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Author: Remi Malahieude Based on: Release FI-A2-engb 2/2008 (1003) – Steve Elliot's Finance Notes from Oct. 30-2006 Date: January 23, 2010 Finance Be aware that beyond the Past Papers, the Faculty Board will post some extremely valuable Revision Exercises in the Faculty Download Area. Those files are not there from the start of term. The Professor will post them right before the minor diet. I highly recommend doing all those prior to any online Case study or Past Paper. Good luck in your finance journey. Module 1 Finance is the economics of allocating resources across time. Financial Markets - Participation is financial markets is driven in part by the desire to shift future resources to the present so as to increase personal consumption, and thus satisfaction. - Or one may shift resources to the future by lending them, buying common stock, etc. In exchange, they get an expectation of increased future resources, in the form of interest, dividends, and/or capital gains. - Where financial investments serve the purpose of reallocating the same resources across time, real asset investment can actually create new future resources. - The provision of funds for real asset investment is important, as is the allocative information that financial markets provide to those interested in making real asset investment. - Financial markets can help tell the investor whether a proposed investment is worthwhile by comparing the returns from the investment with those available on competing uses. - Financial market participants are risk-averse, they would choose the less risky of two otherwise identical investments. Market Interest Rate & Prices - The market interest rate is the rate of exchange between present and future resources. Always positive because lenders keep their money if they are not offered a positive return (MCQ1B1Q1) - Determined by the supply and demand of resources to be borrowed and lent. - At any given time there are numerous market interest rates covering different lengths of time and investment riskiness. Market IR is but one of many interest rates (MCQ1B1Q1) A Simple Financial Market Shifting Resources in Time - A financial exchange line is comprised of any transaction that a participant with an initial amount of money may take by borrowing or lending at the market rate of interest. - 1/55 -
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- The line appears on a graph with CF1, the cash flow later on the vertical axis, and CF0, the now cash flow on the horizontal. - 2/55 -
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- If a participant had $1000 at t0 and wished to borrow whatever he could with a promise to repay $1540 at t1, how much could he borrow? Assume a 10% interest rate. CF1 = CF0 (1+ i) CF1 $1540 CF0 = --------- or ---------- = $1400 (1+ i) 1.10 The participant could borrow $1400 with a promise to repay $1540 at t1. The maximum amount the participant could consume at t0 is thus $2400 (present wealth). $1400 is the present value of $1540. - 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 particular amount of money in the future. - Finding the present value of a future cash flow is often called discounting the cash flow. - Present value is also an accurate representation of what the financial market does when it sets a price on a financial asset. - Present value is the market value of a security when market interest rates or opportunity rates of return are used as discount rates. - Present wealth: total value of a participant’s entire time-specified resources. Investing - Investing in real assets allows for an increase in wealth because it does not require finding someone to decrease their own. - For wealth to increase the present value of the amount given up for real asset investment must be less than the present value of what is gained from the investment. Net Present Value - The present value of the difference between an investments cash inflows and outflows discounted at the opportunity costs (i) of those cash flows. CF1 NPV = -------- – CF0 (1+ i) - It is generally true that NPV = Change in present wealth. - It is also the present value of the future amount by which the returns from the investment exceed the opportunity costs of the investor. Internal Rate of Return - Calculates the average per period rate of return on the money invested. - Once calculated, it is compared to the rate of return that could be earned on a comparable financial market opportunity of equal timing and risk. - IRR is the discount rate that equates the present value of an investment’s cash inflows and outflows. This implies that it is the discount rate that causes an investment’s NPV to be equal to zero. (MCQ1B2) CF1 NPV = 0 = – CF0 + ----------- (1+ IRR) CF1 (1+IRR) = -------- CF0 - An IRR greater than the financial market rate implies an acceptable investment (and a + NPV), an IRR lower than it does not (and a –NPV). - IRR and NPV usually give the same answer as to whether an investment is acceptable, but often give different answers as to which of two investments is better. Corporate Example - The sole task of a company is to maximise the present wealth of its shareholders. - A company would accept investments up to the point where the next investment would have a –NPV or an IRR less than its opportunity cost. - 3/55 -
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- Although shareholders have different consumption preference across time, companies should 1. Ignore the shareholders preferences 2. Allow the market to reallocate resources across time 1. because the financial markets allow shareholders to reallocate resources by borrowing and lending as they see fit. This way allows the company to concentrate on maximising shareholder wealth. (MCQ1B3) More Realistic Financial Markets Multiple Period Finance - Multiple period exchange rates (interest) are written as (1 + in)n, where n is the number of periods. Compound Interest - Compounding means that the exchange rate between two time points is such that interest is earned not only on the initial investment, but also on previously earned interest. The amount of money you end up with by investing CF0 at compounding interest is written CF0 [1 + (i/m)]m t where m is the number of times per period that compounding takes place, and t is the number of periods the investment covers. - The most frequent type of compounding is called continuous. Interest is calculated and added to begin calculating interest on itself without any passage of time between compoundings. This reduces the above formula to CF0(eit), where e is = 2.718…., the base of a natural logarithm. CF0 (eit) = Continuous compounding Multiple Period Cash Flows - To find the present value of a cash flow occurring at any one future time point the following formula is used: CFt PV = --------- (1+ it)t - The present value of a set (stream) of cash flows is the sum of the present values of each of the future cash flows associated with the asset, calculated: CF1 CF2 CF3 PV = --------- + --------- + -------- (1+ i1)1 (1+ i2)2 (1+ i3)3 Multiple Period Investment Decisions - Calculating NPV when the investment decision will affect several future cash flows must include all present and future cash flows associated with the investment. CF1 CF2 CF3 NPV = CF0 + --------- + --------- + -------- (1+ i1)1 (1+ i2)2 (1+ i3)3 - Calculating the IRR of a set of cash flows involves finding the discount rate that causes NPV to equal zero; CF1 CF2 CF3 NPV = 0 = CF0 + ------------ + ------------ + ----------- (1+ IRR)1 (1+ IRR)2 (1+ IRR)3 - The only way to solve for the IRR of a multiple period cash flow stream is with the trial and error technique. - 4/55 -
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Calculating Techniques and Short Cuts in Multiple Period Analysis - The instruction to calculate the PV of a stream of future cash flows is; T CFt PV = Σ --------- (1.2) t=1 (1+ it)t - When discount rates are consistent across the future this changes to; T CFt PV = Σ -------- (1.3) t=1 (1+ i)t Calculation Methods - Start with the CF furthest from the present, discount it one period closer and add the CF from the closer time point, discount that sum one period nearer, etc. Continue process until all cash flows are included and discounted back to t0. PREFERRED METHOD - Use present value tables. Adding up the cash flows after discounting each one for its respective time period. - Tables are valuable when finding the present value of annuities. A constant annuity is a set of cash flows that are the same amount across future time points. - A perpetuity is a cash flow stream assumed to continue forever. Formula is simply a division of the constant per-period CF by the constant per-period discount rate: CF PV = -------- (1.4) i - A slight modification of the above allows for the assumption that the cash flows will continue forever, but will grow or decline at a constant percentage rate during each period (AKA growth perpetuity), CF PV = -------- (1.5) (i – g) where g is the constant per-period growth rate of the cash flow. - This equation will not work when i<g. Interest Rates, Interest Rate Futures and Yields - Interest rates that begin at the present and run to some future time point are called spot interest rates. - The set of spot rates in a financial market is called the term structure of interest rates. - A coupon bond has a face value that is used, along with its coupon rate, to figure a pattern of cash flows promised by the bond. - These cash flows comprise interest payments each period which continue until the maturity period when the face value itself, as a principal payment plus the final interest payment, is promised. The Yield to Maturity (YTM) - The YTM is the IRR of the bonds promised cash flows, or the average per period interest rate on the money invested in the bond. The set of YTMs is known as the yield curve (MCQ1B9) - Bonds can have the same spot rates, cash-flow risk, and number of interest payments, yet have different YTMs. This is caused by a difference in the cash-flow patterns of each bond. - This is dubbed the coupon effect on the YTM. Named as such because the size of the coupon of a bond determines the pattern of its cash flows, and thus how its YTM will reflect the set of spot rates that exist in the market. - It is unwise to make comparisons among securities on the basis of their YTMs unless their patterns of cash flows (or coupons, for bonds) are identical. - YTMs express both earning rates and the amounts invested across time. (MCQ1B9) - Issue price = par value = face value - 5/55 -
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Forward Interest Rates - Interest rates that begin at some time point other than the present (to). - The amount invested in an asset across time can be found by accruing past invested amounts outward at the same rates that were used to discount cash flows back in time. - This amount allows for a calculation of a forward interest rate. - Forward interest rates are usually indicated as ƒ with a left subscript indicating the rates start time point and a right one indicating the ending time point. Therefore: CF1 ( 1 + 1ƒ2 ) = CF2 ( 1 + i2 )2 = ( 1 + i1 ) ( 1 + 1ƒ2 ) = ( 1 + 0ƒ1 ) ( 1 + 1ƒ2 ) ( 1 + i3 )3 = ( 1 + i1 ) ( 1 + 1ƒ2 ) ( 1 + 2ƒ3 ) = ( 1 + 0ƒ1 ) ( 1 + 1ƒ2 ) ( 1 + 2ƒ3 ) ( 1 + i4 )4 = ( 1 + i1 ) ( 1 + 1ƒ4 )3 = ( 1 + i3 )3 ( 1 + 3ƒ4 ) = ( 1 + 0ƒ3 )3 ( 1 + 3ƒ4 ) - This formula calculates the implied forward rate for a bond. - If forward rates are known, the spot rate of interest can be found by multiplying together 1 plus each of the intervening forward rates, taking the n th root of that product (where n = number of periods covered), and subtracting 1. (page 1/35) Interest Rate Futures - The futures market in interest rates allow you to avoid (or hedge) the risk that interest rates might change unexpectedly (therefore, potentially, reducing an NPV to a point where an investment is no longer worthwhile). - Expectations around future interest rates and future values are almost never completely accurate because, between the time the expectation is formed (t0) and the realisation occurs (t1), additional information will have appeared that causes the market to revise its cash flow expectations, its opportunity costs, or both. - Financial futures markets allow participants to guard against this kind of risk by buying and selling commitments to transact in financial securities at future time points – at prices fixed as the present. - Allows a guaranteed set of discount rates for an asset NPV by agreeing to sell securities at set prices across an assets life. - Hedging takes away both good and bad surprises. Interest Rate Risk & Duration - The variability of values due to changes in interest rates is the effect of interest rate risk. - Duration is a kind of index that tells us how much a particular bond value will go up and down as interest rates change. - It is the number of periods into the future where a bonds average value is generated. The greater the duration of a bond, the farther into the future its average value is generated, and the more its value will react to changes in interest rates. - Duration can be calculated by weighting the time points from which cash flows are generated, by the proportion of total value generated at each time: t t x CFt t t x CFt Σ (1+it)t Σ (1+it)t Duration = = t=1 Bond value t=1 Bond NPV - Duration is the starting point for an important aspect of professional bond investing called immunisation. - 6/55 -
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Annualized growth rate calculation Present Value PV = CF x PVIFi,n PVIFi,n= PV Interest Factor [Table A2.1] Present Value of Annuity PVA = CF x PVAIFi,n PVAIFi,n = PV of Annuity Interest Factor [Table A2.2] Time out: for e.g. Year 5-17: 17 – 5 = 13 years <- (5-1) = 4 PVA = CF (PVAIFi,17 – PVAIFi,4) If annuity starts today PVA = CF x PVAIFi,n x (1+i) Future Value FV = PV x FVIFi,n = CF x FVIFi,n = CF0 [1 + (i/m)]m t = PV [1 + (i/m)]m t FVIF = Future Value Interest Factor [Table A2.3] FVIF = FV / PV Future Value of Annuity FVA = CF x FVAIFi,n FVAIFi,n = Future Value Annuity Interest Factor [Table A2.4] YTM Calculation/ Interpolation: FAQ mini case 1.8 and 1.9: r1 = fist YTM rate guess N1 r2 = second guess YTM = r1 + [ ---------- x (r2 – r1) ] N1 = NPV fist guess = I Bond value – First guess I N1+ N2 N2 = NPV second guess = I Bond value – First guess I Ignore negative sign for NPV, take absolute values RevEx1Q6: What us the return offered if invest 1200 now for 6 years and obtain 1900 at the end of that time? FVIFr,n = FV / PV = 1900 / 1200 = 1.5833 (1+i)6 = 1.5833 => i = (1.5833)1/6 = 7.96% RevEx1Q27: What should you pay for an asset that produces a level of cash stream of $50,000 every 6 months for the next 10 years, if your opportunity cost of capital is 8% (annual rate), compounded per period? PVA = CF x PVAIFi,n [Table A2.2] = 50,000 x PVAIF4,20 = 50,000 x 13.59 = 679,500 A cny offer to pay you 200,000 today, it will pay you 30,000 pa at the end of Y5 and then a further 12years. If your cost of capital is 10%, would you accept? This is a 13yr annuity at 10% = 7.1034 [Table A2.2], PVA = CF x PVAIFi,n = 30,000 x 7.1034 = 213,100 CF at the end of Y5, the annuity bring the value back to the start of Y5, so discount rate end of Y4= 0.683 [Table A2.1] = 1/ (1.1)4 => PV = CF x PVIFi,n = 231,100 x 0.683 = 145,550 => don’t accept or (17 year annuity – 4 year annuity) x 30,000 = 145,550 PVA = CF (PVAIFi,17 – PVAIFi,4) - 7/55 -
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RevEx1Q30: 1m paid 100,000 pa starting today vs. a 700,000 one time payment today, which one do you take? Opportunity cost is 8% PVA = CF x PVAIF8%,10 periods [Table A2.2] x (1+r) [as the annuity starts today] = 100,000 x 6.7101 x 1.08 = 724,690.80 MCQ1B5: A bond trade at $110.5 in the market, its coupon is 9%, which has just been paid and next payment is exactly 1 year. T/he bond has 5 years until maturity (at $100). YTM? 9 9 9 9 109 110.5 = -------- + -------- + -------- + -------- + -------- (1+ r)1 (1+ r)2 (1+ r)3 (1+ r)4 (1+ r)5 MCQ1B10: 7% coupon bond paying i semi-annually trades at $98.12 just after the interest payment. Bond has 3 years maturity. YTM? 3.5 3.5 3.5 3.5 3.5 103.5 98.12 = -------- + -------- + -------- + -------- + -------- + -------- (1+ r)1 (1+ r)2 (1+ r)3 (1+ r)4 (1+ r)5 (1+ r)6 - 8/55 -
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Module 2 – Fundamentals of Company Investment Decisions The corporation (plc) is an organization that raises money from capital suppliers by issuing contracts (securities), invests that money in productive assets, operates those assets (perhaps hiring other resources such as management and labour), and distributes the money proceeds from operating those assets to all that have claims on the proceeds. Capital suppliers are those who own equity and debt claims on a company. Investment Decisions & Shareholder Wealth - When a company issues shares to raise money from the capital market it creates a security known as one of the following: ordinary shares, common stock, equity, common shares, ownership capital, etc. Important things to remember about this type of capital claim: 1. It is a residual claim - Equity has no specific contract with the company that requires any particular amounts of money to be paid to shareholders at any particular time. - Shareholders have only the entitlement to vote for the directors of the company. - Directors and management are agents of the shareholders maximising the wealth of its current shareholders. 2. Equity has limited liability - The possible losses that a shareholder can incur are limited to the value of the shares that the shareholder owns. 3. Until all other contracts that the company has entered into have been filled, the shareholders are entitled to nothing. Once met however, the shareholders have an ownership claim on all of the remaining corporate resources. - Shareholder wealth is the market value of the common shares or equity that the shareholders own. - If a company wishes to maximise its shareholders wealth, it should seek to maximise the market value of the shareholders ordinary shares. The Market Value of Common Shares - is the discounted value of all future dividends that the current shareholders are expected to receive. Dividend1 + Value1 Div1 + E1 Div1 Div2 + E2 Value0 = --------------------------------- E0 = ------------- , and E0 = ---------- + ------------- (1 + Equity discount rate) (1 + re) (1 + re) (1 + re)2 So true value: Div CF E0 = ------- PV = ------ (Perpetuity) re i Investment and Shareholder Wealth - The use of a properly calculated investment NPV does in fact result in an increase in the present wealth of shareholders. Investment Decisions in All-Equity Corporations When making an investment; 1. The total value of a company increases by the NPV of the investment plus what it cost to undertake it. 2. The shareholders experience a wealth increase equal to the investment’s NPV. 3. Existing shareholders of the company get a wealth increase equal to the investment’s NPV regardless of who contributes the money necessary to undertake the investment (i.e. forgone dividend, new equity holders, or even the original holders). Investment Decisions in Borrowing Corporations - Corporate NPV is equal to the change in wealth of existing shareholders even if some of the money for an investment comes from creditors/ bondholders instead of equity holders. - 9/55 -
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Share Values and Price/Earnings Ratios - P/E ratios are offered as signals that the market is providing as to the company’s future earnings prospects, growth rate, riskiness, etc. - The P/E ratio is nothing more or less than the ratio between the present value of all the company’s future dividends (its market price) and its expected earnings during the first period. - For certain companies with very simple cash-flow patterns (i.e. constant, or constant growth perpetuities) we can derive a specific relationship between P/E ratios and equity discount rates: Dividend per share Equity per share Price per share = ------------------------- = ---------------------- re re So Price per share 1 P/E = --------------------------- = ----- Earnings per share re - For companies who are not paying out all earnings as dividends: Dividend per share Earnings per share x payout ratio* Price per share = ------------------------- = ----------------------------------------------- ( re – g ) ( re – g ) So Price per share 1 P/E = --------------------------- = ----------- x payout ratio* Earnings per share ( re – g ) * where payout ratio is the percentage of earnings paid as dividend. = dividend payout ratio Dividend Payout Ratio = --------------- Earnings - Caution must be exercised when comparing the P/E rations of different companies to ensure that all but one of the factors influencing market prices are reasonably similar. When a dividend is paid, the share priced falls by that amount e.g. share price = 100p, cny pays 10p dividend, the share price falls to 90p. That dividend is pay out of the share price, it is history (FB/FAQ) 2003 2004 2005 2006 2007 2008 2009 RE2Q6: Dividend 5.8p 6 6.3 6.7 7.1 7.7 8.5 re=14% What is the share price if you base the growth of dividends on (i) the entire period (ii) the last 2 years? (i) g = (8.5/5.8)1/6 = 6.577% P0= (8.5 x 1.065777) / (0.14 – 0.06577) = 122p (ii) g = (8.5/7.1)1/2 = P0= 203p The DGM can be manipulated to give different valuations if you use different spreads of years to calculate the growth rate of dividends. if g>r => multi-stage valuation model (RE2iQ8) The share price is the discounted value of all future Dividends (FAQ/ FB ) (ie. the PV of all future dividends = value of the cny) MCQ2B1 - 10/55 -
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A high P/E ratio usually signifies a cny that is growing fast. Or it might be a cny where profits have almost disappeared. Or cny takeover target and shares have been bid up. IF so, they will usually keep most of their earnings for reinvestment to continue that growth. More value slow growing cnies will pay larger dividends. The payout ratio indicates how much a cny’s earnings are paid out in the form of dividends (the balance being available for reinvestment). FB/FAQ P/E ratio is of limited use. Compare similar cnies (same sector/business). Cnies should have same accounting conventions => earnings based on the same calculations. Adjustments required/needed to deliver measure of earnings close to cash earnings rather than accounting earnings. not across sectors -> meaningless. Accounting figures still subject to manipulation (RE2iQ7) You can’t have a high dividend payout ratio and a high growth rate (g). [FAQ] - 11/55 -
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Module 3 – Earnings, Profit, and Cash Flow Total Corporate Value Change - The increase or decrease in the market value of all of a corporation’s capital claims that would take place if the investment were accepted. Corporate Cash Flows – activity across time - Financial cash flows are the cash amounts that are expected to occur at the times for which the expectations are recorded. Typical Cash Flows (Company with zero debt, 100% equity financed) (‘000s) Now Yr 1 Yr 2 Yr 3 Customers 0 +17 500 +23 500 +4 000 Operations 0 -7 000 -3 830 -5 200 Assets -10 000 -4 000 -2 000 0 Government 0 -4 000 -8 085 +5 600 Capital* (FCF) -10 000 +2 500 +9 585 +4 400 2 500 000 9 585 000 4 400 000 NPV = -10 000 000 + -------------- + ------------- + ------------- = +3 500 000 (1.10) (1.10)2 (1.10)3 1. Customers – The amounts of cash expected to take in from sales and/or selling used assets. 2. Operations – Cash flows that are paid in cash that year, be deductible for taxes that year, and not be a payment to a capital supplier. 3. Assets – While the cash flow is made at time listed, it is not deductible at that point and must therefore be capitalised and depreciated across time. 4. Government – Taxes paid due to the investment. 5. *Capital – The amounts of cash that could be taken out of the corporation by it’s capital suppliers and still have the investment run as planned (AKA Free Cash Flow). The value of all future increases/decreases in dividends expected due to the project (because company is equity financed). Cash Flows and Profits - Cash flows are not the same as he numbers that appear in financial statements of corporations. - One of the biggest differentiation is that accounting figures often report cash flows for time periods other that that which the flow occurs. - 12/55 -
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- Stakeholders = Gouvernment, Employers, Lenders different than shareholders!!!! - Land = Opportunity cost (a cash outflow), in a CF analysis, initial value of land is an outflow, final value of land at the end of the project is an inflow. - Salvage value is part of the depreciation calculation. An Asset is usually fully depreciated, adjusting for any expected salvage value at the end of its useful life. [MCQ3B7] - Debtors = Account receivables The accounting term debtors will include customers who will not pay until the next period, sot it is wrong to include it in a CF. [MCQ3A6] - When constructing project CF figures, Interest payments are excluded because they are not part of the investment decision (FCF*= FCF-ITS) [MCQ3A7] - Depreciation is an expense for tax purpose. [MCQ3A10] - Capitalisation allocates the cost of the asset over a number of time periods. [MCQ3B5] - FCFs and Profits after tax of a project will add up to the same amount. [MCQ3B10] - Profit = Income = Earnings - Your have an accountant’s income statement for 2 projest, one purely equity financed, one partly financed with debt, but identical in all other respects. - The all equity finance project will report a higher income Because in the accounting figures, interest is regarded as an expense, so the debt finance cny will have higher expenses and so lower profit as a result (MCQ4A2) - The debt financed cny will have a greater CF than the equity financed cny (MCQ4B2) - The cash that debt suppliers expect to get in the future = in PV terms to the amount that is raised from them at present, so debt’s wealth is unaffected by the investment. (MCQ4A3) - The figures to use in the WACC calculation are market values of debt and equity. (MCQ4A4) - All equity CFs are the CFs that exclude the ITS. They are the CFs that would exist if the project was only funded by equity. (MCQ4B3) - The appropriate rate to discount all equity CFs in a WACC calculation is the tax shield adjusted discount rate. (MCQ4B4) - What do FCFs of an investment project which are appropriate to be discounted with the project’s WACC include? All changes in the payments between the firm and its capital suppliers induced by the project, were the project to be financed only with equity. - 13/55 -
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Module 4 – Company Investment Decisions using the WACC - The weighed average cost of capital (WACC) is a discount rate that combines the capital costs of all the various types of capital claims that a company issues. Free Cash Flow and Profits for Borrowing Corporations - Financial markets place values on corporate debt claims by discounting with risk-adjusted rates the amounts of cash that the company is expected to pay to those claims. - Debt has a higher priority claim to cash than does equity. - A partially debt financed investment, ceteris paribus, will have higher free cash flows than one which is 100% equity financed. - This is due to tax laws that allow interest on loans to be written-off. - This is called a corporation’s income tax shield ITS. - Income tax shields can be calculated by taking the expected interest payment on each period and multiplying it by the corporate income tax rate. Investment Value for Borrowing Corporations - Debt suppliers wealth should be unaffected by the investment. Figured by taking the interest + principal for each period and dividing by the debt interest rate. - Equity wealth change is figured out by comparing the investment-induced change in equity value to any foregone dividend. Value change is calculated by subtracting principal and interest from the FCF for each period and dividing that by an appropriate discount rate. Overall Corporate Cash Flows and Investment Value - To figure out NPV as a whole, the FCFs must be discounted with a rate commensurate with their risk. - To find this discount rate the debt and equity rates must be combined in proportion to their claims on the corporate cash flow. This value is given by the market value of the two claims: Debt market value Equity market value Overall rate = ------------------------ x Debt required rate + -------------------------- x Equity required rate Total market value Total market value - Valuing the security is now easy: n FCF Value of the project = Σ ---------------------------------- t=0 (1 + overall required rate)t Investment NPV and the WACC - The above technique is the overall NPV method. - Common practice in financial analysis of corporate investment is that when estimating the cash flows of a project, its interest tax shields are not included in the cash flows. - In order to calculate an accurate NPV using cash flows that exclude interest tax shields, the effect must also be included in the discount rate. - The WACC is the discount rate that: a. Reflects the operating risks of the projects. b. Reflects the projects proportional debt and equity financing with attendant financial risks. c. Reflects the effect of interest deductibility for the debt-financed portion of the project. - In order to reflect interest deductibility in the discount rate (WACC), the weighted average must use the company’s after-tax cost of debt rather than the debt suppliers required rate. - Cost of debt in a company with deductible interest is simply debts required return multiplied by the complement of the corporate income tax rate: Debt cost = Debt required return x (1 - Corporate income tax rate) - WACC is therefore calculated as follows; Debt market value Equity market value WACC = ------------------------ x Debt cost rate + -------------------------- x Equity required rate Total market value Total market value - 14/55 -
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- The WACC-NPV analysis of an investment project is performed by discounting the project’s FCF, not including the interest tax shields that the projects financing will generate. - This adjusts for the deductibility of corporate interest in the discount rate as opposed to the CF of the project. - Companies using the WACC-NPV are willing to specify the expected proportions of debt and equity in terms of their market values, but they do not know exactly what the claims will be worth until after the analysis is complete. The Adjusted Present Value Technique - APV does not require knowledge of debt/equity proportions, but does require that the interest tax shields of the project be estimated. - APV is therefore preferred by corporations who are comfortable in estimating the amounts of debt the projects will use. - If performed correctly both APV and WACC-NPV will give the same answers. - APV finds the NPV by first finding the value of an investment as if it were financed only by equity, and then adds the PV of the projects interest tax shields. - All-equity value is calculated by adding all the CFs discounted by the (an) all equity discount rate. - Interest tax shields value is calculated by discounting the shield CFs by the risk-adjusted rate for debt cash flows: APV = (All-equity value) + (Interest tax shield value) – Present cost The Choice of NPV Techniques - When complexities such as tax credits, cash costs, in addition to interest and its deductions (i.e. cost of bankruptcy proceedings), etc. appear relevant to a company’s financial decisions, the APV approach may be easier to use. - The reason for this is that APV treats these cash-flow effects separately, by first estimating the cash flows, then discounting each one at a rate appropriate to their unique risk. - On the negative side, APV does not have the automatic characteristic of being consistent with maintaining an intended ratio between the various kinds of financing (debt / equity) a company uses. - 15/55 -
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Notations Cash Flows FCFt Free cash flow: the amount of cash a company can distribute to its capital suppliers at time t due to an investment. It Interest cash flow at time t Tc Corporate income tax rate ITSt Interest tax shield cash flow ITSt = It x TC FCF*t Unleveraged (ungeared) free cash flow: amount of free cash flow a company is expected to generate at t due to a project, not including income tax shields. FCF*t = FCFt – ITSt. = All equity CFs, ie. CFs that would exist if the project was only funded by equity (MCQ4B3) Market Values Et Market value of the equity of the investment at time t Dt Market value of the debt of the investment at time t Vt Market value of the investment at time t . Vt = Et + Dt Discount Rates re Required return on the equity of the investment. rd Required return on the debt of the investment. rd* Cost of debt as a rate to the investment rd* = rd x (1-Tc) rv Overall weighted average return on the capital claims of the investment. rv = D (rd) + E (re) = Overall capital return/ cost. V V rv* Weighted average cost of capital (WACC) of the investment. rv* = WACC = D (rd*) + E (re) V V ru All-equity unleveraged (ungeared) required return on the investment. Investment Evaluation Techniques WACC-NPV t FCF*t NPV0 = Σ --------- t=0 (1+rv*)t APV t FCF*t ITSt APV0 = Σ [ -------- + -------- ] t=0 (1+ru)t (1+rd)t - WACC reflects the i. Financial and operational risk of the project ii. The interest deductibility involved in the project The project WACC would reflect the project’s proportional debt and equity rather than the actual amount. (MCQ4A6) - 16/55 -
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Module 5 – Estimating Cash Flows for Investment Projects - Estimating investment cash flows means that financial managers must keep the following in mind: 1. Inclusion of all corporate cash flows affected by the investment sometimes means that financial analysts must invoke the idea of economic opportunity costs. 2. Inclusion of all relevant cash flows means that analysts must include cash flows from interactions of the investment with other activities of the corporation. 3. Inclusion of all relevant cash flows also means that analysts must know what things should be omitted from the investments cash flows. I.e. sink costs are to be ignored. An investment should be discontinued if its future cash flows PV is less than the company would obtain by selling or abandoning the project now or later. 4. Inclusion of all relevant cash flows means that analysts must be very careful that the accounting numbers provided for a project are interpreted correctly. I.e. Overhead costs are typically not indicative of the incremental cash flows that a project will require. Accounting numbers can include non-cash expenses (depreciation), and arbitrary activity measures such as floor-space devoted to the manufacture of a product. It is however correct to include as cash outflows the changes or increments to overall corporate expenses caused by the acceptance of the project. - There are many corporate cash flows that should not be included because they are not incremental (i.e. managers salaries); they would not be affected by the acceptance or rejection of a project. Summary - All changes that would be caused in the cash flows of a corporation by its accepting a project must be included in the analysis of the project. - ONLY cash flows are to be included. - Estimate CFs as if project were purely equity financed, no debt, so no interest payments. Operating CF = Operating profit – Change in net Working Capital + Change in Overheads NWC figure comes from changes in receivables, payables, inventory and cash year on year. For project budgeting CF analysis, interest payments are not included as these are payments to capital suppliers. This effect is caught in the discount rate (WACC). [RevEx2(ii)8] Total CA = Account receivable = Cash outflow in terms of NWC Total CL = accounts payable = Cash inflow “ “ “ “ [MCQ5A7] If the cny does not sell the FA at the end of the project, we must include a sum to reflect the benefit the cny gets from their use. [MCQ5A8] - 17/55 -
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Module 6 – Applications of a Company’s Investment Analysis - Real asset investment decisions = capital budgeting The Payback Period - The number of periods until a project’s cash flows accumulate positively to equal its initial outlay. - Companies use this method by picking a maximum period of time beyond which an investment’s payback will be unacceptable, and rejecting all investment proposals that do not promise to recoup their initial outlays in that time or less. - Payback periods and NPV can yield different answers. - Problems with the payback period include: a. It ignores all cash flows beyond the maximum acceptable payback period. b. It does not discount the cash flows within the maximum acceptable period, thereby giving equal weight to all of them. This is inconsistent with shareholder opportunity costs. c. It has too much bias to short term CFs (MCQ6B1) d. It is not concerned with the profitability of the project (MCQ6B1) - Some companies have altered their payback period techniques to be discounted payback periods. Concern ‘a’ above is still valid. - If a company feels it must use the payback period, a rudimentary estimate of the maximum allowable period should be set: 1 1 Payback = ------- - ---------------- rv* rv*(1+rv*)n where n is the number of periods in the projects total lifetime. - This payback is generally only accurate for projects with fairly consistent cash flows each period. - If these restrictions are met, the above will show the number of periods across which, if the original outlay is not returned (in FCF*), the investment will have a negative NPV. The Average (Accounting) Return on Investment (AROI) - Calculates a rate of return on the investment in each period by dividing expected accounting profits by the net book value of the investments assets. - These numbers are then added and the sum is divided by the number of periods for which rates of return have been calculated. The result is then compared to a minimal acceptable return (often an industry or company average). - AROI does not discount cash flows and the numbers used are the wrong ones. - However AROI does have some value as an evaluation of control device to check the progress of an ongoing project on a period-by-period basis. Average profit (over the period in question) AROI = ---------------------------------------------------------------------------------------------- (FAQ +/- AROI) Average investment (if depreciated to zero it’ll be the initial investment divided by 2) Average investment = (Initial value + disposable value) ÷ 2 IRR vs. NPV - When there is an outlay, an inflow, and another outlay (in the form of an opportunity cost), multiple IRRs can exist – Sign changes across time can yield multiple IRRs. - A pattern of sign changes can also produce a project that has a totally upward sloping relationship between NPV and IRR. To correctly accept a project in this case the IRR would have to be less than the hurdle rate. - 18/55 -
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- There are various means that can be used to make the IRR come up with a correct answer in a particular situation. The difficulty being that you must know beforehand that you are going to have a problem with the IRR, and what the solution is. - Another situation in which the IRR can cause problems is in multiple-period cash flow investments which require a different discount rate for each cash flow. The cash flows IRR can still be found, but at which hurdle rate is it compared? The YTM of a security with the same risk and cash flow patterns as the investment would have to be found. - IRR assumes that interim CFs are reinvested at the IRR rate. - NPV “ “ “ “ “ “ “ “ discount “ (MCQ6A8 and Dec 2005Q1.d) IRR vs. NPV in Mutually Exclusive Investment Decisions - In situations where multiple investment options must be compared and subsequently ranked NPV is best. - When IRR must be used the incremental cash flow analysis technique should be used. The algorithm steps are: 1. Take any two projects out of the group. 2. Find the one that has the highest net positive cash flow total (sum of all FCF*). The investment with the highest net cash flow is the defender, the other the challenger. 3. At each time point, subtract the cash flows of the challenger from those of the defender, the resulting stream are the incremental cash flows. 4. Find the IRR of the incremental cash flows. 5. If the IRR is greater than the appropriate hurdle rate, keep the defender and throw out the challenger and vice-versa. 6. Pick the next project out of the group and repeat the process using the winner of step 5 until only one investment remains. 7. Calculate the IRR of the winner. If it is greater than the hurdle rate, accept it; if not then reject all the projects. - This algorithm works because it looks at the IRR of choosing one project over another, instead of each cash projects IRR. - There are also situations in which the incremental cash flow method of choosing among investments should never be used: 1. When the incremental cash flows have more than one change of sign across time. 2. When the projects differ in risk or financing, so that they require different hurdle rates. - IRR is more likely to give incorrect indications of investment ranking among a group of mutually exclusive investments when the investments: i. are of significantly different magnitude ii. “ “ “ “ duration t0 t1 t2 t3 Project CFs, discount rate 10%: No.1: -$2500 +$1200 +$1300 +$1450 No.2: -$2500 +$1300 +$1300 +$1300 1. Take No.1 and No2. 2. No.1 ΣCF= 1450 > No.2 ΣCF= 1400 No.1 defender No.2 challenger 3. Challenger CFs – Defender CFs t0 t1 t2 t3 -$2500 +$1200 +$1300 +$1450 Defender +$2500 -$1300 -$1300 - $1300 Challenger Incremental CF = 0 -$ 100 0 +$ 150 4. Through trial and error IRR = 22.5% of the incremental CFs 5. 22.5% > hurdle rate of 10% => keep Defender No.1, throw out Challenger No.2 6. No next project 7. IRR of the winner (No.1) = 25.9% > hurdle rate 10% => accept winner No1 is the better of the 2 projects The cross-over rate is where the NPV of the 2 projects is equal is also the point where the NPV of the incremental CFs between the projects is equal to zero. - 19/55 -
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The Cost-Benefit Ratio and the Profitability Index The C-B Ratio - The ratio between the present value of the cash inflows and the cash outflows of an investment: - Where Inflowst + Outflowst = FCF*t - An investment is accepted if CBR >1, and rejected is CBR <1. - A CBR >1 would have a positive NPV, and a CBR <1 would have a negative NPV. - When faced with the question of an investments desirability both CBR and NPV will produce the same recommendation. - For mutually exclusive events however, CBR is attracted to those investments that have the greatest ratio differences between inflow and outflow present values instead of actual cash or value differences. The Profitability Index - The ratio of the accumulated present values of future cash flows to the present cash flow of an investment. - The PI is a ratio measure and therefore suffers from the same problems of CBR. - PI is unsuitable for ranking investments because it displays another relative measure, the wealth increase per dollar of initial outlay instead of the wealth increase itself. The CBR and PI techniques of investment analysis give the same indication of investment acceptability which indication agrees with NPV, if investments are dependent. Capital Rationing - The set of methods used to choose a group of projects that will maximise shareholder wealth while having limited funds available is called capital rationing techniques. - When having to choose between a few projects, one simply looks at all the possible combinations of investments that lie within the budget and choose the package with the greatest NPV. This is called exhaustive enumeration. - When confronted with many projects to choose from, one common method is to calculate the profitability indices for the investments, and to list them in declining order of PI. Investments are then accepted in order of PI, until the budget has been exhausted. - A project may be skipped because its outlay is too large, and the next one having a small enough outlay taken as you work down the list. - The PI technique must be used with some caution in ranking investments when the highest PI projects do not use up the entire budget. - Being under capital rationing is an undesirable situation. It can mean that you have not been able to solve internal organisation/communication problems, or that the capital market is unconvinced of your prospects. This implies that you will be forced to forego investments that would have increased the wealth of shareholders. - The existence of high market required rates should not be interpreted as a capital-rationing situation. This is simply a signal that your capital costs are also high. - The capital rationing situation implies that financing beyond the budget constraint carries not a high but an indefinite cost. Soft capital rationing within the organisation Hard capital rationing outside the organisation capital markets Small high risk firms. Markets not sure about the information out of the cny, discount rate offered too high. Better info and good track record lead to easing of this problem. (June 2006 Q1.c) - 20/55 -
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