Finance market Finance is the economics of allocating resources

across time: Borrowing shifts from future to present Lending and investing shift from present to future

Investments are of two kinds Financial: mere reallocation across time Real assets: creates new future resources, such as

buildings and equipment Market provides allocative information: the basis for

comparing the returns of competing uses, including an adjustment for risk.

Market Interest Rates and Prices The market interest rate is the rate of exchange

between present and future resources. This rate is always positive, since no lender is

prepared to receive fewer future resources than they give up in the present.

There are actually many market rates at one time, covering different riskiness and different periods of time.

Present Value Present value is defined as the amount of money to

be invested or lent now to end up with a particular amount in the future. The financial exchange line between present and future

resources has a slope = -(1 + i) A higher interest rate thus translates to a steeper slope: a

greater amount of futures resources having to be exchanged for a present amount

Finding the present value of the future cash flow is called discounting

Present Wealth Present wealth discounts a market participant’s

entire time-specified resources to a single number. This can be used as a benchmark to measure the benefit of

a proposed financial decision This cannot be changed by present financial investments,

since all should have a present value equal to their cost. A company’s sole task is to maximize the present

wealth of its shareholders. The shareholders can then adjust their individual patterns

of resources by dealing in the financial market.

Net Present Value Net Present Value (NPV) is the present value of the

difference between an investment’s cash inflows and outflows. An investor’s opportunity cost is the alternative of earning

a market rate on a financial investment. The NPV of an investment is the discounted value of the

amounts by which the investment’s cash flows differ from those of its opportunity cost.

Internal Rate of Return Internal Rate of Return (IRR) calculates the

average per-period rate of return on the money invested. Alternatively, this can be viewed as the discount

rate that equates an investment’s cash inflows and outflows (NPV = 0).

The IRR can be easily compared to a comparable financial market opportunity of equal timing and equal risk.

Compound Interest Compounding is the simple recognition that the

interest earned on an investment can itself earn interest.

Income stream from an investment at t0 is CF0 [1 + (i/m)]mt, where m is the number of times per period that compounding takes place.

Continuous compounding is based on making the compounding period infinitesimally small: CF0(ert).

Investing

Investing is real assets – such as productive machinery, new production facilities, research or a new product line – creates new cash flows that did not previously exist, and thus new wealth that was not there before.

A good investment will produce more wealth than it consumes; a bad investment will do the opposite.

Multi-Period Cash Flows The future value of a present amount invested at the

rate it for t periods is the invested amount multiplied by (1 + it)t.

The present value of a future amount CFt is: PV = CFt/ (1 + it)t.

The value of an asset that generates a stream of future cash flows is the sum of the present values of each of the future cash flows associated with the asset.

Multi-period investments A constant annuity is a set of cash flows that are the

same amounts across future time points. The present value of $1 per period for t periods implies a constant cash flow per period, and is therefore an annuity. PV of $1 for t periods = [(1 + i)t – 1] / i(1 + i)t

Future value of $1 for t periods = [(1 + i)t – 1] / i A perpetuity is a cash flow stream that is assumed to

continue forever. The formula for the present value of a perpetuity is: PV = CF/ i. For example, $100 per period forever at a discount rate of 10 per cent = $100/0.10 = $1,000.

Multi-period investments, 2 If cash flows continue forever, but grow or decline

at a constant rate g, the formula becomes: PV = CF/ (i – g). This might provide a reasonable approximation for a stream from a long-lived asset.

For example, a cash flow stream that starts at $100 at the end of this period and grows at 5 per cent per period, with a 10 per cent discount: PV = $100/ (0.10 – 0.05) = $2,000.

Interest Rates Interest rates that begin at the present and run to

some future time point are called spot interest rates. If interest rates are 5% between t0 and t1, 6% between t0

and t2 and 7% between t0 and t3, then the one-period spot rate is 5%, the two-period spot rate is 6% and the three-period spot rate is 7%.

The set of all spot rates is called the term structure of interest rates.

Bonds A coupon bond has a face value that is used, along

with its coupon rate, to figure the pattern of cash flows promised by the bond. A cash flow three years out is discounted by the three-

period spot rate; a cash flow two years out by the two period spot rate, etc.

The cash flows comprise interest payments until maturity, when the principal payment plus a final interest payment is promised.

A zero-coupon bond has only the final principal payment and no interim interest payments.

Yield The yield-to-maturity is the rate that discounts a

bond’s promised cash flows to equal its market price, analogous to IRR.

A difference in yields between bonds that have been subjected to the same discount rates is the coupon effect on the yield to maturity. It reflects that a greater or lesser portion of the bond’s value derives from the interest payments – because the interest is valued based on the spot discount rate for that period.

Comparing Yields The YTM’s are expressing not only the earning

rates but also the amounts invested in the bonds across time, i.e., higher interim cash interest payments means that relatively less is invested in the later periods.

The YTM, being a constant per-period average, cannot form the basis of comparison unless the cash flows are identical. Bonds of equal risk must earn the same rates during the same periods.

Forward Interest Rates A forward interest rate is usually noted with the

letter f surrounded by a left subscript indicating the rate’s beginning time point and a right subscript indicating the rate’s ending time point, e.g., the interest rate between t1 and t2 is noted as 1f2.

The implied forward rate can be calculated by extracting the invested amount and comparing to the payment on that amount.

Spot and Forward Rates

The present value of a t2 cash flow can be arrived at: Discounting with the spot rate for two periods Discounting for the forward rates for one period each Therefore: (1 + i2)2 = (1 + 0f1)(1 + 1f2)

If the 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 nth root of that product, and subtracting 1.

Spot and Forward Rates 2

If the spot rates are known, the forward rates can be found by solving first for the forward rate nearest the present, and successively working to rates further in the future.

Interest Rate Futures At t0, a market participant may have certain

expectations about the rates at t1. In the interim, new information may appear that causes the market to revise its cash flow expectations, opportunity costs or both.

The possibility of a rate change can be hedged using interest rate futures.

The value of the futures contract depends on the implicit rate at the time that it is bought or sold. If rates increase, the value of the futures contract decreases.

Duration

Duration is a measure of the number of periods into the future where a bond’s value, on average, is generated.

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

Calculating Duration Sum of: proportions of the present value of the bond

represented by the cash flows, each multiplied by the number of years until the cash flow is received. (i x CFi)/(ri

i x PV), where r = interest rate

This is a particularly valuable concept for coupon bonds where, depending on their coupon rates, the duration of a nine-year bond could be longer than the duration of a ten-year bond.

2. Company Investment Decisions Those having claims upon a company’s assets

include those having contracts (both formal and informal), government (for taxes) and those holding securities (common shares).

The quid pro quo of limited shareholder liability is that equity is a residual claim: all other claimants will be satisfied before a distribution to shareholders.

Share Value Shareholder wealth (market cap) is the market value

of the common shares. To maximize the former is to maximize the latter.

The value of a share is related to the discounted value of the stream of future dividends. Different bids and offers result from the different perceptions of value and of the discount rate.

The Investment’s Effect on Equity

Wealth of existing shareholders is increased by the NPV of the investment, regardless of the source of investment capital. If an investment will generate $X and costs $Y,

the new capital suppliers will get $Y of the $X value increase, thus leaving $X - $Y = NPV for the equity holders of the company.

The Price/ Earnings Ratio The P/E ratio is a complex function of the size,

timing and risk of cash flows, usually based on the preceding period’s earnings (as a proxy for earnings at the end of the current period).

The nexus between the discount rate (which applies only to dividends) and the P/E ratio (which applies only to earnings) is the payout ratio. Price per share0 = dividend per share1 / (re – g) g = re – (dividend per share1 / price per share0) (Price per share0 / earnings per share1) = [payout ratio / (re

– g)]

3. Earnings, Profit and Cash Flow The differences between the timing of cash flows

underpins the creation of the Statement of Cash Flows, to supplement the Income Statement.

A table of changes in cash flows might show amounts attributable to: Customers Operations Assets Government Capital Requirement (the sum of the above)

Free Cash Flow

Free (as in ‘unfettered’) Cash Flow is interpreted to be the amount that could be withdrawn by capital suppliers without impairing the operating expectations. If the amount is negative, it is to be contributed.

Components of Cash Flow Customers: includes sales revenue actually received, but

also later capital dispositions Operations: (1) paid in the current period, (2) tax

deductible in the current period, and (3) not a payment to a capital supplier. These ‘expenses’ do not include interest or depreciation.

Assets: are cash flows at the time listed, but must be capitalized and deducted in future periods.

Government: A negative tax amount for a project will reduce overall tax for the corporation in the current period or allow recovery of taxes through a “carry-back”.

Depreciation

The original cash outlay (less its expected salvage value) is written off in even amounts (straight-line) over the remaining life of the project.

At termination, the salvage value is also written off as an expense at the same time that the asset sale becomes ‘revenue’.

4. Weighted Average Cost of Capital

WACC is a discount rate based on the relative costs of the different capital claims.

This captures in a single discount rate all of the returns necessary to service the company’s capital claims.

Interest Tax Shield Tax laws allow corporations to reduce their taxes by

deducting interest expense: The reduction in income taxes because of interest

deductibility is called its interest tax shield. Dividend payments, which are likewise a payment to a

capital supplier, are not deductible. Companies that pay dividends instead of interest pay more

taxes. The interest tax shield is found by multiplying the

period’s interest expense by the corporate income tax rate.

Project Cash Flows

The 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.

The flows are calculated as if the project will be financed with equity, even if the plan is to finance it with debt.

WACC components & weighting The WACC incorporates the after-tax cost of debt,

rather than the debt supplier’s required rate. Debt cost = Debt required rate x (1 – corporate income tax

rate) This and the required return on equity are weighted

according to the claim of each upon the cash flows. The WACC discounts the ungeared (i.e., unleveraged

by tax shields) cash flows. The WACC-NPV is for the analyst that can specify

the proportions of the financing, even if the size of the components is unknown.

Adjusted Present Value The Adjusted Present Value (APV) allows the

analyst to incorporate various adjustments to cash flows, but this method requires that their dimensions (rather than proportions) be estimated.

APV will find the same NPV as WACC by: (1) discounting the unleveraged cash flows based on financing completely with equity, (2) then adding the discounted (by the pre-tax rate of interest) interest tax shields.

5. Estimating Cash Flows

The analysis must include all changes that are expected to take place in the corporation’s cash flows, and include nothing but cash flows.

Free cash flow = Revenues – Direct Expenses +/- Change in Working Capital +/- Change in Assets +/- Taxes

Issues Issue #1: Valuations should consider economic

opportunity costs (e.g., alternate use of equipment) Issue #2: Changes may result from interactions with

other activities (e.g., the new product results in declining sales of another product, unless this would have happened anyway.)

Issue #3: Cash outlays that have already been made – sunk costs – are to be ignored.

Issue #4: Accounting numbers may relate neither to cash flow nor to the changes caused by the project.

Adjustments I Sales revenue can be converted to cash receipts by

adjusting for the change in accounts receivable, but it is probably preferable to simply adjust for revenues and expenses by adjusting for the change in working capital. Working capital = current assets – current liabilities

Interest and capital repayment are not cash flows, but merely claims on the cash flows created.

Adjustments II If calculating NPV or IRR, the tax calculation should

not include the deduction for interest, since this is already included in the discount rate for NPV, and IRR assumes equity capital only. APV requires an estimate of the tax shields, then discounts at the pre-tax rate.

Overhead allocations are a costing device, and unrelated to the change in cash flows.

6. Company Investment Analysis

Four widely-used alternatives to NPV and APV: Payback period Average (or Accounting) Return on Investment

(AROI) Internal Rate of Return Cost/ Benefit Ratio (CBR) or Profitability Index

(PI)

Payback Period I Payback Period is the number of periods until

a project’s cash flows recoup the investment outlay. It ignores all cash flows (the profit!) beyond the

payback period. The cash flows are not typically discounted, so

that a dollar received at t1 is valued the same as one in t3 so long as both are within the payback period.

Payback Period II The introduction of discounting makes the

calculation more complex, but only overcomes the second deficiency.

A payback period that equals the discount hurdle can be calculated: Payback = (1 / rv*) – (1 / (rv* x (1 + rv*)n), where n is the

number of periods in the project’s lifetime So for a discount rate of 10% and 8 periods, (1 / 0.1) - (1 /

(0.1* x (1.1)8) = 10 – 4.665 = 5.335

Average Return on Investment AROI calculates a rate of return on each period by

dividing expected accounting profits by the net book value of the investment’s assets.

This is the equivalent of dividing the average profit by the average assets. Using accounting profit rather than cash flow fails to

recognize that profits can be earned ahead of being received.

The model does not use discounting, and therefore values a dollar profit in t1 the same as the dollar profit in t3.

Cost Benefit Ratio The Cost – Benefit Ratio (CBR) has the NPV of the

cash inflows in the numerator and the NPV of the outflows in the denominator.

The CBR is greater than 1 if the NPV would have been greater than 0, and less than 1 when the NPV would have been negative.

Capital claimants are typically interested in the quantum of wealth increase, and not in a ratio.

Profitability Index The Profitability Index (PI) is very similar to CBR.

It has the NPV of all future cash flows in the numerator and the initial cash flow in the denominator. It can only be used when the t0 cash flow is an outlay.

It will produce the same ratio as the CBR when the only negative outlay in in the t0 period.

It calculates the NPV of the project per dollar of initial outlay, but is unsuitable for ranking projects because the criterion should be the quantum of wealth increase and not the ratio.

Internal Rate of Return (IRR) Both IRR and NPV are discounted cash flow

methods: IRR calculating a rate (and assuming reinvestment) to get an NPV of 0. The NPV uses the hurdle rate to discount, and assumes reinvestment at that rate, to calculate a change to shareholder wealth.

The IRR is unable to contend with each cash flow having a unique discount rate.

If the sign on the returns changes more than once, the IRR method will calculate a return rate for each additional change in sign.

Incremental Rate Algorithm I If ranking multiple opportunities, the IRR

should be supplemented with the incremental rate algorithm. This examines a pair of projects at a time. If a project turns out to be inferior to another, it is

excluded from the pool of contenders. The last remaining project (the winner) still must

be examined for its suitability, i.e., the best of the field could still be a dog.

Incremental Rate Algorithm II1. For each time period, subtract the cash flows of the

project with the smaller overall cash flow from those of the larger.

2. Determine the IRR of the incremental cash flows.3. If the IRR is greater than the hurdle rate, the higher

cash flow project is superior; if not, the lower cash flow project is superior.

4. Calculating the IRR tests whether one would invest in the difference between the two projects.

Capital Rationing I An investment is acceptable when it returns more

than a company’s shareholders could earn by owning other assets in the capital market.

Preventing a company from taking any number of projects with positive NPV: A constraint on resources, particularly management talent A disagreement with capital providers on the desirability

of the investment (a communications issue?)

Capital Rationing II

To merely select the highest NPV projects within the budget constraint is called exhaustive enumeration.

Where the number of potential projects is large, integer programming software can optimize the selection within the budget.

Investment Relatedness I Economic relatedness runs on a continuum

from very negative to very positive: Purely contingent: cash flows from one would not

exist without the other Somewhat positive Independent Somewhat negative Mutually exclusive: the selection of one precludes

the selection of another

Investment Relatedness II If investments are economically independent,

each can be judged on the basis of its cash flows alone.

Where investments are related, all possible combinations must be specified, along with the unique cash flow for that combination.

If all combinations have been listed, the combinations must be mutually exclusive.

Renewable Investments When considering an investment in different assets

that will be replaced (renewed), the comparison can be facilitated by applying the concept of an annuity.

Divide the NPV of a single cycle for each investment by the annuity present-value factor for the number of years in the asset replacement cycle at the appropriate discount rate. The result is a constant annuity outlay per period that has

the same NPV as the asset.

Inflation I Inflation is an increase in the price unaccompanied

by any other changes (such as quantity or quality). The “inflation-free” return is the real rate, and the

return that compensates for both that and inflation is the nominal rate. (1 + Nominal return) = (1 + Real return) x (1 + Inflation)

We typically quote the nominal rate. The real rate is the difference between the nominal rate and the effects of expected inflation (including uncertainty about it).

Inflation II The most common error in dealing with inflation is

in estimating cash flows. The estimates should include the effect of inflation on the cash flows, and then be discounted with nominal rates.

Inflation has the effect of reducing the value of depreciation deductibility for tax. An optimal method might be determined treating these expenses as generating ‘tax shields’, then comparing the present values from the competing methods.

Leases I In a capital lease, the lessor is usually in the

business of leasing assets, and not in the business of operating those assets.

To be preferable to using debt and purchasing the asset outright, the lease must otherwise accomplish something valuable to the lessee. It does not save money, even before considering the

margin of the lessor. It does not increase the company’s debt capacity, since

most capital suppliers recognize that the lease has nearly equivalent obligations.

Leases II The lease may allow the lessor to capture a tax advantage

when it may not otherwise be able to benefit from the deductibility of interest and depreciation.

Leasing can lower the cost of ‘information asymmetries’ that exist for some assets.

There are ‘economies of scale’ in the management of specialized asset leasing.

An analysis of the whether to purchase or lease should subject the cash flows to discounting at the comparable after-tax rate.

Performance Measurement The application of ‘economic income’ concepts has

become a popular approach to measuring economic performance. A division may be ‘charged’ for the capital invested, and the

period’s income (positive or negative) indicates whether the performance has compensated the company for its opportunity costs.

Activities that produce positive economic profit have positive effects on share value.

The greater difficulty is in implementation, since (1) it is a period by period measure of a longer-term operation, and (2) accounting performance is not the equivalent of economic performance.

7. Risk and Investment Decisions The Security Market Line (SML) describes the

relationship between risk and return: the higher the risk, the higher the required return. It depicts the set of risk-adjusted returns available in the market (i.e., opportunity costs).

An average expected return (a ‘mean’) on a project can be derived from a probability distribution of returns.

To a capital supplier, risk is best measured by the standard deviation of rates of return for a portfolio of assets (and not those of the assets themselves).

Portfolio A portfolio will have less risk than the average of the

securities in it due to the interactions between them. This is the value of diversification.

To the extent that the returns from securities are correlated (unless perfectly so), their risks will cancel each other out. The correlation coefficient runs in a continuum from +1.0 (perfectly correlated) to 0.0 (independent) to –1.0 (perfectly inversely correlated).

The covariance between a pair of assets is given by the product of the standard deviations and their correlation coefficient.

Systematic Risk

If market participants understand the benefits of diversification, only the risk that cannot be diversified away is relevant: the systematic risk of the asset.

There appears to be a lower limit to risk to be obtained by diversification, due to a common correlation among all securities, called the market factor.

Beta The beta () of an asset is a ratio of its standard

deviation of returns x its correlation with the market, over the standard deviation of market return. i = i i / m

This is the same as the covariance over the variance of the market return, or im / 2

m ; the variance – covariance model

This is sometimes called the regression coefficient, as it provides the slope of the regression line between the asset and the market.

Expected Returns

The expected return for the risk in project i is given by: E(ri) = rf + [E(rm) – rf] i

Where rf is the risk-free rate, E(rm) is the expected market rate and i is the beta coefficient

Estimating Systematic Risk The analysis requires a beta.

This reflects the extent to which the returns from a project are expected to accentuate or dampen the returns on the market as a whole.

This analysis might use the beta from a company with risk similar to the project.

It can also be estimated by making various adjustments to the beta of the company or division.

Adjustment 1: Financial Gearing

If the benchmark beta is from a company that has borrowed money, this effect must be removed: u = e (E/V) + d (D/V) Where beta (ungeared) is equal to the observed

market values of the beta’s of equity and debt, weighted for their proportions of the total, V.

Adjustment 2: Revenue Risk

The beta is adjusted for revenue volatility by multiplying the ungeared beta by the ratio of project revenue volatility over company revenue volatility. Revenue adjusted = u x (Project revenue

volatility / Company revenue volatility)

Adjustment 3: Operational Gearing There is a further adjustment for the ratio of fixed

prices in the project and company, because financial results will always be more variable with high fixed costs (operational gearing). Ungeared beta for the project is obtained by multiplying

the revenue-adjusted beta by the ratio of fixed costs in the project and in the company.

Project u = r.a. u (1 + Project fixed cost %/ 1 + Company fixed cost %)

Adjustment 4: Reassembly

The final step is to readjust the reconstructed and ungeared for any financial gearing planned for the project. This changes the proportions in u = e (E/V) + d

(D/V), solving for e

Weighted Average Cost of Capital The WACC of any company is in fact the average of

the risk-adjusted rates of return of the company’s various endeavors, including its asset types and associated future cash flow expectations.

This WACC should not be applied as an investment criterion unless the investment risk is the same as the average risk of the entire company.

Estimating the WACC, I Returning to the formula:

E(ri) = rf + [E(rm) – rf] i

Risk free returns can be obtained from the YTM on a government bond of comparable maturity.

Estimating E(rm) is isolation is more problematic, but: E(rm) is a function of rf The whole term – the difference between the market return

and the risk free rate – is more stable over time than the market return itself: averaging 9.1% in UK and 8.8% in USA.

Estimating the WACC, II

Beta was estimated using the process described above.

The WACC thus derived must yet account for interest deductibility, in order to reflect the returns to the full financing of the project. rv* = D/V (rd*) + E/V (re)

Certainty Equivalents As an alternative to adding a risk premium to the risk

free rate to produce a risk-adjusted discount rate, we could adjust the future cash flows downward according to their risk characteristics, and then discount the (now ‘certain’) cash flow at the risk free rate. CFce = CF – [Covariance(CF, rm) / Variance (rm)] x (E(rm) –

rf) The future cash flow is reduced by a portion of the spread

over the risk free rate, according to its systematic risk. This amount is still a future amount, and must be discounted

by the risk free rate to present value.

Risk Resolution Across Time

If an investment’s cash flows do not have constant risk across time, and can be resolved as time passes, this must be accounted for in the analysis, or the risk may be over-estimated for future cash flows (beyond the resolution point.)

8. Company Dividend Policy The dividend decision is, in mirror image, a cash

retention and cash reinvestment decision. If the were no frictions in transaction costs (taxes,

brokerage fees or flotation costs), the shareholder would be indifferent to the form of wealth: cash or share value. These frictions may give shareholder ‘clienteles’ a preference for one form over another.

There is enough competition amongst capital users that there is little to be gained by catering to a clientele by changing dividend policy, and it may indeed prejudice existing shareholders.

Passive Residual Dividend Policy

1. Retain as much cash as is necessary to make all investments with positive NPVs.

2. Raise new equity only when internally generated funds are insufficient.

3. Cash left over could be paid as a dividend.

Signaling

A company may attempt to establish a pattern of dividend payments, and employ a change from the pattern to communicate with markets and shareholders.

A share dividend may also be used for signaling.

9. Company Capital Structure

For any company, its debt claims require lower returns than its equity, because equity, being residual, must bear greater risk than debt.

Their interaction means that the addition of new debt has the effect of raising the risk to equity. Thus, geared equity is riskier than ungeared equity.

Earnings Before Interest & Taxes Earnings before interest and taxes (i.e., operating

income) is a measure of the total amount of money available to service debt, taxes (the priority dividends paid to an unwelcome equity claimant) and equity.

The more borrowing a company does, the steeper will be the line depicting the EBIT-EPS relationship (hence the term ‘leveraged’).

Modigliani & Miller Franco Modigliani and Merton Miller (M&M), in

ground-breaking analysis, argued that if shareholder wealth was the same regardless of capital structure, then the latter is irrelevant.

An efficient capital market adjusts the returns of debt and equity claimants according to the cost of acquiring the same future cash flow expectations.

Competitive markets abhor an arbitrage opportunity as nature abhors a vacuum. Participants seeking greater wealth create an elegant consistency among security prices.

Borrowing The transaction might be regarded as the sale of a

claim to assets, with an option to repurchase that claim by making interest payments.

The incremental return required on geared equity as the result of increasing debt is often called the implicit cost of borrowing.

As both the equity (re) rate and the debt rate (rd) increase with increases in D/V, the value weight [1 – D/V] on the higher equity rate steadily declines, exactly offsetting the higher proportion of lower-cost debt, so that their weighted average is unchanged.

Taxes The operating cash flows of a company are

transformed by the taxation system before they can be claimed by capital suppliers. This transformation is different depending on the capital structure of the company.

We can think of a company’s value as the sum of its unleveraged value plus the value of its leveraging-based tax benefits.

Interest deductibility makes the company’s cost of capital lower, the more debt it uses.

Agency There are potential conflicts of interest between debt

holders and shareholders. Agency costs are primarily in the form of

inefficiencies in the operation of the company’s assets, caused by actual or potential default.

Monitoring costs, which are priced into the debt contract, are also a type of friction, as debt suppliers ensure that covenants are observed.

This conflict might be resolved either by having the debt be callable (company pays out early) or convertible (debt holder converts claim to shares).

Default The essence is a change in legal ownership of the

company’s assets from the shareholders to the bondholders.

Bankruptcy costs are not the declines in value that precipitate the default – those are independent of capital structure. The true costs are those of the legal process and of the opportunity costs (when compared to equity financing).

The Borrowing Decision I One consideration for the lender is the value of the

debt claim to the total value of the company. A market value of assets might be difficult to obtain, so practitioners often rely on book values. These are thought less vulnerable to upset when the company is in financial distress.

A financial planning exercise, using a simulation model, would compare the financing alternatives under a range of economic outcomes.

The Borrowing Decision II If borrowing, the company must ensure that there is

no likely conflict with covenants or payment schedules.

The company must be fully able to capture the tax benefits, and not merely replacing one tax benefit with another.

Convertibility may reduce risk to the lender, or call provisions the cost to the borrower.

Key financial ratios, particularly gearing ratios, are often compared to industry averages.

10. Working Capital Management Working capital is the set of balance sheet items

included under Current Assets and Current Liabilities.

Their commonality is their concern with the short term (the current operating period, usually one year.

Management decisions to change the amount, timing or risk of cash flows can still affect the wealth of shareholders.

Risk, Return and Term I Short-term assets are less risky because they

possess a much greater amount of liquidity: the capacity to be turned into cash quickly

without much loss in value relative to that of their best use.

Long-term assets tend to be much more specific to the line of business, and more subject to the uncertainties of a particular industry or market.

Risk, Return and Term II Short-term finance tends to be risky in the

sense of requiring the firm frequently to renew the principal amounts of financing outstanding. Financing that is excess to the company’s needs

can be dispensed with (‘reversed’) at the end of its term.

This reversibility characteristic is financing’s counterpart to asset liquidity.

Maturity Matching Maturity matching associates low risk-and-return

assets with high risk-and-return financing (both short term), and high risk-and-return assets with low risk-and-return financing (both long term) The result is a mixture of risks and returns that is both

potentially profitable and survivable. Some current assets have a long-term characteristic, that

is, the company always requires some amount of cash, inventory, debtors regardless of immediate market position.

‘Accounting definition’ assets are presumably fixed assets.

Short-term Optimization Rather than considering the costs and benefits of

short-term assets and financing, managers devise policies to govern the firm’s investment in each type. Types include cash, marketable securities, accounts

receivable and inventory. Efficient management balances costs and benefits to

produce the highest company value. Typically benefits reach a point of diminishing returns,

while costs steadily increase with usage.

Managing Cash Balances I Cash is required for transaction uses, precautionary

and anticipatory reserves and compensating balances (left on deposit with bank).

For cash and securities, the balance is in minimizing the sum of transaction costs and foregone interest. When cash usage is steady, cash replenishment amounts are solved by: $r = sqrt [ (2 x $ D x $T) / i ], where D is the total annual

cash spent by the firm, T is the transaction cost and i is the interest foregone.

The formula equalizes the transaction cost with the cost of foregone interest on the replenishment amount.

Managing Cash Balances II Cash usage is not usually steady:

Cash receipts are cyclical or seasonal Expenditures tend to be ‘lumpy’ At best, a manager may be able to specify a probability

distribution of potential cash balance changes. The company may establish minimum and maximum

cash balances to be held, and will calculate a ‘return point’ to which the balance will be reset when it hits one of those bounds.

Managing Cash Balances III The return point is solved by;

$R = cube root [(3 x $T x s2) / (4 x i)] + $M, where s2 is the variance of the change in cash balances, i is a daily rate and $M is the minimum threshold.

The s2 term is expected cash balance change, squared, times the number of times per day there will be changes: s2 = $c2 x t

This formula gives an upper threshold at three times the differential between the minimum and the return point, plus $M.

Managing Receivables A higher level of receivables may boost credit sales,

but at the costs of a longer collection period and of bad debt.

An attempt to discriminate between good and bad credit risks should continue until the incremental expenditure is equal to the expected gain.

To analyze the effects of a change, accumulate: (1) the NPV of the sales value when received, less the previous NPV, (2) less the change in costs, (3) plus the cost of increased working capital, (4) less the NPV of the recoupment of that capital.

Short-Term Financing To calculate the effective interest rate when a

discount is given (or a premium demanded): i = (1 + [discount% / 1 – discount%])365/ # days

Short-term financial management is best pursued in the context of a company’s cash budgeting. The setting forth of the company’s expectations for its

inflows and outflows of cash over some future time period, usually near-term.

Financial and Ratio Analysis Absolute figures are not helpful by themselves. A

ratio reduces the data to a workable form and makes it more meaningful.

Percentages or ratios permit easy comparison between periods or different corporate entities.

Ratios may suppress poor absolute figures. Differences in definition are ultimately less

important than consistent application. Trends are usually more meaningful that a single

period analysis.

Financial and Ratio Analysis Four types of ratios

– Liquidity: Measure a company’s ability to meet its maturing short-term obligations

– Profitability: Measure management’s overall effectiveness.

– Capital Structure: Examine the asset structure of the company; analyze the company’s dependence on debt (gearing ratios).

– Efficiency (activity or turnover): Indicate the company’s effectiveness in managing its assets.

Ratios I1. Current ratio = Current assets / Current Liabilities2. Quick Ratio = (Current Assets – Inventory) /

Current Liabilities3. Profit Margin = Net profit after taxes / Sales4. Return on Total Assets = Net profit after taxes /

Total Assets5. Return on Owners’ Equity = Net profit after taxes

/ Owners’ Equity

Ratios II6. Fixed to Current Asset Ratio = Fixed Assets /

Current Assets7. Debt Ratio = Total Debt / Total Assets

Creditors look to the owners’ equity to provide a margin of safety.

Companies with low gearing ratios have less risk of loss in economic downturns, but also has lower returns when the economy performs well.

8. Times Interest Earned = (Profit before tax + Interest Charges) / Interest Charges

Ratios III

9. Inventory Turnover = Sales / Inventory10. Average Collection Period = Debtors /

Sales per day11. Fixed Assets Turnover = Sales / Fixed

Assets

One Hundred Percent Statement

In relation to profitability and cost control, a favorite technique is the One Hundred Percent Statement. Sales are set at 100% Each item of cost is calculated as a percentage of

sales.

11. International Financial Mgmt If a company has monetary assets denominated in a

foreign currency, it is exposed to the risk of exchange rate fluctuations.

Purchasing power parity is an application of the assumption that free markets do not allow arbitrage opportunities to exist for long.

Exchange rates portray relationships in wealth exchanges across national borders in much the same manner as interest rates portray wealth exchanges across time.

Exchange Rates Even with its imperfections, there is an impressive

elegance and consistency in exchange rates across currencies based on the general economics of international transactions.

By entering a forward exchange contract, a trader commits to purchase or sell an amount of currency at a fixed rate at a fixed time in the future.

The same result can be achieved by borrowing in the foreign currency, exchanging spot and investing the proceeds in the domestic currency.

Inflation Maintaining purchasing power across time requires

that the forward exchange rates for any two currencies be consistent with the inflation expected in those currencies. Nominal interest rate = Real interest rate + Effect of

inflation (1 + nominal rate)n = (1 + Real rate)n + (1 + inflation rate)n

The connection is that interest rate differentials are caused by inflation differentials, which are the root cause of the observed discount or premium on forward exchange.

Translation In translating future foreign-denominated cash

flows, there is no theoretical difference between: taking the domestic equivalents from forward rates then

discounting with the domestic discount rate. discounting the foreign currency by its own rate, then

exchanging with the spot rate. The want of forward rates beyond near terms makes

the second strategy preferable.

Monetary and Real Assets Monetary assets are those whose returns are

expected to be fixed in monetary or money terms in the future, regardless of the inflation rate in the economy. Only these are serious candidates for the hedging of

exchange risk. Real assets are not fixed in foreign currency value,

but will increase in value with increases in foreign inflation. This applies to plant and equipment, but also other longer-

term productive assets.

12. Financial Engineering

With respect to an option, the text mysteriously describes the extrinsic value as the premium.

Valuing a Binomial Option I The value can be calculated using an option

equivalent portfolio. Requirements (for a call): The nominal payouts at the up outcome (Cu) and

down outcome (Cd): max[market – strike, 0] The proportion of the up or down outcome to the

strike: multipliers u and d respectively The current share price: S0.

Valuing a Binomial Option II

The equivalent number of shares purchased (negative if sold): Y = (Cu - Cd) / (S0 x (u – d))

The equivalent lending at the risk-free rate (borrowing if negative): Z = (uCd – dCu) / [(u – d)(1 + rf)]

C0 = (Y x S0) + Z

Valuing a Binomial Option III

Alternatively: uS0 – mCu = dS0 – mCd

Therefore, m = [S0 x (u – d)] / (Cu – Cd) Where m is the hedge ratio

Black-Scholes Model I

There are five variables in determining option value: Underlying security price: S Exercise price: K Risk-free rate of interest: r Standard deviation of the underlying security

price: Time until expiration: t

Black-Scholes Model II

C = SN(d1) – Ke-rt N(d2) Where d1 = [ln(S/K) + rt + ((2/2)t)] / [ t0.5]

d2 = d1 - t0.5

N(d1) is the cumulative normal distribution equal to the “delta”

cumulative normal distribution returns the probability of the outcome of the input value or less, given the mean and standard deviation

Real Options When an investment proposal carries with it an

option to alter, curtail or extend a project’s cash flows at some future time, classic NPV is an inadequate valuation technique.

Project cash flows after the exercise, discounted back to the time of the exercise, represent the option payout. This payout, discounted to the present, represents the S0 value.The exercise price is the premium.

Agency An agent is an individual, group or organization to

whom a principal has designated decision-making authority.

The primary engines driving agency situations are conflicts of interest. Typically, the interests of shareholders conflict with managers or bondholders.

Agency concepts can explain real market actions that at first seem irrationally complex or outside the scope of traditional financial economics.

Solving Agency Problems Any solution to an agency problem requires that:

There be an overall gain to solving the problem The agent has an incentive to participate in the solution.

Many economists think that an efficient market for company takeovers is an important solution to the agency problem of manager – shareholder conflict.

Derivatives

A derivative is simply any financial security whose return or outcome set is derived from some other asset’s value or return outcome.

The well-publicized derivatives trading disasters tend to be manifestations of control failure, regardless of whether the sufferer had intended to hedge or speculate.

Swaps and Exotics A swap is a transaction in which one party

exchanges one stream of cash flows for another. One or both of these streams may be based on an index.

The market for such transactions has grown due to economic efficiency and the ability of dealers to customize to meet user needs.

Exotics are combinations of derivatives, financially engineered to meet the very specific risk objectives of a single firm.