing

before looking at external financing. This is because internal financing does not send out any bad

signals to investors. As such, the theory establishes an implied order of most preferred to least

preferred methods of financing.

1. Internal Funds (Retained Earnings, cash and marketable securities)

2. Issue Debt

3. Issue Hybrids

Capital Structure


4. Issue Equity

Capital Structure Theories and Reality

In reality, there is no one theory that can specify what the optimal capital structure for a

firm should be. Looking at real data, we see that different firms in different countries and industries

can have completely no debt at all to almost completely debt financed.

Thus, each firm should look at its own business risk levels, asset characteristics, industry, tax

position, financial performance etc. to find its optimal capital structure. This being said, surveys

indicate that most firms have either no capital structure target or have a very flexible one indicating

that most firms simply take what is appropriate when required.

Most firms also take less debt on so that they have financial flexibility. This means that when

they really require debt, they have the capacity to take on that debt instead of increasing financial

risk to a point where bankruptcy is more probable.

Dividend Policy


Dividend Policy

Background

Dividends are the payments a firm makes to its investors from retained earnings. A firm has

choices into how much and what type of dividends they should deliver or if they should even deliver

dividends at all.

Cash Dividends

Cash dividends are pretty self explanatory; the company gives out cash to shareholders.

There are four different types of cash dividends; these being:

Regular

Payments the firm regularly makes at set intervals.

Extra

Additional payments that may be repeated.

Special

Additional payments that will not be repeated.

Liquidating

Payments as a result of the firm liquidating.

Dividends are first declared by the company and from that day, shares trade with the

dividend entitlement (cum-dividend) until four days before the record date. This is because share

trades are settled 3 days after the trade on the ASX so four days is the required time. Four days

before the record date, shares sell ex-dividend (with no dividend entitlement). The ex-dividend price

of the share is expected to be the cum-dividend price minus the dividend per share.

Dividend Irrelevance Theory

The Dividend Irrelevance Theory was developed by Modigliani and Miller (the same people

who proposed the M&M theory in Capital Structure). It states that dividends are irrelevant because

firm value is defined by its earning power and business risk, not its dividends.

As with before, this theory comes loaded with assumptions:

Perfect capital markets

No tax

No transaction costs

Information is widely and freely available

Investors are price takers and rational

Investors all have the same wants and needs

Investment decisions are not affected by dividend decisions

No agency costs

This theory also states that shareholders are indifferent to dividend policy because they can

use a homemade dividend policy by reinvesting dividends that have been paid out or selling shares

Dividend Policy


off. Thus, an investor will not want to pay more for a share with high dividends than one with low

dividends.

The Tax Preference Theory

Generally, the assumptions made in the dividend irrelevancy theory are wild in that there is

no way it is possible to assume in reality

finance notes

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