print summaries 50 mcq

7/26/2019 Print Summaries 50 MCQ

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Author: Remi MalahieudeBased on: Release FI-A2-engb 2/2008 (1003) Steve Elliot's Finance Notes from Oct. 30-2006 Date: January 23, 2010

Finance

Be aware that beyond the Past Papers, the Faculty Board will post some extremely valuable Revision Exercisesin the Faculty Download Area. Those files are not there from the start of term. The Professor will post them rightbefore the minor diet. I highly recommend doing all those prior to any online Case study or Past Paper.

Good luck in your finance journey.

Module 1

Finance is the economics of allocating resources across time.

Financial Markets- Participation is financial markets is driven in part by the desire to shift future resources to

the present so as to increase personal consumption, and thus satisfaction.- Or one may shift resourcesto the future by lending them, buying common stock, etc. In

exchange, they get an expectation of increased future resources, in the form of interest,dividends, and/or capital gains.

- Where financial investmentsserve the purpose of reallocating the same resources acrosstime, real asset investmentcan actually create new future resources.

- The provision of funds for real asset investment is important, as is theallocativeinformationthat financial markets provide to those interested in making realasset investment.

- Financial markets can help tell the investor whether a proposed investment is worthwhile bycomparing the returns from the investment with those available on competing uses.

- Financial market participants are risk-averse, they would choose the less risky of twootherwise identical investments.

Market Interest Rate & Prices- The market interest rateis the rate of exchange between present and future resources.

Always positive because lenders keep their money if they are not offered a positive return (MCQ1B1Q1

- Determined by the supply and demand of resources to be borrowed and lent.- At any given time there are numerous market interest rates covering different lengths of

time and investment riskiness.Market IR is but one of many interest rates (MCQ1B1Q1)

A Simple Financial Market

Shifting Resources in Time- A financial exchange lineis comprised of any transaction that a participant with an initial

amount of money may take by borrowing or lending at the market rate of interest.- The line appears on a graph with CF1, the cash flow lateron the vertical axis, and CF0, the

nowcash flow on the horizontal.


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- If a participant had $1000 at t0and wished to borrow whatever he could with a promise torepay $1540 at t1, how much could he borrow? Assume a 10% interest rate.

CF1 = CF0(1+ i)

CF1 $1540CF0= --------- or ---------- = $1400

(1+ i) 1.10

The participant could borrow $1400 with a promise to repay $1540 at t1. The maximumamount the participant could consume at t0is thus $2400 (present wealth). $1400 is the

present value of $1540.- Present valueis defined as the amount of money you must invest or lend at the presenttime so as to end up with a particular amount of money in the future.

- Finding the present value of a future cash flow is often called discountingthe cash flow.- Present value is also an accurate representation of what the financial market does when it

sets a price on a financial asset.- Present value is the market value of a security when market interest rates or opportunity

rates of return are used as discount rates.- Present wealth: total value of a participants entire time-specified resources.

Investing- Investing in real assets allows for an increase in wealth because it does not require finding

someone to decrease their own.- For wealth to increase the present value of the amount given up for real asset investment

must be less than the present value of what is gained from the investment.

Net Present Value- The present value of the difference between an investments cash inflows and outflows

discounted at the opportunity costs (i) of those cash flows.

CF1NPV = -------- CF0

(1+ i)

- It is generally true that NPV = Change in present wealth.- It is also the present value of the future amount by which the returns from the investment

exceed the opportunity costs of the investor.

Internal Rate of Return- Calculates the average per period rate of return on the money invested.- Once calculated, it is compared to the rate of return that could be earned on a comparable

financial market opportunity of equal timing and risk.- IRR is the discount rate that equates the present value of an investments cash inflows and

outflows. This implies that it is the discount rate that causes an investments NPV to beequal to zero. (MCQ1B2)

CF1NPV = 0 = CF0 + -----------

(1+ IRR)

CF1(1+IRR) = --------

CF0

- An IRR greater than the financial market rate implies an acceptable investment (and a + NPVIRR lower than it does not (and a NPV).

- IRR and NPV usually give the same answer as to whether an investment is acceptable, butoften give different answers as to which of two investments is better.

Corporate Example- The sole task of a company is to maximise the present wealth of its shareholders.- A company would accept investments up to the point where the next investment would

have a NPV or an IRR less than its opportunity cost.


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- Although shareholders have different consumption preference across time, companiesshould1. Ignore the shareholders preferences2. Allow the market to reallocate resources across time

1. because the financial markets allow shareholders to reallocate resources by borrowingand lending as they see fit. This way allows the company to concentrate on maximisingshareholder wealth. (MCQ1B3)

More Realistic Financial Markets

Multiple Period Finance- Multiple period exchange rates (interest) are written as (1 + in)

n, where n is the number of

periods.

Compound Interest- Compounding means that the exchange rate between two time points is such that interest

is earned not only on the initial investment, but also on previously earned interest. Theamount of money you end up with by investing CF0at compounding interest is written

CF0 [1 + (i/m)]m t

where m is the number of times per period that compounding takes place, and t is thenumber of periods the investment covers.

- The most frequent type of compounding is called continuous. Interest is calculated andadded to begin calculating interest on itself without any passage of time betweencompoundings. This reduces the above formula to CF0(e

it), where e is = 2.718., the base

of a natural logarithm.

CF0(eit) = Continuous compounding

Multiple Period Cash Flows- To find the present value of a cash flow occurring at any one future time point the following

formula is used:

CFtPV = ---------

(1+ it)t

- The present value of a set (stream) of cash flows is the sum of the present values of eachof the future cash flows associated with the asset, calculated:

CF1 CF2 CF3PV = --------- + --------- + --------

(1+ i1)1

(1+ i2)2

(1+ i3)3

Multiple Period Investment Decisions- Calculating NPV when the investment decision will affect several future cash flows must

include all present and future cash flows associated with the investment.

CF1 CF2 CF3NPV = CF0 + --------- + --------- + --------

(1+ i1)1

(1+ i2)2 (1+ i3)

3

- Calculating the IRR of a set of cash flows involves finding the discount rate that causesNPV to equal zero;

CF1 CF2 CF3NPV = 0 = CF0 + ------------ + ------------ + -----------

(1+ IRR)1

(1+ IRR)2 (1+ IRR)

3

- The only way to solve for the IRR of a multiple period cash flow stream is with the trial anderror technique.


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Calculating Techniques and Short Cuts in Multiple Period Analysis

- The instruction to calculate the PV of a stream of future cash flows is;

T CFtPV = --------- (1.2)

t=1 (1+ it)t

- When discount rates are consistent across the future this changes to;

T CFt

PV = -------- (1.3)t=1 (1+ i)t

Calculation Methods- Start with the CF furthest from the present, discount it one period closer and add the CF

from the closer time point, discount that sum one period nearer, etc. Continue process untilall cash flows are included and discounted back to t0. PREFERRED METHOD

- Use present value tables. Adding up the cash flows after discounting each one for itsrespective time period.

- Tables are valuable when finding the present value of annuities. A constant annuity is a setof cash flows that are the same amount across future time points.

- A perpetuityis a cash flow stream assumed to continue forever. Formula is simply adivision of the constant per-period CF by the constant per-period discount rate:

CFPV = -------- (1.4)

i

- A slight modification of the above allows for the assumption that the cash flows willcontinue forever, but will grow or decline at a constant percentage rate during each period(AKA growth perpetuity),

CFPV = -------- (1.5)

(i g)

where g is the constant per-period growth rate of the cash flow.

- This equation will not work when i


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Forward Interest Rates- Interest rates that begin at some time point other than the present (to).- The amount invested in an asset across time can be found by accruing past invested

amounts outward at the same rates that were used to discount cash flows back in time.- This amount allows for a calculation of a forward interest rate.- Forward interest rates are usually indicated as with a left subscript indicating the rates

start time point and a right one indicating the ending time point. Therefore:

CF1( 1 + 12) = CF2

( 1 + i2)2 = ( 1 + i1) ( 1 + 12) = ( 1 + 01) ( 1 + 12)

( 1 + i3)3 = ( 1 + i1) ( 1 + 12) ( 1 + 23) = ( 1 + 01) ( 1 + 12) ( 1 + 23)

( 1 + i4)4 = ( 1 + i1) ( 1 + 14)

3= ( 1 + i3)

3 ( 1 + 34) = ( 1 + 03)

3 ( 1 + 34)

- This formula calculates the impliedforward ratefor a bond.- If forward rates are known, the spot rate of interest can be found by multiplying together 1

plus each of the intervening forward rates, taking the n th root of that product (wheren=number of periods covered), and subtracting 1. (page 1/35)

Interest Rate Futures- The futures market in interest rates allow you to avoid (or hedge) the risk that interest rates

might change unexpectedly (therefore, potentially, reducing an NPV to a point where aninvestment is no longer worthwhile).

-

Expectations around future interest rates and future values are almost never completelyaccurate because, between the time the expectation is formed (t0) and the realisationoccurs (t1), additional information will have appeared that causes the market to revise itscash flow expectations, its opportunity costs, or both.

- Financial futuresmarkets allow participants to guard against this kind of risk by buying andselling commitments to transact in financial securities at future time points at prices fixedas the present.

- Allows a guaranteedset of discount rates for an asset NPV by agreeing to sell securities atset prices across an assets life.

- Hedging takes away both good and bad surprises.

Interest Rate Risk & Duration- The variability of values due to changes in interest rates is the effect of interest rate risk.- Durationis a kind of index that tells us how much a particular bond value will go up and

down as interest rates change.- It is the number of periods into the future where a bonds average value is generated. The

greater the duration of a bond, the farther into the future its average value is generated,and the more its value will react to changes in interest rates.

- Duration can be calculated by weighting the time points from which cash flows aregenerated, by the proportion of total value generated at each time:

t t

Duration = = t=1 t=1

- Duration is the starting point for an important aspect of professional bond investing calledimmunisation.

t x CFt(1+it)

t

Bond value

t x CFt(1+it)

t

Bond NPV


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Annualized growth rate calculation

Present Value PV = CF x PVIFi,n

PVIFi,n= PV Interest Factor [Table A2.1]

Present Value of Annuity PVA = CF x PVAIFi,n

PVAIFi,n = PV of Annuity Interest Factor [Table A2.2]

Time out: for e.g. Year 5-17: 17 5 = 13 years i = (1.5833)

1/6 = 7.96%

RevEx1Q27: What should you pay for an asset that produces a level of cash stream of $50,000 every 6months for the next 10 years, if your opportunity cost of capital is 8% (annual rate), compounded perperiod?

PVA = CF x PVAIF i,n [Table A2.2] = 50,000 x PVAIF4,20 = 50,000 x 13.59 = 679,500

A cny offer to pay you 200,000 today, it will pay you 30,000 pa at the end of Y5 and then a further 12years.If your cost of capital is 10%, would you accept? This is a 13yr annuity at 10% = 7.1034 [Table A2.2], PVA = CF x PVAIFi,n= 30,000 x 7.1034 = 213,100

CF at the end of Y5, the annuity bring the value back to the start of Y5, so discount rate end of Y4= 0.683[Table A2.1] = 1/ (1.1)

4 => PV = CF x PVIFi,n= 231,100 x 0.683 = 145,550 => dont accept

or

(17 year annuity 4 year annuity) x 30,000 = 145,550 PVA = CF (PVAIFi,17 PVAIFi,4)


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RevEx1Q30: 1m paid 100,000 pa starting today vs. a 700,000 one time payment today, which one do you

take? Opportunity cost is 8%PVA = CF x PVAIF8%,10 periods [Table A2.2] x (1+r) [as the annuity starts today]= 100,000 x 6.7101 x 1.08 = 724,690.80

MCQ1B5: A bond trade at $110.5 in the market, its coupon is 9%, which has just been paid and nextpayment is exactly 1 year. T/he bond has 5 years until maturity (at $100). YTM?

9 9 9 9 109110.5 = -------- + -------- + -------- + -------- + --------

(1+ r)1

(1+ r)2 (1+ r)

3 (1+ r)

4 (1+ r)

5

MCQ1B10: 7% coupon bond paying i semi-annually trades at $98.12 just after the interest payment. Bondhas 3 years maturity. YTM?

3.5 3.5 3.5 3.5 3.5 103.598.12 = -------- + -------- + -------- + -------- + -------- + --------

(1+ r)1

(1+ r)2 (1+ r)

3 (1+ r)

4 (1+ r)

5 (1+ r)

6


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Module 2 Fundamentals of Company Investment Decisions

The corporation (plc) is an organization that raises money from capital suppliers by issuing contracts(securities), invests that money in productive assets, operates those assets (perhaps hiring other resourcessuch as management and labour), and distributes the money proceeds from operating those assets to all thathave claims on the proceeds.

Capital suppliers are those who own equity and debt claims on a company.

Investment Decisions & Shareholder Wealth- When a company issues shares to raise money from the capital market it creates a security

known as one of the following: ordinary shares, common stock, equity, common shares,ownership capital, etc.

Important things to remember about this type of capital claim:1. It is a residual claim

- Equity has no specific contract with the company that requires any particularamounts of money to be paid to shareholders at any particular time.

- Shareholders have only the entitlement to vote for the directors of the company.- Directors and management are agentsof the shareholders maximising the wealth

of its current shareholders.2. Equity has limited liability

- The possible losses that a shareholder can incur are limited to the value of theshares that the shareholder owns.

3. Until all other contracts that the company has entered into have been filled, theshareholders are entitled to nothing. Once met however, the shareholders have anownership claim on allof the remaining corporate resources.

- Shareholder wealth is the market value of the common shares or equity that theshareholders own.

- If a company wishes to maximise its shareholders wealth, it should seek to maximise themarket value of the shareholders ordinary shares.

The Market Value of Common Shares- is the discounted value of all future dividends that the current shareholders are expected to

receive.

Dividend1 + Value1 Div1+ E1 Div1 Div2+ E2Value0= --------------------------------- E0= ------------- , and E0 = ---------- + -------------

(1 + Equity discount rate) (1 + re) (1 + re) (1 + re)2

So true value:

Div CFE0= ------- PV = ------ (Perpetuity)

re i

Investment and Shareholder Wealth- The use of a properly calculated investment NPV does in fact result in an increase in the

present wealth of shareholders.

Investment Decisions in All-Equity Corporations

When making an investment;1. The total value of a company increases by the NPV of the investment plus what it cost to

undertake it.2. The shareholders experience a wealth increase equal to the investments NPV.3. Existing shareholders of the company get a wealth increase equal to the investments NPV

regardless of who contributes the money necessary to undertake the investment (i.e.forgone dividend, new equity holders, or even the original holders).

Investment Decisions in Borrowing Corporations- Corporate NPV is equal to the change in wealth of existing shareholders even if some of

the money for an investment comes from creditors/ bondholders instead of equity holders.


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Share Values and Price/Earnings Ratios- P/E ratios are offered as signals that the market is providing as to the companys future

earnings prospects, growth rate, riskiness, etc.- The P/E ratio is nothing more or less than the ratio between the present value of all the

companys future dividends (its market price) and its expected earnings during the firstperiod.

- For certain companies with very simple cash-flow patterns (i.e. constant, or constantgrowth perpetuities) we can derive a specific relationship between P/E ratios and equitydiscount rates:

Dividend per share Equity per sharePrice per share = ------------------------- = ----------------------

re re

So

Price per share 1P/E = --------------------------- = -----

Earnings per share re

- For companies who are not paying out all earnings as dividends:

Dividend per share Earnings per share x payout ratio*

Price per share = ------------------------- = -----------------------------------------------( re g ) ( re g )

So

Price per share 1P/E = --------------------------- = ----------- x payout ratio*

Earnings per share ( re g )

* where payout ratio is the percentage of earnings paid as dividend.= dividend payout ratio

Dividend

Payout Ratio = ---------------Earnings

- Caution must be exercised when comparing the P/E rations of different companies toensure that all but one of the factors influencing market prices are reasonably similar.

When a dividend is paid, the share priced falls by that amount e.g. share price = 100p, cny pays 10p dividend,the share price falls to 90p. That dividend is pay out of the share price, it is history (FB/FAQ)

2003 2004 2005 2006 2007 2008 2009RE2Q6: Dividend 5.8p 6 6.3 6.7 7.1 7.7 8.5 re=14%What is the share price if you base the growth of dividends on (i) the entire period (ii) the last 2 years?(i) g = (8.5/5.8)1/6 = 6.577% P0= (8.5 x 1.065777) / (0.14 0.06577) = 122p(ii) g = (8.5/7.1)1/2 = P0= 203p

The DGM can be manipulated to give different valuations if you use different spreads of years to calculate thegrowth rate of dividends. if g>r => multi-stage valuation model (RE2iQ8)

The share price is the discounted value of all future Dividends (FAQ/ FB )(ie. the PV of all future dividends = value of the cny) MCQ2B1


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A high P/E ratio usually signifies a cny that is growing fast. Or it might be a cny where profits have almostdisappeared. Or cny takeover target and shares have been bid up. IF so, they will usually keep most of theirearnings for reinvestment to continue that growth. More value slow growing cnies will pay larger dividends.

The payout ratio indicates how much a cnys earnings are paid out in the form of dividends (the balance beingavailable for reinvestment). FB/FAQ

P/E ratio is of limited use. Compare similar cnies (same sector/business). Cnies should have same accountingconventions => earnings based on the same calculations. Adjustments required/needed to deliver measure ofearnings close to cash earnings rather than accounting earnings.

not across sectors -> meaningless. Accounting figures still subject to manipulation(RE2iQ7)

You cant have a high dividend payout ratio and a high growth rate (g). [FAQ]


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Module 3 Earnings, Profit, and Cash Flow

Total Corporate Value Change- The increase or decrease in the market value of all of a corporations capital claims that

would take place if the investment were accepted.

Corporate Cash Flows activity across time

- Financial cash flows are the cash amounts that are expected to occur at the times for whichthe expectations are recorded.

Typical Cash Flows (Company with zero debt, 100% equity financed) (000s)

Now Yr 1 Yr 2 Yr 3Customers 0 +17 500 +23 500 +4 000Operations 0 -7 000 -3 830 -5 200

Assets -10 000 -4 000 -2 000 0

Government 0 -4 000 -8 085 +5 600Capital* (FCF) -10 000 +2 500 +9 585 +4 400

2 500 000 9 585 000 4 400 000NPV = -10 000 000 + -------------- + ------------- + ------------- = +3 500 000

(1.10) (1.10)2 (1.10)

3

1. Customers The amounts of cash expected to take in from sales and/or selling used assets.2. Operations Cash flows that are paid in cash that year, be deductible for taxes that year,

and not be a payment to a capital supplier.3. Assets While the cash flow is made at time listed, it is not deductible at that point and

must therefore be capitalisedand depreciated across time.4. Government Taxes paid due to the investment.5. *Capital The amounts of cash that could be taken out of the corporation by its capital

suppliers and still have the investment run as planned (AKA Free Cash Flow). The value ofall future increases/decreases in dividends expected due to the project (because companyis equity financed).

Cash Flows and Profits- Cash flows are not the same as he numbers that appear in financial statements of

corporations.- One of the biggest differentiation is that accounting figures often report cash flows for time

periods other that that which the flow occurs.


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- Stakeholders = Gouvernment, Employers, Lenders different than shareholders!!!!

- Land = Opportunity cost (a cash outflow), in a CF analysis, initial value of land is an outflow, final value ofland at the end of the project is an inflow.

- Salvage value is part of the depreciation calculation. An Asset is usually fully depreciated, adjusting for anyexpected salvage value at the end of its useful life. [MCQ3B7]

- Debtors = Account receivablesThe accounting term debtors will include customers who will not pay until the next period, sot it is wrong toinclude it in a CF. [MCQ3A6]

- When constructing project CF figures, Interest payments are excluded because they are not part of theinvestment decision (FCF*= FCF-ITS) [MCQ3A7]

- Depreciation is an expense for tax purpose. [MCQ3A10]

- Capitalisation allocates the cost of the asset over a number of time periods. [MCQ3B5]

- FCFs and Profits after tax of a project will add up to the same amount. [MCQ3B10]

- Profit = Income = Earnings

- Your have an accountants income statement for 2 projest, one purely equity financed, one partly financedwith debt, but identical in all other respects.- The all equity finance project will report a higher income

Because in the accounting figures, interest is regarded as an expense, so the debt finance cny will havehigher expenses and so lower profit as a result (MCQ4A2)

- The debt financed cny will have a greater CF than the equity financed cny (MCQ4B2)

- The cash that debt suppliers expect to get in the future = in PV terms to the amount that is raised from themat present, so debts wealth is unaffected by the investment. (MCQ4A3)

- The figures to use in the WACC calculation are market values of debt and equity. (MCQ4A4)

- All equity CFs are the CFs that exclude the ITS. They are the CFs that would exist if the project was onlyfunded by equity. (MCQ4B3)

- The appropriate rate to discount all equity CFs in a WACC calculation is the tax shield adjusted discountrate. (MCQ4B4)

- What do FCFs of an investment project which are appropriate to be discounted with the projects WACCinclude?All changes in the payments between the firm and its capital suppliers induced by the project, were theproject to be financed only with equity.


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Module 4 Company Investment Decisions using the WACC- The weighed average cost of capital (WACC) is a discount rate that combines the capital

costs of all the various types of capital claims that a company issues.

Free Cash Flow and Profits for Borrowing Corporations- Financial markets place values on corporate debt claims by discounting with risk-adjusted

rates the amounts of cash that the company is expected to pay to those claims.- Debt has a higher priority claim to cash than does equity.- A partially debt financed investment, ceteris paribus, will have higher free cash flows than

one which is 100% equity financed.- This is due to tax laws that allow interest on loans to be written-off.- This is called a corporations income tax shield ITS.- Income tax shields can be calculated by taking the expected interest payment on each

period and multiplying it by the corporate income tax rate.

Investment Value for Borrowing Corporations- Debt suppliers wealth should be unaffected by the investment. Figured by taking the

interest + principal for each period and dividing by the debt interest rate.- Equity wealth change is figured out by comparing the investment-induced change in equity

value to any foregone dividend. Value change is calculated by subtracting principal andinterest from the FCF for each period and dividing that by an appropriate discount rate.

Overall Corporate Cash Flows and Investment Value- To figure out NPV as a whole, the FCFs must be discounted with a rate commensurate with

their risk.- To find this discount rate the debt and equity rates must be combined in proportion to their

claims on the corporate cash flow. This value is given by the market value of the twoclaims:

Debt market value Equity market valueOverall rate = ------------------------ x Debt required rate + -------------------------- x Equity required rate

Total market value Total market value

- Valuing the security is now easy:n FCF

Value of the project = ----------------------------------

t=0 (1 + overall required rate)

t

Investment NPV and the WACC

- The above technique is the overallNPV method.- Common practice in financial analysis of corporate investment is that when estimating the

cash flows of a project, its interest tax shields are not included in the cash flows.- In order to calculate an accurate NPV using cash flows that exclude interest tax shields, the

effect must also be included in the discount rate.

- The WACC is the discount rate that:a. Reflects the operating risks of the projects.b. Reflects the projects proportional debt and equity financing with attendant financial risksc. Reflects the effect of interest deductibility for the debt-financed portion of the project.

- In order to reflect interest deductibility in the discount rate (WACC), the weighted averagemust use the companys after-tax cost of debtrather than the debt suppliers required rate.

- Cost of debt in a company with deductible interest is simply debts required return multipliedby the complement of the corporate income tax rate:

Debt cost = Debt required return x (1 - Corporate income tax rate)

- WACC is therefore calculated as follows;

Debt market value Equity market valueWACC = ------------------------ x Debt cost rate + -------------------------- x Equity required rate

Total market value Total market value


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- The WACC-NPV analysis of an investment project is performed by discounting the projectsFCF, not including the interest tax shields that the projects financing will generate.

- This adjusts for the deductibility of corporate interest in the discount rate as opposed to theCF of the project.

- Companies using the WACC-NPV are willing to specify the expected proportions of debtand equity in terms of their market values, but they do not know exactly what the claims willbe worth until after the analysis is complete.

The Adjusted Present Value Technique- APV does not require knowledge of debt/equity proportions, but does require that the

interest tax shields of the project be estimated.- APV is therefore preferred by corporations who are comfortable in estimating the amounts

of debt the projects will use.- If performed correctly both APV and WACC-NPV will give the same answers.- APV finds the NPV by first finding the value of an investment as if it were financed only by

equity, and then adds the PV of the projects interest tax shields.- All-equity value is calculated by adding all the CFs discounted by the (an) all equity

discount rate.- Interest tax shields value is calculated by discounting the shield CFs by the risk-adjusted

rate for debt cash flows:

APV = (All-equity value) + (Interest tax shield value) Present cost

The Choice of NPV Techniques- When complexities such as tax credits, cash costs, in addition to interest and its deductions

(i.e. cost of bankruptcy proceedings), etc. appear relevant to a companys financialdecisions, the APV approach may be easier to use.

- The reason for this is that APV treats these cash-flow effects separately, by first estimatingthe cash flows, then discounting each one at a rate appropriate to their unique risk.

- On the negative side, APV does not have the automatic characteristic of being consistentwith maintaining an intended ratio between the various kinds of financing (debt / equity) acompany uses.


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Notations

Cash FlowsFCFt Free cash flow: the amount of cash a company can distribute to its capital suppliers at time t

due to an investment.

It Interest cash flow at time t

Tc Corporate income tax rate

ITSt Interest tax shield cash flow ITSt = It x TC

FCF*t Unleveraged (ungeared) free cash flow: amount of free cash flow a company is expected togenerate at t due to a project, not including income tax shields.

FCF*t = FCFt ITSt. = All equity CFs,ie. CFs that would exist if the project was only funded by equity (MCQ4B3)

Market ValuesEt Market value of the equity of the investment at time tDt Market value of the debt of the investment at time tVt Market value of the investment at time t .

Vt = Et + Dt

Discount Ratesre Required return on the equity of the investment.rd Required return on the debt of the investment.rd

* Cost of debt as a rate to the investment

rd*= rd x (1-Tc)

rv Overall weighted average return on the capital claims of the investment.

rv = D (rd) + E (re) = Overall capital return/ cost.V V

rv* Weighted average cost of capital (WACC) of the investment.

rv* = WACC = D (rd*) + E (re)

V V

ru All-equity unleveraged (ungeared) required return on the investment.

Investment Evaluation Techniques

WACC-NPV

t FCF*tNPV0= ---------

t=0 (1+rv

*)t

APV

t FCF*t ITStAPV0= [ -------- + -------- ]

t=0 (1+ru)

t (1+rd)

t

- WACC reflects thei. Financial and operational risk of the projectii. The interest deductibility involved in the projectThe project WACC would reflect the projects proportional debt and equity rather than the actual amount.(MCQ4A6)


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Module 5 Estimating Cash Flows for Investment Projects

- Estimating investment cash flows means that financial managers must keep the following inmind:

1. Inclusion of all corporate cash flows affected by the investmentsometimes meansthat financial analysts must invoke the idea of economic opportunity costs.

2. Inclusion of all relevant cash flowsmeans that analysts must include cash flowsfrom interactions of the investment with other activities of the corporation.

3. Inclusion of all relevant cash flows also means that analysts must know what thingsshould be omitted from the investments cash flows. I.e. sink costsare to beignored. An investment should be discontinued if its future cash flows PV is lessthan the company would obtain by selling or abandoning the project now or later.

4. Inclusion of all relevant cash flowsmeans that analysts must be very careful thatthe accounting numbers provided for a project are interpreted correctly. I.e.Overhead costs are typically not indicative of the incremental cash flows that aproject will require. Accounting numbers can include non-cash expenses(depreciation), and arbitrary activity measures such as floor-space devoted to themanufacture of a product. It is however correct to include as cash outflows thechanges or increments to overall corporate expenses caused by the acceptance ofthe project.

- There are many corporate cash flows that should not be included because they are notincremental (i.e. managers salaries); they would not be affected by the acceptance orrejection of a project.

Summary- All changes that would be caused in the cash flows of a corporation by its accepting a

project mustbe included in the analysis of the project.- ONLY cash flows are to be included.- Estimate CFs as if project were purely equity financed, no debt, so no interest payments.

Operating CF = Operating profit Change in net Working Capital + Change in Overheads

NWC figure comes from changes in receivables, payables, inventory and cash year on year.

For project budgeting CF analysis, interest payments are not included as these are payments to capitalsuppliers. This effect is caught in the discount rate (WACC). [RevEx2(ii)8]

Total CA = Account receivable = Cash outflow in terms of NWCTotal CL = accounts payable = Cash inflow [MCQ5A7]

If the cny does not sell the FA at the end of the project, we must include a sum to reflect the benefit the cny getsfrom their use. [MCQ5A8]


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Module 6 Applications of a Companys Investment Analysis

- Real asset investment decisions = capital budgeting

The Payback Period

- The number of periods until a projects cash flows accumulate positively to equal its initialoutlay.

- Companies use this method by picking a maximum period of time beyond which an

investments payback will be unacceptable, and rejecting all investment proposals that donot promise to recoup their initial outlays in that time or less.

- Payback periods and NPV can yield different answers.- Problems with the payback period include:

a. It ignores all cash flows beyond the maximum acceptable payback period.b. It does not discount the cash flows within the maximum acceptable period, thereby

giving equal weight to all of them. This is inconsistent with shareholder opportunitycosts.

c. It has too much bias to short term CFs (MCQ6B1)d. It is not concerned with the profitability of the project (MCQ6B1)

- Some companies have altered their payback period techniques to be discounted paybackperiods. Concern a above is still valid.

- If a company feels it must use the payback period, a rudimentary estimate of the maximum

allowable period should be set:

1 1Payback = ------- - ----------------

rv* rv

*(1+rv

*)n

wherenis the number of periods in the projects total lifetime.

- This payback is generally only accurate for projects with fairly consistent cash flows eachperiod.

- If these restrictions are met, the above will show the number of periods across which, if theoriginal outlay is not returned (in FCF*), the investment will have a negative NPV.

The Average (Accounting) Return on Investment (AROI)- Calculates a rate of return on the investment in each period by dividing expected

accounting profits by the net book value of the investments assets.- These numbers are then added and the sum is divided by the number of periods for which

rates of return have been calculated. The result is then compared to a minimal acceptablereturn (often an industry or company average).

- AROI does not discount cash flows and the numbers used are the wrong ones.- However AROI does have some value as an evaluation of control device to check the

progress of an ongoing project on a period-by-period basis.

Average profit (over the period in question)AROI = ---------------------------------------------------------------------------------------------- (FAQ +/- AROI)

Average investment (if depreciated to zero itll be the initial investment divided by 2)

Average investment = (Initial value + disposable value) 2

IRR vs. NPV- When there is an outlay, an inflow, and another outlay (in the form of an opportunity cost),

multiple IRRs can exist Sign changes across time can yield multiple IRRs.- A pattern of sign changes can also produce a project that has a totally upward sloping

relationship between NPV and IRR. To correctly accept a project in this case the IRR wouldhave to be lessthan the hurdle rate.


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- There are various means that can be used to make the IRR come up with a correct answerin a particular situation. The difficulty being that you must know beforehand that you aregoing to have a problem with the IRR, and what the solution is.

- Another situation in which the IRR can cause problems is in multiple-period cash flowinvestments which require a different discount rate for each cash flow. The cash flows IRRcan still be found, but at which hurdle rate is it compared? The YTM of a security with thesame risk and cash flow patterns as the investment would have to be found.

- IRR assumes that interim CFs are reinvested at the IRR rate.- NPV discount (MCQ6A8 and Dec 2005Q1.d

IRR vs. NPV in Mutually Exclusive Investment Decisions- In situations where multiple investment options must be compared and subsequently

ranked NPV is best.- When IRR must be used the incremental cash flowanalysistechnique should be used.

The algorithm steps are:1. Take any two projects out of the group.2. Find the one that has the highest net positive cash flow total (sum of all FCF

*). The

investment with the highest net cash flow is the defender, the other the challenger.3. At each time point, subtract the cash flows of the challenger from those of the

defender, the resulting stream are the incremental cash flows.4. Find the IRR of the incremental cash flows.5. If the IRR is greater than the appropriate hurdle rate, keep the defender and throw

out the challenger and vice-versa.6. Pick the next project out of the group and repeat the process using the winner of

step 5 until only one investment remains.7. Calculate the IRR of the winner. If it is greater than the hurdle rate, accept it;

if not then reject all the projects.

- This algorithm works because it looks at the IRR of choosing one project over another,instead of each cash projects IRR.

- There are also situations in which the incremental cash flow method of choosing amonginvestments should never be used:

1. When the incremental cash flows have more than one change of sign across time.2. When the projects differ in risk or financing, so that they require different hurdle rates

-

IRR is more likely to give incorrect indications of investment ranking among a group ofmutually exclusive investments when the investments:i. are of significantly different magnitudeii. duration

t0 t1 t2 t3Project CFs, discount rate 10%: No.1: -$2500 +$1200 +$1300 +$1450

No.2: -$2500 +$1300 +$1300 +$1300

1. Take No.1 and No2.2. No.1 CF= 1450 > No.2 CF= 1400

No.1 defender No.2 challenger3. Challenger CFs Defender CFs

t0 t1 t2 t3-$2500 +$1200 +$1300 +$1450 Defender+$2500 -$1300 -$1300 - $1300 Challenger

Incremental CF = 0 -$ 100 0 +$ 150

4. Through trial and error IRR = 22.5% of the incremental CFs5. 22.5% > hurdle rate of 10% => keep Defender No.1, throw out Challenger No.26. No next project7. IRR of the winner (No.1) = 25.9% > hurdle rate 10% => accept winner

No1 is the better of the 2 projects

The cross-over rate is where the NPV of the 2 projects is equalis also the point where the NPV of the incremental CFsbetween the projects is equal to zero.


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The Cost-Benefit Ratio and the Profitability Index

The C-B Ratio- The ratio between the present value of the cash inflows and the cash outflows of an

investment:

- Where Inflowst+ Outflowst= FCF*t

- An investment is accepted if CBR >1, and rejected is CBR 1 would have a positive NPV, and a CBR


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Capital rationing tends to occur when cnies have complicated management structures which cause problems in informationflows.

Investment Inter-relatedness- This is when the acceptance or rejection of one investment affects the expected cash flows

on another.- Mutual exclusivity is a form of economic inter-relatedness.- Combinations due to capital-rationing are also inter-related.

Economic Inter-relatedness of Investment Cash-Flows- When dealing with economic relatedness among investment proposals companies must

specify all possible combinations of inter-related investments along with their unique cashflows and NPV. The combination with the highest NPV is chosen.

Renewable Investments- When companies must choose among investments in real assets where the life span and

cash costs are different for each option the equivalent annual costtechnique is used.- The technique is as follows:

1. The NPV of a single cycle for each asset is found.2. Divide each NPV by the annuity present value factor for the number of years in

each assets replacement cycle at the appropriate discount rate.3. The result is the constant annuity outlay per period that has the same NPV as the

asset.4. Compare the per-period equivalent annuity outlay for each asset and choose the

one with the lowest cost per period.

NPV Annuity PV Factor Cst annual equivalent CFs

Largemouth -$21,461 2.4868* = $8,630 acceptLunker -$15,678 1.7355* = $9,034 reject*appendice 2 (Table A2.2) 10% discount rate, 3 periods for Largemouth and 2 for Lunker

2 machines with the same EAC chose the shorter life cycle ie. life as it would give theoption of updating the technology more quickly.

Positive Neither Negative

PurelyContingent

SomewhatPositive

SomewhatNegative

MutuallyExclusiveIndependent


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Inflation and Company Investment Decisions- The real rateof return is the difference between the nominal rateand the expected

influence of inflation on required rates for some time in the future. Because there is no wayto measure such expectations effects, the real rate is not measurable.

- Nominalcash flows and nominaldiscount rates should be used when dealing withinflation on corporate investment decisions. If the analysis is performed carefully, theimpact of inflation on the investment, and on shareholder wealth, will appear in the NPV.

- A common error is for cash flows to be stated in real terms, those observable today.Analysts should always be explicit in requesting inflated future cash flow estimates.

- Another trait is that because many governments require production assets be depreciatedacross time, when inflation occurs, the costs of assets will increase across time faster thanthe rate of inflation. This results in FCF

*increasing at a slower rate than inflation.

- Accelerating depreciation schedules have been put in place to help offset this effect. Forexample double-declining balance, or sum-of-the-years digitsmethods.(June2009Q1d)

- Debt suppliers can be particularly concerned about inflation and required rates. The reasonfor this is that debt contracts promise specific amounts of nominal cash at particular timesin the future. If the nominal interest rate that suppliers get at the inception of theirinvestment turns out to be a poor estimate of actual inflation, debt suppliers will achieve areal return different from their initial expectations.

NOMINAL means the actual number of $$ that would change hands at the time the purchase is madeREAL price is the number of $$ that would have been exchanged to purchase something before the

inf. took place

Inflation-free return = REAL rate

(1+N) = (1+R) (1+I)

In an inflationary environment, the net effect of inflation on depreciation expenses for CF purpose istaxes will increase faster than the inflation rate and FCF will increase at a rate less than inflation.

If inflation is going to fall steeply and stay at a low level and market prices do not reflect thisexpectation, a cny would replace long term debt with short term debt. As IR will tend to fall withinflation. [Practice final examination MCQ10]

Leasing- A contractual agreement between an asset owner (lessor) and a company that will actually

operate the asset without owning it (lessee)- The most common type of lease is a financialor capitallease where the lessor is

usually in the business of leasing assets.

The Economics of LeasingAdvantages- Leasing allows for higher tax benefits than the alternative of borrowing and purchasing an

asset.- Information asymmetriesexist on certain types of assets, and leasing can serve to lower

the costs of such information problems.- There are economies of scalein the management of specialised asset leasing.Misconceptions- Leasing saves money because the lessee does not have to make a large capital outlay to

purchase an asset.- Lessee debt capacity is higher since they do not need to borrow money to buy the asset.

Evaluating Leases- Cash flows used would include: cost of purchasing, lost depreciation tax shields, lease

payments, and lease payment tax shields.- The correct discount rate for performing an NPV is the after tax interest rate (rd

*).

- It is important to know what lease rate would allow for a positive NPV when negotiatinglease agreements with a lessor.


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December 2006 Q1e:The lease or buy decision is another capital budgeting problem. Workout the PV of the lease CFs and setthese against the cost of actually buying the asset.Operating CFs irrelevant as theyd be the same purchased or leased.The lease effectively displaces debt, as debt would be used to finance the purchase, so the disc. rate isthe after-tax cost of debt [rd*= rd (1-Tc)].Salvage value = complicating factor = outflow for the lease PV, discount rate = cny WACC because it is arisky CF.

Managing the Investment Process / Biases-

All depends on the quality of the CF forecast. To avoid too rosy a picture hence poorinvestment decisions, directly relate management compensation to shareholder wealthoutcomes.

Biases In capital Budgeting (June 2009 Q1c)- Overconfidence: over-optimistics CFS- Projects that particular managers want done overstating everything- Overly cautions and avoid risky projects- Too low a discount rate- Treatment of inflation. Nominal CF only or Real CF only, no mix upReward managers for the amount of wealth created by their projects

EVA analysis.

Using Economic Income Performance Measurement(EVA = Economic Value Added, EP Economic Profit, etc.)See June 2007 Q1.d

- Charging a capital cost against the net CFs of a company division in a given period, andseeing if theres anything left over. Typically calculated by WACC x invested amount = $capital cost. If positive left over, revenue covered costs and opportunity costs of its capitalsuppliers, leaving and economic profit for its shareholders.

- Nothing more than period-by-period applications of WACC-NPV.- EPs strength is to uncover company operations that are profitable in an accounting sense,

but not in an economic sense.- ++ EP => positive effect on share value; no ++ EP => declining share value

=> EP tied to shareholder wealth, hence an excellent management performance measure.


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Module 7 Risk and Company Investment Decisions

- The security market lineor SML describes the relationship between risk and return asbeing positive: the higher the risk, the higher the required return. (MCQ7A1)

Risk and Individuals- To an individual capital supplier, risk is best measured by the standard deviation of rates on

return on the entire portfolio of assets or by the extent to which possible outcomes arelikely to differ from the mean expected outcome.

- In order to figure out the riskiness of a set of securities one must quote the probabilities ofvarious rates of return or the probability distributions of returns, for example:

Portfolio probability distribution

Rate of Return Probability8.5% 35%11.0% 10%13.5% 30%16.0% 25%

- The next step is to calculate the mean return of these probabilities, or:

0.085 x 0.35 = 0.02975 Mean return+ 0.11 x 0.10 = 0.01100 + 0.135 x 0.30 = 0.04050 + 0.16 x 0.25 = 0.04000 Sum 0.12125Mean = 12.125% = Expected return

- The standard deviation is calculated:

(0.085 - 0.12125)2

x 0.35 = 0.00045992(0.110 - 0.12125)

2 x 0.10 = 0.00001266

(0.135 - 0.12125)2 x 0.30 = 0.00005672

(0.160 - 0.12125)2 x 0.25 = 0.00037539

Sum = 0.00090469 = VARIANCE0.00090469 = 0.03008 = Standard deviation

= 3.008% = Standard deviation

- The result is a reflection of the risk inherent in a portfolio.- Unfortunately, studies to date show that the empirical relationship between risk (measured

as standard deviation of return) and the actual level of return earned is not good.- In the 1950s Harry Morowitz was the first to show that company security holders are

indeed risk-averse, and require higher returns when the risk is higher.- He also showed that the resulting positive relationship between return and standard

deviation of return would only be true for the entire portfolio and not for the individualassets within.

- This is because part of the standard deviation of return for individual assets is diversifiedawaywhen included in a portfolio with others.

A risk averse investor is one who prefers higher returns and lower risk. (MCQ7B4)

Return

Risk

SML


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Risk, Return, and Diversification- Continuing with the above example:

Return outcome ProbabilityAsset A 10% 45%

20% 55%Asset B 7% 65%

12% 35%

- Expected returns per asset are:

A: (0.10 x 0.45) + (0.20 x 0.55) = 0.155 or 15.5%

B: (0.07 x 0.65) + (0.12 x 0.35) = 0.0875 or 8.75%

- Standard deviations are:

A: (0.10 - 0.155) x 0.45 = 0.00136(0.20 - 0.155)

2x 0.55 = 0.00111

= 0.002470.00247 = 0.0497 or 4.97%

B: (0.07 - 0.0875) x 0.65 = 0.00020(0.12 - 0.0875)

2x 0.35 = 0.00037

= 0.000570.00057 = 0.0239 or 2.39%

- The logical way to find the risks and returns of the portfolio formed therefore seems to be totake the average of the returns and standard deviations for the two individual assets:

Avg Return: (0.5 x 0.1550) + (0.5 x 0.0875) = 0.12125 or12.125%(sameas the portfolios expected rate of return above!)

Avg Std Deviation(0.5 x 0.0497) + (0.5 x 0.0239) = 0.0368 or3.68%

(differsfrom the std deviation for the portfolio of 3.008%)

- Obviously the weighted average standard deviation of return of individual assets in theportfolio is nota correct way to calculate the std deviation of return of the portfolio.

- In order to derive the portfolios return probability distribution, we must know how individualasset returns interact. This information comes in the form of a joint probability distribution:

- Each cell inside a box describes the probability of a particular set of returns being

simultaneously earned by both assets A and B.- The joint (interior) probabilities must sum in rows and columns to equal the original

probabilities of the individual security returns while the sum of all cells must equal 100%(1.0).

Portfolio Events and Probabilities

- The whole portfolio has less risk than the average risk of the securities within it due todiversification. [see December 2006 Q2.1]

- An easier method for figuring out risk of a portfolio is using the correlation coefficient.


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The Market Model and Individual Asset Risk

- William Sharpe and John Lentner ascertained the only relevant risk in a market whereeveryone understands the benefits of diversification is the undiversifiable or systematicrisk of an asset.

- The reason for a minimum level of risk even in a well-diversified portfolio is that there is acommon correlation present in all securities, and this limits the amount of diversificationpossible. This common factor is called the market factor(Riskm).

- The systematic risk of securities is thus based upon the extent to which their returns areinfluenced by the market. The actual measure of the undiversifiable risk of a security (j) is:

Systematic Riskj = Std. Deviation of returnj x Correlation ofjwith the market.

- A security with a correlation close to +1 will have a systematic risk close to its standarddeviation not much of its risk will be diversifiable.

- A security with low correlation to the market will have much of its risk diversified away whenheld in a portfolio with other securities, and thus has a low systematic risk.

- A simple manipulation gives a more commonly used formula:

Betaj j Standard deviation of returnj Correlation ofj with market

Standard deviation of market return

Or j jjm j j mjm j jm Covariance jmm m m Variance m

where jis the beta coefficient forj; jmis the covariance ofjand the market; and 2

mis the

variance of the market.

- Also known as the regression coefficient. Provides the same information as the previoussystematic risk measure, but scaled to the risk of the market as a whole.

- For example, a of 1.0 indicates that an xpercent increase or decrease in the return on themarket is associated with an xpercent increase or decrease in the return on that security,while a of 1.5 indicates an xpercent increase or decrease in the market will result in a1.5xreturn on the security. The coefficient:

- The steeper the slope (the higher the coefficient), the greater will the returns on thesecurityjamplify or gear upward (or downward) the returns on the market portfolio.


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The more positively assets are related in a portfolio, the less there will be to gain from diversification (MCQ7A5).

As correlation declines, the benefits of diversification increased (MCQ7A5).

A positive value for covariance means that the assets move together, range +1 to -1.

Portfolio risk (s= Standard deviation) is equal to the weighted average (linear combination) of the risks ofindividual assets when the individual asset risks are perfectly correlated, ie. corr = +1.0

coefficient is a measure of the undiversifiable or systematic risk.

The REGRESSION coefficient is produced when a regression analysis is done on two variables. The reg. Coef.will indicate the steepness of the slope of the line of best fit through the different observation (Figure 7.5) that isthe regression line that runs through the different points, and the is the reg. coef indicating the steepness ofthe relationship between the share and the market.

The Market Model or Security Market Line- If the financial market sets securities returns based on their risks when held in well

diversified portfolios, systematic risk will be an appropriate measure of risk for individualassets and securities, and the SML as depicted below will dictate the set of risk-adjustedreturns available in the market:

- Above relates the amount of systematic risk inherent in the returns of a security (its ) tothe returns required on that security by the market. The relationship is positive in that thehigher the systematic risk ofj, the higher its required return.

- The SML is located with repect to two important points, the risk-free rate (rf) and the market

portfolios risk-return location (m). m has a return of E(rm) and (by definition) a of 1.0- The quantitative relationship between risk and return is:

E(rj) = rf + [ E(rm) rf ]j CAPM formula = rf + (rm rf) (7.1)

- The SML based returns are the opportunity costs of capital suppliers of companies, andthus can form the basis for evaluating company investments.

- These investments must offer returns in excess of the capital suppliers opportunity costs inorder to be acceptable.

The central idea behind the CAPM is that you get higher return for taking on greater risk.(Dec2006Q2.2)

If investors hold the market portfolio, they will have diversified away all their specific risk and be lewith just the market risk. The measure of a shares market risk in the portfolio will be its beta.

The reason why a portfolios risk cannot be reduced to zero by diversification is that there is acommon factor/ influence (the market) among most investments which causes their returns to bepositively correlated.

j

rf

m

E(rj)

E(rm)

SML

1.0


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Using the Capital Asset Pricing Model in Evaluation Company Investment Decisions

- The CAPM or SML is a system that generates required rates of return based upon theriskinesses of assets.

- The WACC of any company is in fact an average of the risk-adjusted rates of return of thecompanys various endeavours, including its asset types and associated future cash flowexpectations.

- In order to be acceptable, an investment must offer an expected return in excess of the

return depicted on the SML for the investments systematic risk level. This means that goodinvestments would plot above the SML, perpendicularly above their systematic risk.- In the above example, investment A is above the WACC, thereby implying it is acceptable.

However it is below the SML which indicates that it does not offer a return high enough tocompensate for its risk. Investment B has the opposite problem.

- A company should not generally apply its WACC as an investment criterion. It will only givea correct answer when an investments risk is the same as the average risk of the entirecompany. (MCQ7B7)

- Most companies are aware that projects can differ in risk, and that some adjustment ofcriterion is advisable. Usually this takes on the form of fixed increments or decrements tothe companys average criterion.

Estimating Systematic Risk of Company Investments- To use the SML for estimating required returns, the amount of systematic risk (size of the

coefficient) of a project must be specified. There are several ways to do this:a. If project is of the same risk as the existing company, and its shares are traded on

the stock market, one can merely look up the coefficient of the companys sharesin one of the financial reporting services that supply such data.

b. If risk differs (+ or -) from the company average, the investment may be similar toanother companys. In such situations, the coefficient of the other company canbe used. This is also valuable when the shares of the investing company are nottraded, but those of a similar company are, and the investment is simply a scalechange.

- When market generated coefficients are unavailable, the systematic risk measure mustbe constructed artificially. The best approaches to such estimates begin with a coefficientfor the company / division thinking of undertaking the project, and adjusting that coefficientfor the differences between the project and the company or division.

- In constructing coefficients from the characteristics of the investment itself, it is necessaryto concentrate upon the underlying factors affecting the returns on the project.

Some Considerations- If the projects revenues are expected to be quite volatile in reaction to overall market

activity, relative to the divisional / company average, an adjustment to the coefficientmust be made.

- Similarly, on the cost side, if fixed costs of a project comprise a relatively high proportion ofits total cost, the coefficient of the project must be adjusted upwards this is describedas operational gearing. = CF Total cost (MCQ7B8)Retail operations have high FC investments in their stores, once covered, extra salesgenerates high level of profit.

ReturnA

E(rj)

ARISKWACCB

ReturnB

WACC

SML

j

B

A

WACC


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- One preliminary adjustment that must be performed when constructing . If the beginningvalue is from a company that has borrowed money, the value must be purified before theother adjustments are made. This is done by:

u = eE + dD = weighted average of the 2(D+E)V V

Where eand d are observed equity and debt coefficients, E and D are theirobserved market values, and V= E + D.

- Once uis solved it must be adjusted for revenue risk differentials .To adjust for revenue risk differential, uis multiplied by the ratio of the investmentsrevenue volatility to that of the company:

Revenue-adjusted = u Project revenue volatility oCompany revenue volatility

- Next is adjusted for operational gearing: Fixed Cost Adjustment

Project u = Revenue-adjustedx2 (1 + Project fixed cost %) 2(1 + Company fixed cost %)

- The final step that remains is to re-adjust the reconstructed and ungeared coefficient forany financial gearing planned for the project . In order to do so, we must know the coefficient for the debt that will be issued for the project as well as the gearing ratio. With

these two items as well as the ungeared coefficient of the project, the equity coefficientcan be calculated using:

u = eE + dDV V

Estimating the WACC of an Investment- Invoking the SML relationship will allow us to find the return required on the equity of the

project.

E(rj) = rf + [ E(rm) rf ]j CAPM formula = rf + (rm rf) (7.1)

is determined as above

rf is given by government bond interest rates (YTMs) for comparable maturityinvestments in such bonds.E(rm), the expected return on the market portfolio, is a function of the risk-free rate andtherefore it makes more sense to estimate the difference between E(rm) and rf. Thisfigure is the historical average market (i.e. LSE, NYSE) return abovethe risk-free rate.

Equity risk premium = Market risk premium = Stock market risk premium = (rm rf)

- Once the equity required return is determined one can find the after tax cost of capitalusing the same equation (if applicable).

- The next step is to find the WACC of the project:

rv* = WACC = D (rd*) + E (re)V V

The correct time to use a cny to estimate the discount rate for a project is when the project is small in sizecompared to the existing cny. MCQ7A10


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Other Considerations on Risk and Company Investments

Certainty Equivalents- It is possible to adjust downward the expected future cash flow itself for its risk

characteristics, creating a certainty-equivalentcash flow, and to discount that cash flowat the risk-free rate.

- The SML equation must be changed to state cash-flows:

CFce= CF o E(rm) rf ox Covariance (CF,rm)

Variance (rm)- The certainty equivalent cash flow (CFce) is found by subtracting from the expected risky

cash flow (CF) an adjustment for its systematic risk.- That adjustment uses a variant of the market price of risk, [E(rm) rf]/ Variance (rm),

multiplied by a measure of the systematic risk of the cash flow, Covariance (CF, r m).Variance (rm) is the variance (standard deviation

2) of the market return, and the covariance

(CF, rm) is the covariance (coefficient of the CF x variance of the market return) of thecash flow with the overall market.

Risk Resolution across Time- A commonly encountered complexity in investment analysis is that the risk of an investment

can be foreseen to change as time passes, yet a decision as to whether to undertake theinvestment must be made now.

-

A common error in this situation would be to treat the investments entire cash flow set ashaving the same risk.- The basic question is whether to undertake an initial outlay, where the desirability of that

outlay depends upon the outcome of the test. For example in giving up $500 000 now thereis a 50% chance of receiving 0 and a 50% chance of receiving $2 500 000 one periodhence. Expected payoff is thus:

0(0.5) + 2 500 000(0.5) = 1 250 000

- In order to be undesirable, the discounted certainty equivalent of the $1 250 000 wouldhave to be less than $500 000.

Conclusion- If shareholders are already well diversified, diversification at the company level is irrelevant

(and probably costly) to them.


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Module 8 Company Dividend Policy

- Dividends are the amounts of cash that a company distributes to its shareholders as theservicing of that type of capital.

- Since any residual cash not paid as dividendsis still owned by shareholders, this retainedcash is reinvested in the company on behalf of shareholders. The dividend decision is thusalso a cash-retentionor reinvestmentdecision.

Dividend Irrelevancy I

- The net result of changing a companys dividend is the substitutability of capital gains(i.e.share value increases) as the dividend is reduced for cash when it is paid.- Increased dividends = decreased market value, and vice versa.- The investment / dividend decision:

- The connection is a truly organic one for the company: if dividends are changed, and noother action undertaken, the companys investments will also change. Using the abovefigure, an increase in dividends would be shown as a widening of the dividend pipe and anarrowing of the retention pipe resulting in a smaller investment amount.

- To isolate the effect of dividend choices, the companys investment plans must be keptintact as dividends change.

- Increase in dividends = increase in new equity (more shares issued)- Decrease in dividends = decrease in new equity (less shares issued)

-

The company share value in total is unchanged, therefore existing shareholder wealth isthe same.- When the effect of company financial decisions upon shareholders portfolios can be

undone by the offsetting actions of shareholders, the company financial decision isirrelevant.

Dividends and Market Frictions

Taxation of Dividends- From the shareholders perspective, it is after-tax dividends that are of interest. The

dividend substitute - capital gains, are also potentially liable for taxation.- Of the two it is usually dividends that are taxed more heavily.- In countries where dividends are net of company taxes, and the dividends paid are taxed at

the shareholder level, dividend payment is expensive.- In such a tax system where double taxation of dividends is unavoidable, there is a strong

tax incentive against the payment of dividends for companies seeking to please theirshareholders.

- Some countries have imputationsystemswhich impute an amount of company taxes toshareholders based upon the dividends that companies pay, and then give shareholders acredit on their taxes for that amount.

- This only balances the double paymenteffect if personal income tax liabilities ofshareholders = the tax credit.

Dividend taxes are a market friction but not a transaction cost of dividends. MCQ8B4


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Transactions Costs of Dividend Payments / Preference of shareholders- Brokerage fees to be paid for transactions.- Shareholders may prefer one dividend policy to another depending on their preferences for

consuming wealth across time and the costs they would pay to achieve the desiredconsumption pattern.

Flotation Costs- Companies themselves incur costs in raising money from capital markets when they pay

dividends so high as to require new shares to be issued.These costs are called Flotation Costs.

- Depending on the mechanism of sale, these flotation costs can be significant (5-25% oftotal value of issued shares).

Combined Frictions- Taxes, transaction costs and flotation costs and information costs net bias in most cases is

against the payment of dividends.- The resulting optimal dividend policy would be to find all the investments with positive

NPVs and retain as mush cash as is necessary to undertake them; if there is cash left over,a dividend could be paid; only raise new equity capital when funds insufficient for allinvestment sometimes called a passive residual dividend policy (not optimal).

Dividend Clienteles: Irrelevancy II- Different groups of shareholders have come to be called clientelesin finance. The

interpretation is that they comprise groups that would be willing to pay extra to get the typeof dividend policy that is best suited to their own tax and consumption proclivity.

- It is unlikely however that a company choosing one policy over another will be of benefit toshareholders because there are likely to be no relatively under-serviced clienteles willing topay a premium for the change.

- A better term than irrelevancy is probably inertia.- A company switching policies can actually be costly to its existing clientele, so whatever a

companys current policy is, it is likely to be optimal.

Other Considerations in Dividend Policy

Dividends and Signalling- Gives indication about future performance of the cny.

- It is in the interests of both managers and shareholders to have share prices reflect newinformation (good or bad) as quickly as possible.- Alterations in dividend policy are a subtle way to communicate this information.- In order to be truly effective though, dividend payout must be relatively smooth over time.- Share dividend: instead of dividend, additional partial share of the company is paid.

Preserve cash for investment purpose, can reduce taxes, can increase borrowing capacity,increasing risk for shareholders.

- Share splitting: a two for one split is the same as a 100% share dividend.Might be a sign of financial difficulty and this is one way of freeing up cash to repaybondholders.

A one for two share split (reverse stock split -> raises the share price) means you have halfthe number of shares, but they are worth twice as much as before.Cnies undertake share splits because

1. Their shares have become too expensive2. It improves their liquidity3. It signals growth prospects

Liquidity of share = ease and efficiency of trading in the market (financial market liquidity).

Signalling: (i) reverse stock split, (ii) share repurchase, (iii) increase in payout ratio


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Dividends and Share Repurchase- Share repurchases are nothing more than a cash dividend to shareholders.- Company claims of investing in itselfare bogus as long as there is one share

outstanding.- In some countries money received in share repurchase transactions is taxed more lightly or

not at all. Share repurchases on the open market also show signs of being signallingattempts that receive a positive response from holders.

- One type of share repurchase that is not so positive for shareholders is a targetedsharerepurchase. This is a transaction wherein a company offers to repurchase only particularshares (usually held by potential buyers). The repurchase price is at a significant premiumover the market price.

The traditional view of dividends says that shareholders prefer dividends now with high payout ratios rather thancapital gains (the bird in the hand argument) MCQ81A

The bird in the hand argument is wrong because the riskiness of distant dividends is already accounted for inthe discount rate. MCQ8A3

The bird in the hand argument regards dividends paid now as being more valuable than uncertain capital gains.FAQ M8

In perfect market environment, if dividends are reduced, market value will be higher because fewer new shareare issured. You release more cash for investment => thus reduce the need for issuing more shares, so any

increase in NPV will be captured by the old shareholders. MCQ8B2

The risky position in the perfect market is reducing dividends, because it means that the shareholders isactually receiving less cash from the cny and more of his wealth is tied up in share value. MCQ8B3

Important factors to consider when deciding the size of dividends Profitability of cny (and prospects for profits over business cycle) Cnys need for additional finance (liquidity position) The ability of the cny to raise additional finance on the markets Its shareholders dividend preferences Gearing level which might limit the cnys ability to pay dividend

Raising money from the markets is expensive, so the passive policy saves on flotation coasts. Theunpredictability of dividend payments is the strongest argument against passive policy. Shareholders likepredictable dividends. MCQ8A4

Information costs cnies are constrained on what they can tell to investors, so theres no free flow of informationbetween the cny and the investor. The cny will favor a dividend policy that is stable and predictable which theycan use the dividend information to the investors. (profiler final exam 1: dividends)

In the real world with market frictions, optimal dividend policy = passive residual dividend policy.


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Module 9 Company Capital Structure

- A companys capital structure is the extent to which it is financed with each of its capitalsources (debt and equity).

- Straight debenture: the companys assets in general are to be pledged as collateral for the loan. (MCQ 9.5)It has a floating charge on the cnys asset, whereas the Secure Debenture has a fixed charge on a specific asset.

Capital Structure, Risk and Capital Costs- Debt is not more expensive than equity supposedly due to debt carrying required (higher-

priority of senior) interest payments whereas equity does not. It ignores the fact thatdividend payments are legitimate capital costs of the company.

- Debt is not cheaper than equity since the issuance of debt increases the attendant returnsrequired on equity (often called the implicit costof borrowing).

- Performing a comparison of EBIT-EPS for two companies enforces this rule.- Results can be charted on an EBIT-EPS chart. (Figure 9.2 p9/8)- The differences in the level of steepness in EPS ranges are verbally described as gearing

or leverage(the variability of operating income is amplified). Financial risk.

Capital Structure Irrelevancy I: M & M (Merton Miller and Franco Modigliani)- The M&M economics of company capital structure predicted that it would make no

difference to shareholder wealth whether the company borrows money or not. Financialmarkets will ensure this.

-

Because shareholders can borrow and lend on the same basis as companies, any benefit(or detriment) residing in company borrowing can be duplicated (or canceled) byshareholders borrowing or lending transactions in their own personal portfolios.So company capital structure does not matter.

- A wealth increase is impossible since identicalfuture cash flow expectations can beachieved in a different manner, and less expensively. Shares of any company mustsell forjust what it would otherwise cost to acquire the same future cash flow expectations.

Arbitrage and Prices A Digression- Arbitrageis a transaction wherein an instantaneous risk-free profit is realized.- Efficient financial markets abhor arbitrage, and arbitrage opportunities cannot be expected

to exist for any significant time in a market with well-informed investors.- Market prices must adjust to cause all equivalent future cash flows to sell for the same

price.- This adjustment occurs naturally with the forces of demand and supply.

Summation of Capital Structure Irrelevancy I- The M & M ideas make clear that the total value of the company must be unaffected by a

change in its capital structure. E.g.: Capital structure & company values (w/o taxes):


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Capital Structure and capital cost without taxes- The below illustrates the behavior of the required rates of return and overall capital cost of

the company: it alters the companys capital structure.

- M&M argument over capital structure stated that cnys average cost of capital is notaffected by the level of debt or equity. MCQ9A4

- With respect to specific weighted average relationships determining rv (overall capitalreturn/ cost), we can imply:

rv = D (rd) + E (re) rv = D (rd) + (1-D) (re)V V V V

- The higher proportion of lower-cost debt exactly offsets the lower proportion of higher cost-equity, such that their weighted average is unchanged (rv=cst).

Capital Structure Decisions and Taxes- Companies are taxed by the government on the amount of incomeor profitthat they

make.- Recall interest tax shields: ITS = It x Tc- When taxes exist, and when interest is deductible by companies, companies will tend to

use debt as their primary source of capital.- Debt is therefore cheaperin the sense that the total of taxes paid by companies and their

shareholders will be lower than if the companies were to issue equity.

Summation of Capital Structure relevance with Taxes- Operating cash flows that a company produces are transformed by the taxation system

before they can be claimed by capital suppliers. This transformation is different dependingon the capital structure of the company.

- Because of the tax advantage in company borrowing, a company with debt in its structurewill be more valuable than an otherwise identical company that does not borrow.

- To find the value of this tax benefit (ITS is a stream of cash flows):

VITS = ITSRd

- The entire firm could be valued by either debt plus equityor the following APV typesituation (Value unleveraged + leveraging-based tax benefits):

V = VU + VITS


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- The relationship between changes in capital structure and changes in capital claim andcompany values are as follows:

Capital Structure and Company values with taxes

Capital Structure and Capital cost with taxes

- Effects on required returns and capital costs:

The WACC (rv*) is the discount rate that gives the correct valuation when applied to a companysungeared free cash flow (FCF*), not including ITS.

- Notice that the companys cost of capital (WACC) steadily declines as the companysubstitutes debt for equity in its capital structure. This is because even though a companysvalue is increasing, its ungeared FCF* must (by definition) be unchanged as D/Vincreases. So by the relationship

V = FCF* rv*must be declining as D/V increases.rv*

- A companys cost of capital (WACC ie. rv*) is therefore lower the higher its proportion ofdebt.

Capital Structure Irrelevancy II: Taxes (June 2007 Q2.3)- Merton Miller has argued that as more and more borrowing is undertaken by companies in

economies with progressive personal taxes, the interest rates necessary to sell bonds tohigh personal-tax investors will increase causing the benefits of company borrowing todisappear.

- The tax benefits of company borrowing compete with other mechanisms used to reducetaxes (depreciation, credits) which tends to reduce debts advantages, particularly when theamounts of income that require shelter from taxes is uncertain.

- Borrowing to obtain tax benefits is less desirable in an uncertain world than when futureincome streams are known with certainty.

Capital Structure and Agency Problems (see module 12 as well)- Agencydeals with situations where the decision-making authority of a principal

(shareholder or bondholder) is delegated to an agent(managers of a company).- Agency considerations concern themselves with the instances where

conflicts of interestmay arise among principals and agents, and how they are resolved.- One important mechanism used to resolve conflicts of interest is by the issuance of

complex debt contracts. For example, some debt claims carry a convertibilityprovision.This means that under certain conditions, at the option of the lender, a bond can beexchanged for common shares. Therefore avoiding certain agency costs.


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- Another instance of agency conflict occurs when a company in financial distress is unwillingto undertake a profitable investment because the resulting effect would be to helpbondholders, not shareholders.

Least helpful in resolving an agency conflict would be secured debentures. It does not stop managersembarking on risky projects. MCQ9Q6Vs. restrictive covenants/ convertible bonds/ maintenance of minimal financial ratios.

Convertible bonds, equity warrants, executive share options are issued by the cny so they form part of thecny capital structure. Equity traded options are an exchange created investment not issued by the cny so

do not form part of the capital structure. MCQ9A1

Equity traded options are the most common type of equity for derivatives. They provide the right, but notthe obligation, to buy (call) or sell (put) a quantity of stock, at a set price (the strike price), within a certainperiod of time (prior to the expiration date).

Dividend payments represent CF leaving the cny and going to shareholders. In certain situationsbondholders may be worried that the cash leaving the cny might impair the cnys ability to service its debtobligations. As a result clauses in debt contracts limiting dividend payout.

Default and Agency Costs- The true costs of bankruptcy or financial distress are:

a. Legal costs and administrative costsThe costs involved in pursuing the legal process of realigning the claims on the assets of the companyfrom those specified in the original borrowing contract.

b. Loss of profits as a resultThe implicit and opportunity costs incurred in this effort relative to what would have happened had thecompany financed instead by equity capital.

c. Loss of customersd. Loss of credit

- Unless there is some unique benefit to the issuance of a particular type of claim (such asthe interest deductibility of debt), there is no reason to think that one type of claim will bebetter than another.

Magnitude of bankruptcy costs, most to the least:(a) aeroplane manufacturer, (b) photocopier cny, (c) construction cny, (d) supermarket cny.

Other Agency Considerations- Perk consumption beyond the point where management productivity is efficiently

enhanced.- Conglomerationto increase the size and reduce the CF risk of the company, thus

stabilising management remuneration, with no benefit to shareholders holding welldiversified portfolios.

Making the Company Borrowing Decision- No quantitative method.- One point that stands out as likely to be of importance to the optimal amount of borrowing

is tax considerations. But the practitioner must be very careful to judge the nettax benefitsof borrowing.

- There is a common notion in practitioner finance that risky business should borrow less (orbe lent less) than companies that are not so risky. This is more of a Darwinian rule of

thumbthan a thought out, validated notion. This ruleprobably works due to agency costs risk is likely to make agency costs higher.

The borrowing decision contains signalling power to investors.By increasing borrowing management is signalling that they have confidence in the strength ofcash flows in the future. MCQ9A9


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Book Values and Borrowing

- Practitioners argue book valuesshould be used for measuring the extent of companyborrowing while academic types argue that market valuesare the correct measure.

- The use of book values in the real world makes sense. They are a good measure of theextent to which values will not be upset by financial distress when the company is engagedin borrowing.

When using debt and equity weights to calculate the WACC, we use market values these willreflect the current required rate of return on the assets, the markets perception of the risk ofthe company. It reflects the value of these assets today. Book Value is likely to be out of date,may reflect decisions taken years ago and not to be relevant today.

Techniques of Deciding upon Company Capital Structure

1. Examine what companies in similar lines of businesshave decided about the amounts they willborrow.

- The best way to do this is to look at company averages for borrowing ratios in the industryof interest.

- The distance of a companys debt ratio from the industry average determines the borrowingdecision.

2. Financial planning a detailed examination of the companys future cash-flow expectations(including those associated with the borrowing alternatives under consideration) so as to decideupon the best choice of financing method.

- The company financial planner, in possession of a capacity to simulate the cash flow andfinancial statements of the company across the future, asks a series of what-ifsof theplanning model.

- The result is a set of possible future outcomes for the company under the sets of conditionsand financing alternatives that the planner examines.

Suggestions for Deciding about Capital Structure

1. The company should use simulation to attempt to forecast its cash flows and financial stat

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