The Basic Ideas, Scope, and Tools of Finance Finance is the economics of allocating resources across time. The market interest rate is the rate of exchange between present and future resources. Any transaction that a participant might make by borrowing or lending at the market interest rate of interest will produce a result that lies on the Financial Exchange Line. The expression that moves us up or down the exchange line is: CF(1) = CF(0) (1 + I) Present Value Present Value is defined as the amount of money you must invest or lend at the present time so as to end up with a paticular amount of money in the future. Present value is also an accurate representation of what the market does when it sets a price on a financial asset. The present value of all present and future resources (cash flows) is known as present wealth. It is a useful benchmark or standard to judge whether an individual will be better or worse off when undertaking a proposed financial decision. One cannot change present wealth merely bey transacting at the market rate. Borrowing and lending at this rates simply moves you up and down the exchange line--so it impacts only time allocation. (Only investing in real assets can increase present wealth. This produuces a parallel shift in the financial exchange line.) The amount of parallel shift in the exchange line can be calculated using the present value equation. PV = CF(0) + CF(1) (1 + i) Net Present Value PV (inflow - outflow) = - CF(0) + CF(1) (1 + i) The number produced by this expression is exactly equal to the change in present wealth.

Internal Rate of Return (IRR)

1 / 40

1) Average per period rate of return on the $$ invested. 2) The discount rate that equates the present values of investment’s cash inflows and outflows (rate that causes NPV to equal 0). NPV = 0 = -CF(0) + CF(1) (1 + IRR) Multiple Period Finance PV = CF(2) (1 + I(2))^2 Compound Interest CF(0) x [1+ (i/m)] ^mt m = number of times/period compounding takes place t = Number of periods Continuous Compounding CF(0) x (e^it) Multiple Period Cash Flows PV = CF(1) + CF(2) + CF(3) (1+i(1)) (1+i(2))^2 (1+i(3))^3 NPV = CF(0) + CF(1) + CF(2) + CF(3) ( 1+i(1)) (1+i(2))^2 (1+i(3))^3 Finding IRR in these situations is more complicated, but still is found by setting NPV = 0, and solving for discount rate. Usually found with good calculator, or by trial and error. Math Summary: PV = Σ CF(t) (1+ i(t))^t From t=1 to T. Reduces to 1+i when the discount rate is the same across all periods.

Present Value Tables Helpful when calculating far off periods. Find interest rate, and period. Multiply times actual amount.

2 / 40

Perpetuity PV = CF i When CF grows or declines at a constant rate: PV = CF (i - g) Where g is the constant per period growth rate of the cash flow. Interest Rates, Interest Future Rates, and Yields The relationship between spot rates (those which begin at the present, and run to some future point), forward rates (rates that begin at some point in the future), and and YTM (yield to maturity--the IRR of a bond’s promised cash flows, total yield given term structure and rates), can be seen as follows: Spot Rates: $923 = $40 + $40 + $1040 (1.05) (1.06)^2 (1.07)^3 Forward Rates: $923 = $40 + $40 + (1.05) (1.05)(1.07) YTM: $923 = $40 + $40 + $1040 (1.069) (1.069)^2 (1.069)^3 $1040 (1.05)(1.07)(1.09)

Summarizing: (1 + i(2))^2 = (1 + 0f(1))(1 + 0f(2)) Example: (1 + i(3))^3 = (1 + 0f(1)) (1 + 1f(2)) (1 + 2f(3)) (1.07)^3 = (1.05) (1.07) (1 + 2f(3))

3 / 40

2f(3)= 9% Bond YTM Yield’s can be different even if discount rates are the same due to the coupon effect on the yield to maturity--that is, cash flow amounts that occur in different spot rate periods ipact the yield. YTM’s reflect not only rates, but amounts invested. Interest Future Rates Financial markets allow you to guard against the risk of an interest rate change giving your investment a negative NPV (whereas formerly, it was positive). One tactice would be to sell an interest rate futures contract in the aproximate amounts and timings of the cash inflows of the project. Example: Investment has following cash flows: t(0) -$1,700 i(1) = 10% i(2) = 11% NPV = -1700 + 1000 + 1000 (1.10) (1.11)^2 The forward rate implied by this term structure is : (1 + i(2))^2 = (1+ i(1))(1 + 1f(2)) (1 + 1f(2)) = (1 + i(2))^2/ (1+ i(1)) (1 + 1f(2)) = (1.11)^2/(1.10) 1f(2) = 12.0009% t(1) $1000 t(2) $1000

Suppose the 1f(2) rate changes to 15%. Then, by plugging this into the equation above, i(2) becomes 12.4722%. By doing an NPV, we get NPV = -1700 + 1000 + 1000 (1.10) (1.124722)^2 =- $.40

4 / 40

The positive NPV became negative due to the change in interest rates. You could hedge by selling a $1000 futures contract at a forward interest rate of 12.009%. (if the forward rate increases, the price of your security will decline, but, since you have a contract to sell at a higher price, the value of your contract will increase. The increase offsets the NPV of your investment. Futures price = $1000 (1 + 1f(2) ) = $1000/1.12009 = $892.79 If forward rates gor to 15, then price of the cash flow is 1000/1.15=869.57. You sold at a higher price, so your investment value increases by 892-869=21.11, offsetting the NPV decrease.

5 / 40

Module 2 - Fundamentals of Company Investment Decisions Corporate Equity: 1) A residual claim 2) Limited Liability 3) No contract as in bondholders, but have rights to all leftover resources What determines the value of equity? Dividends (and/or retained earnings) alone. Key Points : 1) Corporations in making financial decisions attempt to maximize the wealth of their existing shareholders. 2) Shareholder wealth consists essentially of the market value of the comon shares or equity of the company. 3) So the company in maximizing the wealth of its shareholders must attempt to maximize the market value of its common shares. 4) The market value of the common shares of a company is the present value of the future dividends ( or retained earnings) expected to be paid to currently existing shares of the company. Investment Decisions in All Equity Corporations Regardless of who pays the initial outlay (retained earnings from forgone dividends or issueing new shares), the NPV of the investment stays the same regardless. Investment Decisions in Borrowing Corporations If an investment is undertaken by borrowing, the NPV does not change as in the case of an all equity company. Share Values and P/E Ratios 1) The P/E ratio is nothing more nor less than the ratio between the present value of all the company’s future dividends (its market price), and its expected earnings during the first period. 2) A company’s P/E ratio is a very complex number in terms of 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. 3) For certain companies with very simple cash flow patterns (such as constant or constant growth perpetuities) we can derive a specific relationship between P/E ratios and equity discount rates. But for most companies, the relationship is much too complex

6 / 40

to make numerical estimation worthwhile. 4) If we are careful, we could use the P/E ratios for example, to: a) Infer that expected future growth rates for dividends and earnings will be above average of other companies within the same industry. b) Other

7 / 40

Module 3 - Earnings, Profit and Cash Flow Financial cash flows are the cash amounts that are expected to occur at the times for which the expectations are recorded. They are not to be confused with accounting numbers. FCF-’Free Cash Flow’: The amounts of cash that can be taken by capital suppliers from the company as a result of the investment while leaving all of the plans of the company intact. Corporate NPV: Total corporate value change less cost of investment. Government tax credits are viewed as negative taxes. Conclusions to Module 3 1) Investment NPV is correctly calculated by discounting to the present all of the changes that will occur in the cash flows of the corporation as a whole, were it to accept the project. The net of the amounts is called the free cash flow. 2) These corporate cash flows can be conveniently depicted at one level of generality by listing all of the outside groups with whom the corporation transacts. 3) Free cash flow is defined as the net amounts of cash that the company could pay to its capital suppliers from the proceeds of the project at each time point, and not upset the expectations associated with the project. This essentially means that free cash flow is the amounts that are expected to be left over or ‘residual’ after all commitments and contracts other than those to capital suppliers have been satsified according to the market’s expectations. 4) Cash flows are not the same as the numbers that appear in financial statements of corporations. Included in items such as Revenues and Expenses are non-cash items that cause accounting numbers to differ from cash flows (changes in debtors or accounts receiveable, and creditors or accounts payable , and depreciation, are examples.). There are also certain cash flows that are not included in accounting figures at the times when they occur (such as outlays for depreicable assets, and collections of receivables and payment of payables.) If accounting data are to be used as the basis for cash flow estimates, all necessary adjustments must be made to result in cash flow estiamtes at each time point of the investment.

8 / 40

Module 4 - Investment Decisions Weighted Average Cost of Capital WACC-’Weighted Average Cost of Capital’ companies with complex capital structures composed of both debt and equity. Calculation of WACC is complicated by the fact that debt has interest tax shields associated with it. WACC is the discount rate which: 1) Reflects the operating risks of the project; 2) Reflects the project’s proportional debt and equity financing 3) Reflects the effect of interest deductibility for the debt financed portion of the project. Overall Rate= Debt Market Rate x Debt Required Rate + Equity Market Value x Equity Required Rate Total Market Value Total Market Value Debt Cost = Debt Required Rate x (1-Corporate Income Tax Rate) Debt Cost is debt’s required rate multiplied by the complement of the project’s corporate income tax rate. (In other words, the after tax effective cost of debt given the interest tax shields.) WACC is used when the proportions of debt and equity can be determined. What’s needed to calculate WACC? 1) Required rate for equity 2) Debt’s after tax cost rate 3) “All equity” free cash flows 4) Proportions intended fordebt and equity financing. WACC-NPV NPV(0) = Σ FCF(t) * (1 + rv*)^t Where: rv* = The WACC of the investment; equal to: D (rd*) + E (re) V V Where:

9 / 40

FCF(t) * = Unleveraged (ungeared) free cash flow: the amount of free cash flow that the company is expected to generate at time t due to the project not including interest tax shields. rd* = Cost of debt as a rate to the investment; equal to rd x (1-T(c)), rd = Required return on the debt of the investment re = Required return on equity of the investment D = Market value of debt E = Market value of the equity V = Market value of the investment The Adjusted Present Value Technique (APV) APV- When amounts of debt that projects will use are known--but not proportions. Method: 1) Calculate present value assuming all equity financing 2) Calculate present value of tax shield 3) All Equity Value + Interest Tax Shield Value - Present Outlay = APV APV(0) = Σ FCF*(t) + ITS (1 + ru)^t ( 1 + rd)^t Where: Σ from t=0 to n, FCF*(t) = Unleveraged (ungeared) free cash flow: the amount of free cash flow that the company is expected to generate at time t due to the project not including interest tax shields. ru = All-equity or unleveraged (ungeared) required return on investment; the rate that would be required on the investment were it to be financed purely with equity. rd = The required return on the debt of the investmen ITS = Interest tax shield cash flow: the reduction in corporate income taxes at time t caused by interest deductibility of the debt issued for the investment. Equal to interest cash flow x coporate tax rate.

Summary: There are four major components of conducting a WACC-NPV, or an APV as follows: 1) Determine cash flows

10 / 40

a) What is the free cash flow amount? b) What is the interest cash flow? c) What is the corporate tax rate? d) What is the interest tax shield amount? 2) Determine market values a) What is the market value of equity? b) What is the market value of debt? c) What is the market value of the total investment? 3) Determine discount rates a) What is the required return on equity? b) What is the required return on debt? c) What is the true cost of debt less interest tax shields? d) What is the overall weighted average discount rate --factoring in equity’s return, and the true cost of debt? 4) Use the investment evaluation techniques WACC-NPV a) Use NPV if proportions of debt and equity are known b) Discount rate properly reflects debt/equity proportions APV a) Use APV is actual amounts of debt and equity are known b) Calcualtes Ungeared NPV of free cash flows, plus the NPV of the interest tax shields using debt’s required return.

11 / 40

Module 5 - Estimating Cash Flows for Investment Projects When estimating cash flows, its important to work the procedures in the correct order, so one procedure isn’t interrupted for another. Cash Flow Estimation Steps #1- Calculate Depreciation Expenses for Tax Purposes Note: Straight line depreciation involves equal amounts for each year. Salvage value is registered in year asset is liquidated. #2- Calculate Change in Taxes Should Company Accept the Project Requires Creation of Income Statement: Sales Revenue Other Revenue Subtotal Direct Expense Labor Other Management Marketing Subtotal Depreciation Subtotal Total Expense Profit Before Tax (Total Revenue Less Total Expense) Less Taxes Total Income #3-Calculate Working Capital Accounts Receivable Accounts Payable Cash and Inventories Use to calculate changes in net working capital Note: a) Add these together, but they should be noted as negative changes to net working capital. b) Don’t forget total liquidation value at final period. This is a positive entry. #4-Project Cash Flows Sales Revenue

12 / 40

Total Direct Expense Change in Net Working Capital Assests Taxes FCF-Free Cash Flow (Generally, all of the above are subtracted from sales revenues, except possible liquidation pluses in the final period.) Summary 1) Include all changes that will occur in the cash flows of the corporation were it to accept the project, at the time points when those cash flow changes are expected to take place. Those cash flows comprise all transactions that the corporation would undertake with suppliers of labor and management skills, with suppliers of materials and assets, and with government. Operational opportunity costs are legitimately included in a projects cash flows, but cash flows to and from capital suppliers are not. 2) When the cash flows are being estiamted for an NPV or an IRR analysis, it is not necessary to estimate the interest tax shields for the project: the cash flows are ‘allequity’ flows. When an APV analysis is to be done, interest tax shields must also be estimated, based upon the debt issued to finance the project. Important Notes: 1) Cash inflow timing is often different from that reflected in accounting records 2) Cash outflows for apital outlays etc. follow a pattern different from accounting records. 3) The accounting expenses for overhead, depreciation, and interest generally differed from cash flows, but had cash flow implications. << Note only changes to cash flows.>> <<Record Cash Flows, and only cash flows>>

13 / 40

Module 6 - Applications of Company Investment Analysis There are several alternatives to the NPV advocated by the business world. It can be demonstrated that NPV is superior to all. NPV Alternatives Payback Period: Time until investment is recouped. Problems: 1) Ignores all cash flows beyond the minimal acceptable payback period. 2) It does not discount cash flows during the minimum acceptable period--so inconsistent with investor opportunity costs. What would be a reasonable payback period? 1/rv*- 1/ (rv*(1+ rv*)^n ) where rv* is the weighted average cost of capital and n is the number of periods in the project’s total lifetime. Accurate only for fairly constant cash flows. Average (Accounting) Return on Investment Dividing expected accounting profits by net book value (depreciated value). These numbers are added together, divided by number of periods, and compared to standard. Problems: 1) Does not discount cash flows 2) Uses the wrong numbers IRR vs. NPV W/O Question, the NPV is superior as an investment decision criteria. Why? IRR has the following limitations: 1) Multiple sign changes in cash flows can produce multiple IRR’s. 2) IRR’s in cases of multiple discount rates in multiple periods is a problem. 3) IRR is a problem when evaluating competing projects because completing projects cash flow patterns often ‘cross over’ at a discount rate < IRR. IRR can be used to compare projects with the incremental cash flow analysis. Follow the steps below to use this method: 1) If you have a lot of projects to pick from, think of them as being in a pot, and pick any

14 / 40

two from the pot. 2) Find the one that has the highest net positive cash flow total (the simple sum of all its FCF*’s, which can be thought of as an NPV calculated with a discount rate of 0. Call the project with the highest net positive cash low total “the defender”, call the other one the challenger. 3) At each time point, subtract the cash flows of the challenger from those of the defender, and call the resulting stream the ‘incremental cash flows’. 4) Find the IRR of the incremental cash flows. 5) If the IRR of the incremental cash flows is greater than the appropriate hurdle rate, keep the defender, and throw out the challenger. If the IRR of the incremental cash flows is less than the appropriate hurdle rate, keep the challenger, and throw out the defender. 6) Omitting the thrown out projects and keep the survivor--keep goin until there’s only one left. That’s the winner. 7) Calculate the IRR of the winner. If it exceeds the hurdle rate, accept the winner, if lower, all in the pot get rejected. Cost Benefit Ratio CBR= Σ Inflows (1 + rj)^t Σ Outflows ( 1 + rj)^t

Investment is accepted if ratio is >1, rejected if < 1. On the plus side: It’s really a form of NPV Problem: Answer is a ratio of values, not value itself and can give wrong answers.

Profitability Index (PI) PI= Σ FCF*t (1 + rv)^t -FCF*(0)

15 / 40

PI>1 OK < 1 Reject The PI is used only when the present cash flow FCF*(0) is a net outlay. Because it is a ratio, has same problem as CBR--displays “wealth increase per dollar of initial outlay” instead of net total wealth increase. Capital Rationing. All calculations up to now assume that there is enough money available to pursue all projects. How to decide on investment projects when capital is limited? 1) Rank investments in order of NPV’s, and choose highest NPV’s. 2) Rank both in terms of NPV and PI 3) For interdependent investments, combinations can be studied as single investment packages. Renewable Investments Some company investments have different renewal cycles. How to compare ‘apples to apples’? 1) Find NPV of a single cycle of each asset. 2) Divide that number by the annuaity present value factor for the number of years in each asset replacement cycle, at the appropriate discount rate. This procedure converts actual cash flows associated with each investment to a constant annuity cash outlay. Inflation Be sure you are consistent when using “real” & “nominal” rates.

16 / 40

Module 7 - Risk and Company Investment Decisions The securities market line (SML) describes the relationship between risk and return. Risk is best measured by the standard deviation of rates of return on the entire portfolio of assets. Probability Distribution of Returns Example: Rate of Return 8.5% 11.0% 13.5% 16% Probability 35% 10% 30% 25%

The mean,(average expected return), is found by multiplying the individual rates of return by the probabilities, and summing. In this case, the mean is .12125 or 12.125%. Standard Deviation of Returns Found by squaring the difference between the mean, and individual returns, muliplying times the probability of the individual return, and summing: _________________ SD= √ Σ (ir - bar x)^2 * Pn from 1 to n ir equals the return of the individual investment. In the case of the above numbers, SD= (.085 - .12125)^2 * .35 = .00045992 (.11 - .12125)^2 * .1 = .00001266 (.135 - .12125)^2 * .3 = .00005672 (.16 -.12125)^2 * .25 = .00037539 =.0009046 taking the square root; = .03008 =3.0008% Problem: The SD of return has not proven to be a valid indicator of performance. It has little empirical validity. The positive relationship between risk and return is only true for entire portfolio, not individual assets within it. (Reason: part of the SD for individual assets is “diversified away”).

17 / 40

Can not use the weighted average standard deviation of return of individual assets--must use “joint probability distribution” Examples: Asset B Returns 7% 10% Asset A Returns 20% .3 .65 .25 .35 .55 .35 12% .1 .45

Probability is higher for one asset returning low, while another is returning high. Average SD was wrong because it ignored interaction of returns. Can deal directly with this issue by handling the interrelatedness of asset returns via the correlation coefficient. Main lesson: Portfolio risk is not the same as average individual security risk. Undiversifiable/Systematic risks: Extent to which securities are influenced by common factors (the market). Actual Measure: Systematic Risk of Security j =SD of Return j x Correlation of j with market. Typical Measure: βj = SD of Return x Correlation with Market SD of Market Return Example: β of 1.5 x % change in market gives 1.5 x % change in return of a security. The market only compensates for undiversifiable risks, therefore, correct measure of risk is that which exists after diversification. How much compensation? rf : Risk free market return E (rj) = rf + [E(rm) -rf] βj Required return on a security is composed of compensation for time (rf) + compensation for risk [E(rm) - rf] βj.

18 / 40

Summary: 1) The total risk of an individual asset or security can be separated into two types of risk, that which can be diversified away, and that which cannot. 2) The risk that cannot be diversified away is related to an underlying ‘market factor’ that is common to all assets and securities, and is thus a common correlation limiting the amount of risk reduction through diversification that is possible by including a security in the portfolio. 3) This undiversifiable or systematic risk can be measured by the β coefficient (SD times correlation with the market) of the security in question. 4) If the financial market sets securities’ returns based upon their risks when held in well diversified portfolios, systematic risk will be the appropriate measure of risk for individual assets and securities, and the SML as depicted in Fig. 7.6 and formula 7.1 will dictate the set of risk adjusted returns available in the market. 5) These SML-based returns are the opportunity costs of capital suppliers of companies, and thus can form the basis for evaluating internal company investments. These investments must offer retuns in excess of capital supplier’ opportunity costs in order to be acceptible. Capital Asset Pricing Model The Capital Asset Pricing Model, or security market line, the system which generates required rates of return based upon the riskiness of assets . WACC should not generally be used as an investment criteria. It will only give a correct answer when the investments risk is the same as the average risk of the entire company. (For example the WACC is in fact an average of the risk adjusted rates of return of the company’s various asset risks--it includes mix of both high and low risks.) Estimating Systematic Risks for Company Projects 1) Estimate β : (If not known, stock market β comparison on similar ventures.) 2) Establish “benchmark β“: Gearing--adjusting due to operations (fixed cost), financial (debt content), etc. Finding Beta: a) Find Ungeared beta: βu =βe E/V + βd D/V The ungeared beta is found by the above formula. This is the beta that would exist if the company had no debt outstanding.

19 / 40

b) Adjust for revenue and operational gearing Revenue adjusted β = βu Project Revenue Volatility Company Revenue Volatility Poject βu = Revenue adjusted β ( 1 + Project fixed cost %) ( 1 + Company fixed cost %) Now the beta of the equity of the project can be found by the formula given above: βu =βe E/V + βd D/V: The idea here is to plug in the ungear beta numbre for the project, the proportions of debt and equity, and the given beta of the debt to solve for beat of the equity. Estimate WACC using β 1) Find E(rj): expected return on equity by: 2) Finding rf: usually government bond rates 3) Finding [ E(rm) - rf]: typically found in stock market “excess” gain over time. (in UK, the rate is 9.1, and in US, 8.8% hisotrically). 4) Apply these figures to the equation for the SML including the beta for the project: E (rj) = rf + [E(rm) -rf] βj 5) At step 4, we have the required return for equity, but if project is also financed with debt, so we need to find the WACC for the project (rv*) 6) Find E(rd) by plugging in the beta for the debt in the SML equation from step four. (Equation is same, just use debt beta instead of equity beta.) 7) Apply the effect of interest tax shields to debt’s required return to find the true cost of debt (rd*). 8) Now we know (rv*) ,(rd*), and thr proportions of debt and equity for the project, so we can now calculate the WACC for the project. Certainty Equivalents How much money would I agree to accept in the futurefor certain in exchange for a risky cash flow? CF(ce) = CF - E(rm) - rf Cov. (CF,rm) Var.(rm) Where Var.(rm) = the variance (the squared SD) of the market return, and Cov. (CF,rm) = β x the variance of the market return

20 / 40

What we are doing here is subtracting out from a risky cash flow an adjustment for systematic risk. Remember: you are to receive this cash flow in the future (t1), so don’t forget to discount one period. Summary: 1) Diversification reduces risks. An investment will include diversifiable and undiversifiable risks. diversifiable risks disappear in a diversified portfolio. 2) Capital suppliers require higher returns for bearing higher risks, but the risk they bear is only that which is undiversifiable. 3) The market prices securities as if they were held in well diversified portfolios. 4) The pricing process of financial markets is captured in the SML equation which is a function of beta. 5) The SML relationship can be used to estimate the appropriate risk-adjusted discount rates for company investment projects. 6) The WACC can be used for an investment project only if the project is similar to the company WACC. 7) If the investment differs from the company, a project specifc WACC can be found by using a beta of another company consistent with the risk and activities of the project under consideration. 8) If there is no beta available to be observed for the investment, the beta must be artificially constructed. This process uses a bench mark beta adjusted for various gearing ratios. 9) It is possible to construct an SML relationship which can generate certainty equivalent cash flows. 10) Analyses are more complicated for cash flows who’s risk are not constant across time. Change in risk across time must be accounted for.

21 / 40

Module 8 - Company Dividend Policy Key Issues Involved in Company Dividend Policy 1) The dividend decision is a cash retention or reinvestment decision. 2) When the effect of company financial decisions upon shareholder’s portfolios can be undone by offsetting actions of shareholders, the company financial decision is irrelevant. 3) A company’s dividend change is the substitutability of capital gains (i.e. share value increases) when the dividend is reduced, for cash when the dividend is paid. 4) One argument for dividends is the “bird in the hand” argument. Capital gains are uncertain, current dividends are not. However, uncertainty has a price, and its price is factored into the price of the shares. 5) Shareholders may prefer one dividend policy over another due to transaction costs. (i.e. those who prefer cash incur costs in selling shares.) 6) Dividends are taxable, so some shareholders may prefer capital gains over dividends. (in the UK, this is sometimes alleviated by various tax policies) 7) Companies incur flotation costs when raising new shares. 8) One optimal dividend policy is would be to find all investments with positive NPV’s, retain enough cash to undertake the investments, only raise new equity capital when internally generated funds are insufficient, and pay any remaingin cash out as dividends. (the passive residual dividend policy). 9) Given different clienteles seeking to add shares into their portfolio of companies with particular dividend philosphies, and many different companies serving different interests, there is nothing to be gained by changing dividend policy. 10) Companies are restricted as to what information they can release to the market. Dividends play a role in signalling messages to investors. 11) Share repurchases are really payments of cash dividends.

22 / 40

Module 9 - Company Capital Structure Should money be borrowed ? Or should it be raised from shareholders? Argument #1: Debt is more expensive than equity in a company’s capital structure because debt carries required interest payments whereas equity does not.” False: Equity requires shareholder returns, no less a cost of capital than interest payments. Argument #2: Equity’s returns must be higher than debts’ because equity’s claims are residual, so their risk is higher. Because risk higher, returns are higher, so equity is more expensive than debt.” False: This argument ignores important interactions within the set of a company’s required capital returns Debt renders more risky its capital claims--therefore, it could be said that the gains that are had from issueing low interest debt might well be offset by increases in in the risk and attendant returns required by shareholders. Debt in the capital structure increases risk. Why? 1) Risk is related to beta. 2) Beta is related to the variation in return. (The SD of return.) 3) Since debt is first in line, debt amplifies the variability of return. The terms “gearing” or “leverage” is a description of this amplification of variability idea. See example below: Ungeared Company EBIT outcome 15000 120000 150000 Geared Company EBIT outcome 15000 120000 150000 Interest outcome 40000 40000 40000 Equity outcome EPS outcome -25000 80000 110000 -5 16 22 Probability .1 .55 .35 EPS outcome 1.5 12.00 15.00 Probability .1 .55 .35

This type of risk is called financial risk to distinguish from business operating risk. M&M argue that it would make no difference to shareholder wealth whether the

23 / 40

companies borrowed money or not. Financial markets would ensure that this is so. What happens to the wealth of shareholders when the companies capital structure is altered by borrowing? The wealth of the shareholders is unchanged. It can’t increase or decrease as in an efficient market, it must sell for what it would otherwise cost to acquire the same future cash flow expectations. Summary: 1) Company captial structure does not matter--in regard to shareholder wealth. 2) Company capital strucutre does affect the risk and return of equity. Arbitrage and Prices Market prices must adjust to cause all equivalent future cash flows sold in whatever form as single securities or as portfolios of holdings to sell for the same price. Capital Structure and Taxes Because interest payments are generally deductible in some fashion, and directly benefit shareholders, it would seem obvious that companies would make use of this benefit, and tend to be financed by debt. This is not what we see. Why? For one thing, companies can take many types of write offs--including depreciation. So, companies could in effect show no income (due to heavy depreciation write offs), and therefore pay no taxes. So why then borow? Also, the amount of income a company will earn is uncertain, however, the amount of interest payments is fixed, making borrowing undesirable. Capital Structre and Agency Problems Agency problems deal with issues such as conflicts of interest among principals or angents. For instance, lenders wish to ensure that borrowers don’t do things that make their returns more risky. (Like borrowing in order to undertake one investment, and instead doing another.) How to resolve: Lender Covenants, other arrangments such as complex debt contracts.

Agency costs can make borrowing less attractive. A positive covenant is the convertibility provision which some debt claims carry.

24 / 40

(Meaning, under certain conditions, bonds can be exchanged for shares.) Default Bankruptcy is a positive attribute of borrowing. Why? 1) Bankruptcy does not cause economic conditions which precipitate bankruptcy. 2) Bankruptcy ensures order transfer of assets from shareholders to bondholders--and reduces costs (for instance, no litigation). Other Agency Issues 1) Agency problems between shareholders and managers 2) Takeovers, mergers, conglomeration Book Values and Borrowing Academics say extent of borrowing is related to market value of company. Practitioners argue for book value as appropriate standard. Market Value: based on future cash flow expectation Book value: Value of assets Techiques of Deciding on Capital Structure #1- Do what other companies in similar circumstances do. #2- Financial planning using what if simulations Debentures: debt collateralized by the overal assets and cash flow of the company. Suggestions for Deciding About Capital Structure 1) Use cash flow simulations to obtain worst case view where the existence of borrowing might lead to financial distress. 2) Borrowing should be avoided if simulations indicate high possiblity of violating covenants. 3) If simulations indicate that borrowing tax benefits simply replace other tax benefits, then little reason to borrow.

4) If the company’s value is largely in tangible assets, more borrowing is sustainable than if the same value is dependent upon intangibles (like future profitability of investments not yet undertaken, or skill skill of managers to find new opportunities). Industry gearing ratios are useful to see the amounts of borrowing which other similar companies have been able to sustain.

25 / 40

5) Company should consider attachment of covenants to bonds which would alleviate degree of concern of unfavorable actions toward bondholders. 6) There are reasons why companies would choose to avoid new equity issuances (loss of ownership and control) and such considerations outweigh negative aspects of borrowing. 7) When a tentative conclusion is reached, see if the result is inconsistent with the capital structures of other companies in the same line of business.

26 / 40

Module 10 - Working Capital Management A company’s ‘working capital’ is its short term investments in cash, marketable securities, receivables (debtors), and short term financings. Because of the short term nature of these assets and financings, an entirely different set of financial mangement techniques is used in dealing with them. Working Capital = Current assets and current liabilities Combining Risks and Rates of Return on Assets and Financing Assets Short Term Low Risk Low Return Financings Short Term High Risk High Return Long Term Low Risk Low Return Long Term High Risk High Return

Use maturity matching using the rule of thumb, “finance short term assets with short term liabilities and long term assets with long term liabilities” Short Term Asset Benefits and costs Asset Type Cash Marketable Securities Accounts Inventories Benefit Highest Liquidity Liquidity Increased Revenues More efficient production schedule, sales flexibility Cost Foregone interest Zero NPV Delayed, uncertain cash receipts Capital costs, transaction costs

Management of Cash Balances Transaction uses of cash: Paying debts, etc. Precautionary and anticipatory reserves: Unanticipated need for cash. Compensating balances: Bank reserve requirements, covenants, etc. Cost of cash balances: Transaction costs of switching between securities and their differential interest rates. Optimizing Cash Replenishment Amounts In idealized sawtooth waveform representing use of cash down to some minimal amount,

27 / 40

and then replenishing with bulk amount, use this formula: $r = [(2 x $D x $T)/ i] ^1/2 where: r is the optimal amount of cash replenishment D is the total amount spent by the firm i is interest foregone due to liquidity of asset T is transaction costs Upper Limit Return Point $R = [(3 x $T x s^2)/4i]^1/3 s^2 is the variance of the changes in the cash balances from the probability distribution described earlier. s^2 = $c^2 x t $c = cash balance change per hour Express interest differential in daily rate t in hours per day (8) The upper limit is: $U = $M + 3($R - $M) M is minimum point, R is the desired point. Management of Receivables Accounts receivable and inventory stocks. Inventory management is a seperate subject. Accounts Receivable There is a deterioration in the quality of customer credit which accompanies an increase in the amounts owed to the company. There are many techniques available to determine creditworthiness including discriminant analysis. But at some point, rejecting the marginal customer ceases to be worthwhile.

Expected Profit from Not Reviewing Creditworthiness Expected Profit = Number of good customers x Profit per customer + Number of Bad Customers x Loss per customer

28 / 40

Expected Profit Using Credit Analysis Expected Profit = Number of good customers x Profit per customer + Number of bad customres x Loss per customer - Costs of credit analyses Sometimes, profit can be higher when not reviewing creditworthiness. Analyzing Change In Terms NPV = Change in PV of Sales Receipts - Change in Costs - Change in Working Capital Investment Example: * S/W sales @ 100 packages/day @ $250 & costs of $175 * Payment on average 35 days from sale * Bad debt loss 3% of sales * Daily interest rate: .04% (15.7%/annum) * Working capital is 20% of sales NPV = (125 x 250)(1- .04) (1.0004)^40 - (100 x 250)(1- .03) (1.0004)^35

[(125 x 175) - (100 x 175)] -.20 x [(125 x 250) - (100 -250)] + .20 x [{(125 x 250)/ (1.0004)^40} - {100 x 250)/(1.0004)^35}] = $1,206.30 Management of Short Term Financings In aggregregate, short term financing is best considered a function of two phenomena, the company’s line of business, and maturity matching with short term assets. One important source of short term financing is credit extended by vendors. Question: Should you pay early, and take a vendor discount? Or pay on time with no discount?

The annual equivalent interest rate of 2 % over 20 days is: .02 x 1-.02 i = ( 1 + 365/20 365 20 )^365/20 -1 = 44.58%

29 / 40

Not a good deal. Better to borrow if you have to, and take the discount. Cash Budgeting Short term financial management is best pursued within the context of a company’s cash budgeting. Cash budgeting is the setting forth of the company’s expectations for its inflows and outflows of cash over some future time period, usually near term. Final Key Points Working capital management involves two levels of activity: 1) The hands on application of management techniques to specific asset and financing decisions. 2) The optimal setting of policies for such decisions, so that each of these small decisions is almost automatically determined by the company’s well considered policy. Liquidity Ratios Current Ratio Current Ratio= Current Assets Current Liabilities Cach and assets expected to turn into cash during the current year--liabilities to be paid during the current year. Quick Ratio (Acid Test) Quick Ratio = Current Assets - Inventory Current Liabilities Backing inventory out of assets is a more rigorous test of company’s ability to pay obligations.

Profitability Ratios Profit Margin Profit Margin = Net Profit After Taxes Sales Return on Total Assets

30 / 40

Return on Total Assets = Net Profit After Taxes Total Assets Return on Specific Assets Return on Specific Assets = Net Profit After Taxes Inventory Return on Owner’s Equity Return on Owner’s Equity = Net Profit After Taxes Owner’s Equity Capital Structure Ratios Fixed to Current Asset Ratio Fixed to Current Asset Ratio = Fixed Assets Current Assets Debt Ratio Debt Ratio = Total debt Total Assets Note: Total debt would include deferred taxation, current liabilities, loans, investment grants Times Interest Earned Times Interest Earned = Profit Before Tax and Interest Charges Interest Charges

Efficiency Ratios Inventory Turnover Inventory Turnover = Sales Inventory Average Collection Period Average Collection Period = Debtor Sales Per Day

31 / 40

Note: Also called “days sales outstanding” Fixed Assets Turnover Fixed Assets Turnover = Sales Fixed Assets

32 / 40

Module 11 - International Financial Management Firms deal with exchange rates between currencies of different countries when buying or selling to different countries. Exchange rates fluctuate over time, firms must deal with this risk. Undertaking foreign operations is also impacted by exchange rates. Other concerns involve determining the location, security, and currency in which to borrow. Finannly, government controls and subsidies. Exchange Rates and the Law of One Price Exchange rates bear the relationship to each other that they do due to purchase power parity and the law of one price. Interest rates preserve wealth across time, exchange rates preserve wealth across borders. Spot and Forward Exchange Rates The following is an example of spot and forward rates between pounds and dollars: Spot 180 Day Forward Dollar/Pound 1.5960 1.5780 Pound/Dollar .6266 .6337

Example of How to Use Spot and Forward Rates: 1) A UK firm wants to sell product in July 87 in the US, and not receive payment in dollars until Jan 88. 2) To avoid uncertainty, the firm can buy sterling forward at .6337 per dollar buy entering into a forward exchange contract. 3) If amount is 100k, the firm would receive 63,370 sterling six months hence. 4) The firm could accomplish the same transaction by : a) borrowing dollars today at the six months interest rate in the US, and exchange these dollars for sterling at the existing exchange rate, b) calculate exactly how many dollars it can borrow so as to pay off the dollar loan with the dollars expected from collecting receivables six months hence, c) Formula is: Amount borrowed = $ receivables/(1 + Six Month $ interest rate)

33 / 40

d) Assume six month dollar rate is annual rate of 6.5% Amount borrowed = 100k/(1.065)^1/2= 96,900 e) The loan proceeds are switched to sterling at spot: Sterling Proceeds = .6266 x 96,900 = 60,717 f) Sterling invested at the UK six month sterling rate of 8.94%/annual Sterling( 22 January 1988) = 60714 x (1.0894)^1/2 = 63,373 Cash proceeds are exactly the same as the forward interest rate. This is a necessity due to interest rate parity. Interest rate parity in forward exchange markets is similar to purchasing power parity in spot markets. Therefore: Relative Interest Rates = Relative Forward exchange discount or premium Forward Exchange, Interest Rates, and Inflation Expectations Nominal Interest Rate = Real Interest Rate + Effect of Inflation (1+ Nominal Rate)^n = (1+ Real Rate)^n x (1 + Inflation rate)^n Bottom line is that interest rate differentials between countries are caused by inflation differentials between countries. Hedging International Cash Flows 1) Buying a forward exchange option: Has benefits, but also costs associated with it. 2) Investing in Foreign Real Assets Financing Sources for Foreign Investment Should funds be sourced locally, or domestically? Or a third location? Real assets in foreign locations tend to increase in value as inflation increases, monetary assets do not. Don’t overlook other investment risks, such as takeover by foreign governments. Agency theory helps correct for this--by building automatic and irreversible counter-incentives. Assume all parties will act in their own best interests, so structure the deal accordingly. Companies need not expose themselves to serious risks due to exchange fluctuations, they should hedge. Also, be careful to ake into account inflation and exchange rate biases in reporting from foreign subsidiaries.

34 / 40

35 / 40

Module 12 - Advanced Topics: Options and Agency Option Characteristics Options are properly termed “contingent claims” because their value depends upon the value outcome of some underlying asset. Call Option Allows you to purchase (‘call’) another security or asset at a fixed price at a fixed time. Summary: 1) You own a call option for 100 shares at $1.25/share between now and the end of the year.. 2) $1.25 is the strike price. 3) Shares are the underlying assets. 4) The last time you can exercise is the expiration date. Suppose the stock is trading now at $1.50 per share. You can now exercise the call. 1) You pocket $25 (difference between 100 x $1.25 & 100 x 1.50) less price of option. 2) When an option can be exercised profitably, it is said to be in the money, when it cannot, it is out of the money. Note: Remember-Options are optional. Futures contracts are not. The pruchaser of a futures contract is forced to complete the transaction, even if its detrimental. Exercise Time Exercising only at expiration: European options. Exercising at any time before or at expiration: American options. Options Valuation The market value of the option is always somewhat higher than the market value of the asset itself. (The ‘premium’ of the option.) Even when the market value is zero, the option is higher than zero. Though immediate excersize nets you nothing, event excersize could net you something.

Calculating the Value of a Simple Option

36 / 40

q=.6 So = $1.50 1-q =.4

uS = 1.6 x $1.5 = $2.40

dS = .6 x 1.5 = $.9

So = the current price of the underlying security = 1.5 q = the liklihood of the underlying security price increase = .6 uSo = the underlying security increased price result = $2.4 dSo = the underlying security reduced price result = $.9 u = upward multiplier for underlying security price = 1.6 d = downward multiplier of the security price = .6 The payoff is Cu 2.40 -1.25 = 1.15 at a strike price of 1.25 when the security price is up, and 0 when its down. Your chances are Cd 60% of hitting, and 40% missing it. So what is your option worth? The law of one price says that two portfolios with the same financial performance are priced the same. So, we find the value of the call option by constructing a portfolio with the same performance. This portfolio must have payoffs equal to Cu and Cd with the same liklihoods as those of the option. Also: rf = the risk free interest rate (either borrowing or lending) for the period of the option; assume this is 10%. Y = the number of underlying shares to puchase (or negative to sell short) Z = the amount lending (if positive) or borrowing (if negative) at the risk free rate SoCu = YuSo + Z(1+rf) Cd = YdSo + Z(1+rf)

Then: Y = Cu-Cd = 1.15-0 So(u-d) 1.5(1.6-.6) = .7666

37 / 40

Z= uCd-dCo = 1.6(0) -.6(1.15) = -.62727 (u-d)(1+rf) 1.6-.6 (1 + .1) This means that if you purhase .7666 of a share of the underlying asset, and at the same time, borrow .62727, you will have the same future cash flow expectations. Then Yso + Z = .766(1.5) -.62727 = .5227 this is the market value of the option. Some Observations Regarding the Simple Valuation Model 1) The formula does not include probabilities. 2) The valuation process is simpler than those for typical securities discussed earlier. For instance, you are not valuing discounted future cash flows. This is a highly efficient valuation mechanism, in part because we are dealing with a contingent claim. the market has already valued the underlying security. 3) Use the priciple of no arbitrage. 4) American and European options will have the same value Valuing More Realistic Options 1) The binomial model deals only with two possible security values. A realistic model must allow for many possible prices. 2) Instead of putting in multiple prices, the model can be made to deal with multiple periods. 3) Periods can be set to any desired length. This model is conceptually simple, but numerical complexity would render it inefficient. The Black-Scholes Model Black & Scholes reformulated the binomial model and made it continuous. Co = SoN(d1) -Xe^-rfT *N(d2) d1 = [ln(So/X) + rfT]/σ(T^1/2) +.5σ(T^1/2) and d2 = d1 - σ(T^1/2)

There are five variables which determine option value: So: Underlying security price X: Exercise or striking price rf: Risk free rate of interest σ: Standard deviation of underlying security price (volatility,β) T: Time until expiration

38 / 40

Applications of Option Valuation Consider the equity of a firm with debt in its capital stucture. This equity is actually a call option: if interest and principal are paid to creditors, shareholders own the underlying assets of the firm; if interest and principal are defaulted, creditors will end up with the assets. Black Scholes can be used to value a company in this maner--for instance: 1) The ratio of underlying asset value to excersize price. (So/X). For the option held as equity by shareholders, the underlying asset value is the total value of the company’s assets, and the strike price is the interest and principal promises to creditors. 2) If the ratio is high (in the money), implies low debt. If low, a highly geared company. Agency Deals with principals, agents, and conflicts of interest. Takeovers--an important solution to manager shareholder conflict of interest. Agency solutions: 1) Must be overall incentive to solve--overall gain 2) Agent has incentive to participate in the solution Information asymetries can cause agency problems to arise. Bondholders can issue call provisions on the bond to solve agency problems. Convertible bonds: bonds can be converted into shares to take advantage of equity increase over debt should equity take on riskier investment than agreed upon. Convertible bond problems can be solved using binomial option valulation equations. In any case, the value of the convertible bond will be the same regardless of high or low risk investment--and their will be no incentive to take one over the other. Alternative Option Valuation-Perfectly Hedged Security uSo -mCu = dSo -mCd m = So(u-d) Cu-Cd m is the hedge ratio, it tells you how many call options to write for every one share held.

39 / 40

So = the current price of the underlying security q = the liklihood of the underlying security price increase uSo = the underlying security increased price result dSo = the underlying security reduced price result Portfolio value = Perfectly Hedged Return Risk Free Discount @ one period Then: So-mCo=X Call option Co = X/So-m

40 / 40

Internal Rate of Return (IRR)

1 / 40

1) Average per period rate of return on the $$ invested. 2) The discount rate that equates the present values of investment’s cash inflows and outflows (rate that causes NPV to equal 0). NPV = 0 = -CF(0) + CF(1) (1 + IRR) Multiple Period Finance PV = CF(2) (1 + I(2))^2 Compound Interest CF(0) x [1+ (i/m)] ^mt m = number of times/period compounding takes place t = Number of periods Continuous Compounding CF(0) x (e^it) Multiple Period Cash Flows PV = CF(1) + CF(2) + CF(3) (1+i(1)) (1+i(2))^2 (1+i(3))^3 NPV = CF(0) + CF(1) + CF(2) + CF(3) ( 1+i(1)) (1+i(2))^2 (1+i(3))^3 Finding IRR in these situations is more complicated, but still is found by setting NPV = 0, and solving for discount rate. Usually found with good calculator, or by trial and error. Math Summary: PV = Σ CF(t) (1+ i(t))^t From t=1 to T. Reduces to 1+i when the discount rate is the same across all periods.

Present Value Tables Helpful when calculating far off periods. Find interest rate, and period. Multiply times actual amount.

2 / 40

Perpetuity PV = CF i When CF grows or declines at a constant rate: PV = CF (i - g) Where g is the constant per period growth rate of the cash flow. Interest Rates, Interest Future Rates, and Yields The relationship between spot rates (those which begin at the present, and run to some future point), forward rates (rates that begin at some point in the future), and and YTM (yield to maturity--the IRR of a bond’s promised cash flows, total yield given term structure and rates), can be seen as follows: Spot Rates: $923 = $40 + $40 + $1040 (1.05) (1.06)^2 (1.07)^3 Forward Rates: $923 = $40 + $40 + (1.05) (1.05)(1.07) YTM: $923 = $40 + $40 + $1040 (1.069) (1.069)^2 (1.069)^3 $1040 (1.05)(1.07)(1.09)

Summarizing: (1 + i(2))^2 = (1 + 0f(1))(1 + 0f(2)) Example: (1 + i(3))^3 = (1 + 0f(1)) (1 + 1f(2)) (1 + 2f(3)) (1.07)^3 = (1.05) (1.07) (1 + 2f(3))

3 / 40

2f(3)= 9% Bond YTM Yield’s can be different even if discount rates are the same due to the coupon effect on the yield to maturity--that is, cash flow amounts that occur in different spot rate periods ipact the yield. YTM’s reflect not only rates, but amounts invested. Interest Future Rates Financial markets allow you to guard against the risk of an interest rate change giving your investment a negative NPV (whereas formerly, it was positive). One tactice would be to sell an interest rate futures contract in the aproximate amounts and timings of the cash inflows of the project. Example: Investment has following cash flows: t(0) -$1,700 i(1) = 10% i(2) = 11% NPV = -1700 + 1000 + 1000 (1.10) (1.11)^2 The forward rate implied by this term structure is : (1 + i(2))^2 = (1+ i(1))(1 + 1f(2)) (1 + 1f(2)) = (1 + i(2))^2/ (1+ i(1)) (1 + 1f(2)) = (1.11)^2/(1.10) 1f(2) = 12.0009% t(1) $1000 t(2) $1000

Suppose the 1f(2) rate changes to 15%. Then, by plugging this into the equation above, i(2) becomes 12.4722%. By doing an NPV, we get NPV = -1700 + 1000 + 1000 (1.10) (1.124722)^2 =- $.40

4 / 40

The positive NPV became negative due to the change in interest rates. You could hedge by selling a $1000 futures contract at a forward interest rate of 12.009%. (if the forward rate increases, the price of your security will decline, but, since you have a contract to sell at a higher price, the value of your contract will increase. The increase offsets the NPV of your investment. Futures price = $1000 (1 + 1f(2) ) = $1000/1.12009 = $892.79 If forward rates gor to 15, then price of the cash flow is 1000/1.15=869.57. You sold at a higher price, so your investment value increases by 892-869=21.11, offsetting the NPV decrease.

5 / 40

Module 2 - Fundamentals of Company Investment Decisions Corporate Equity: 1) A residual claim 2) Limited Liability 3) No contract as in bondholders, but have rights to all leftover resources What determines the value of equity? Dividends (and/or retained earnings) alone. Key Points : 1) Corporations in making financial decisions attempt to maximize the wealth of their existing shareholders. 2) Shareholder wealth consists essentially of the market value of the comon shares or equity of the company. 3) So the company in maximizing the wealth of its shareholders must attempt to maximize the market value of its common shares. 4) The market value of the common shares of a company is the present value of the future dividends ( or retained earnings) expected to be paid to currently existing shares of the company. Investment Decisions in All Equity Corporations Regardless of who pays the initial outlay (retained earnings from forgone dividends or issueing new shares), the NPV of the investment stays the same regardless. Investment Decisions in Borrowing Corporations If an investment is undertaken by borrowing, the NPV does not change as in the case of an all equity company. Share Values and P/E Ratios 1) The P/E ratio is nothing more nor less than the ratio between the present value of all the company’s future dividends (its market price), and its expected earnings during the first period. 2) A company’s P/E ratio is a very complex number in terms of 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. 3) For certain companies with very simple cash flow patterns (such as constant or constant growth perpetuities) we can derive a specific relationship between P/E ratios and equity discount rates. But for most companies, the relationship is much too complex

6 / 40

to make numerical estimation worthwhile. 4) If we are careful, we could use the P/E ratios for example, to: a) Infer that expected future growth rates for dividends and earnings will be above average of other companies within the same industry. b) Other

7 / 40

Module 3 - Earnings, Profit and Cash Flow Financial cash flows are the cash amounts that are expected to occur at the times for which the expectations are recorded. They are not to be confused with accounting numbers. FCF-’Free Cash Flow’: The amounts of cash that can be taken by capital suppliers from the company as a result of the investment while leaving all of the plans of the company intact. Corporate NPV: Total corporate value change less cost of investment. Government tax credits are viewed as negative taxes. Conclusions to Module 3 1) Investment NPV is correctly calculated by discounting to the present all of the changes that will occur in the cash flows of the corporation as a whole, were it to accept the project. The net of the amounts is called the free cash flow. 2) These corporate cash flows can be conveniently depicted at one level of generality by listing all of the outside groups with whom the corporation transacts. 3) Free cash flow is defined as the net amounts of cash that the company could pay to its capital suppliers from the proceeds of the project at each time point, and not upset the expectations associated with the project. This essentially means that free cash flow is the amounts that are expected to be left over or ‘residual’ after all commitments and contracts other than those to capital suppliers have been satsified according to the market’s expectations. 4) Cash flows are not the same as the numbers that appear in financial statements of corporations. Included in items such as Revenues and Expenses are non-cash items that cause accounting numbers to differ from cash flows (changes in debtors or accounts receiveable, and creditors or accounts payable , and depreciation, are examples.). There are also certain cash flows that are not included in accounting figures at the times when they occur (such as outlays for depreicable assets, and collections of receivables and payment of payables.) If accounting data are to be used as the basis for cash flow estimates, all necessary adjustments must be made to result in cash flow estiamtes at each time point of the investment.

8 / 40

Module 4 - Investment Decisions Weighted Average Cost of Capital WACC-’Weighted Average Cost of Capital’ companies with complex capital structures composed of both debt and equity. Calculation of WACC is complicated by the fact that debt has interest tax shields associated with it. WACC is the discount rate which: 1) Reflects the operating risks of the project; 2) Reflects the project’s proportional debt and equity financing 3) Reflects the effect of interest deductibility for the debt financed portion of the project. Overall Rate= Debt Market Rate x Debt Required Rate + Equity Market Value x Equity Required Rate Total Market Value Total Market Value Debt Cost = Debt Required Rate x (1-Corporate Income Tax Rate) Debt Cost is debt’s required rate multiplied by the complement of the project’s corporate income tax rate. (In other words, the after tax effective cost of debt given the interest tax shields.) WACC is used when the proportions of debt and equity can be determined. What’s needed to calculate WACC? 1) Required rate for equity 2) Debt’s after tax cost rate 3) “All equity” free cash flows 4) Proportions intended fordebt and equity financing. WACC-NPV NPV(0) = Σ FCF(t) * (1 + rv*)^t Where: rv* = The WACC of the investment; equal to: D (rd*) + E (re) V V Where:

9 / 40

FCF(t) * = Unleveraged (ungeared) free cash flow: the amount of free cash flow that the company is expected to generate at time t due to the project not including interest tax shields. rd* = Cost of debt as a rate to the investment; equal to rd x (1-T(c)), rd = Required return on the debt of the investment re = Required return on equity of the investment D = Market value of debt E = Market value of the equity V = Market value of the investment The Adjusted Present Value Technique (APV) APV- When amounts of debt that projects will use are known--but not proportions. Method: 1) Calculate present value assuming all equity financing 2) Calculate present value of tax shield 3) All Equity Value + Interest Tax Shield Value - Present Outlay = APV APV(0) = Σ FCF*(t) + ITS (1 + ru)^t ( 1 + rd)^t Where: Σ from t=0 to n, FCF*(t) = Unleveraged (ungeared) free cash flow: the amount of free cash flow that the company is expected to generate at time t due to the project not including interest tax shields. ru = All-equity or unleveraged (ungeared) required return on investment; the rate that would be required on the investment were it to be financed purely with equity. rd = The required return on the debt of the investmen ITS = Interest tax shield cash flow: the reduction in corporate income taxes at time t caused by interest deductibility of the debt issued for the investment. Equal to interest cash flow x coporate tax rate.

Summary: There are four major components of conducting a WACC-NPV, or an APV as follows: 1) Determine cash flows

10 / 40

a) What is the free cash flow amount? b) What is the interest cash flow? c) What is the corporate tax rate? d) What is the interest tax shield amount? 2) Determine market values a) What is the market value of equity? b) What is the market value of debt? c) What is the market value of the total investment? 3) Determine discount rates a) What is the required return on equity? b) What is the required return on debt? c) What is the true cost of debt less interest tax shields? d) What is the overall weighted average discount rate --factoring in equity’s return, and the true cost of debt? 4) Use the investment evaluation techniques WACC-NPV a) Use NPV if proportions of debt and equity are known b) Discount rate properly reflects debt/equity proportions APV a) Use APV is actual amounts of debt and equity are known b) Calcualtes Ungeared NPV of free cash flows, plus the NPV of the interest tax shields using debt’s required return.

11 / 40

Module 5 - Estimating Cash Flows for Investment Projects When estimating cash flows, its important to work the procedures in the correct order, so one procedure isn’t interrupted for another. Cash Flow Estimation Steps #1- Calculate Depreciation Expenses for Tax Purposes Note: Straight line depreciation involves equal amounts for each year. Salvage value is registered in year asset is liquidated. #2- Calculate Change in Taxes Should Company Accept the Project Requires Creation of Income Statement: Sales Revenue Other Revenue Subtotal Direct Expense Labor Other Management Marketing Subtotal Depreciation Subtotal Total Expense Profit Before Tax (Total Revenue Less Total Expense) Less Taxes Total Income #3-Calculate Working Capital Accounts Receivable Accounts Payable Cash and Inventories Use to calculate changes in net working capital Note: a) Add these together, but they should be noted as negative changes to net working capital. b) Don’t forget total liquidation value at final period. This is a positive entry. #4-Project Cash Flows Sales Revenue

12 / 40

Total Direct Expense Change in Net Working Capital Assests Taxes FCF-Free Cash Flow (Generally, all of the above are subtracted from sales revenues, except possible liquidation pluses in the final period.) Summary 1) Include all changes that will occur in the cash flows of the corporation were it to accept the project, at the time points when those cash flow changes are expected to take place. Those cash flows comprise all transactions that the corporation would undertake with suppliers of labor and management skills, with suppliers of materials and assets, and with government. Operational opportunity costs are legitimately included in a projects cash flows, but cash flows to and from capital suppliers are not. 2) When the cash flows are being estiamted for an NPV or an IRR analysis, it is not necessary to estimate the interest tax shields for the project: the cash flows are ‘allequity’ flows. When an APV analysis is to be done, interest tax shields must also be estimated, based upon the debt issued to finance the project. Important Notes: 1) Cash inflow timing is often different from that reflected in accounting records 2) Cash outflows for apital outlays etc. follow a pattern different from accounting records. 3) The accounting expenses for overhead, depreciation, and interest generally differed from cash flows, but had cash flow implications. << Note only changes to cash flows.>> <<Record Cash Flows, and only cash flows>>

13 / 40

Module 6 - Applications of Company Investment Analysis There are several alternatives to the NPV advocated by the business world. It can be demonstrated that NPV is superior to all. NPV Alternatives Payback Period: Time until investment is recouped. Problems: 1) Ignores all cash flows beyond the minimal acceptable payback period. 2) It does not discount cash flows during the minimum acceptable period--so inconsistent with investor opportunity costs. What would be a reasonable payback period? 1/rv*- 1/ (rv*(1+ rv*)^n ) where rv* is the weighted average cost of capital and n is the number of periods in the project’s total lifetime. Accurate only for fairly constant cash flows. Average (Accounting) Return on Investment Dividing expected accounting profits by net book value (depreciated value). These numbers are added together, divided by number of periods, and compared to standard. Problems: 1) Does not discount cash flows 2) Uses the wrong numbers IRR vs. NPV W/O Question, the NPV is superior as an investment decision criteria. Why? IRR has the following limitations: 1) Multiple sign changes in cash flows can produce multiple IRR’s. 2) IRR’s in cases of multiple discount rates in multiple periods is a problem. 3) IRR is a problem when evaluating competing projects because completing projects cash flow patterns often ‘cross over’ at a discount rate < IRR. IRR can be used to compare projects with the incremental cash flow analysis. Follow the steps below to use this method: 1) If you have a lot of projects to pick from, think of them as being in a pot, and pick any

14 / 40

two from the pot. 2) Find the one that has the highest net positive cash flow total (the simple sum of all its FCF*’s, which can be thought of as an NPV calculated with a discount rate of 0. Call the project with the highest net positive cash low total “the defender”, call the other one the challenger. 3) At each time point, subtract the cash flows of the challenger from those of the defender, and call the resulting stream the ‘incremental cash flows’. 4) Find the IRR of the incremental cash flows. 5) If the IRR of the incremental cash flows is greater than the appropriate hurdle rate, keep the defender, and throw out the challenger. If the IRR of the incremental cash flows is less than the appropriate hurdle rate, keep the challenger, and throw out the defender. 6) Omitting the thrown out projects and keep the survivor--keep goin until there’s only one left. That’s the winner. 7) Calculate the IRR of the winner. If it exceeds the hurdle rate, accept the winner, if lower, all in the pot get rejected. Cost Benefit Ratio CBR= Σ Inflows (1 + rj)^t Σ Outflows ( 1 + rj)^t

Investment is accepted if ratio is >1, rejected if < 1. On the plus side: It’s really a form of NPV Problem: Answer is a ratio of values, not value itself and can give wrong answers.

Profitability Index (PI) PI= Σ FCF*t (1 + rv)^t -FCF*(0)

15 / 40

PI>1 OK < 1 Reject The PI is used only when the present cash flow FCF*(0) is a net outlay. Because it is a ratio, has same problem as CBR--displays “wealth increase per dollar of initial outlay” instead of net total wealth increase. Capital Rationing. All calculations up to now assume that there is enough money available to pursue all projects. How to decide on investment projects when capital is limited? 1) Rank investments in order of NPV’s, and choose highest NPV’s. 2) Rank both in terms of NPV and PI 3) For interdependent investments, combinations can be studied as single investment packages. Renewable Investments Some company investments have different renewal cycles. How to compare ‘apples to apples’? 1) Find NPV of a single cycle of each asset. 2) Divide that number by the annuaity present value factor for the number of years in each asset replacement cycle, at the appropriate discount rate. This procedure converts actual cash flows associated with each investment to a constant annuity cash outlay. Inflation Be sure you are consistent when using “real” & “nominal” rates.

16 / 40

Module 7 - Risk and Company Investment Decisions The securities market line (SML) describes the relationship between risk and return. Risk is best measured by the standard deviation of rates of return on the entire portfolio of assets. Probability Distribution of Returns Example: Rate of Return 8.5% 11.0% 13.5% 16% Probability 35% 10% 30% 25%

The mean,(average expected return), is found by multiplying the individual rates of return by the probabilities, and summing. In this case, the mean is .12125 or 12.125%. Standard Deviation of Returns Found by squaring the difference between the mean, and individual returns, muliplying times the probability of the individual return, and summing: _________________ SD= √ Σ (ir - bar x)^2 * Pn from 1 to n ir equals the return of the individual investment. In the case of the above numbers, SD= (.085 - .12125)^2 * .35 = .00045992 (.11 - .12125)^2 * .1 = .00001266 (.135 - .12125)^2 * .3 = .00005672 (.16 -.12125)^2 * .25 = .00037539 =.0009046 taking the square root; = .03008 =3.0008% Problem: The SD of return has not proven to be a valid indicator of performance. It has little empirical validity. The positive relationship between risk and return is only true for entire portfolio, not individual assets within it. (Reason: part of the SD for individual assets is “diversified away”).

17 / 40

Can not use the weighted average standard deviation of return of individual assets--must use “joint probability distribution” Examples: Asset B Returns 7% 10% Asset A Returns 20% .3 .65 .25 .35 .55 .35 12% .1 .45

Probability is higher for one asset returning low, while another is returning high. Average SD was wrong because it ignored interaction of returns. Can deal directly with this issue by handling the interrelatedness of asset returns via the correlation coefficient. Main lesson: Portfolio risk is not the same as average individual security risk. Undiversifiable/Systematic risks: Extent to which securities are influenced by common factors (the market). Actual Measure: Systematic Risk of Security j =SD of Return j x Correlation of j with market. Typical Measure: βj = SD of Return x Correlation with Market SD of Market Return Example: β of 1.5 x % change in market gives 1.5 x % change in return of a security. The market only compensates for undiversifiable risks, therefore, correct measure of risk is that which exists after diversification. How much compensation? rf : Risk free market return E (rj) = rf + [E(rm) -rf] βj Required return on a security is composed of compensation for time (rf) + compensation for risk [E(rm) - rf] βj.

18 / 40

Summary: 1) The total risk of an individual asset or security can be separated into two types of risk, that which can be diversified away, and that which cannot. 2) The risk that cannot be diversified away is related to an underlying ‘market factor’ that is common to all assets and securities, and is thus a common correlation limiting the amount of risk reduction through diversification that is possible by including a security in the portfolio. 3) This undiversifiable or systematic risk can be measured by the β coefficient (SD times correlation with the market) of the security in question. 4) If the financial market sets securities’ returns based upon their risks when held in well diversified portfolios, systematic risk will be the appropriate measure of risk for individual assets and securities, and the SML as depicted in Fig. 7.6 and formula 7.1 will dictate the set of risk adjusted returns available in the market. 5) These SML-based returns are the opportunity costs of capital suppliers of companies, and thus can form the basis for evaluating internal company investments. These investments must offer retuns in excess of capital supplier’ opportunity costs in order to be acceptible. Capital Asset Pricing Model The Capital Asset Pricing Model, or security market line, the system which generates required rates of return based upon the riskiness of assets . WACC should not generally be used as an investment criteria. It will only give a correct answer when the investments risk is the same as the average risk of the entire company. (For example the WACC is in fact an average of the risk adjusted rates of return of the company’s various asset risks--it includes mix of both high and low risks.) Estimating Systematic Risks for Company Projects 1) Estimate β : (If not known, stock market β comparison on similar ventures.) 2) Establish “benchmark β“: Gearing--adjusting due to operations (fixed cost), financial (debt content), etc. Finding Beta: a) Find Ungeared beta: βu =βe E/V + βd D/V The ungeared beta is found by the above formula. This is the beta that would exist if the company had no debt outstanding.

19 / 40

b) Adjust for revenue and operational gearing Revenue adjusted β = βu Project Revenue Volatility Company Revenue Volatility Poject βu = Revenue adjusted β ( 1 + Project fixed cost %) ( 1 + Company fixed cost %) Now the beta of the equity of the project can be found by the formula given above: βu =βe E/V + βd D/V: The idea here is to plug in the ungear beta numbre for the project, the proportions of debt and equity, and the given beta of the debt to solve for beat of the equity. Estimate WACC using β 1) Find E(rj): expected return on equity by: 2) Finding rf: usually government bond rates 3) Finding [ E(rm) - rf]: typically found in stock market “excess” gain over time. (in UK, the rate is 9.1, and in US, 8.8% hisotrically). 4) Apply these figures to the equation for the SML including the beta for the project: E (rj) = rf + [E(rm) -rf] βj 5) At step 4, we have the required return for equity, but if project is also financed with debt, so we need to find the WACC for the project (rv*) 6) Find E(rd) by plugging in the beta for the debt in the SML equation from step four. (Equation is same, just use debt beta instead of equity beta.) 7) Apply the effect of interest tax shields to debt’s required return to find the true cost of debt (rd*). 8) Now we know (rv*) ,(rd*), and thr proportions of debt and equity for the project, so we can now calculate the WACC for the project. Certainty Equivalents How much money would I agree to accept in the futurefor certain in exchange for a risky cash flow? CF(ce) = CF - E(rm) - rf Cov. (CF,rm) Var.(rm) Where Var.(rm) = the variance (the squared SD) of the market return, and Cov. (CF,rm) = β x the variance of the market return

20 / 40

What we are doing here is subtracting out from a risky cash flow an adjustment for systematic risk. Remember: you are to receive this cash flow in the future (t1), so don’t forget to discount one period. Summary: 1) Diversification reduces risks. An investment will include diversifiable and undiversifiable risks. diversifiable risks disappear in a diversified portfolio. 2) Capital suppliers require higher returns for bearing higher risks, but the risk they bear is only that which is undiversifiable. 3) The market prices securities as if they were held in well diversified portfolios. 4) The pricing process of financial markets is captured in the SML equation which is a function of beta. 5) The SML relationship can be used to estimate the appropriate risk-adjusted discount rates for company investment projects. 6) The WACC can be used for an investment project only if the project is similar to the company WACC. 7) If the investment differs from the company, a project specifc WACC can be found by using a beta of another company consistent with the risk and activities of the project under consideration. 8) If there is no beta available to be observed for the investment, the beta must be artificially constructed. This process uses a bench mark beta adjusted for various gearing ratios. 9) It is possible to construct an SML relationship which can generate certainty equivalent cash flows. 10) Analyses are more complicated for cash flows who’s risk are not constant across time. Change in risk across time must be accounted for.

21 / 40

Module 8 - Company Dividend Policy Key Issues Involved in Company Dividend Policy 1) The dividend decision is a cash retention or reinvestment decision. 2) When the effect of company financial decisions upon shareholder’s portfolios can be undone by offsetting actions of shareholders, the company financial decision is irrelevant. 3) A company’s dividend change is the substitutability of capital gains (i.e. share value increases) when the dividend is reduced, for cash when the dividend is paid. 4) One argument for dividends is the “bird in the hand” argument. Capital gains are uncertain, current dividends are not. However, uncertainty has a price, and its price is factored into the price of the shares. 5) Shareholders may prefer one dividend policy over another due to transaction costs. (i.e. those who prefer cash incur costs in selling shares.) 6) Dividends are taxable, so some shareholders may prefer capital gains over dividends. (in the UK, this is sometimes alleviated by various tax policies) 7) Companies incur flotation costs when raising new shares. 8) One optimal dividend policy is would be to find all investments with positive NPV’s, retain enough cash to undertake the investments, only raise new equity capital when internally generated funds are insufficient, and pay any remaingin cash out as dividends. (the passive residual dividend policy). 9) Given different clienteles seeking to add shares into their portfolio of companies with particular dividend philosphies, and many different companies serving different interests, there is nothing to be gained by changing dividend policy. 10) Companies are restricted as to what information they can release to the market. Dividends play a role in signalling messages to investors. 11) Share repurchases are really payments of cash dividends.

22 / 40

Module 9 - Company Capital Structure Should money be borrowed ? Or should it be raised from shareholders? Argument #1: Debt is more expensive than equity in a company’s capital structure because debt carries required interest payments whereas equity does not.” False: Equity requires shareholder returns, no less a cost of capital than interest payments. Argument #2: Equity’s returns must be higher than debts’ because equity’s claims are residual, so their risk is higher. Because risk higher, returns are higher, so equity is more expensive than debt.” False: This argument ignores important interactions within the set of a company’s required capital returns Debt renders more risky its capital claims--therefore, it could be said that the gains that are had from issueing low interest debt might well be offset by increases in in the risk and attendant returns required by shareholders. Debt in the capital structure increases risk. Why? 1) Risk is related to beta. 2) Beta is related to the variation in return. (The SD of return.) 3) Since debt is first in line, debt amplifies the variability of return. The terms “gearing” or “leverage” is a description of this amplification of variability idea. See example below: Ungeared Company EBIT outcome 15000 120000 150000 Geared Company EBIT outcome 15000 120000 150000 Interest outcome 40000 40000 40000 Equity outcome EPS outcome -25000 80000 110000 -5 16 22 Probability .1 .55 .35 EPS outcome 1.5 12.00 15.00 Probability .1 .55 .35

This type of risk is called financial risk to distinguish from business operating risk. M&M argue that it would make no difference to shareholder wealth whether the

23 / 40

companies borrowed money or not. Financial markets would ensure that this is so. What happens to the wealth of shareholders when the companies capital structure is altered by borrowing? The wealth of the shareholders is unchanged. It can’t increase or decrease as in an efficient market, it must sell for what it would otherwise cost to acquire the same future cash flow expectations. Summary: 1) Company captial structure does not matter--in regard to shareholder wealth. 2) Company capital strucutre does affect the risk and return of equity. Arbitrage and Prices Market prices must adjust to cause all equivalent future cash flows sold in whatever form as single securities or as portfolios of holdings to sell for the same price. Capital Structure and Taxes Because interest payments are generally deductible in some fashion, and directly benefit shareholders, it would seem obvious that companies would make use of this benefit, and tend to be financed by debt. This is not what we see. Why? For one thing, companies can take many types of write offs--including depreciation. So, companies could in effect show no income (due to heavy depreciation write offs), and therefore pay no taxes. So why then borow? Also, the amount of income a company will earn is uncertain, however, the amount of interest payments is fixed, making borrowing undesirable. Capital Structre and Agency Problems Agency problems deal with issues such as conflicts of interest among principals or angents. For instance, lenders wish to ensure that borrowers don’t do things that make their returns more risky. (Like borrowing in order to undertake one investment, and instead doing another.) How to resolve: Lender Covenants, other arrangments such as complex debt contracts.

Agency costs can make borrowing less attractive. A positive covenant is the convertibility provision which some debt claims carry.

24 / 40

(Meaning, under certain conditions, bonds can be exchanged for shares.) Default Bankruptcy is a positive attribute of borrowing. Why? 1) Bankruptcy does not cause economic conditions which precipitate bankruptcy. 2) Bankruptcy ensures order transfer of assets from shareholders to bondholders--and reduces costs (for instance, no litigation). Other Agency Issues 1) Agency problems between shareholders and managers 2) Takeovers, mergers, conglomeration Book Values and Borrowing Academics say extent of borrowing is related to market value of company. Practitioners argue for book value as appropriate standard. Market Value: based on future cash flow expectation Book value: Value of assets Techiques of Deciding on Capital Structure #1- Do what other companies in similar circumstances do. #2- Financial planning using what if simulations Debentures: debt collateralized by the overal assets and cash flow of the company. Suggestions for Deciding About Capital Structure 1) Use cash flow simulations to obtain worst case view where the existence of borrowing might lead to financial distress. 2) Borrowing should be avoided if simulations indicate high possiblity of violating covenants. 3) If simulations indicate that borrowing tax benefits simply replace other tax benefits, then little reason to borrow.

4) If the company’s value is largely in tangible assets, more borrowing is sustainable than if the same value is dependent upon intangibles (like future profitability of investments not yet undertaken, or skill skill of managers to find new opportunities). Industry gearing ratios are useful to see the amounts of borrowing which other similar companies have been able to sustain.

25 / 40

5) Company should consider attachment of covenants to bonds which would alleviate degree of concern of unfavorable actions toward bondholders. 6) There are reasons why companies would choose to avoid new equity issuances (loss of ownership and control) and such considerations outweigh negative aspects of borrowing. 7) When a tentative conclusion is reached, see if the result is inconsistent with the capital structures of other companies in the same line of business.

26 / 40

Module 10 - Working Capital Management A company’s ‘working capital’ is its short term investments in cash, marketable securities, receivables (debtors), and short term financings. Because of the short term nature of these assets and financings, an entirely different set of financial mangement techniques is used in dealing with them. Working Capital = Current assets and current liabilities Combining Risks and Rates of Return on Assets and Financing Assets Short Term Low Risk Low Return Financings Short Term High Risk High Return Long Term Low Risk Low Return Long Term High Risk High Return

Use maturity matching using the rule of thumb, “finance short term assets with short term liabilities and long term assets with long term liabilities” Short Term Asset Benefits and costs Asset Type Cash Marketable Securities Accounts Inventories Benefit Highest Liquidity Liquidity Increased Revenues More efficient production schedule, sales flexibility Cost Foregone interest Zero NPV Delayed, uncertain cash receipts Capital costs, transaction costs

Management of Cash Balances Transaction uses of cash: Paying debts, etc. Precautionary and anticipatory reserves: Unanticipated need for cash. Compensating balances: Bank reserve requirements, covenants, etc. Cost of cash balances: Transaction costs of switching between securities and their differential interest rates. Optimizing Cash Replenishment Amounts In idealized sawtooth waveform representing use of cash down to some minimal amount,

27 / 40

and then replenishing with bulk amount, use this formula: $r = [(2 x $D x $T)/ i] ^1/2 where: r is the optimal amount of cash replenishment D is the total amount spent by the firm i is interest foregone due to liquidity of asset T is transaction costs Upper Limit Return Point $R = [(3 x $T x s^2)/4i]^1/3 s^2 is the variance of the changes in the cash balances from the probability distribution described earlier. s^2 = $c^2 x t $c = cash balance change per hour Express interest differential in daily rate t in hours per day (8) The upper limit is: $U = $M + 3($R - $M) M is minimum point, R is the desired point. Management of Receivables Accounts receivable and inventory stocks. Inventory management is a seperate subject. Accounts Receivable There is a deterioration in the quality of customer credit which accompanies an increase in the amounts owed to the company. There are many techniques available to determine creditworthiness including discriminant analysis. But at some point, rejecting the marginal customer ceases to be worthwhile.

Expected Profit from Not Reviewing Creditworthiness Expected Profit = Number of good customers x Profit per customer + Number of Bad Customers x Loss per customer

28 / 40

Expected Profit Using Credit Analysis Expected Profit = Number of good customers x Profit per customer + Number of bad customres x Loss per customer - Costs of credit analyses Sometimes, profit can be higher when not reviewing creditworthiness. Analyzing Change In Terms NPV = Change in PV of Sales Receipts - Change in Costs - Change in Working Capital Investment Example: * S/W sales @ 100 packages/day @ $250 & costs of $175 * Payment on average 35 days from sale * Bad debt loss 3% of sales * Daily interest rate: .04% (15.7%/annum) * Working capital is 20% of sales NPV = (125 x 250)(1- .04) (1.0004)^40 - (100 x 250)(1- .03) (1.0004)^35

[(125 x 175) - (100 x 175)] -.20 x [(125 x 250) - (100 -250)] + .20 x [{(125 x 250)/ (1.0004)^40} - {100 x 250)/(1.0004)^35}] = $1,206.30 Management of Short Term Financings In aggregregate, short term financing is best considered a function of two phenomena, the company’s line of business, and maturity matching with short term assets. One important source of short term financing is credit extended by vendors. Question: Should you pay early, and take a vendor discount? Or pay on time with no discount?

The annual equivalent interest rate of 2 % over 20 days is: .02 x 1-.02 i = ( 1 + 365/20 365 20 )^365/20 -1 = 44.58%

29 / 40

Not a good deal. Better to borrow if you have to, and take the discount. Cash Budgeting Short term financial management is best pursued within the context of a company’s cash budgeting. Cash budgeting is the setting forth of the company’s expectations for its inflows and outflows of cash over some future time period, usually near term. Final Key Points Working capital management involves two levels of activity: 1) The hands on application of management techniques to specific asset and financing decisions. 2) The optimal setting of policies for such decisions, so that each of these small decisions is almost automatically determined by the company’s well considered policy. Liquidity Ratios Current Ratio Current Ratio= Current Assets Current Liabilities Cach and assets expected to turn into cash during the current year--liabilities to be paid during the current year. Quick Ratio (Acid Test) Quick Ratio = Current Assets - Inventory Current Liabilities Backing inventory out of assets is a more rigorous test of company’s ability to pay obligations.

Profitability Ratios Profit Margin Profit Margin = Net Profit After Taxes Sales Return on Total Assets

30 / 40

Return on Total Assets = Net Profit After Taxes Total Assets Return on Specific Assets Return on Specific Assets = Net Profit After Taxes Inventory Return on Owner’s Equity Return on Owner’s Equity = Net Profit After Taxes Owner’s Equity Capital Structure Ratios Fixed to Current Asset Ratio Fixed to Current Asset Ratio = Fixed Assets Current Assets Debt Ratio Debt Ratio = Total debt Total Assets Note: Total debt would include deferred taxation, current liabilities, loans, investment grants Times Interest Earned Times Interest Earned = Profit Before Tax and Interest Charges Interest Charges

Efficiency Ratios Inventory Turnover Inventory Turnover = Sales Inventory Average Collection Period Average Collection Period = Debtor Sales Per Day

31 / 40

Note: Also called “days sales outstanding” Fixed Assets Turnover Fixed Assets Turnover = Sales Fixed Assets

32 / 40

Module 11 - International Financial Management Firms deal with exchange rates between currencies of different countries when buying or selling to different countries. Exchange rates fluctuate over time, firms must deal with this risk. Undertaking foreign operations is also impacted by exchange rates. Other concerns involve determining the location, security, and currency in which to borrow. Finannly, government controls and subsidies. Exchange Rates and the Law of One Price Exchange rates bear the relationship to each other that they do due to purchase power parity and the law of one price. Interest rates preserve wealth across time, exchange rates preserve wealth across borders. Spot and Forward Exchange Rates The following is an example of spot and forward rates between pounds and dollars: Spot 180 Day Forward Dollar/Pound 1.5960 1.5780 Pound/Dollar .6266 .6337

Example of How to Use Spot and Forward Rates: 1) A UK firm wants to sell product in July 87 in the US, and not receive payment in dollars until Jan 88. 2) To avoid uncertainty, the firm can buy sterling forward at .6337 per dollar buy entering into a forward exchange contract. 3) If amount is 100k, the firm would receive 63,370 sterling six months hence. 4) The firm could accomplish the same transaction by : a) borrowing dollars today at the six months interest rate in the US, and exchange these dollars for sterling at the existing exchange rate, b) calculate exactly how many dollars it can borrow so as to pay off the dollar loan with the dollars expected from collecting receivables six months hence, c) Formula is: Amount borrowed = $ receivables/(1 + Six Month $ interest rate)

33 / 40

d) Assume six month dollar rate is annual rate of 6.5% Amount borrowed = 100k/(1.065)^1/2= 96,900 e) The loan proceeds are switched to sterling at spot: Sterling Proceeds = .6266 x 96,900 = 60,717 f) Sterling invested at the UK six month sterling rate of 8.94%/annual Sterling( 22 January 1988) = 60714 x (1.0894)^1/2 = 63,373 Cash proceeds are exactly the same as the forward interest rate. This is a necessity due to interest rate parity. Interest rate parity in forward exchange markets is similar to purchasing power parity in spot markets. Therefore: Relative Interest Rates = Relative Forward exchange discount or premium Forward Exchange, Interest Rates, and Inflation Expectations Nominal Interest Rate = Real Interest Rate + Effect of Inflation (1+ Nominal Rate)^n = (1+ Real Rate)^n x (1 + Inflation rate)^n Bottom line is that interest rate differentials between countries are caused by inflation differentials between countries. Hedging International Cash Flows 1) Buying a forward exchange option: Has benefits, but also costs associated with it. 2) Investing in Foreign Real Assets Financing Sources for Foreign Investment Should funds be sourced locally, or domestically? Or a third location? Real assets in foreign locations tend to increase in value as inflation increases, monetary assets do not. Don’t overlook other investment risks, such as takeover by foreign governments. Agency theory helps correct for this--by building automatic and irreversible counter-incentives. Assume all parties will act in their own best interests, so structure the deal accordingly. Companies need not expose themselves to serious risks due to exchange fluctuations, they should hedge. Also, be careful to ake into account inflation and exchange rate biases in reporting from foreign subsidiaries.

34 / 40

35 / 40

Module 12 - Advanced Topics: Options and Agency Option Characteristics Options are properly termed “contingent claims” because their value depends upon the value outcome of some underlying asset. Call Option Allows you to purchase (‘call’) another security or asset at a fixed price at a fixed time. Summary: 1) You own a call option for 100 shares at $1.25/share between now and the end of the year.. 2) $1.25 is the strike price. 3) Shares are the underlying assets. 4) The last time you can exercise is the expiration date. Suppose the stock is trading now at $1.50 per share. You can now exercise the call. 1) You pocket $25 (difference between 100 x $1.25 & 100 x 1.50) less price of option. 2) When an option can be exercised profitably, it is said to be in the money, when it cannot, it is out of the money. Note: Remember-Options are optional. Futures contracts are not. The pruchaser of a futures contract is forced to complete the transaction, even if its detrimental. Exercise Time Exercising only at expiration: European options. Exercising at any time before or at expiration: American options. Options Valuation The market value of the option is always somewhat higher than the market value of the asset itself. (The ‘premium’ of the option.) Even when the market value is zero, the option is higher than zero. Though immediate excersize nets you nothing, event excersize could net you something.

Calculating the Value of a Simple Option

36 / 40

q=.6 So = $1.50 1-q =.4

uS = 1.6 x $1.5 = $2.40

dS = .6 x 1.5 = $.9

So = the current price of the underlying security = 1.5 q = the liklihood of the underlying security price increase = .6 uSo = the underlying security increased price result = $2.4 dSo = the underlying security reduced price result = $.9 u = upward multiplier for underlying security price = 1.6 d = downward multiplier of the security price = .6 The payoff is Cu 2.40 -1.25 = 1.15 at a strike price of 1.25 when the security price is up, and 0 when its down. Your chances are Cd 60% of hitting, and 40% missing it. So what is your option worth? The law of one price says that two portfolios with the same financial performance are priced the same. So, we find the value of the call option by constructing a portfolio with the same performance. This portfolio must have payoffs equal to Cu and Cd with the same liklihoods as those of the option. Also: rf = the risk free interest rate (either borrowing or lending) for the period of the option; assume this is 10%. Y = the number of underlying shares to puchase (or negative to sell short) Z = the amount lending (if positive) or borrowing (if negative) at the risk free rate SoCu = YuSo + Z(1+rf) Cd = YdSo + Z(1+rf)

Then: Y = Cu-Cd = 1.15-0 So(u-d) 1.5(1.6-.6) = .7666

37 / 40

Z= uCd-dCo = 1.6(0) -.6(1.15) = -.62727 (u-d)(1+rf) 1.6-.6 (1 + .1) This means that if you purhase .7666 of a share of the underlying asset, and at the same time, borrow .62727, you will have the same future cash flow expectations. Then Yso + Z = .766(1.5) -.62727 = .5227 this is the market value of the option. Some Observations Regarding the Simple Valuation Model 1) The formula does not include probabilities. 2) The valuation process is simpler than those for typical securities discussed earlier. For instance, you are not valuing discounted future cash flows. This is a highly efficient valuation mechanism, in part because we are dealing with a contingent claim. the market has already valued the underlying security. 3) Use the priciple of no arbitrage. 4) American and European options will have the same value Valuing More Realistic Options 1) The binomial model deals only with two possible security values. A realistic model must allow for many possible prices. 2) Instead of putting in multiple prices, the model can be made to deal with multiple periods. 3) Periods can be set to any desired length. This model is conceptually simple, but numerical complexity would render it inefficient. The Black-Scholes Model Black & Scholes reformulated the binomial model and made it continuous. Co = SoN(d1) -Xe^-rfT *N(d2) d1 = [ln(So/X) + rfT]/σ(T^1/2) +.5σ(T^1/2) and d2 = d1 - σ(T^1/2)

There are five variables which determine option value: So: Underlying security price X: Exercise or striking price rf: Risk free rate of interest σ: Standard deviation of underlying security price (volatility,β) T: Time until expiration

38 / 40

Applications of Option Valuation Consider the equity of a firm with debt in its capital stucture. This equity is actually a call option: if interest and principal are paid to creditors, shareholders own the underlying assets of the firm; if interest and principal are defaulted, creditors will end up with the assets. Black Scholes can be used to value a company in this maner--for instance: 1) The ratio of underlying asset value to excersize price. (So/X). For the option held as equity by shareholders, the underlying asset value is the total value of the company’s assets, and the strike price is the interest and principal promises to creditors. 2) If the ratio is high (in the money), implies low debt. If low, a highly geared company. Agency Deals with principals, agents, and conflicts of interest. Takeovers--an important solution to manager shareholder conflict of interest. Agency solutions: 1) Must be overall incentive to solve--overall gain 2) Agent has incentive to participate in the solution Information asymetries can cause agency problems to arise. Bondholders can issue call provisions on the bond to solve agency problems. Convertible bonds: bonds can be converted into shares to take advantage of equity increase over debt should equity take on riskier investment than agreed upon. Convertible bond problems can be solved using binomial option valulation equations. In any case, the value of the convertible bond will be the same regardless of high or low risk investment--and their will be no incentive to take one over the other. Alternative Option Valuation-Perfectly Hedged Security uSo -mCu = dSo -mCd m = So(u-d) Cu-Cd m is the hedge ratio, it tells you how many call options to write for every one share held.

39 / 40

So = the current price of the underlying security q = the liklihood of the underlying security price increase uSo = the underlying security increased price result dSo = the underlying security reduced price result Portfolio value = Perfectly Hedged Return Risk Free Discount @ one period Then: So-mCo=X Call option Co = X/So-m

40 / 40