Basic Concepts Introduction to Financial Mathematics The Valuation of a Firm’s Securities Capital Budgeting Capital Budgeting Applications – Part 1 Capital Budgeting Applications – Part 2 Risk and Return The Capital Asset Pricing Model Cost of Capital and Raising Capital Capital Structure Dividend Policy Copyright © Ka Hei Yeh 2009 First Edition published October 2009. Revised February 2010) This work is licensed under the Creative Commons Attribution Attribution-Non-CommercialNo Derivative Works 2. 5 Australia Licence. To view a copy of this license, visit http://creativecommons.
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Do not rely on them; these notes are not intended to serve as a replacement for your own own. Business Finance– Semester 2 2009 2 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 owner’s 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. Business Finance– Semester 2 2009 3Basic Concepts • The Financing Decision This is the decision about how to structure the firm’s 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 firm’s shares, the goal of financial management is sometimes shortened to, “maximising the firm’s 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 SocietyThe 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).Business Finance– Semester 2 2009 4 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 firm’s 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-equityFailure by the corporation to adhere to these covenants can trigger the debtholder to immediately ask for full repayment. Business Finance– Semester 2 2009 5 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 you’re simply buying again from people who have previously bought it from a “shop”. Business Finance– Semester 2 2009 6 Introduction to Financial Mathematics 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 year’s 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 •Business Finance– Semester 2 2009 7 Introduction to Financial Mathematics 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 r is the interest rate. 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. Business Finance– Semester 2 2009 8 Introduction to Financial Mathematics 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+ Example: We have a rate which is 9% p. a. which is compounded monthly.
To find the effective annual rate: = 1+ 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. 0. 09 12 ? 1 = 9. 38% ? 1 Business Finance– Semester 2 2009 9 The Valuation of a Firm’s Securities The Valuation of a Firm’s Securities Background A firm is valued by looking at both: • • The present value of cash flows generated by the firm’s productive assets (such as plant, equipment etc. ) The present value of the sum of cash flows generated by the firm’s 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 firm’s needs and wants because both debt and equity have their advantages and disadvantages.Debt Do not gain ownership of the firm Do not gain voting rights in the firm Interest is tax deductible Must repay interest and principal amounts First 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. Equity Gain ownership of the firm Gain voting rights in the firm Dividends are not tax-deductible Dividends do not have to be paid Residual claim if the firm goes bankrupt Business Finance– Semester 2 2009 10 The Valuation of a Firm’s Securities 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 bond’s 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 paymentsThe 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 bond’s 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 Discount bonds Premium bonds (FV = Bond Value) (FV > Bond Value) (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 theBusiness Finance– Semester 2 2009 11 The Valuation of a Firm’s Securities • 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 bond’s 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.
Business Finance– Semester 2 2009 12 The Valuation of a Firm’s Securities 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 firm’s: • • • 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 offers as retained profit.
We assume that this is reinvested at the company’s 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 ?.
Business Finance– Semester 2 2009 13 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. 2. 3. 4. 5.
Generate Project Proposals Screen Projects Evaluation Implementation and Control 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 Business Finance– Semester 2 2009 14 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 ook 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. Business Finance– Semester 2 2009 15 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 project’s 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. Business Finance– Semester 2 2009 6 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 isn’t 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.Business Finance– Semester 2 2009 17 Capital Budgeting Applications– Part 1 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 project’s 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 it’s 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 IRR’s 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. Business Finance– Semester 2 2009 18 Capital Budgeting Applications– Part 1 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 project’s IRR is. The Crossover rate is the discount rate at which both Project A and Project B’s 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. Business Finance– Semester 2 2009 19 Capital Budgeting Applications– Part 1 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 project’s costs equals the present value of the project’s terminal value. As such, we can deduce that the formula is: = ? 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. Business Finance– Semester 2 2009 20 Capital Budgeting Applications– Part 1 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. Business Finance– Semester 2 2009 21 Capital Budgeting Applications– Part 1Tax Tax is an outflow of cash and needs to be deducted from operating cash flows to find a firm’s 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. Business Finance– Semester 2 2009 22 Capital Budgeting Applications– Part 2 Capital Budgeting Applications – Part 2 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. Business Finance– Semester 2 2009 23 Capital Budgeting Applications– Part 2 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 ith 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. Note that in this approach, we divide by the equivalent “PVIFA year” and not a normal year.If a project had 10% WACC and was for 3 years, we would divide by 2. 4869 instead of 3. • 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 project’s NPV to changes in assumptions in the project (such as assumptions in inflation, taxes etc. ) The three Business Finance– Semester 2 2009 24 Capital Budgeting Applications– Part 2 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 it’s doing well or just scrap the entire project if it is failing. In reality, a firm would not continue a project if it is doing considerably bad compared to forecasts. Capital budgeting analysis, however, assumes that management will continue this even in the face of negative profits for the rest of the project’s life. Real Options Analysis corrects this by setting any chances of a negative profit to $0 instead. When a project has an option to be abandoned, the expected cash flows from a project increases and the overall risk of the project decreases.This is true since we have the ability to simply call off the project if it becomes unprofitable.
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.Business Finance– Semester 2 2009 25 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 in Company B. Business Finance– Semester 2 2009 26 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 portfolio’s 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 portfolio’s standard deviation is: + Business Finance– Semester 2 2009 +2 27 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 with the following formula: Correlation Coefficient = ? 12 = ? 12 / ? 1 ? 2 Where ? 12 is the covariance between the two stocks.Rearranging this formula, we find that the covariance is equal to the correlation coefficient multiplied by the standard deviations of both stocks. To find the covariance, 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. Add both 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 correlation coefficient, however, measures the strength of the association, and is usually better than the covariance. 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. This is explained further in the next section. • Business Finance– Semester 2 2009 28 The Capital Asset Pricing Model 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 asset’s 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 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 stock’s beta and multiplying it by the market risk premium.
Business Finance– Semester 2 2009 29 The Capital Asset Pricing Model 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 stock’s beta and multiplying it by the risk premium. Mathematically: k = kRF + ? kRP Where: k is the required return on the asset, kRF is the risk free asset, ? is the beta for the asset and kRP is the market risk premium. A company’s position on the line is thus, vulnerable to being changed based on the above factors such as change in the company’s beta and changes in risk aversion. The company’s 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 company’s 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.The steeper the line is, the more risk averse the average investor 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. Business Finance– Semester 2 2009 30 The Capital Asset Pricing Model Capital Asset Pricing Model Uses The CAPM allows us to easily: • • Benchmark portfolio performance Identify under or overvalued assets If the CAPM indicates a higher price than the current one in the market, it is undervalued. Likewise, if it indicates a lower price, then it is overvalued.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. An incorrect estimation can skew results. Beta estimation issues. The beta may not always be constant and stable. It is a model that looks into the future using past data. Generally, we should not use historical data to predict future events. • 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. Business Finance– Semester 2 2009 31 Cost of Capital and Raising Capital 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: = ? + + ? + 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 firm has $2,000 of equity which costs 10% per year and $5,000 of debt which costs 8% per year, the firm’s WACC would be: = 0. 08 ? 5,000 2,000 + 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 firm’s 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 premiumBusiness Finance– Semester 2 2009 32 Cost of Capital and Raising Capital • 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: = 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.It is also useful to look at the firm’s credit rating to find its risk. 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 firm’s owners (the shareholders of the firm).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 firm’s shares on the share market, we can simply use the following formula to find the discount rate. = + 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. Business Finance– Semester 2 2009 33 Cost of Capital and Raising Capital This analysis is easy; however, not all companies always pay out dividends.To date, Microsoft has not paid a single dividend in the entire entity’s life. Many other 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: = + [ ? ] 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 (the risk premium).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 for the market risk premium 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: = + 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. This is the same formula as the one to find the equity cost of capital. 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 firm’s 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 Business Finance– Semester 2 2009 34 Cost of Capital and Raising Capital 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 to calculate the WACC for equity is the same as the one used in 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).That is: = 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: = ? [ + ] + [1 ? ] ? [ + ] 1? + Where: TC is the corporate tax rate of the firm.Business Finance– Semester 2 2009 35 Cost of Capital and Raising Capital 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: = ? [1 ? ] ? [ + ] + ? [ + ] Under an imputation system, the appropriate before-tax WACC is: = Where: ? [ + ] + 1? [1 ? ] ? [ + ] is the proportion of 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 firm’s other undertakings. This risk will usually not alter the firm’s 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 (Beta 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 firm’s beta coefficient.It is, however, the most difficult to estimate. After we have evaluated the project’s 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 predetermined discount rate is applied to it. While this method may not be very accurate, it is very quick to determine. • • Business Finance– Semester 2 2009 36 Cost of Capital and Raising Capital Security Market Line Approach This method takes the SML equation and states that the required rate of return on the project is equal to: + +Where Rf is the risk free rate, RM is the market return and ? A is the project’s beta. The problem here lies in how to find the project’s beta. This formula is the same as the formula used for the normal Security Market Line except that it uses the project’s beta instead of the firm’s beta. We can find the project’s beta 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 project’s cost of capital. This method is very useful if the project is not similar to other projects the firm is undertaking in terms of risk but is only really useful for large projects. Suitable firms to compare to may also be hard to find. For instance, if a company normally sells furniture but wishes to enter the personal and business computer market, it may look at companies like Dell since they mainly do this line of business. The Accounting Beta Method In this method, the beta is estimated by regressing the firm’s accounting return against a large number of other firms.Business Finance– Semester 2 2009 37 Capital Structure Capital Structure Background The capital structure of a company is the proportion of debt, equity and hybrids used to comprise the firm’s 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 firm’s 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. Business Finance– Semester 2 2009 38 Capital Structure Another proposition the theory makes is that the WACC is independent of the firm’s capital structure.This means no matter how much or little debt the company has, WACC will not change. Thus, the WACC formula is the same as the one we use the estimate company-wide WACC (Refer to page 32). Thus our formula is very simple. The value of a leveraged (VL) and unleveraged (VU) firm is the same. = Homemade Leverage Homemade leverage is the ability for the investor to change the level of debt and equity they are taking on. Suppose that a company has 60% debt and 40% equity but then switches to a 50% debt and 50% equity structure. If an investor wants to keep the old structure, they would do the exact opposite of what the firm did.That is: Sell 10% of their shares and lend out those proceeds (depositing into a bank is considered lending to a bank). This would return the investor back to a 60% debt and 40% equity structure. 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. 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 firm’s 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. These are considered indirect bankruptcy costs (incurred to stop the business from going into bankruptcy). + Business Finance– Semester 2 2009 39 Capital Structure Direct bankruptcy costs are costs that arise as a result of legal and administrative expenses occurred when a firm does go bankrupt. This means that not all debtholders will be able to get what they are owed. 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. = + ? 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: = + ? + ? Where PVACe is the present value of agency costs associated with equity and PVACd is the present value of agency costs associated with debt.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 Business Finance– Semester 2 2009 40 Capital Structure 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. It can be considered an outcome of the Signalling Theory. . 2. 3. 4. Internal Funds (Retained Earnings, cash and marketable securities) Issue Debt Issue Hybrids 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. Business Finance– Semester 2 2009 41 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. Typically one-off occasions. 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 sharesBusiness Finance– Semester 2 2009 42 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. The real world has taxes, uncertainties, asymmetrical information, transaction costs and agency costs just to name a few. The tax preference theory states that investors are more inclined towards capital growth instead of dividends.This is because dividends are taxed twice under a classical tax system while taxes associated with capital gains can be deferred until the shareholder sells their shares. Under an imputation tax system, this also holds but it applies less because there is less tax on dividends. The Bird-in-the-Hand Theory The Bird-in-the-Hand Theory drops the assumption that all investors want the same things. Some investors are risk averse and would rather want certain dividend payments now than uncertain capital gains in the future. Thus, investors value firms that have high dividend payouts compared to one with low dividend payouts.Shareholders would thus, require a higher capital return on shares with little or no dividends. Information Content Effect The information content effect is the observed change in share price as a result of news of changes in dividend policies. Share prices usually rise when an announcement is made regarding an increase in dividends while share prices usually fall when an announcement is made regarding a decrease in dividends. Asymmetric information between managers and investors allows managers to use this as a signal to investors. An increase in dividends means confidence in the firm’s future while a decrease means little confidence.The Clientele Effect The Clientele Effect results from people who have different wants. Some investors prefer high dividend stocks while some prefer low dividend stocks. Different firms attract different types of clientele (investors) with their dividend policies. As such, a firm should not change its dividend policy too greatly; otherwise it will cause investors in the firm to be unhappy that it’s changed too much. There is a general knowledge amongst managers that you should not change something that has settled on for a while too much, otherwise, it will cause backlash, no matter if it is a good change or a bad change.Factors affected choice of Dividend Policy As we can see, dividend policy choice is affected by many factors. On the next page is a list of factors that affect either a low or high dividend policy. Business Finance– Semester 2 2009 43 Dividend Policy Low Dividend Policy Taxes under Classical System Flotation Costs Dividend Restrictions Liquidity Issues Ownership Dilution Desire for capital gains over dividends High Dividend Policy Taxes under Imputation System Good for tax-exempt investors Cost of trading shares Desire for certain and current income So with all this information, how much do we pay in dividends then?We have four different types of policies we can use to determine how much to pay. Residual Dividend Approach This approach is self explanatory in that we give out all our residual earnings as dividends. The firm needs to have a target capital structure for this approach however. We take however much net income the firm got from the last investment and deduct from that the required equity in the next project. Any remaining equity here is known as the residual and distributed out as dividends. A strict residual dividend approach is bad for a variety of reasons because it is not a stable approach.The residual amount is most certainly to be different each time leading to an unstable dividend which can give out wrong signals to shareholders about the profitability of the firm. Constant Payout Approach This approach is where the firm pays a constant percentage of earnings at each defined payment date (usually annually or bi-annually). They may also choose to pay it out over an earning cycle instead which can be a different period of time. Constant Dividend Growth This approach was discussed previously and it is where dividends increase at a set percentage each year.Low Regular and Extra This method is where the firm pays a regular low dividend and only pays an extra dividend when earnings are high enough to warrant one. This can be bad in the long run though because investors will come to expect an extra dividend and when there isn’t one, investors will believe the firm is not doing well (bad signal). Constant Nominal Payout This is simply paying out the same fixed amount of dividends every period. The dividend is only increased when management is fully confident that the firm can support a higher dividend for perpetuity.In doing this, firms should not cut back on projects just to pay dividends, avoid cutting dividends, avoid selling equity and maintain targeted debt to equity and dividend payout ratios. Business Finance– Semester 2 2009 44 Dividend Policy Dividend Reinvestment Plans Alternatives to cash dividends exist and one of them is a dividend reinvestment plan. This is where shareholders are option to automatically reinvest all or part of their cash dividends in new shares. This is partially irrelevant to the investor because they can use a homemade dividend policy to do this by themselves.The only bonus to this is that there are less transaction costs. These are still considered dividends for tax purposes. Some firms may also allow open enrolment where shareholders can, if they wish, to buy even more shares by paying more when a dividend reinvestment plan is available. This allows shareholders to buy even more shares while avoiding brokerage fees. The amount of shares a shareholder is entitled to, is found by multiplying the cash dividend by the number of shares, then dividing it by the difference between share price and the discount if any exists.Dividend reinvestment plans can be advantageous for a firm because they can issue new equity without having to go through the normal long and costly procedures of a normal sale. It also allows the firm to re-evaluate its dividend policy. If the majority of investors are opting for the plan, then the firm would be better off paying less dividends and concentrating on capital growth. The reverse is also true. Bonus Issues Bonus issues are where a firm issues additional new shares on a pro-rata basis for free to investors. What this does is increase the amount of shares on the market but it also decreases the per share price, EPS and DPS.This is an intended effect so that share prices do not get too high. Share Splits Share splits are where each share is split up into more shares. These have the same similar effect as bonus issues do. Both bonus issues and share splits are typically interpreted by investors and shareholders as a good signal that management is confident about its future because it is concerned that share prices will get too high. It is also good for investors because the more shares that are traded at once, the cheaper transaction costs get. Reverse Splits This is a complete reverse of a share split. Shares are grouped and replace with one new share instead.This has the opposite effect of share splits and bonus issues in that they increase share price, EPS and DPS. This sends a negative signal to investors as aggregate dividends will usually decrease. Firms may choose to do this to reduce transaction costs and improve liquidity (very low price shares have high costs in percentage terms than higher priced shares). Business Finance– Semester 2 2009 45 Dividend Policy Share Repurchase/Buyback A share repurchase/buyback is where a firm uses cash to buy back their own shares. This is done by firms to reduce the amount of shares in the market, increase share price and EPS.Firms can either purchase directly from the share market or make an offer to shareholders to purchase shares. If we assume perfect capital markets, shareholders will be indifferent between buybacks and dividends. Managers use share buybacks because it is a way of distributing cash without it technically being a dividend. Thus, it provides financial flexibility for the manager who does not want to increase dividends temporarily as this would cause a wrong signal to be sent when they are brought down again. It can also be useful for managers to alter the capital structure of the firm.They can issue debt and use that money to buy back shares. This increases the debt of the firm and decreases equity, thus, changing the firm’s capital structure. However, this is only really useful for large changes in the capital structure. Share buybacks give positive signals to the market that management believes that equity is undervalued. Firms that do so tend to outperform the market for months after a buyback has occurred. Shareholders themselves also like share buybacks because, unlike dividends, they have a choice whether to sell those shares or not for cash.This also gives them tax flexibility. No buyback means no tax, and buying back means tax. Having a choice is valuable for a shareholder who may not want more tax liability. However, share buybacks are disadvantageous in that some shareholders may prefer cash dividends over anything else. They may view it as a negative signal because the firm may have to buyback at a very high price compared to the market. In the long-run, this causes share price to fall and thus, disadvantages all shareholders who did not sell their shares. This document ends here. Business Finance– Semester 2 2009 46