Finance

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
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 such rates at one time, covering different riskiness and different periods of time.
Present Value (PV) The amount of money to be invested or lent now to end up with a particular amount in the future.• Called discounting
Present Wealth A market participant’s entire time-specified resources discounted to a single number.• This can be used as a benchmark to measure the benefit of a proposed financial decision as it is a company’s sole task for it to be maximised.
Net Present Value (NPV) Present value of difference between cash inflows and outflows discounted at opportunity cost
Internal Rate of Return (IRR) The average per-period rate of return on the money invested.• Can be viewed as the discount rate that equates an investment’s cash inflows and outflows (NPV = 0).
Compound Interest 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.
Annuity A set of cash flows that are the same amounts across future time points• PV = C[ (1-(1+r)^-t)/r]• FV = C[((1+r)^t – 1)/r]
Perpetuity A cash flow stream that is assumed to continue forever• PV= C/r
Growing cash flow in perpetuity If cash flows continue forever, but grows 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.
term structure of interest rates. The set of all spot rates
Spot Rates • Interest rates that begin at the present and run to some future time point.• 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%.
Yield The rate of return anticipated on a bond if held until the end of its lifetime.
Bond Valuation The present value of the annuity (or possibly multiple period cash flows) + the present value of the lump sum• If equal payments. PV = (C[(1-(1+r)^-t)/r]) + (FV/(1+r)^t) Where: FV = Face Value C = Face Value / coupon rate r = YTM t = time to maturity
The interest rate is equal to the coupon rate when the bond is priced at par.
A bond priced above par (a premium bond) has a coupon rate higher than the interest rate
a bond priced below par has a coupon rate lower than the interest rate.
Yield Curve A line that plots the interest rates, at a set point in time, of bonds having equal credit quality, but differing maturity
Coupon Effect If maturity and a bond’s initial price remain constant, the higher the coupon, the lower the volatility, and the lower the coupon, the higher the volatility.
The higher the coupon the lower the volatility
The lower the coupon the higher the volatility
Factors that affect volatility of bonds coupon rate: lower coupons — higher volatilityduration: higher duration — higher volatilitymaturity: higher maturity — higher volatilityYTM: lower YTM — higher volatility
Bonds of similar RISK and maturity will have similar YTM (even if the coupon rates are different).
The YTM of bonds with different maturity or risk cannot be compared
Forward Interest rates A rate applicable to a financial transaction that will take place in the future
Futures Contract A contract to sell/buy an asset at a later date, at a price agreed upon well in advance.
Purpose of Futures Contracts A form of insurance. The buyer of a future would rather take the bird in the hand with a price that’s guaranteed today, rather than the possibility of two (or zero) in the bush later, protecting himself from low prices while forgoing the chance to profit off high ones• Contract which can be bought or sold as such are often used for speculation and arbitrage.
The difference between futures and option A future is both right and obligation. When the time comes, you’re legally bound to sell or buy the underlying asset.
The first equation uses the spot rates, the second uses the forward interest rates, and the last uses the bond’s YTM. 923 = 40/1.05 + 40/1.06^2 + 1040/1.07^3923 = 40/1.05 + 40/(1.05 x 1.07) + 1040/(1.05 x 1.07 x 1.09)923 = 40/1.069 + 40/1.069^2 + 1040/1.069^3
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 … Generalized formula(1+it)t = (1+z1) (1+1f2) (1+2f3) (1+3f4) … (1+it)t = (1+it-1)t-1 (1+t-1ft)examples(1+ 1f2 )=(1+ i2 )^2/(1+0f1 )(1+ 2f3 )=(1+i3)^3/(1+0f1)(1+1f2)Multiple period examples(1 + i5)^5 = (1 + i3)^3 * (1 +3f5)^2
Duration A measurement of how long, in years, it takes for the price of a bond to be repaid by its internal cash flows. It is an important measure for investors to consider, as bonds with higher durations carry more risk and have higher price volatility than bonds with lower durations.
Duration calculated Macaulay duration is defined as: (sum of (PV of (period number * cash flow))/priceSteps: a. Multiply each cash flow by the period number it will be paid in b. Find the present value of each of the above c. Sum the above PV values d. Divide the above sum by the current price
Influences on Interest rates • Inflation• Changes in creditworthiness of bond issuers• Real-asset returns
Corporate Equity • a security known variously as ‘ordinary shares’, ‘common stock’, ‘equity’, ‘common shares’, ‘ownership capital’ etc. • Has no specific contract with the company that requires any particular amounts of money to be paid • Is a residual claim, shareholders have agreed to stand last in queue for the corporate largesse, in exchange for everything that is left over.
Limited Liability possible losses that a shareholder can incur are limited to the value of the shares• nice but not free, the company would be able to borrow money more cheaply if its creditors also got a claim on the personal resources of the company’s shareholders.
Constant dividend The firm will pay a constant dividend foreverThe price is computed using the perpetuity formulaP0 = D / R
Dividend Growth Model Dividends are expected to grow at a constant percent per period.• P0 = D0(1+g)/(R-g)Which also equals• D1/(R-g)The price will grow at the same rate as the dividends
Stock Price Sensitivity to Dividend Growth (Required Return) As the growth rate approaches the required return the price and sensitivity increases significantly
Holding period return (selling price + dividends – buying price) / buying price
Cost of Capital P = D1 /(r-g)Therefore, to calculate the cost of Capital (r)r = (D1/P) +g
Shareholders’ Rights • Share proportionally in declared dividends• Share proportionally in remaining assets during liquidation• Pre-emptive right – first shot at new stock issue to maintain proportional ownership if desired
Dividends are not a liability of the firm until a dividend has been declared by the Board therefore … a firm cannot go bankrupt for not declaring dividends
Dividend payments… are not considered a business expense and are not tax deductible In Canada,
Dividends received by individual shareholders … are partially sheltered by the dividend tax credit
Imputation systems mitigates double taxation of dividends
Factors to consider in finance decisions • the cost of retained earnings in relation to the opportunity cost — how funds can be used elsewhere.• Pecking order — internal financing is generally thought to be less expensive for the firm than external financing, • no transaction costs • affects shareholder wealth without paying the taxes associated with dividends• New shareholders dilute ownership• an all-equity project will report higher net income, because in the accounting figures interest is regarded as an expense, so the debt-financed company will have higher expenses and lower profits as a result. • conversely debt will have lower taxes and more free cash flow
Existing shareholders of the company get a wealth increase equal to … NPV regardless of who contributes the money necessary to undertake the investment (i.e. forgone dividend, new equity holders, the original holders i.e. new shares going to existing shareholders, or creditors).
The Price Earnings Rati0 The ratio between the present value of all the company’s future dividends (its market price) and its expected earnings (for example: earnings x payout rate x growth) during the first period.
A company’s P/E ratio is a very complex number in terms of the information that can influence it. It is affected by • the pattern of dividends that a company pays,• its payout ratio, • the riskiness of the company as evidenced by the discount rate of its equity, • and the stream of earnings that the company is expected to be able to generate across the future.
High P/E Ratios • a signal of the market’s high opinion of a company’s shares, • a sign that the company’s share prices may be too high. • might be a growth company or where profits have almost disappeared, but the stockmarket may see this as being a temporary episode. • could be that the company is a takeover target and the shares have been bid up.
Using P/E to compare companies • only be used to compare similar companies that also have similar capital structures. • should not be used to compare companies across sectors..
Types of Cash Flow • Customers• Operations • Assets • Government• Capital Suppliers
Customers Cash Flows The amounts of cash taken in from sales When the money actual changes hands (ie not credit sales)
Operations Cash Flows Cash flows that are paid in cash that year, be deductible for taxes that year, and not be a payment to a capital supplier.
Assets Cash Flows While the cash flow is made at time listed, it is not deductible at that point and must therefore be capitalised and depreciated across time.
Government Cash Flows Taxes paid due to the investment.
Capital Suppliers Cash Flows The amounts of cash that could be taken out by capital suppliers from the company as a result of the investment while leaving all of the plans of the company unchanged (AKA Free Cash Flow)
Cash Flows differ from Accounting Statement in terms of accounts payable/receivable Cash flows simply state that companies receive cash from, and pay cash out to, various groups during each period.• companies rarely pay cash ‘on the spot’ for the assets or services that they buy, and customers often take some time to pay their bills. • something the company sells right now does not result in a cash payment from a customer until next period.
Effect of depreciation on Cash Flow • Considered a non-cash expense• Depreciation does have an indirect effect on cash flow, When a company prepares its income tax return, • Depreciation only exists because it is associated with a fixed asset. When that fixed asset was originally purchased, there was a cash outflow to pay for the asset. Thus, the net positive affect on cash flow of depreciation is nullified by the underlying payment for a fixed asset.
Interest payments and cash flows Interest payments are a payment to a capital supplier so they should be excluded. They are part of the financing decision, not the investment decision. To include interest payments would result in an underestimation of the NPV of a project.
Non-cash items depreciation and overheads
After tax cash flow A measure of financial performance that looks at the company’s ability to generate cash flow through its operations. It is calculated by adding back non-cash accounts such as amortization, depreciation, restructuring costs and impairments to net income.
Free Cash Flow The net amounts of cash that the company could pay to its capital suppliers from the proceeds of a project at each time point without upsetting the expectations associated with the project.
Free Cash Flow and Profit If we separately add up the free cash flows and after tax profits they will amount to the same figure. They will not be the same figures at the same time periods, reflecting the timing differences between accounting figures and cash flows
Weighted Average Cost of Capital WACC A discount rate based on the relative costs of the different capital claims. It is calculated by multiplying the cost of each source of finance by the relevant weight and summing the products up.
Interest Tax Shield Tax laws allow corporations to reduce their taxes by deducting interest expense:• The interest tax shield is found by multiplying the period’s interest expense by the corporate income tax rate.
Covenants / indenture provisions contractual arrangement for periodic payment of money (e.g. interest)
What Makes a Good Decision Criteria? • Does the decision rule adjust for the time value of money?• Does the decision rule adjust for risk?• Does the decision rule provide information on whether we are creating value for the firm?
NPV – Decision Rule • If the NPV is positive, accept the project• A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners.
Debt Market Value The Initial Investment + interest payments• debt suppliers’ wealth is unaffected by the success or failure of the investment.
Equity Market Value The sum of the expected Free Cash Flow values excluding debt market value discounted at an appropriate rate
project’s NPV Equity Market Value – Debt Market Value• it is not one of the more commonly used techniques in the modern company, there is a tendency to use techniques that do not separate the cash flows into those going to the various capital claims, but instead merely deal with the company’s cash flows as a whole.
Total Market Value Equity Market Value + Debt Market Value
overall project rate a market-value weighted average of the rates required by the various capital claims upon the investment.• Rates debt and equity are based on their proportional claims upon the corporate cash flow.• ((Debt Market Value / Total Market Value) x Debt rate) + ((Equity Market Value / Total Market Value) x Equity rate)• Gives a discount rate that can be used to calculate the NPV of a project
The Weighted Average Cost of Capital WACC is a discount rate that reflects … • the operating risks of the project;• the project’s proportional debt and equity financing with attendant financial risks; and• the effect of interest deductibility for the debt-financed portion of the project.
Weighted Average Cost of Capital – formula WACC = (weight of debt x cost of debt) + (weight of equity x cost of equity)• Weight of debt is calculated by taking the (current value of debt)/( current value of debt + current value of equity) given the percentage of investment in debt• The weights are based on the target market values of the relevant components. But if no market values are available we base the weights on book values.• Costs are after taxes i.e. (rate *(1 – corporate tax rate)
Weighted Average Cost of Capital – Example • Value of debt = 30• Value equity = 70• Cost of debt = 4%• Cost of equity = 3 %• = ((30 / (30 + 70) ) x 0.04) + ((70/(30 + 70)) x 0.03)
Adjusted Present Value An investment appraisal technique similar to net present value method. However, instead of using weighted average cost of capital as the discount rate, ungeared cost of equity is used to discount the cash flows from a project and there is an adjustment for the tax shield provided by related debt capital and possibly for issuing costs.• Ungeared NPV + financing effects (tax shield benefit and issue costs (if necessary…may not be if the loan is directly from the government)
Calculating APV for an all equity investment • Calculate issue costs • Equity amount – (Equity amount/(1 – issue cost rate))• Calculate the ungeared NPV • The sum of (fcf*/(1+rate)^t) – initial investment• Substract the issue costs from the ungeared NPV
Calculating APV for an investment using debt financing • Calculate issue costs using — loan amount – (loan amount/(1 – issue cost rate))• Add issue costs to loan amount for the remaining calculations• Calculate after tax interest costs for 1 year using — Interest costs = loan amount × borrowing rate × (1 – corporate tax rate) • Calculate the PV of the interests costs until the end of the loan using — (Corporate debt rate, length of loan annuity factor) × interest costs • Calculate the PV of of the loan repayment using — loan amount/(1- corporate debt rate) ^t• Calculate the npv of loan using (loan amount – pv of int pmts – pv of loan repayment)• Calculate the ungeared NPV using –the sum of (fcf*/(1+rate)^t) – initial investment• Substract the npv of the loan from the ungeared npv
Factors to consider when choosing NPV/WACC as the NPV technique • Does not require that actual amounts of debt to be issued be known • Requires that the proportions of debt and equity market values be known• It adjusts for the deductibility of corporate interest in the discount rate as opposed to the cash flows of the project• Finds the present value by discounting the combined claims’ cash flows
Factors to consider when choosing APV as the NPV technique • Requires that actual amounts of debt to be issued be known• Does not require that the proportions of debt and equity be known• Requires that the interest tax shields of the project’s debt be estimated.• Finds present values by splitting up the cash flows into the all-equity cash flows) and the interest tax shield cash flows. These are each then discounted separately at rates appropriate to their individual risks.Easier to adjust to changing capital structure — no need to recalculate WACC• highlights the present value benefit of the borrowing they are doing.• useful in isolating the benefits of government subsidies and the costs of financial distress.
Internal Rate of Return IRR Rate of return that makes the NPV equal to zero (NPV= 0)
Advantages of IRR • Knowing a return is intuitively appealing• It is a simple way to communicate the value of a project to someone who doesn’t know all the estimation details• If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task• Generally leads to the same answers as the NPV method
Disadvantages of IRR • May result in multiple answers or no answer with non-conventional cash flows, if the cash flows change sign• IRR usually unsuccessful when cash flows have differing discount rates• May lead to incorrect decisions in comparisons of mutually exclusive investments
IRR and Non-Conventional Cash Flows • When the cash flows change sign more than once, there is more than one IRR• When you solve for the IRR, you are solving for the root of an equation. When you cross the x-axis more than once, there will be more than one return that solves the equation
Two projects with different cash flows can produce a conflict between NPV and IRR. Example:Two Projects, the required rate of return is 10 %Initial Investment A : 500 B : 400Year 1 A : 325 B : 325Year 2 A : 325 B : 200NPV A : 64.05 B : 60.74 (A is better)IRR A : 19.43 B : 22.17 (B is better)The cross over rate is the discount rate at which the NPV of the two projects is equal
Reasons for conflicts between NPV and IRR • Timing of cash flows• Scale of cash flows
The Cross-Over Rate is calculated by by taking the difference between the Cash Flows from the two Projects and finding the IRR
If the required return is higher than the cross over point … the NPV will favour one of the projects. If lower it will favour the other
Types of Project Cash Flows • Initial Investment Outlay• Operating Cash Flow over a Project’s Life• Terminal-Year Cash Flow
Initial Investment Outlay • These are the costs that are needed to start the project, such as new equipment, installation, etc.• Include opportunity costs as a negative cash flow
Terminal-Year Cash Flow • This is the final cash flow, both the inflows and outflows, at the end of the project’s life; for example, potential salvage value at the end of a machine’s life.• The key metrics for determining the terminal cash flow are salvage value of the asset, net working capital and tax benefit/loss from the asset.
Examples of Terminal Year Cash Flows • Return of net working capital +$300• Salvage value of the machine +$800• Tax reduction from loss (salvage < BV) +$80• Net terminal cash flow $1,180
Sunk Costs The initial outlays required to analyse a project that cannot be recovered even if a project is accepted. As such, these costs will not affect the future cash flows of the project and should not be considered when making capital-budgeting decisions.
Opportunity Cost The cost of not going forward with a project or the cash outflows that will not be earned as a result of utilizing an asset for another alternative.
Calculating Free Cash Flow • changes in net working capital = changes in current assets – current liabilities • Operating revenues (sales – returns)• Operating profit = operating revenues – operating expenses• Operating cash flow = operating profit – changes in NWC• Fixed Asset Cash flow = Fixed Asset Sales – Fixed Asset Purchases• Free cash flow = Operating cash flow + Fixed-asset cash flow – Income tax • Adjust to FCF*, by taking out the interest tax shields
Payback Period How long does it take to get the initial cost back in a nominal sense?• Decision Rule – Accept if the payback period is less than some preset limit
Example of Computing Payback For The Project Assume we will accept the project if it pays back within two years.• Year 1: 165,000 – 63,120 = 101,880 still to recover• Year 2: 101,880 – 70,800 = 31,080 still to recover• Year 3: 31,080 – 91,080 = -60,000 project pays back in year 3If the preset limit is 3 years, do we accept or reject the project?
Payback Period – Advantages • Easy to understand• Adjusts for uncertainty of later cash flows• Biased towards liquidity
Payback Period – Disadvantages • Ignores the time value of money• Requires an arbitrary cutoff point• Ignores cash flows beyond the cutoff date• Biased against long-term projects, such as research and development, and new projects
Average (Accounting) Return on Investment (AROI) provides a quick estimate of a project’s worth over its useful life. • is calculated by finding a capital investment’s average operating profits before interest and taxes but after depreciation and amortization (also known as “EBIT”) and dividing that number by the book value of the average amount invested. It can be expressed as the following:• Average Profit / Average Investment• The result is expressed as a percentage• The higher the AROI, the better.
Example of an AROI calculation A project requiring an average investment of $1,000,000 and generating an average annual profit of $150,000 would have an ARR of 15%
Disadvantages of an AROI calculation • Does not discount cash flows, ignores the time value of money • Using accounting profit rather than cash flow fails to recognize that profits can be earned ahead of being received• Exists for historic reasons (focus on accounting profits) but use on the decline.• Can be useful for monitoring progress of an ongoing project on a period-by-period basis.
The Cost-Benefit Ratio (CBR) Transformation of the NPV from a difference into a ratio• Sum of all discounted inflows divided by sum of all discounted outflows• 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 (PI) Same as CBR but assumes :• First flow is outflow and rest are inflows• An index of 1.1 implies that for every $1 of investment, we create an additional $0.10 in value
Profitability Index (PI) Advantages • Closely related to NPV, generally leading to identical decisions• Easy to understand and communicate• May be useful when available investment funds are limited, being a ratio, it ignores the scale of investment
Profitability Index (PI) Disadvantages May lead to incorrect decisions in comparisons of mutually exclusive investments
Reasons for Capital Rationing Upper management may specify spending limits for each department or for the company as a whole. This is contrary to the rational view of shareholder wealth maximisation but might be necessary because• An absolute limit on the amount of finance available is imposed by the lending institutions.• Internal reasons for capital rationing include management worries about the organisation’s ability to manage an expanded level of investment.,. Human resource constraints may also limit a company’s ability to manage expansion.
Capital Rationing The purpose is to find a way to determine the combination of projects that will maximise the firm’s NPV within the constraint on capital.• consider the size of the NPV in relation to the capital invested using profitability index to rank projects (assumes projects are independent and divisible)• As the funds are consumed it may be necessary to skip a project if the initial outlay will exceed the remaining funds.• There are many Inexpensive software packages that aid in capital rationing involving: Integer programming, operational research, management science
If investments are economically independent, they may be considered individually and judged on the basis NPV alone but if there is any Investment Interrelatedness… Economic relatedness is a scale that ranges from positive to negative. If a group of projects exhibits any shading of interrelatedness, the financial manager must first specify all possible combinations of interrelated investments, along with their unique cash flows and NPVs. Next, the combination with the highest NPV is chosen.
Positive Investment Interrelatedness Pure contingency: the cash flows of a particular project cannot exist unless those associated with another investment are accepted
Neutral Investment Interrelatedness Economic independence implies that the acceptance or rejection of one project has no effect upon the cash flows of the projects with which it is economically independent.
Negative Investment Interrelatedness Mutual exclusivity: the acceptance of a particular alternative implies the rejection of the cash flows of all that are mutually exclusive of it
Renewable Investments — Equivalent annual cost (EAC) is often used as a decision making tool in capital budgeting when comparing renewable investment projects of unequal lifespans. • For example if project A has an expected lifetime of 7 years, and project B has an expected lifetime of 11 years it would be improper to simply compare the net present values (NPVs) of the two projects because after project A completes in 7 years then an outlay of cash would be required to restart it.
Calculating Equivalent annual cost (EAC) technique NPVs/(PVAs/NPVs)Where • NPVs = NPV of a single cycle• PVAs = Present value of an Annuity if NPVs was the paymentExample• 21461/((21461*(1-(1.1)^-3)/0.1)/21461)
Inflation An increase in price unaccompanied by any other changes (such as quantity, quality, and so forth).
A `Nominal´ price The actual number of £s (or whatever currency) that would change hands at the time the purchase is made.• the real cash flows for each time point multiplied by (1 + inflation rate)^t
A `Real´ price The number of £s (or whatever currency) that would have been exchanged to purchase something before the inflation took place.
Investment analysts should always be explicit in requesting inflated future cash flow estimates. The real rate is not measurable because there is no way to measure the expected influence of inflation therefore nominal cash flows and nominal discount rates should be used when dealing with inflation on corporate investment decisions.• The most common error that investment analysts make in dealing with inflation is using nominal discount rates with real cash flows.
Accelerating depreciation schemes A method of alleviated the negative impact of inflation on the ta deductibility of depreciation. • When inflation occurs, the costs of productive assets will increase across time more or less with other cash flows, but depreciation expenses for assets bought in the past will not. • The net effect can be to make taxes increase across time faster than the inflation rate
The double-declining balance accelerated depreciation method allows a deduction equal to twice what the straight-line amount would be if calculated on the depreciable amount and time remaining in each period.
The sum-of-the-years’-digits accelerated depreciation method allows a deduction equal to the proportion found by dividing the remaining depreciable life of the asset by the sum of the years of the asset’s total life.
An example of the double declining method of depreciation A business purchased a delivery truck for $30,000 that it expected to last for 10 years, after which it would be worth $3,000 (its salvage value), the company would deduct the remaining $27,000 as $2,700 per year for 10 years under straight-line depreciation. Using the double-declining balance method, however, it would deduct 20% (double 10%) of $27,000 in year 1 ($5,400), 20% of $21,600 ($27,000 minus $5,400) in year 2 ($4,320), and so on.• Because the double declining balance method results in larger depreciation expenses near the beginning of an asset’s life and smaller depreciation expenses later on, it makes sense to use this method with certain assets that lose value quickly
an example of the sum-of-the-years’-digits accelerated depreciation method If an asset was expected to last for five years, the sum of the years’ digits would be obtained by adding: 5 + 4 + 3 + 2 + 1 to get a total of 15.Year 1: 5/15 = 33%Year 2: 4/15 = 27%Year 3: 3/15 = 20%Year 4: 2/15 = 13%Year 5: 1/15 = 7%The percentages should add up to 100%.
Advantages of Leasing • Leasing allows for higher tax benefits that the alternative of borrowing and purchasing an asset.• Information asymmetries exist on certain types of assets, and leasing can serve to lower the costs of such information problems. particularly the schedule of obsolescence . A lease can be written in such a manner as to allow the lessee to take advantage of ‘new and improved’ or upgraded assets, and thus avoid the risk of costly obsolescence• There are economies of scale in the management of specialised asset leasing.
Misconceptions of leasing • 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; Saving the initial 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 negotiating lease agreements with a lessor.
Using Economic Income in Performance Measurement (EVA, EP, etc.) Charging a capital cost against the net cash flows of a company division in a given period, and seeing if there is anything left over. • This cost is typically calculated by multiplying a WACC by an invested amount to produce a target profit amount that can be compared to the division’s revenues.
Advantages of using Economic Income as a measure of performance • recognise that all capital suppliers, not just creditors, require adequate returns. Using WACC allows for the measurement of such compensation• Can be used to uncover company operations that are profitable in an accounting sense, but not in an economic sense.
Disadvantages of using Economic Income as a measure of performance • Differences between accounting numbers and cash flows, particularly depreciation• How can this be used to evaluate a new division that can reasonably be expected to produce negative cash flows in its earlier years, which are only compensated later?• Economic income measures are not present values of streams of income, as is NPV
Standard Deviation The square root of the Variance
Variance of a return sum of [(rate -mean) ^2 x probability)]Steps:1) Determine the mean return by• multiply the rates of potential return by the probability of their occurrence. • sum these products. (use this value in the next step)2) subtract each potential outcome from the mean return3) square those differences, 4) multiply these differences by the likelihoods of their occurring,5) sum above
An Example of Joint Probability Event, AssetA, AssetB, Return(combined), Probability1 10%, 7%, 8.5%, 35%2 10%, 12%, 11.0%, 10%3 20%, 7%, 13.5%, 30%4 20%, 12%, 16.0%, 25%There are significant chances that when asset A is generating a high (20 per cent) return, asset B will be generating a low (7 per cent) return: and vice versa. This means that the risks of the two securities will to some extent cancel each other out.
Standard deviation is a decent measure of risk of an individual security but not if it is held in a portfolio. Harry Markowitz invented a detailed model of how capital suppliers make decisions. William Sharpe and John Lintner, independently and almost simultaneously, extended the idea• When individual assets are held in a portfolio, the risk associated with the portfolio is not simply the average risk of the assets.• The risk of individual assets can to some extent cancel each other out when in a portfolio.• The extent to which that risk will cancel depends upon how positively the returns are related. • One way to measure that relatedness is by the correlation coefficient of a pair of returns
Covariance of two sets of returns Steps1) calculate the average return for each set returns2) find the difference between the return and the average for each item in the first set and multiple it by the difference between the corresponding return and average of the second set3) Sum the above4) The last step is to divide the result by one less than the sample size.(Sum of ( return1 – average1) * (return2 – average2))/ (sample size -1)
Beta Measures how volatile that investment is compared to the overall market• Covariance(return,market)/variance(market) • The market is determined using an appropriate index
Systematic risk That part of a security’s risk that is common to all securities of the same general class (stock or bonds) and thus cannot be eliminated by diversification• The reduction of risk due to diversification seems to have a limit, but there is a level of risk below which portfolios do not go, regardless of how well diversified. • if you want to know how much systematic risk a particular security, fund or portfolio has, you can look at its beta
Most likely reason for systematic risk In a given country, much of the basic economic activity that generates returns in securities markets is common to all companies whose shares and bonds are traded on those markets. You can think of this as ‘overall economic activity’
The level of systematic risk is determined by … • The sensitivity of the firm to the level of economic activity in the economy• The proportion of fixed to variable costs
A beta of greater than 1 means … The investment has more systematic risk than the market
A beta of less than 1 means … Means less systematic risk than the market
A beta of equal to 1 means .. The same systematic risk as the market.
The general idea behind CAPM is … Investors need to be compensated in two ways: • time value of money (rf) and• risk (beta).
The expected return for the risk in project i is given by… • E(ri) = rf + [E(rm) – rf] Bi• Where rf is the risk-free rate, E(rm) is the expected market rate and Bi is the beta coefficient
market premium E(rm) – rf
The security market line –SML. Graphs the relationship between risk (beta) and expected return.• Graphs the results from the capital asset pricing model (CAPM) formula. The x-axis represents the risk (beta), and the y-axis represents the expected return. • All correctly priced assets lie on the SML.
If a security is priced above the SML … it is undervalued.
If a security is priced below the SML … it is overvalued.
Using the SML to determine whether or not to buy a security Example• The current real rate of return 19%• The current risk-free rate is 5%.• The market is expected to return 12% next year. • The beta of the security is 1.9.• Expected return = 5% + 1.9*(12% – 5%) = 18.3% We expect the asset to return 18.3% and be plotted on the SML. However, the current real rate of return for the asset is 19%. The asset would be plotted above the SML. Therefore, it is undervalued and should be bought.
Advantages of the Capital Asset Pricing Model • CAPM likely to produce a superior NPV than WACC• CAPM produces an NPV discount rate which is tailor made to the level of systematic risk of the individual project. The WACC only reflects the company’s existing AVERAGE systematic risk level• CAPM describes the market relationships which will result in equilibrium if investors behave in the manner prescribed by the portfolio theory (e.g. diversification, risk-averse investor)
Estimating risk based on an existing project If project is of the same risk as the company investing in the project, and its shares are traded on the stock market, one can merely look up the β coefficient of the company’s shares.• If risk differs (+ or -) from the company average, the investment may be similar to another company’s. In such situations, the β coefficient of the other company can be used. • If the the shares of the investing company are not traded, but those of a similar company are its beta can be used• For example: a company seeks out companies with a product line that is similar to the line for which the company is trying to estimate the beta. Once these companies are found, the company would then take an average of those betas to determine its project beta
Factors to consider when Estimating Risk when a market generated beta is unavailable • If the project’s revenues are expected to be quite volatile relative to the company or divisional average, an adjustment to the coefficient must be made. (revenue volatility)• Similarly, if the fixed costs of a project comprise a relatively high proportion of its costs, the β coefficient of the project must be adjusted upwards (operational gearing)
Technique for Estimating Risk when a market generated beta is unavailable Begin with a ‘benchmark’ β coefficient (from a company or division that can be either similar to or different from the project in question) and then successively multiply that coefficient by the ratios of the project’s volatilities to those of the benchmark• ungear the published beta • Multiply the ungeared ratio by the revenue volatility ratio between the benchmark and the project • Do the same for the operational gearing ratio• regear the ungeared beta using the project’s own gearing ratio
Steps invovled in Estimating Risk when a market generated beta is unavailable 1. βu = βe (E/V) + βd (D/V)2. Revenue adjusted β = βu x (Project revenue volatility / Company revenue volatility)3. Project βu = Revenue adjusted β x (1 + Project fixed cost %/ 1 + Company fixed cost %)4. βu = βe (E/V) + βd (D/V), solving for βe
Estimating the WACC Use SML to calculate rd*• E(rd) = rf + [E(r m ) – rf] βi• Risk free returns (rf) can be obtained from the YTM on a government bond of comparable maturity.• [E(r m ) – rf] … the difference between the market return and the risk free rate is relatively stable over time: averaging 9.1% in UK and 8.8% in USA.use project levels of debt and equity to calculate rv, the WACC of the project• rv = D/V (rd) + E/V (re)
Certainty equivalents SML Equation and the Certainty Equivalent equation require the same information and give the same answers. The only difference is that the former you learn what risk-adjusted discount rate to use, while from latter you learn what risk-adjusted cash flow to discount with the risk-free rate.`
Certainty equivalents equation CFce = CF – [E(rm) – rf]/variance(rm) * covariance(CF, rm)•The certainty equivalent cash flow (CFce) is found by subtracting from the expected risky cash flow (CF) an adjustment for its systematic risk.
Why must a change in divendend policy be accompanied by a changing in the capital being raised from outside Any increase in dividends will reduce retained earnings, and any reduction in dividends will increase retained earnings and so company’s investments will also change.
Any increase in dividends must be accompanied by… cash being raised from outside
Any reduction in dividends must be accompanied by… would require less cash to be raised from outside .
Dividend Irrelevancy • if the shareholder were unhappy with a policy of reducing dividends , he can sell enough shares to duplicate the cash dividend that was not received and vice versa• When the effect of company financial decisions upon shareholders portfolios can be undone by the offsetting actions of shareholders, the company financial decision is irrelevant
Bird-in-the-Hand Theory Dividends are preferable to capital gains because the former is actual cash in hand, and the latter is based upon future dividends not yet received. Thus a policy that substitutes future uncertain dividends for current certain dividends is by its very nature designed to increase the riskiness of the company’s shares.
MM’s dividend-irrelevance theory Investors can affect their return on a stock regardless of the stock’s dividend. For example, suppose, from an investor’s perspective, that a company’s dividend is too big. That investor could then buy more stock with the dividend that is over the investor’s expectations. Likewise, if, from an investor’s perspective, a company’s dividend is too small, an investor could sell some of the company’s stock to replicate the cash flow he or she expected. As such, the dividend is irrelevant to investors
Taxation of Dividends • It is generally the case that dividends are more heavily taxed than capital gains.• Often the amounts of cash available to pay dividends are net of company taxes, and the dividends paid are taxed again at the shareholder level. • When dividends are not paid, shareholders receive no cash, but neither do they pay taxes. they retain their full claim. • (Although taxes may be required when the capital gain is realised (but this could be at a lessor rate and the timing is at the discretion of the shareholder.)
Does the double taxation of dividends affect share price ? In tax system where ‘double taxation’ of dividends is unavoidable, there is a strong tax incentive against the payment of dividends for companies. • empirical evidence as to whether high dividend-paying companies’ shares are adjusted in price for the taxability of the dividends is mixed
Imputation Systems ‘imputation’ systems make some attempt to alleviate the double taxation of dividends by giving shareholders a credit on their taxes. • Often there is a personal tax liability that is higher than the tax credit received (because of higher personal tax brackets by shareholders).
Imputation Systems in the UK The imputed shareholder dividend tax is paid in advance. • Advance corporation tax (ACT) must be paid by the company even if there is no company income tax. The company can set this off against its income tax – mainstream corporation tax (MCT) – if and when this is eventually paid. • the time value of money results in a loss the to the company
Transaction Costs of Dividend Payments Brokerage fees to be paid by shareholders to shift between shares and cash.
Shareholders may prefer one dividend policy to another depending upon .,. • their preferences • the costs they would pay to achieve the desired consumption pattern.
Flotation Costs The costs incurred by companies in raising money from capital markets• Depending on the mechanism of sale these flotation costs can be significant (5-25% of total value of shares issued).
Company dividends is that they tend to be smooth over time one explanation for the `smoothing´ across time of company dividends is … Signalling• The dividend announcement can be made to be a `surprise´ (either good or bad) to the market. Based upon the past pattern of dividends either with respect to time or relative to other measures such as earnings• It is in the interests of both managers and shareholders to have share prices reflect new information (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.
Dividend Clienteles: Irrelevancy II • Some shareholders (commonly called `fat cats´) want low payouts because of high personal income tax brackets. • Others (`widows and orphans´) want high payouts because of low personal taxes and preferences to consume their wealth in the form of cash payments. • However, it is unlikely that a company choosing one policy over another will be of benefit to its shareholders because there are likely to be no relatively under-served clienteles willing to pay a premium for the company to change its policy.• A company switching policies can actually be costly to shareholders, so whatever a company’s current policy is likely to be optimal.
Share repurchases are nothing more than a cash payment to shareholders in the form of capital gains, which is preferred because of the tax implications. Why? • there is seldom a reason why the company could not simply issue new shares to employees and merger candidates so repurchase is not needed to for employee ownership programs or to fight mergers • Company claims of investing in itself are bogus as long as there is one share outstanding. In such a case there will always be a 100 per cent equity claim outstanding, and since that single share would claim the entire firm, it would take the entire equity value of the company to repurchase it.
Share repurchases on the open market also be used to … signalling
One type of share repurchase that is not so positive for shareholders, the targeted share repurchase. This is a transaction wherein a company offers to repurchase only particular shares (usually held by investors whose motives frighten existing management). The targeted share repurchase. This is a transaction wherein a company offers to repurchase only particular shares (usually held by investors whose motives frighten existing management).
Characteristics of a targeted share repurchase • The repurchase price is usually at a significant premium above the existing market price. • Share prices usually decline even more than would have been expected.• Evidently the market thinks that targeted share repurchases are bad, in that existing managers will now be left to make decisions without the implied oversight.
Dividend Policy — agency considerations Dividends can be used to shift assets out of the company and therefore from the potential claim of creditors.
“Debt is more expensive than equity in a company’s capital structure because debt carries required interest payments whereas equity does not” is a fallacy. What is the truth dividend payments (and capital gains depending on dividend policy) are capital costs so equity carries the equivalent of interest costs
“Equity must always be a more costly capital source than debt because of debt’s higher position in the hierarchy of capital claims” is a fallacy. What is the Truth ? Debt is ‘cheaper’ in the sense of carrying an interest rate but debt’s prior claim increases the risk of equity so it is not necessarily a ‘cheap’ The gains from issuing low-interest debt might be offset by increases in the risk and returns required by shareholders
Why does the existence of debt in a company’s capital structure causes its equity to be riskier The range of possible returns to shareholders is much greater for Geared than for Ungeared. • Geared’s equity must therefore be more risky.
The differences in steepness of the Geared and Ungeared lines in EBIT- EPS graphs are verbally described as … gearing or leverage.
the line depicting the EBIT-EPS relationship… will be steeper ( often called financial risk to distinguish it from the underlying `line of business´ or operating risk that resides in EBIT ).
Why might with shareholders’ limited liability pay a negative EPS Shareholders probably would pay because unless they do, creditors can foreclose on the debt and take over the assets
The basic M&M proposition is based on the following key assumptions • No taxes • No transaction costs • No bankruptcy costs • Equivalence in borrowing costs for both companies and investors • Symmetry of market information, meaning companies and investors have the same information
‘M&M’, Miller and Modigliani — Capital Structure is generally Irrelevant because … • If cash flows will be divided up differently between debt and equity, the total value of each class of security will change, but not the total of both added together. • Miller and Modigliani – also states that if an investor is not happy with the capital structure it is possible from them to mimic a different capital structure
if an investor would prefer a company to be more highly geared … this can be simulated by buying shares and borrowing against them.
If an investor would prefer the company to be less highly geared this can be simulated this by buying a combination of its debt and equity.
There are extensions to MM theory which suggest that the actions of market forces makes gains that can be made by adjusting capital structure will be fairly small. Why ? • if a company’s capital structure made it more valuable that would drive up the price of its shares• tax treatment of debt and equity income in the hands of investors (personal tax)
Arbitrage A transaction wherein an instantaneous risk-free profit is made
The forces of demand and supply will … cause prices to adjust so as to destroy the arbitrage opportunity.
If two portfolios have wildly different securities in them, but portfolios’ aggregate future expectations are identical then … The portfolios must be equally valuable
As gearing ratio increases: • Both r(e) and r(d) increase• But [cheaper] r(d) weight (proportion) increases while the weight (proportion) [more expensive] r(e) decreases • Therefore total r(v) remains constant
The deductibility of interest payments by companies should cause there to exist a bias in company capital structures toward the use of borrowing instead of equity capital. • Even when both companies and shareholders are able to deduct interest payments, shareholders are still better off with the gearing on the company level because the company tax benefit cannot be recouped by shareholders through deductible personal borrowing. • The tax benefit of borrowing is common to almost all developed economies, and persists even when shareholders themselves pay personal income taxes such as ‘imputation’ systems
The interest tax shield (ITS) is equal to the interest payment (I) multiplied by the company income tax rate (Tc)– ITS = I(Tc), that amount is a cash flow, however, and not a value. So the value of the tax benefit must be equal to: VITS = ITS / rd
The value of the entire firm as an APV-type valuation V = VU + VITS• instead of thinking of the company’s value as the sum of its debt and its equity values the company’s value as the sum of its value if it were unleveraged plus the value of its leveraging-based tax benefits.
The interest tax shield becomes more valuable as … gearing increases because the deductible interest payments increase
a company that financed itself entirely with debt would … pay no taxes, since all of its distributions to capital claimants would be in the form of deductible interest payments
Example of an Agency Problem – Mutually Exclusive Projects, conflict of interest between bondholders and shareholders Example – two projects BOTH with $8000 debtProject A – 50% chance of returning 8000, 50% of returning 14000Project B – 50% chance of returning 2000, 50% of returning 20000Return to SHAREholders• Project A – either 0 or 6000• Project B – either 0 or 12000Return to DEBT holders• Project A – always 8000• Project B – either 2000 or 0Project B has a higher potential return to shareholders (considering limited liability)Project A has a lower risk to bondholdersThe lender will recognise that the company has an incentive to switch from Project A to Project B because management would more partial to the interests of the shareholders
Addressing a conflict of interest between bondholders and shareholders One of the more important mechanisms is the issuance of complex debt contracts for exampel constraints on the way a company can operate its assets including the maintenance of various financial ratios, limitations upon dividend payments, and so forth. • This solution would require expensive monitoring
An instance of agency conflict between bondholders and shareholders A company in financial distress (where its is unwilling to undertake a profitable investment because the resulting effect would be to help bondholders, not shareholders.
Convertibility Provision Under certain conditions (for a specified period and at a given price or exchange ratio), at the option of the lender, a bond can be exchanged for common shares. Used to address conflict between bondholders and shareholders• Shareholders do not gain at the expense of debtholders• bondholders do not require as stringent a set of restrictive or ‘negative’ covenants • would not be forced to charge for agency monitoring costs.• usually carry a lower rate of interest than a normal bond• new equity would incur dilution self liquidating
Call Provision The capacity on the part of the company to repurchase its bonds at a fixed price for a given period of time
Default and Agency Costs • litigation• delay in using/selling assets• Operational constraints (suppliers unwilling to extend credit; customers worried about warranties)• Opportunity costs
Bankruptcy’s essential effect To change the legal ownership of the company’s assets from shareholders to bondholders
bankruptcy is only possible if there are creditors. But it is not true that the possibility of bankruptcy is a drawback of borrowing, bankrupt is a positive, not a negative attribute of borrowing. Explaine The shareholders’ right to walk away from company debt will be priced originally in the company’s shares and bonds.• Limit liability has a price. When a limited company sells bonds and shares on the market it receives more for its shares and less for its bonds (i.e. paid lower returns to shareholders and higher interest rates to bondholders) than an unlimited company.
The interests of managers and shareholders are usually congruent because… shareholders elect the board of directors of the company, who in turn hire and fire management
A takeover bid is oftern the cause of a conflict of interest between mangagers and shareholders It is effectively asking shareholders to replace one management group with another. This is likely to be a more significant constraint upon managers to perform in the interests of shareholders
Actions that managers can take that augment their wealth to the detriment of shareholders • ‘perk’ consumption beyond the point where management productivity is efficiently enhanced (e.g. a slightly larger and more plush company jet, a more beautiful – or handsome – secretary• asset operations that benefit managers instead of shareholders, such as conglomeration (the merging of unrelated firms) to increase the size and reduce the cash-flow risk of the company, thus making management remuneration higher and more stable, with no accompanying benefits to shareholders who own already well diversified portfolios
Bonds and Security • Collateral – secured by financial securities• Mortgage – secured by real property, normally land or buildings• Debentures – unsecured debt with original maturity of 10 years or more• Notes – unsecured debt with original maturity less than 10 years• Seniority – Should the company go bankrupt or face another liquidating event, holders of the senior-most security will be in line to receive repayment• Sinking Fund – Account managed by the bond trustee for early bond redemption
A Call Provision Might include: • Call premium – Amount the call price > par value.• Deferred call – a provision prohibiting the issuer from redeeming the bond before a specific date.• Call protected – a provision that specifies a period in which the bond cannot be redeemed by the issuer
Protective Covenants A part of an bond agreement that limits certain actions a company may take during the term of the bond to protect the lender’s interests.• Negative covenants• Positive covenants
Put bond bondholder can force the company to buy the bond back prior to maturity Lower required return
n very simple tax structures, debt tends to have an advantage over equity but not always, explaine ? • Miller’s argument regarding taxes at personal level• Companies with quite low taxable income• companies with other means of reducing their taxes, such as credits, depreciation and depletion allowances, and so forth, debt-based tax reductions must not simply replace the deductibilities from other sources or there is really no company-wide benefit from borrowing.
There is a common notion in practitioner finance that risky businesses should borrow less (or somehow be lent less) than companies that are not so risky. Seems irrelevant, Risk can be priced. Explain ? • Agency costs are probably the reason why lenders and borrowers are less attracted to risky situations. • The difficulties in monitoring the actions of the firm, • odds of incurring distress costs.
Techniques of Deciding upon Company Capital Structure • examine what companies in similar lines of business have decided about the amounts they will borrow. Look at company averages in the industry. This depends heavily upon the ‘Darwinian rule of thumb’ argument. • financial planning. Simulate the cash flow and financial statements of the company across the future, asks a series of ‘What if?’ questions of the planning model. A computer spreadsheet programs are currently much in vogue for this, and are increasingly easy to set and manipulate
Suggestions for Deciding about Capital Structure • Forecast cash flows and concentrate on “worst case”• Avoid borrowing where: covenants and contracts could jeopardize operations or if tax benefits will simply replace other tax benefits• Increase borrowing where: value is largely in tangible assets or if necessary to avoid new equity issuances (possibly to avoid loss of ownership control) • Consider covenants and convertible provisions if lenders fear company decisions may be detrimental to their interests• Compare tentative conclusions with capital structures of others in same industry. Deviations may signal omissions or represent improvements
Short-term assets • cash, marketable securities, receivables and inventories. • Lower risk (liquidity), lower return (unlikely to carry high ‘monopolistic’ returns)
Long-term assets • plant, equipment, real estate, and certain valuable intangibles.• higer risk ( less easily converted to cash and more uncertain value), higher return ( generated by the higher-risk activities )
Practitioners argue book values should be used for measuring the extent of company borrowing while academic types argue that market values are the correct measure. What are the advantages of books values • In times of bankruptcy or severe distress assets are unlikely to be generating their usual operating cash flows, and may well be offered for sale in liquidation. Book (historic, depreciated) values are here probably better indicators of lender expectations• The very nature of tangible assets as collateral for loans may also play a part in the reliance of finance practitioners upon book values. • tangible assets tend to be those that appear on the balance sheets of companies making book values a proxy for the extent to which a company’s market value is based upon tangible assets. tangible assets present fewer problems than do intangible ones in the presence of borrowing.
Short-term financing • tends to be risky in the sense of requiring the firm frequently to renew the principal amounts of financing outstanding. This could become a problem in hard times. • there is no tendency for short-term interest rates to be higher or lower than long-term rates• short durations make them more easily reversed — less costly to discontinue when unnecessary• Higher risk, higher return
long-term financing • Even in bad times, the company is required only to abide by its contractual obligations • not as easily cancelled therefore higher costs to cancel• lower risk, lower returns
Reversibility • short durations make them more easily reversed• financing’s counterpart to asset liquidity
rule of thumb in finance – maturity matching • Finance short-term assets with short-term liabilities, and long-term assets with long-term liabilities.’
Risks of NOT using maturity matching Short term assets – long term financing• Low risk but costly because the company would have to carry the debt for a long time for a low return investmentLong term asset – short term financing• High risk the company may not have the financing it needs to cover its obligations
Short-term asset benefits and costs – Cash • Cash• Highest liquidity• Forgone interest
Short-term asset benefits and costs – Marketable securities • Liquidity• Zero NPV
Short-term asset benefits and costs – Accounts receivable • Increased revenue• Delayed, uncertain cash receipts
Short-term asset benefits and costs – Inventories • More efficient production schedule, sales flexibility• Capital costs, transaction costs
Cash is required for… • Transaction balances• Precautionary/anticipatory reserves• Compensating balances (cash amounts contractually left on deposit with banks)
The costs of cash balances are: • transactions costs • differential interest rate earned.
Management of working capital requires that… There is enough cash on hand to meet the requirements of the company, while minimising costs
A simple model of cash usage • The higher the reorder amount, the fewer the reorder transactions and the lower that cost, but the higher will be the interest forgone because of the higher average cash balances held.• The optimising of cash replenishment amounts in this situation is solved by: £r = [(2 x £D x £T)/i]^(1/2)where £r is the optimal amount of cash replenishment, £D is the total amount of cash the company expect to disperse during the year (discoverable due to the steady rate of cash disbursements).£T a (fixed) transaction costi is the interest penalty (interest foregone)
A more realistic picture is one where a company’s cash expenditure is lumpy and cash receipts are more seasonal/cyclical. • The manager cannot know in advance either the directions or amounts of cash balance changes in the future When cash falls to £M (mimimum) enough interest bearing securities are cashed to return the balance to £R (return point). When cash balances increase to £U (upper), securities are bought with excess cash to again bring the balance to £R.£R = [(2x £T x s2)/4i]^(1/3) + £Mwhere£T a (fixed) transaction costi is the interest penalty (interest foregone)s2 is expected cash balance change, squared, times the number of times per day there will be changes: s2 = $c^2 x t• example: ZYX plc has an expected cash-balance change of £c = £4000 per hour for an 8 hour working day, s2= (£4000)^2 × 8 = £128 000 000:• Formula to calculate £U£U = £M + 3(£R – £M)
The future of working capital mangement One note of caution is that technological change has and will continue to relegate much of the above analysis to little practical significance due to electronic funds transfers
Management of Receivables — accounts receivable (debtors) and inventory (stocks). A higher level of receivables results in: more sales but… longer waits until the actual receipt of cash and the likelihood of never being paid (bad debt).
The deterioration in the quality of customer credit accompanying an increase in the amounts owed to the company. Ways of discerning who should receive credit are … • Credit-reporting agencies supply information to a company at a cost.• A company’s own records of customer payment histories• Sophisticated statistical analysis (i.e. discriminant analysis).
At some point rejecting the marginal customer ceases to be worthwhile. This is the point where incremental expenditure for search and evaluation exceeds the expected gain from discriminating • Caution: a company who accepts everybody must keep it private or else the ratio of bad to good customers will rise. Formula Expected profit =( number of good customers x profit per customer) – (number of bad customers x loss per customers) – cost of analysis
One other approach to the management of receivables is to calculate the NPV associated with a proposed change in credit terms for a company FormulaNPV= change in PV of sales receipts – change in variable costs – change in working capital investment
To calculate the effective interest rate when a discount is given (or a premium demanded): i = (1 + [discount% / 1 – discount%]) ^365/ # days
Purpose of ratio analysis • compare the performance of the company this period with last, • compare the performance of the company (department) with that of competitors or other departments, and • detect areas of weakness
Data is produced for statistical analysis by the various ‘clearing houses’ Some of these organisations are operated for profit in the private sector, while others are run by government departments
A word of warning about ratios A word of warning about ratios • they can be used to suppress poor absolute figures ie 300% growth over a bad result may still be a bad result.• The goal of ratio analysis is simplify comparison which will be defeated if too many ratios are calculated • it is important to study the trend of the ratios calculated rather than attempting to arrive at sound conclusions based on one accounting period’s ratios
In ratio analysis the one hundred per cent statement (or common size) can be used in place of standard accounting statements. A financial statement in which the items are expressed as percentages instead of amounts. For example, A common-size statement is most useful when one attempts to compare a company to similar companies of different size.
groups of financial ratios • Liquidity ratios. • Profitability ratios. • Capital structure ratios. • Efficiency ratios.
Current Ratio (liquidity) Current assets / current liabilities• position of a company to meet its current obligations• It is often stated as a rule of thumb that a current ratio of 2 indicates a sound financial situation Not necessarily as there are many ways to access financing (particularly the marketability of stock) – but it is definitely a good sign
Quick Ratio (sometimes called the Acid Test) (liquidity) Current assets – inventory/ current liabilities • current assets sometimes includes inventory that is slow moving • quick ratio backs inventory out of the calculation • The industrial average is slightly greater than the widely accepted rule of thumb of 1 times
Profit Margin (Profitability) Typically, net profit after taxes / sales.• Some analysts therefore are beginning to move towards net profit before taxes
Return on Total Assets (Profitability) Net profit after taxes / total assets• Profit is not only a function of sales but also closely related to the assets employed by the company to produce the profit.• Note: total assets are normally used: a case can be made for using just the productive assets, omitting such items as goodwill and investments. The industrial sector the average is calculated on total assets.
Return on Specific Assets (return on inventory) (Profitability) Net profit after taxes / Inventory• Could show a company is carrying too much inventory, locking up cash in inventory, the greater the risk of some part of it becoming obsoleteCould also mean the company is carrying more in inventory to give them a trading advantage for example a stocking-up in advance of a major sales drive, or a rise in raw material price, or a risk of irregular and short supplies
Return on Owners’ Equity (Profitability) Net profit after taxes / owners’ equity• Perhaps the most important profitability ratio• investors are more concerned with relating their returns with the current market price of their shares rather than with the ‘book value’ of their investment. one normally considers an increase in this ratio to be a good sign but further analysis is required to determine whether or not a disproportionate increase in debt caused the improvement in this ratio.
Fixed to Current Asset Ratio (Capital Structure) Fixed assets / current assetsexamines the asset structure of the company
• The effect of debt financing on ownership and control If the owners have provided only a small proportion of total financing, the risks of the enterprise are borne mainly by the creditors. On the other hand, by raising funds through debt, the owners gain the benefits of maintaining control of the firm with a limited investment of their own.
• Gearing ratios (Capital Structure) A company with a high gearing ratio may be more vulnerable to economic downturns. This is because it has to make interest paymentsThe flipside of this argument is that leverage works well during good times
Debt Ratio (Capital Structure) Total debt / total assetsThis ratio measures the proportion of assets that are financed by debt. Debt includes current liabilities and all loans and bonds.
Times Interest Earned (Capital Structure) (EBIT) / interest• Uses the profit and loss account in order to measure the gearing position and margin of safety in relation to earningsmeasures the extent to which earnings can decline without the company finding itself unable to meet the annual interest costs.
Inventory Turnover (Efficiency) Sales / Inventory• Sales occur over the entire year, whereas the inventory figure is taken from the closing balance sheet. Different industries have significantly different inventory turnovers. Metals and engineering are slow because of the length of the production process; retail shops are very rapid, indicating that they need low inventories to service their sales levels.
Average Collection Period (Efficiency) the average accounts receivable balance divided by average credit sales per day.• sometimes called days’ sales outstanding.represents the average length of time that a company must wait after making a sale before receiving cash.
Fixed Assets Turnover (Efficiency) Sales / fixed assetsFixed assets are acquired by a company to produce sellable products: it is therefore not unreasonable to relate the investment in fixed assets to the level of sales generated from them.
Financial Analysis and Internal Accounting Managers, however, also have access to internal accounting information that permits them to engage in a more penetrating analysis. • The chart is a hierarchical tree structure• The right side of the chart develops the turnover ratio• The left side of the chart develops the profit margin on sales.If management considers that the return on total investment is not satisfactory, it can trace back through the chart
Exchange Rates and the Law of One Price is based on the assumption that differences between prices are eliminated by market participants taking advantage of arbitrage opportunities, for example • different prices for a single identical good in two location (not difference in cost)• sellers have an incentive to sell their goods in the higher-priced location, driving up supply lowering the price• consumers move to the lower-priced location in order to buy the good at the lower price, demand increases driving up pricesStops when the two prices are equal
Interest rates generate the expectation that wealth is preserved across time, exchange rates do the same thing for purchasing power across countries,However … impediments to free exchange can be imposed by governments. • These impediments can be negative such as import and export restrictions to currency movement constraints• or positive such as subsidisations Even with its imperfections there is an impressive consistency in exchange rates across currencies
Spot and Forward Exchange Rates the exchange rate at which a bank agrees to exchange one currency for another at a future date The forward exchange rate is determined by a parity relationship among the spot exchange rate and differences in interest rates between two countries..
Interest rate parity ensures that borrowing or lending in one currency at the interest rates applying to that currency will produce the same final wealth as borrowing or lending in any other currency at the interest rates applying to the other currencies. For example … Country X’s currency is trading at par with Country Z’s currency, • X interest rate 6%• Z interest rate 3%.makes sense to borrow to borrow at 3% (Z) invest at 6% (X)However, to repay the loan in currency Z, one must enter into a forward contract to exchange the currency back from X to Z . A covered interest rate parity exists when the forward rate of converting X to Z eradicates all the profit from the transaction Therefore, an important determinant of the forward exchange rate between any two currencies is the expectation of differential inflation rates in the two countries
When you lend money, the return you contract to receive is usually stated in … nominal terms
The Fisher Effect The Fisher Effect defines the relationship between real rates, nominal rates and inflation(1 + R) = (1 + r)(1 + h) where:R = nominal rater = real rateh = expected inflation rate
The ratio between the inflation rates of the two countries will … equal the ratio between the nominal interest rates which in turn will equal the ratio between the forward and spot rates
Currency risk When companies conduct business across borders, they must exchange foreign currencies for home currencies when dealing with receivables, and vice versa for payables. Foreign exchange risk is the risk that the exchange rate will change unfavorably before payment is made or received in the currency .
Options are usually more expensive more expensive than futures
common hedges are … forward contractsoptions
Factors to consider when choosing between an option and a future Buying a forward contract hedges exchange risk exactly.• An option, however, does not hedge; it actually creates a position that insures against a bad turn in exchange rates but retains the advantages of a beneficial movement in exchange. Unless there is some reason for a company to think it can predict future exchange rates better than the foreign exchange options market, there is no reason for exchange options to be used in transactions
‘Currency Swap’ involves the exchange of principal and interest in one currency for the same in another currency. I
‘Currency Swap’ – Example A U.S.-based company needs to acquire Swiss francs and a Swiss-based company needs to acquire U.S. dollars. These two companies could arrange to swap currencies by establishing an interest rate, an agreed upon amount and a common maturity date for the exchange. Currency swaps were originally done to get around exchange controls. .
In concept there is no risk of interest rate or exchange rate movement that could not be hedged by forward or futures transactions instead of a swapSwaps exist because…• they are cheaper to undertake• the type contract need is not offered.• to avoid certain kinds of costly national securities regulations or adverse taxation consequencesThat swap transactions are important is without question. Within the last few years there has been a huge increase in the number and size of swaps, both in terms of interest-based and exchange-based risks and opportunities
Within the last few years there has been a huge increase in the number and size of swaps … both in terms of interest-based and exchange-based risks and opportunities indicating that they are quite important
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.
Call Equivalent Portfolio To determine the current value of option we can use the law of one price and create a call-equivalent portfolio that contains a number of shares of the underlying asset along with enough financing that will produce the same cash flow. The law of one price ensures that investments that produce the same cash flows are priced the same and so the value of this portfolio will be the same as the option
Example of the binomial model of option valuation Variables:• Price of underlying asset (S0) : $500• Call option exercise price (X) : $600• Risk-free rate for the period: 1%• Price change each period: 30% up or down : $650 (uS0) or $350 (dS0). • If the underlying asset ends up being less than $600, the value of the call option would be zero. if the underlying asset exceeds the exercise price of $600, the value of the call option would be the difference between the price of the underlying asset and the exercise price. • In this exampleCu=max(0,(uS0-X)) ] (would be max((X-uS0),0) if it was a put) : max(0,(650-600)) = 50Cd=max(0,(dS0-X)) max(0,350-600) = 0 u = uS0/S0 650/500 = 1.3d = dS0/S0 350/500 = 0.7• To determine value create a call-equivalent portfolio that contains a number of shares of the underlying asset along with enough financing that will produce the same cash flow. •
Observations about the binomial model • This model ignores probabilities• It only works for European options where the option cannot be exercise before the expiry date• Valuation much simpler than for base securities since it is contingent on another valuation• Based on assumption of no arbitrage
Shortcomings of the simple binomial mode Multiple pricesMultiple periods
Binomial Tree diagram to address multiple periods Each level represents a (very short) period• Leaves represent final pricesMany (very short) periods approximates continuous model
Black-Sholes continuous model – 5 input variables S0 –Price of underlying asset • X — Call option exercise price • rf — Risk-free rate for the period• σ – standard deviation of security priceT – Time until expiration
Black-Sholes continuous model Formula also requires… N () – cumulative normal unit distributionln () – natural logarithme — Euler’s constant (2.7182)
Black-Sholes continuous model Formulas d1 = [ln (S0/X) + rfT]/σ(T^1/2) + 0.5 σ(T^1/2)d2 = d1 + σ(T^1/2)C0 = (S0 x N(d1)) – (X x e)^( -(rfx x T)x N(d2))
Options – Out of the money significantly cheaper than in the money or at the money options• They become cheaper as expiry time approachedoffer the biggest leverage or bang for the buck if the option trader’s view proves to be correct.For example, suppose the exercise price is 100p, the share price is 90p, the option price is 6p. This 6p is entirely time value, the exercise price is 10p out of the money.
Options – At the money Both call and put options will be simultaneously “at the money.”• has no intrinsic value, but may still have time value. • This option will be 100% time value.• Options trading activity tends to be high when options are at the money• Tend to carry the highest premiums
Options – In the money option Market value is always above exercise value• Not always worth exercisingexample : an option the gives the right to buy the stock for $12 that could immediately sell for $15, a gain of $3. Wouldn’t net any profit if it the holder paid $3.50 for it. But it would still be considered in the money
Put-Call Parity A portfolio comprising a call option and an amount of cash equal to the present value of the option’s strike price has the same value as a portfolio comprising the corresponding put option and the underlier. For European options, early exercise is not possible.
Put-Call Parity – Formula c + PV(x) = p + sWhere:• c = the current price or market value of the European call• PV(x) = the present value of the strike price • p = the current price or market value of the European puts = the current market value of the underlyer
What causes the price of call options to be higher higher risk free interest rate• higher the time to expiryhigher the volatility of the underlying asset
What applications can the Black Scholes option model have in company finance? Take the case of the equity of a firm with debt in its capital structure, the equity is actually a call option: o If interest and principal are paid to the creditor, shareholders own the underlying assets of the firm: o if interest and principal are defaulted creditors will end up with the assets. These assets were sold provisionally to the creditors when debt was issued, but can be repurchased by shareholders at the option of shareholders through payment of interest and principal to creditors.
When applying the concept of an option to equity by shareholders of the company, underlying asset value is the total value of the company’s assets, and exercise price is the interest and principal promises to creditors. If this ratio is high, the option is well “in the money” which implies a low proportion of debt in the company’s capital structure, If the ratio is low the company has lots of debt. A ratio of 1.0 implies that all the current value of the company is promised to creditors
Other concepts that would apply when viewing the shareholder equity as an option The absolute (exercise) value of the company equity is highest when there is no debt.• Equity has its most advantageous option characteristics when the company is very highly geared (‘at the money’) • Time to expire: this can be seen in the longer the maturity of the company’s debt. The higher is the equity value (other things being held the same).Volatility: higher volatility would imply that the operating assets of the company are more risky e.g. by shifting into a riskier line of business the firm can increase the value of its shares.
An Example of a Real Option Decision The cash flows that will result from the project are uncertain. It could be very good or very bad. Much of this uncertainty has to do with the project’s not actually beginning for several periods into the future. As time actually passes the nature of the project’s cash flows will become more evident• The current project valuation results in a negative NPVThink of it as a call option. Today the project does not look so good, but that could change between now and the time the project would be undertaken. The company can position itself now with the ability to decide periods hence whether or not to pursue it by buying equipment, buying another company, completing an enabling project etc.
Evaluating a future project as if it was a call option The exercise price, • initial investment of the projectthe time until expiration, • the point in the future when the above outlay would be madeunderlying asset value• project’s cash flows from beyond the date of exercise, discounted to the present (excluding initial investment) (calculate as regular cash flow problem and bring result to back to present)risk free interest rateoption value • needs to be at least the NPV of reserving the opportunity (buying a company, equipment, positioning project etc.) (so use this value in the calculation)standard deviation of underlying asset value• can be calculated using the above values and the Black Scholes formula (assuming the option value = the NPV of the positioning)the higher is the standard deviation of the project’s underlying asset value (the more it ‘bounces up and down’ across time), the higher are the odds that the cId project will ‘turn good’ between now and the expiration date
Another Real Option example Consider the situation where a project can either be operated or liquidated at various points during its projected lifetime. • At each of the potential liquidation points there is effectively a put option that allows the company to sell the project instead of operating it for its remaining lifetime (or at least until the next liquidation option point). The company would choose to liquidate the project if the exercise price (the liquidation value) is greater than the present value of the remaining project cash flows plus the value of the additional options to liquidate further in the future. And therefore the NPV’s associated with operating the project through its lifetime must be augmented with the put option values inherent in the ability to abandon or liquidate the project. Ignoring abandonment or liquidation options can produce misleading investment NPVs.
Agent An individual, group or organisation to whom a principal has designated decision-making authority.
Principals Those who feel the ultimate effects of the decisions taken by agents.
Agency Problem Usually refers to a conflict of interest between a company’s management and the company’s stockholders. • The shareholder-bondholder conflict of interest Can also arise when `information asymmetries´ exist.
Solving the Agency Problem for Shareholder- management conflict The manager can be motivated to act in the shareholders’ best interests through incentives such as • performance-based compensation, • direct influence by shareholders, • the threat of firing and the threat of takeovers.
Solving the Agency Problem for shareholder-bondholder conflict One solution to this agency problem may be to issue a security more complex than a simple bond, such as the call-provisioned bond
information asymmetries occur when a buyer and seller in a transaction may have different amounts or quality of information about the decision at hand. Potentially, this could be a harmful situation because one party can take advantage of the other party’s lack of knowledge• technology has made information dissemination increasingly ubiquitous and timely. It is important to note that not all information is good information; that is, just having information that others don’t have doesn’t necessarily make that information valuable or even correcttrading on asymmetric information may be illegal.
An Example of Information asymmetry A seller wants to sell shares before some bad news is available to the public. Once the company’s problems are made public, it is likely that the shares will plummet. Essentially, the seller is taking advantage of the buyer’s lack of knowledge.
Information asymmetry exists when a project was to be undertaken and the shareholders had a better understanding of the project’s NPV Eventually, of course, if the project is undertaken, its NPV will be revealed by its outcome, and bond prices will increase. The problem with this situation is that bondholders instead of shareholders will receive at least part of the NPV of the project, as bond prices increase. With that foreseeable, the shareholders may not allow the project to be undertaken in the first place
Derivatives any financial security whose return or outcome set is derived from some other asset’s value or return outcome. . For example forward and futures contracts
Properly used, derivatives serve to reduce risk The most common type of transaction is derivative markets is the hedging of risk but could also be used for speculation
Derivatives have a reputation as being very complicated and dangerous? • There has evidently been a tendency on the part of some financial security issuers to offer some frighteningly complicated derivative securities, the risks of which even they do not understand. And even simple derivatives can be very dangerous when misapplied.With a large position one could lose (or make) a lot of money very quickly, particularly if bought on margin (leveraging), as is typically done.
The potential benefits are very large for many organisations, if done correctly but because of the nature of derivatives companies should Take careful control and oversight of those responsible for committing firms to positions in derivative markets.Have someone in the organisation who understands enough about these markets to appreciate the risks inherent in a proposed commitment
The Types of Derivatives Interest rateStock MarketForeign ExchangeMortgageReal AssetHybrids and Exotics
Interest rate Derivatives Forward contractsFuture contractsOptionsSwaps
Stock Market Derivatives Future contracts on Market indexesOptions on market indexesOptions on individual securities
Foreign Exchange Derivatives Forward contractsFutures contractsOptionsSwaps
Real Asset Derivatives Forward contractsFutures ContractsOptions Contracts
‘Exotics’ formulated from combinations or mixtures of other types of derivatives. • are tailored to the very specific risk exposures of a single firm, • can be very complicated – s there have been instances where that even the inventor of the security did not fully comprehend the potential range of outcomes• Interest rate- and currency-swaps were considered exotic when they first appeared in the 1980s, • Similarly, proprietary products originally developed to meet the needs of particular clients may in time diffuse more widely into the market.
An example of an exotic is: A swap on which the client makes out well as long as interest rates stay within a relatively narrow range–“the wedding band”–but that turns into a loser if rates move either below the band or above it.
Are exotic transactions useful? Apparently so, or we should not expect to see anything like the volume that we do.
The Definition of Financial Engineering It is closely intertwined with the ideas and markets of derivative securities and risk hedging.• It is the basis of designing a hybrid or exotic financial security to fit very specific risk-shaping intentions of a firm.Embodies the notion that there are a few elemental building blocks or financial contracts that can be combined in a rigorous fashion to produce an almost unlimited variety of non-standard cash flow expectations.
Purpose of Financial Engineering can be employed to design purchases and sales of various financial securities that serve to reduce the risks of adverse movement in each of the risk exposures implied by the project, and to reduce the costs of national regulations and taxation.
The Elements of Financial Engineering Conceptually, the idea is that all familiar financial securities can be thought of as having some combination of;• Credit extension (such as loans, bonds, etc.)• Price fixing (such as futures and forward contracts)Price Insurance (such as call and put options)The invention of new or hybrid financial securities to fit exactly some requirement of an individual financial market participant is a matter of combining these elements into a package of claims that will produce a profile of cash flow expectations meeting this need.
What is a passive dividend policy Using dividends as a source of finance rather than raising money from the market.
Advantages of a passive dividend policy • Raising money from the markets is expensive, so the passive policy saves on flotation costs,• Shareholders like predictable dividends. • Would result in lower taxes.
Disadvantages of a passive dividend policy . The unpredictability of dividend payments is the strongest argument against passive policy.
What is a share dividend The shareholder is accepting shares instead of a cash dividend.
Share dividend advantages • Reduces taxes• Increases the number of shares in issue this will reduce gearing so will allow the company to borrow more.
Share dividend disadvantages Increases risk
What is a share split Old shares are replaced with new shares.
Example of a one for two share split In this case two old shares will be replaced with one new share. The value of the holding will remain the same. So if you have 200 shares at $5 before the stock split, you will have 100 shares at $10 after the split
Discriminant analysis used to assess the credit worthiness of customers
Factoring A financial transaction in which a business sells its accounts receivable
Annualized Return [(1+R1) x (1+R2)… x (1+Rn)] ^ (1/n)
Why is best to discount foreign cash flow with foreign discount rate then translate into the domestic currency using spot rate rather than forecasting the exchange rates and use the domestic rate to discount) The forward exchange markets do not really exist beyond 1 year; foreign exchange forecasting beyond 1 year is extremely risky
Calculating foreign exchange rate Forward rate for foreign per 1 domestic = (( 1 + foreign interest rate) /(1+domestic interest rate)) * spot for foreign per 1 domesticNOTE : in the above calculation the ratio between the interest rates will equal the ratio between the nominal interest rates which in turn will equal the ratio between the forward and spot ratesNOTE: this for the forward rates Multiply by the spot rate. If you are calculating the current rate it would a divisionNOTE: make sure to annualise the interest rates in the ratio before calculating if the looking for 6 month or 3 month rates
An example of calculating the foreign exchange rate UK interest rate = 4%, US interest rate = 2%, spot rate = $1.45/ £1. What is the 1 year forward rate? The dollar is the foreign currency, the US interest rate is the foreign interest rate, and the £ is the domestic unit. Putting this into the formula:=(1.02/1.04) * 1.45
Forward discounts and premiums are defined by the relationship between spot and forward rates in a pair of currencies. Since the forward dollar price of sterling ($1.5780) is lower than the spot price ($1.5960) there is a forward discount on sterling(often quoted as an annual percentage rate, here approximately 2 × (1.5780 − 1.5960)/1.5960 or 2.26 per cent) and a forward premium on dollars.We multiply by 2 because the forward premium or discount is expressed as an annual rate, and the forward rate we have calculated is the six-month rate.NOTE: make sure interest rates are annualised
Overvalued Currency – Advantages – Downward pressure on inflation i.e. imported goods will be cheaper – More imports can be bought – High value of currency forces domestic producers to improve their efficiency to be more competitive in the international market.
Overvalued Currency – disadvantages – Overvalued currency will make exports uncompetitive in the international market which will hurt the export industries- Imports are relatively cheaper to buy due to overvalued currency. Consumers will go in for more imports which will damage to domestic industries
If volatility increases what happens to the price of call options? of put options? Both types of option values will increase, because there is more likelihood of bigger share price movements.
The company is owned by the shareholders Some of the questions used shareholders when I expected company
what are covered puts The writer covers the put with shares or money. It defines and limits risk
what are naked call – inherently risky, as there is limited upside potential and (theoretically) unlimited downside potential should the stock rise above the exercise price of the options that have been sold.- Only experienced investors who strongly believe that the price of the underlying stock will fall or remain flat should undertake this advanced strategy. – The margin requirements are often very high for this strategy as well due to the propensity for open-ended losses- The upside to the strategy is that the investor could receive income in the form of premiums without putting up a lot of initial capital.
Euromarkets Because of the lighter regulatory regime it is cheaper to borrow in the euromarkets. It does not need excessive regulation because it is largely a professional market; private investors are effectively shut out of the market. The eurodollar has exactly the same exchange rate as the domestic dollar. The interest rate charged on a eurodollar loan will be slightly lower than one in a domestic bond market
About swaps Swaps are better for the longer term positions, where it is difficult to get coverage with futures and forward agreements. These products tend to be used for durations of up to 1 year. Swaps allow companies to take advantage of market imperfections in that a company may be charged different rates for borrowing fixed or floating and they can use their comparative advantage in one form of borrowing to allow everyone in the swap transaction to benefit. Swaps are cheaper because you would have to be renewing futures or forward contracts continually to get the same coverage if the coverage was required for periods exceeding one year.
estimating portfolio risk A portfolio’s risk can never be any higher than the linear combination of the risks of its component assets. When assets within a portfolio are perfectly positively correlated, portfolio risk is a weighted average (linear combination) of the risks of the component assets. When correlation is less than perfectly positive, portfolio risk will be less than the linear combination. Correlations cannot be greater than perfectly positive.
exercise value of an option For a call, S0 – X (share price – exercise price)For a put, X-S0
Time Value of an option option price – the exercise value
Discuss the agency problems associated with too little debt Equity is more forgiving than debt (debt is hard, equity is soft). Managers in the company with little debt will be more able to miss targets and invest in poor projects without punishment.
Calculating forward rates over time The forward rates are obtained by multiplying the current spot rate by the interest rate differential (calculated in (a)). This is extended for years two to five by raising the interest rates to the power of the number of years.

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