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# Corporate Finance FINC 3511

GPA 3.83

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This 105 page Class Notes was uploaded by Justus Rippin on Tuesday October 27, 2015. The Class Notes belongs to FINC 3511 at University of West Georgia taught by Ronald Best in Fall. Since its upload, it has received 80 views. For similar materials see /class/230217/finc-3511-university-of-west-georgia in Finance at University of West Georgia.

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Date Created: 10/27/15

CHAPTER 4 Financial Ratio Problems Types of problems and the approach to ratio problem solving Overall There are several steps that should be followed for all ratio problems Following these steps will make it easier to correctly solve each problem These steps provide a way to approach all ratio problems First always identify all ratios mentioned in the problem and write the formulas down Second determine what you are trying to find Third identify the data that you have available and try to determine the type of problem you are facing see next Page Fourth enterthe data in the ratios and solve for your answer Types of problems Ratio problems are hard to classify since there are many combinations and many ways to solve them However in general there are three basic types of ratio problems you will see PIug nchug multiplicative nowandIater PIugnChug The plugnchug problems are the easiest Such a problem is one where all but one item in a ratio is given to you and all you have to do is solve for the remaining one Example Your firm had net income of 1000000 last year and had total assets of 5000000 What was the firm s return on assets The only ratio mentioned is return on assets so we write that formula ROA is what we are finding ROA net income total assets We next identify what we know Net incomel 000000 Total assets5000000 This is a plugn chug problem since we know all entries for the ratio except the ROA which we can solve for ROA 1000000 5000000 20 20 Multiplicative I call the next type multiplicative problems These types of problems generally require you to multiply or divide several ratios to get a solution Example Your return on assets was 20 last year You financed 30 of your assets with debt What was your return on common equity Two ratios are directly mentioned ROA and ROE ROA NITA ROE NICE 01 ROENPMTATR11 DR We are looking for the ROE We know ROA 20 30 of assets were financed with debt this is actually telling us the debt ratio since the debt ratio s definition is that it tells us the percentage of assets financed with debt debt ratio total liabilities total assets To solve the problem we also need to recognize the relationship of the various ratios NOTE NPM net income sales TATR sales total assets Thus NPM TATR net income sales sales total assets NPM TATR net income total assets ROA Thus ROE ROAll debt ratio ROE 20 ll 30 02857 2857 This is actually an example of the DuPont Equation that we discussed earlier in the lecture notes Nowandlater The third type of problem is the nowandlater It usually gives you information about the firm at one time and then wants you to solve for information for a different period EX RRR starget current ratio is 30 Presently the current ratio is 40 based on current assets of 10 million lf RRR expands its current assets using current liabilities how much additional financing can it get before it reaches its target current ratio The only ratio mentioned is the current ratio CR CA CL To solve one of these types of problems we always need to know everything about the present situation before trying to solve for future information Currently CR 40 Thus 4 10 CL Current assets CA 10 so 4CL10 and CL25 After we know all present information we can focus on the future information We know that the target current ratio is 30 To change to CR30 from CR40 we must change the CL andor CA accounts we will be either adding or subtracting In this case the problem says we are increasing CA by using CL Thus however much CL goes up is the same amount CA goes up We must start with the current balances for CA and CL and determine the change CR CA CL target CR30 3 10 X 25 X 325X10X 753x10X 2x25 X 125 CHECK CR 10 12525 125 3 COMPANY NAME TICKER SIC 3M Company IVIMIVI 2670 Abbott Labs ABT 2834 Abercrombie amp Fitch ANF 5651 Adobe Systems ADBE 7372 Advanced Micro DeV AMD 3674 ABS Corp AES 4991 Affiliated Computer ACS 7374 Agilent Technologies A 3825 Air Products amp Chem APD 2810 Akamai Technologies AKAM 7370 Alcoa Inc AA 33 50 Allegheny Energy AYE 491 1 Allegheny Techn ATI 33 12 Allergan Inc AGN 2834 Allied Waste AW 4953 Altera Corp ALTR 3674 Altria Group MO 21 11 Amazoncom AMZN 5961 Amer Elec Power AEP 4911 Amer Tower A AMT 4899 Ameren Corp AEE 491 1 AmerisourceBergen ABC 5122 Amgen AMGN 2836 Anadarko Petroleum APC 131 1 Analog DeVices ADI 3674 AnheuserBusch BUD 2082 Apache Corp APA 131 1 Apollo Group A APOL 8200 Apple Inc AAPL 3571 Applied Biosystems ABI 3826 Applied Materials AMAT 3559 Archer Daniels Midl d ADM 2070 Ashland Inc ASH 5160 ATampT Inc T 481 3 Autodesk Inc ADSK 7372 Automatic Data Proc ADP 7374 AutoNation Inc AN 5500 AutoZone Inc AZO 5531 Avery Dennison AVY 2670 Avon Products AVP 2844 Baker Hughes BHI 3533 Ball Corp BLL 3411 Bard CR BCR 3841 Barr Pharmac BRL 2834 Baxter Int l Inc BAX 2836 Becton Dickinson BDX 3841 Bed Bath amp Beyond BBBY 5700 Bemis Co BMS 2670 Best Buy Co BBY 5731 Big Lots Inc BIG 5331 Biogen Idec Inc BIIB 2836 BJ Services BJS 1389 Black amp Decker BDK 3540 Block HampR HRB 7200 BMC Software BMC 7372 Boeing BA 3721 Boston Scientific BSX 3841 BristolMyers Squibb BMY 2834 Broadcom Corp A BRCM 3674 Brunswick Corp BC 3730 Burlington Northern BNI 401 1 CH Robinson CHRW 4731 CA Inc CA 7372 Cameron Int l Corp CAM 3533 Campbell Soup CPB 2030 Cardinal Health CAH 51 22 Carnival Corp CCL 4400 Caterpillar Inc CAT 3531 CBS Corp B CBS 4833 Celgene Corp CELG 2834 CenterPoint Energy CNP 4931 CenteX Corp CTX 1531 CenturyTel Inc CTL 4813 Chesapeake Energy CHK 131 1 Chevron Corp CVX 291 1 Ciena Corp CIEN 3661 Cintas Corp CTAS 2320 Cisco Systems CSCO 3576 CitriX Sys CTXS 7372 Clorox Co CLX 2842 CMS Energy Corp CMS 4931 Coach Inc COH 3100 CocaCola KO 2080 CocaCola Enterprises CCE 2086 Cognizant Technology CTSH 7370 ColgatePalmolive CL 2844 Computer Sciences CSC 7370 Compuware Corp CPWR 7372 ConAgra Foods CAG 2000 ConocoPhillips COP 291 1 CONSOL Energy CNX 1220 Consol Edison ED 4931 Constellation Brands STZ 2084 Constellation Energy CEG 4931 Convergys Corp CVG 73 89 Cooper Inds CBE 3640 Corning Inc GLW 3679 Costco Wholesale COST 5399 Coventry Health Care CVH 8011 Covidien Ltd COV 3845 CSX Corp CSX 4011 Cummins Inc CMI 3 510 CVS Caremark Corp CVS 5912 Danaher Corp DHR 3823 Darden Restaurants DRI 58 1 2 Dean Foods DF 2020 Deere amp Co DE 3523 Dell Inc DELL 3 571 Devon Energy DVN 131 1 Dillard s Inc DDS 531 1 DIRECTV Group The DTV 4841 Disney Walt DIS 4833 Dominion Resources D 491 1 Donnelley RR amp Sons RRD 2750 Dover Corp DOV 3559 Dow Chemical DOW 2821 DTE Energy DTE 491 1 Du Pont DD 2820 Duke Energy DUK 4931 Dynegy Inc A DYN 1311 Eastman Chemical ElIN 2821 Eastman Kodak EK 3861 Eaton Corp EIN 3714 eBay Inc EBAY 7370 Ecolab Inc ECL 2842 Edison Int l EIX 491 1 El Paso Corp EP 4922 Electronic Arts ERTS 7372 Embarq Corp EQ 4813 EMC Corp EMC 3572 Emerson Electric ElIR 3600 ENSCO Int l ESV 1381 Entergy Corp ETR 491 1 EOG Resources EOG 131 1 EquifaX Inc EFX 73 20 Exelon Corp EXC 491 1 EXpedia Inc EXPE 4700 EXpeditors Int l EXPD 4731 Exxon Mobil Corp XOM 291 1 Family Dollar Stores FDO 53 31 FedEX Corp FDX 4513 FirstEnergy Corp FE 491 1 Fiserv Inc FI SV 7374 Fluor Corp FLR 1600 Ford Motor F 371 1 Forest Labs FRX 2834 Fortune Brands F0 3490 FPL Group FPL 491 1 Freep t McMoRan CampG FCX 1000 GameStop Corp GIVIE 5734 Gannett Co GCI 271 1 Gap The Inc GPS 5651 Gen l Dynamics GD 3730 Gen l Electric GE 9997 Gen l Mills GIS 2040 Gen l Motors GM 371 1 Genuine Parts GPC 501 3 Genzyme Corp GENZ 2836 Gilead Sciences GILD 2836 Goodrich Corp GR 3728 Goodyear Tire GT 3011 Google Inc GOOG 7370 Grainger WW GWW 5000 Halliburton Co HAL 13 89 HarleyDavidson HOG 3751 Harman Int l HAR 3651 Hasbro Inc HAS 3944 Heinz HJ HNZ 2030 Hercules Inc HPC 2890 Hershey Co HSY 2060 Hess Corp HES 2911 HewlettPackard HPQ 3570 Honeywell Int l HON 3728 Horton DR DHI 1531 Hospira Inc HSP 2834 Illinois Tool Works ITW 3540 IMS Health RX 8700 IngersollRand IR 3560 Integrys Energy TEG 4931 Intel Corp INTC 3674 Interpublic Group IPG 731 1 Int l Business Mach IBM 7370 Int l Flavors amp Frag IFF 2860 Int l Game Tech IGT 3990 Int l Paper IP 2600 Intuit Inc INTU 7372 Intuitive Surgical ISRG 3845 ITT Corp ITT 3812 Jabil Circuit JBL 3672 Jacobs Engineering JEC 1600 JDS Uniphase JDSU 3663 Johnson amp Johnson JNJ 2834 Johnson Controls J CI 2531 Jones Apparel Group JN Y 23 30 Juniper Networks JNPR 3576 KB Home KBH 1 5 3 1 Kellogg K 2040 KimberlyClark KlVIB 2621 King Pharmac KG 2834 KLATencor KLAC 3827 Kohl s Corp KSS 5311 Kraft Foods KFT 2000 Kroger Co KR 5411 L3 Communic LLL 3663 Laboratory Corp LH 8071 Lauder Estee EL 2844 Leggett amp Platt LEG 2510 Lennar Corp LEN 1531 Lexmark Int l A LXK 3577 Lilly Eli LLY 2834 Limited Brands LTD 5621 Linear Technology LLTC 3674 Liz Claiborne LIZ 23 30 Lockheed Martin LMT 3760 Lowe s Cos LOW 5211 LSI Corp LSI 3674 Macy s Inc M 531 1 Manitowoc Co MTW 3530 Marathon Oil Corp lVIRO 291 1 Marriott Int l MAR 701 1 Masco Corp MAS 2430 Mattel Inc MAT 3942 McCormick amp Co MKC 2090 McDonald s Corp MCD 5812 McGrawHill MHP 273 1 McKesson Corp MCK 5122 MeadWe stvaco MWV 263 1 Medco Health Solutions MHS 5912 Medtronic Inc MDT 3845 MEMC Elec Mat ls WFR 3674 Merck amp Co lVIRK 2834 Meredith Corp MDP 2721 Microchip Technology MCHP 3674 Micron Technology MU 3674 Microsoft Corp MSFT 7372 Millipore Corp MIL 3826 MoleX Inc MOLX 3678 Molson Coors Brewing TAP 2082 Monsanto Co MON 100 Monster Worldwide lINST 731 1 Moody s Corp MCO 7320 Motorola Inc MOT 3663 Murphy Oil Corp MUR 291 1 Mylan Inc MYL 2834 Nabors Inds NBR 13 81 National Oilwell Varco NOV 3533 National Semic NSM 3674 NetApp Inc NTAP 3572 New York Times NYT 2711 Newell Rubbermaid NWL 3089 Newmont Mining NEM 1040 Nicor Inc GAS 4924 NIKE Inc B NKE 3021 NiSource Inc NI 4931 Noble Corp NE 1381 Noble Energy NBL 131 1 Nordstrom Inc JWN 5651 Norfolk Southern NSC 401 1 Northrop Grumman NOC 3 8 1 2 Novell Inc NOVL 7370 Novellus Sys NVLS 3559 Nucor Corp NUE 3312 NVIDIA Corp NVDA 3674 Occidental Petroleum OXY 13 1 1 Office Depot ODP 5940 OfficeMaX OMX 51 10 Omnicom Group OMC 731 1 Oracle Corp ORCL 7372 PACCAR Inc PCAR 371 1 PactiV Corp PTV 3089 Pall Corp PLL 3569 ParkerHannifin PH 3490 Patterson Cos PDCO 5047 PaycheX Inc PAYX 8721 Peabody Energy BTU 1221 Penney JC JCP 5311 Pepco Holdings POM 491 1 Pepsi Bottling Group PEG 2086 PepsiCo Inc PEP 2080 PerkinElmer Inc PKI 3826 Pfizer Inc PFE 2834 PGampE Corp PCG 4931 Philip Morris Int l PM 2111 Pinnacle West Capital PNW 4911 Pitney Bowes PBI 3579 Plum Creek Timber PCL 2400 Polo Ralph Lauren A RL 2320 PPG Inds PPG 2851 PPL Corp PPL 4911 Praxair Inc PX 28 1 0 Precision Castparts PCP 3728 Procter amp Gamble PG 2840 Progress Energy PGN 491 1 Public Serv Enterprise PEG 4931 Pulte Homes PHM 1531 QLogic Corp QLGC 3674 Qualcomm Inc QCOM 3663 Quest Diagnostics DGX 8071 Questar Corp STR 4923 Qwest Communic Q 4813 Radio Shack Corp RSH 5731 Range Resources Corp RRC 1311 Raytheon Co RTN 3 812 Reynolds American RAI 21 11 Robert Half Int l RHI 7363 Rockwell Automation ROK 3620 Rockwell Collins COL 3728 Rohm and Haas ROH 2821 Rowan Cos RDC 1381 Ryder System R 75 10 Safeway Inc SWY 541 1 SanDisk Corp SNDK 3572 Sara Lee Corp SLE 2000 ScheringPlough SGP 2834 Schlumberger Ltd SLB 13 89 Scripps EW A SSP 4833 Sealed Air SEE 2670 Sears Holdings SHLD 53 31 Sempra Energy SRE 4932 SherwinWilliams SHW 2851 SigmaAldrich SIAL 2836 Smith Int l Inc SII 2890 Snapon Inc SNA 3420 Southern Co SO 4911 Southwest Airlines LUV 45 12 Southwestern Energy SWN 4923 Spectra Energy SE 4923 Sprint Nextel Corp S 48 1 2 St Jude Medical STJ 3845 Stanley Works SWK 3420 Staples Inc SPLS 5940 Starbucks Corp SBUX 5812 Starwood Hotels HOT 701 1 Stryker Corp SYK 3842 Sun Microsystems JAVA 3571 Sunoco Inc SUN 291 1 SUPERVALU INC SVU 541 1 Symantec Corp SYMC 7372 Sysco Corp SYY 5140 Target Corp TGT 53 31 TECO Energy TE 4931 Tellabs Inc TLAB 3661 Tenet Healthcare THC 8062 Teradyne Inc TER 3825 TereX Corp TEX 3531 Tesoro Corp TSO 2911 Texas Instruments TXN 3674 Textron Inc TXT 3721 Thermo Fisher Sci TMO 3826 Tiffany amp Co TIF 5944 Time Warner TWX 4841 TJX Companies TJX 5651 Total System Sycs TSS 73 89 Transocean Inc RIG 13 81 Tyco Electronics TEL 3678 Tyco Int l TYC 9997 Tyson Foods A TSN 2011 US Steel Corp X 3312 Union Pacific UNP 401 1 Unisys Corp UIS 7373 United Parcel Serv UPS 4210 United Technologies UTX 3720 UST Inc UST 2100 VF Corp VFC 2300 Valero Energy VLO 291 1 Varian Medical Sys VAR 3845 VeriSign Inc VRSN 73 72 Verizon Communic VZ 4813 Vulcan Materials VMC 1400 Chapters 5 and 6 The Financial Environment Markets Institutions and Interest Rates Financial markets Types of financial institutions Determinants of interest rates Yield curves What is a market A market is a place where goods and services are exchanged A financial market is a place where individuals and organizations wanting to borrow funds are brought together with those having a surplus of funds Financial Markets I Financial markets bring together people and organizations wanting to borrow money With those having surplus funds There are many different financial markets in a developed economy each dealing with a different type of instrument serving a different set of customers or operating in a different part of the country Markets Physical assets vs Financial assets I Physical asset markets also called quottangiblequot or quotrealquot asset markets are the markets for such products as Wheat autos real estate computers and machinery I Financial asset markets deal with stocks bonds notes mortgages and other claims on real assets Markets Spot vs Futures 39 Spot markets are markets in which assets are bought or sold for on the spot delivery I Futures markets are markets in which participants agree today to buy or sell an asset at a future date Markets Money vs Capital I Money markets are the markets for shortterm highly liquid debt securities those securities that mature in less than one year 39 Capital markets are the markets for longterm debt and corporate stocks Markets Primary vs Secondary I Primag markets are the markets in which corporations sell newly issued securities to raise capital 39 Second markets are the markets in which existing already outstanding securities are traded among investors What is an Initial Public Offering IPO market An IPO Market is a subset of the primary market Firms go public by offering shares of their stock to the public for the first time Markets Public vs Private I Private markets are the markets where transactions are worked out directly between two parties I Public markets are the markets where standardized contracts are traded on organized exchanges Three Primary Ways Capital s Transferred Between Savers and BorrovErs Direct transfer Investment banking house Financial intermediary Direct transfer I Direct transfers of money and securities occur when a business sells its stocks or bonds directly to savers Without going through any type of financial institution Securities Business Dollars Saver I Financiallntermediary I I Transfers through financial intermediaries occur when a bank or mutual fund obtains funds from savers issues its own securities in exchange and then uses these funds to purchase other securities I Intermediaries literally create new forms of capital The existence of intermediaries greatly increases the efficiency of money and capital markets Savers Bus secs Business Intermediary 1 Int SBCS39 Types of Financial ntermediaries Commercial banks Savings and loan associations Mutual savings banks Credit unions Pension funds Life insurance companies Mutual funds I Investment Bankers I Transfers through an investment banking house occur when a brokerage firm such as Merrill Lynch serves as a middleman and facilitates the issuance of securities I These middlemen help corporations design securities that will be attractive to investors buy these securities from the corporations and then resell them to savers in the primary markets Business saVerS Stock Markets I The stock market is one of the most important markets to financial managers because it is here that the price of each stock and hence the value of all publicly owned firms is established There are two basic types of stock markets I The physical location exchanges typi ed by the New York Stock Exchange NYSE and the American Stock Exchange AMEX are tangible physical entities I The electronic dealer markets include the Nasdaq stock market the less formal overthecounter market and the recently developed electronic communications networks ECNs What do we call the price or cost of debt capital The interest rate What do we call the price or cost of equity capital Required Dividend Capital return yield gain What four factors affect the cost of money Production opportunities Time preferences for consumption Risk Expected inflation Real Versus Nominal Rates k Real riskfree rate Tbond rate if no inflation 1 to 4 k Any nominal quoted rate Rate on Treasury securities kkPDRPLPMRP Here k required rate of return on a debt security k real riskfree rate IP inflation premium DRP default risk premium LP liquidity premium MRP maturity risk premium Yield Curve The term structure of interest rates describes the relationship between long and shortterm interest rates The yield curve is the graph of interest rates for similar risk securities for different maturities 20 Hypothetical Treasury Yield Curve Interest Rate 15 Maturity risk premium In ation premium Real riskfree rate Years to Maturity 1 1o 20 21 What kind of relationship exists between the Treasury yield curve and the yield curves for corporate issues Corporate yield curves are higher than that of the Treasury bond However corporate yield curves are not neces sarily parallel to the Treasury curve The spread between a corporate yield curve and the Treasury curve widens as the corporate bond rating decreases 22 Hypothetical Treasury and Corporate Yield Curves Interest Rate 15 BBRated 1 AAARated 5 M Treasu Ty 59 390 Yield Curve 52 Years to o Maturity o 1 5 1o 15 20 23 Pure Expectations Hypothesis The PEH contends that the shape of the yield curve depends on investor s expectations about future interest rates If interest rates are expected to increase LT rates will be higher than S T rates and viceversa Thus the yield curve can slope up down or even bow 24 Assumptions of the PEH Assumes that the maturity risk premium for Treasury securities is zero Longterm rates are an average of current and future shortterm rates lf PEH is correct you can use the yield curve to back out expected future interest rates 25 Conclusions about PEH Some would argue that the MRP 0 and hence the PEH is incorrect Most evidence supports the general view that lenders prefer S T securities and view LT securities as riskier Thus investors demand a MRP to get them to hold LT securities ie MRP gt 0 26 Other factors that influence interest rate levels Federal reserve policy Federal budget surplus or deficit Level of business activity International factors 27 Risks associated with investing overseas Exchange rate risk If an investment is denominated in a currency other than US dollars the investments value will depend on what happens to exchange rates Country risk Arises from investing or doing business in a particular country and depends on the country s economic political and social environment 28 CHAPTER 13 Capital Structure and Leverage I Business and financial risk I Optimal capital structure I Operating Leverage I Capital structure theory What s business risk I Uncertainty about future operating income EBIT ie how well can we predict operating income Low risk EEBIT EBIT Prob Some factors that affect business risk I Uncertainty about demand unit sales I Uncertainty about output prices I Uncertainty about input prices I Product types of other liability I Degree of operating leverage DOL What is operating leverage and how does it affect a firm s business risk I Operating leverage is the use of fixed costs rather than variable costs I If most costs are fixed hence do not decline when demand falls then the firm has a high DOL More operating leverage leads to more business risk for then a small sales decline causes a big profit decline Rev Rev TC TC FC FC QEE Sales QBE sales Low operating leverage Prob High operating leverage K EBITL EBITH EBIT Typical situation Can use operating leverage to get higher EEBT but risk increases What is financial leverage Financial risk I Financial leverage is the use of debt and preferred stock I Financial risk is the additional risk placed on common stockholders as a result of financial leverage Business Risk vs Financial Risk I Business risk depends on business factors such as competition product liability and operating leverage I Financial risk depends only on the types of securities issued More debt more financial risk Concentrates business risk on the stockholders An example Illustrating effects of financial leverage Two firms with the same operating leverage business risk and probability distribution of EBIT Only differ with respect to their use of debt capital structure Firm U Firm L No debt 10000 of 12 debt 20000 in assets 20000 in assets 40 tax rate 40 tax rate Firm U Unleveraged Economy Bad Avg Good Prob 025 050 025 EBIT 2000 3000 4000 Interest 0 0 0 EBT 2000 3000 4000 Taxes 40 800 1 I200 1 I600 NI 1200 1800 2400 Firm L Leveraged Economy Bad Avg Good Prob 025 050 025 EBIT 2000 3000 4000 Interest 1200 1200 1200 EBT 800 1800 2800 Taxes 40 320 720 1120 NI 480 1080 1680 Same as for Firm U Ratio comparison between leveraged and unleveraged firms FIRM U Bad Avq Good BEP 100 150 200 ROE 60 90 120 TIE FIRM L Bad Avq Good BEP 100 150 200 ROE 48 108 168 TIE 167x 250x 330x 12 Risk and return for leveraged and unleveraged firms Expected Values Firm U Firm L EBEP 150 150 EROE 90 108 ETIE 25x Risk Measures Firm U Firm L OROE 212 424 CVROE 024 039 The effect of leverage on profitability and debt coverage I For leverage to raise expected ROE must have BEP gt kd I Why If kd gt BEP then the interest expense will be higher than the operating income produced by debtfinanced assets so leverage will depress income I As debt increases TlE decreases because EBIT is unaffected by debt and interest expense increases lnt Exp de Conclusions Basic earning power BEP is unaffected by financial leverage L has higher expected ROE because BEP gt kd L has much wider ROE and EPS swings because of fixed interest charges lts higher expected return is accompanied by higher risk Optimal Capital Structure That capital structure mix of debt preferred and common equity at which P0 is maximized Trades off higher EROE and EPS against higher risk The taxrelated benefits of leverage are exactly offset by the debt s riskrelated costs The target capital structure is the mix of debt preferred stock and common equity with which the firm intends to raise capital Finding Optimal Capital Structure I The firm s optimal capital structure can be determined two ways I Minimizes WACC I Maximizes stock price I Both methods yield the same results Other factors to consider when establishing the firm s target capital structure Industry average debt ratio TIE ratios under different scenarios Lenderrating agency attitudes Reserve borrowing capacity Effects of financing on control Asset structure Expected tax rate N95 ny How would these factors affect the target capital structure Sales stability High operating leverage Increase in the corporate tax rate Increase in the personal tax rate Increase in bankruptcy costs Management spending lots of money on lavish perks 9999 Table for calculating WACC and determining the minimum WACC Amount DA EA borrowed ratio ratio ks kd1 T WACC 0 000 10000 1200 000 1200 250 1250 8750 1251 480 1155 500 2500 7500 1320 540 1125 750 3750 6250 1416 690 1144 1000 5000 5000 1560 840 1200 Amount borrowed expressed in terms of thousands of dollars 20 Table for determining the stock price maximizing capital structure Amount Borrowed L Po 0 300 1200 2500 250000 326 1251 2603 500000 355 1320 2689 750000 377 1416 2659 1000000 390 1560 2500 21 Why do the bond rating and cost of debt depend upon the amount borrowed I As the firm borrows more money the firm increases its financial risk causing the firm s bond rating to decrease and its cost of debt to increase 22 What effect does increasing debt have on the cost of equity for the firm I If the level of debt increases the riskiness of the firm increases We have already observed the increase in the cost of debt However the riskiness of the firm s equity also increases resulting in a higher ks 23 The Hamada Equation Because the increased use of debt causes both the costs of debt and equity to increase we need to estimate the new cost of equity The Hamada equation attempts to quantify the increased cost of equity due to financial leverage Uses the unlevered beta of a firm which represents the business risk of a firm as if it had no debt 24 The Hamada Equation 13 Bu1 1 T DIE Suppose the riskfree rate is 5 and the market risk premium is 7 The unlevered beta of the firm is 10 Total assets are 2000000 and the debt equals 250000 The tax rate is 40 25 Calculating levered betas and costs of equity 3L 10 1 06250I1750 3L 10857 Leveraged ks kRF kM kRF 13L k5 50 70 10857 k5 126 Unleveraged k5 50 7010 12 26 Who are Modigliani and MillerMM I They published theoretical papers which changed the way people thought about financial leverage I They won Nobel prizes in economics because of this work 27 What assumptions underlie the Independence Hypothesis No brokeragetransaction costs No taxes No bankruptcy costs Investors have the same information about the firm s future as management Investors borrow at the same rate as corporations EBIT is not affected by the use of debt 28 I Without corporate taxes the Independence Hypothesis says Firm value is not affected by the level of debt in the firm THEORY Main contribution is that it shows the items that can cause debt to affect firm value 29 What if interest is tax deductible Corporate Taxes I Even if the costs of debt and equity were the same before taxes with interest deductibility the cost of debt would be less than the cost of equity after taxes I Replacing higher cost equity with lower cost debt would result in a lower WACC and higher firm value 30 What if interest is tax deductible and there are bankruptcy costs I The tax advantage for debt still has the same effect as before I However the existence of bankruptcy costs causes ALL investors to recognize that increased debt means more risk I More risk means more expected return 31 I The cost of equity and debt will increase as the level of debt used increases I Initially this increase will likely be small so that the benefit of debt exceeds its cost I Eventually costs will exceed benefits I This is the Tradeoff Theory 32 Relationship between capital costs and leverage when corporate taxes and bankruptcy risk are considered Cost of Capital 20 40 60 80 100 Dethalue Ratio 33 Implications of Tradeoff Theory I The firm s value is the discounted value of future CFs The appropriate discount rate is WACC The firm s value will be maximized when the WACC is at its lowest I The optimal capital structure will be where the WACC is at its lowest which results in firm value at its highest 34 Cost of Capital or Firm Value I Firm I I I rmT 20 40 60 80 100 Dethaue Ratio 35 Information asymmetry Signaling I It is difficult to accept that investors know as much about the firm s future prospects as managers If this is not true we say information asymmetry exists 36 I Managers cannot simply tell investors what they know because investors may not believe them I With information asymmetry present the old saying action speaks louder than words becomes paramount I Investors know watch managers actions for clues 37 Logically when would managers use debt instead of equity financing I Debt has a set payment amount If it is not met the firm can be forced into bankruptcy I Equity only promises residual payments if there are profits they belong to shareholders 38 I Generally this means managers are more likely to use debt when they view the future as favorable In such a situation they see no reason to fear fixed payment amounts They are more likely to choose equity when prospects are more uncertain 39 Signaling Theory I Financing choices provide a signal to investors Debt financing good news Equity financing bad news This may lead managers to maintain reserve borrowing capacity 40 Agency costs I In many corporations the managers of the firm own relative small portions of the company I Thus they may have incentives to operate in a manner which is not most beneficial to shareholders 41 I Some have argued that this incentive is greater if the managers have access to large amounts of unrestricted CFs free CF I Since debt imposes fixed payments that must be met its use may help alleviate agency costs 42 Chapter 2 Time Value of Money Future value Present value Rates of return Amortization Time lines show timing of cash flows 0 1 2 3 i I CFo CF1 CF2 CF3 Time 0 is today Time 1 is the end of Period 1 or the beginning of Period 2 If you deposit 100 in an account that pays 6 annual interest what amount will you expect to have in the account at the end of the year i6 3 o o I Future value I 100 starting value present value PV 6 interest 006100 6 106 ending value future value FV FV PV PV change FV PV 1 change FV PV 1 i What if we leave the money for two vears 100 present value PV 6 interest 100006 6 106 future value year1 FV1 636 interest 106006 636 11236 future value year 2 FV2 How do we come up with a formula for multiple periods 106100 1 006 FV1PV1i 11236 106 1 006 FV2 FV1 1 i but from above FV2PV1i1i FV2 PV 1 i2 Future value In general for any number of periods FVn PV 1 in If interest is compounded during the year we change the formula to Fvn PV 1 imnm Four Ways to Find FVs Solve the equation using a regular calculator Use tables Use a financial calculator Use a spreadsheet What s the FV of an initial 100 after 3 years if i 10 10 0 FV o o A N II w Finding FVs is compounding Solve equation Fv3 PV1 i3 1001103 1001331 13310 On calculator 110 3E1331 100 1331 B 13310 Using tables I 2 4 6 8 10 1 10200 10400 10600 10800 11000 21040410816112361166412100 3 10612 11249 11910 12597 4 5 10824 11699 12625 13605 1 11041 12167 13362 14693 16105 Fv3 PV FVIF 100 13310 13310 Financial Calculator Solution There are 4 variables lf 3 are known the calculator will solve for the 4th 3 10 IE 13310 Set PIYR 1 END I Spreadsheet Excel I Formulas can be entered into spreadsheets to calculate the time value of money or you can use available financial functions FVratenperpmtpvtype rate is the interest rate per period Inper is the number of periods pmt is the payment amount per period pv is the starting value type indicates whether payments occur at the beginning or end of each period Spreadsheet Excel I NOTE pmt and type are for annuities For lump sum problems set pmt equal to zero and ignore type Enter FVO130100 13310 Answer Present value When we talk about present values of future cash flows we use the same type of analysis All we do is rearrange the equation to solve for the present value What s the PV of 13310 due in 3 years if i 10 Finding PVs is discounting and it s the reverse of compounding Solve FVn PV1 i n for PV FVn 1 PV W FVHW 1 3 PV 13310 100PVFi n 1331007513 100 I Financial Calculator Solution I 3 1o 0 100 This means that if you put in 100 today earning 10 per year you would have 13310 after 3 years We will deal with 3 different rates nominal or quoted or stated rate per year E periodic rate 5 l effective annual 7quot rate iNom is stated in contracts Periods per year m must also be given Examples 0 8 Quarterly 0 8 Daily interest 365 days 20 Periodic rate iPer iNomlm where m is number of compounding periods per year m 4 for quarterly 12 for monthly and 360 or 365 for daily compounding Examples 8 quarterly iPer 8I4 2 8 daily 365 iPer 8I365 0021918 21 Effective Annual Rate EAR EFF The annual rate that causes PV to grow to the same FV as under multiperiod compounding i m EFF 1 gm 1 2 1 21 10 1052 10 01025 1025 22 Will the FV of a lump sum be larger or smaller if we compound more often holding the stated I constant Why If compounding is more frequent than once a yearfor example semiannually quarterly or dailyinterest is earned on interest more often 23 Will the PV of a lump sum be larger or smaller if we compound more often holding the stated I constant Why If compounding is more i once a yearfor example semiannually quarterly or dailyinterest is earned on interest more often so you can start with a smaller amount and reach the same goal in the same amount of time 24 On a financial calculator llrlllquot lquotl 2 10I2 100 E 11025 EAR 11025 100 1025 Any PV would grow to same FV at 1025 annually or 10 semiannually The EAR is used to compare returns on investments with different compounding 25 What is the FV of 100 after 3 years under 10 semiannual compounding 3x2 10l2 100 13401 26 What is the PV of 500 received in 3 years under 10 semiannual compounding 3x2 1012 500 E 37311 27 Annuities are sets of equal payments received at equal time intervals Ordinary Annuity o 1 2 3 I i I I I I I I I PMT PMT PMT Annuity Du o 1 2 3 i PMT PMT PMT 28 What s the FV of a 3year ordinary annuity of 100 at 10 29 Financial Calculator Solution I INPUTS OUTPUT 3 10 100 E 33100 You should be in end mode when you calculate the answer 30 What s the PV of this ordinary annu y o 1 2 3 I 10 I I I I I I I 100 100 100 9091 39 I 8264 7513 24868 PV 31 INPUTS 3 10 100 l OUTPUT 24869 Again make sure you are in end mode when you calculate the answer 32 What s the value at the end of Year 3 of the following CF stream if the quoted interest rate is 10 compounded semiannually 0 1 2 3 5 I I I I I I I 100 100 100 10 compounded semian nually is 5 each 12 year 33 a The cash flow stream is an annual annuity First find EAR 010 2 EAR 17 11o25 b Calculate FV using EAR as interest rate 1025 100 3 E 33180 Find the FV and PV if the annuity were an annuity due with annual compounding of interest 0 1 2 3 l 10 I I I I I I 100 100 100 35 Switch from End to Begin INPUTS 3 10 100 OUTPUT 36410 INPUTS 3 10 100 OUTPUT 27355 36 What is the PV of this uneven cash flow stream f 3 4 100 300 300 50 9091lt 39 I 24793 22539 3415 53008 PV 37 Input in CFLO register CFo 0 CF1 100 CF2 300 CF3 300 CF4 50 Enter 10 then press NPV button to get NPV 53009 Here NPV PV 38 Amortization Construct an amortization schedule fora 100010 annual rate loan with 3 equal payments 39 Step 1Find the required annual payments 0 1 10 2 3 l I 1000 PMT PMT PMT INPUTS 3 10 1000 0 ll OUTPUT 40211 4o Step 2 Find the interest paid in Year 1 INTt Beg balt i INT1 1000o10 100 Step 3 Find repayment of principal in Year 1 Repmt PMT INT 40211 100 41 Step 4 Find ending balance after Year 1 End bal Beg bal Repmt 1000 30211 69789 Repeat steps 24 for Years 2 and 3 to complete the amortization table 42 BEG PRIN END YR BAL PMT INT PMT BAL 1 1000 402 100 302 698 2 698 402 70 332 366 3 366 402 37 366 0 TOT 1120634 20634 1000 43 40211 30211 magma a IIIII IIIIIIIIg 4 4 IIII was messesssssssssssssss quotmm messesssssssssssssss IIIIIIIIIIII fIIIIIIIIII 0 3 Level payments lnterest declines because outstanding balance declines Lender earns 10 on loan outstanding which is falling 44 CHAPTER 8 Risk and Rates of Return Standalone risk Portfolio risk Risk amp return CAPM The basic goal of the firm is to maximize shareholder wealth Investment returns The rate of return on an investment can be calculated as follows Amount received Amount invested Return Amount invested For example if 1 000 is invested and 1100 is returned after one year the rate of return for this investment is 1100 1000 1000 10 What is risk Risk is the possibility that more than one outcome may occur Risk pertains to the possibility that actual returns will be different from the expected return The greater the Chance and range of returns being different from the expected return the riskier the investment 3 Probability distribution Rate of 70 o 15 100 Return Expected Rate of Return Selected Realized Returns 1926 2004 Average Standard Smallcompany stocks Largecompany stocks LT corporate bonds LT government bonds US Treasury bills Source Based on Stocks Bonds Bills and Inflation Valuation Edition 2005 Yearbook Chicago Ibbotson Associates 2005 28 Return Deviation 175 331 124 203 62 86 58 93 38 31 5 If an asset has no risk it is called riskfree The closest approximation we have are government securities Tbills return their promised return regardless of the economy This is why we use Tbills as a proxy for the riskfree rate Do Tbills promise a completely riskfree return NO Tbills are still exposed to the risk of inflation However not much unexpected inflation is likely to occur over a relatively short period Risk Tolerance of Individuals Risk aversion is a dislike for risk Risk averse individuals consider a tradeoff between risk and return in making decisions Risk averse investors require higher expected rates of return to compensate them for assuming higher levels of risk Required return Investors will expect to receive the risk free rate of return for any investment since it can be obtained without any risk They also will require additional expected return to compensate them for the risk of the asset The return on any asset can be described by the following equation Asset s Riskfree Asset s rate of risk reqUIred return premlum return NOTE It is important to note that investors make their decision based on expected returns and risk Actual returns may differ from expected returns so actual returns are not always higher for higher risk investments in the shortrun In the longrun higher returns do generally occur for higher risk assets Risk depends on what could happen versus what is expected to happen So we need to be able to determine what return is expected for a particular asset Expected rate of return on an individual asset A k expected rate of return Pi probability the ith outcome will occur ki return for ith possible outcome Expected Rate of Return Outcomg Return Probabm Better 22 X 03 Same 12 X 05 Worse 8 X 02 Exp Return 66 60 16 110 Risk and Return Risk can be measured in many differentways There are two main ways of looking at risk Standalone risk Portfolio risk What is standalone risk Standalone risk considers all risk It is measured by the dispersion of returns about the mean and is relevant only for assets held in isolation Risk Measures Standalone risk measures standard deviation coefficient of variation Market risk measure beta How do we calculate standard deviation Standard deviation measures total risk n A 039 Variance Z1ki k2Pi I measure of standalone risk the larger the c the lower the probability that actual returns will be close to expected returns I Coefficient of Variation CV I Standardized measure of dispersion about the expected value Std dev g A CV Mean k Shows risk per unit of return still a standalone risk measure Diversification Generally we do not hold assets in isolation We own many assets at any one time This is what is meant by the term diversification simply holding more than one asset Diversification has several benefits for investors 20 Diversification s main benefit is easily seen Since not all investments go up or down at the same time combining several assets together means that it will be likely that when some are doirhg poorly others will be doing we I This results in returns being closer to the average or expected return over time which means that there is less risk 21 Returns Distributions for Two Perfectly Negatively Correlated Stocks r 10 and for Portfolio WM 25 15k 0 Stock W Stock M Portfolio WM V 10 l l v2m 10 1 I 22 Returns Distributions for Two Perfectly Positively Correlated Stocks r 10 and for Portfolio MM Stock M Stock M Portfolio MM MUM iZl 0 39 lV v v 23 Risk that only affects an individual asset company specific risk is removed when many assets are held together Ifyou could own a portfolio of all assets all company specific risk could be eliminated Only the risk that affects all assets would remain 24 By forming portfolios we can eliminate about half the riskiness of individual stocks 35 vs 20 op 35 CompanySpecific Risk StandAlone Risk op 20 Market Risk 0 39 39 39 39 vA 10 20 30 40 2000 Stocks in Portfolio 25 Standalone Market Firmspecific risk 39 risk risk Market risk is that part of a security s standalone risk that cannot be eliminated by diversification and it is measured by beta Firmspecific risk is that part of a security s standalone risk that can be eliminated by proper diversification 26 What is company specific risk Caused by company specific events eg lawsuits strikes winning or losing major contracts etc Effects of such events on a portfolio can be eliminated by diversification 27 What is market risk l Stems from such external events as war inflation recession and interest rates lBecause all firms are affected simultaneously by these factors market risk cannot be eliminated by diversification l Market risk is also known as systematic risk since it shows the degree to which a stock moves systematically with other stocks 28 If you chose to hold a onestock portfolio and thus are exposed to more risk than diversified investors would you be compensated for all the risk you bear 29 I NO Standalone risk as measured by a stock s G or CV is not important to a welldiversified investor Rational riskaverse investors are concerned with 0 which is based on market risk 30 There can only be one price hence market return for a given security Therefore no compensation can be earned for the additional risk of a one stock portfolio 31 Portfolio Return and Standard Deviation The expected return for a portfolio will be the weighted average return for all assets in the portfolio Portfolio standard deviation is generally less than the weighted average of the standard deviations of the individual assets in the portfolio 32 Portfolio return n kp 2 wi ki i1 wi fraction of funds invested in asset i ki exp return for ith asset 33 Expected Return for a Portfolio Asset Invested Return AAA BBB CCC DDD 2000 25 4000 20 6000 16 8000 10 34 I Expected Return for a Portfolio I Determine the fraction of total funds in each asset multiply times the return and sum the resulting values Asset Invested Return AAA 2000 20000 X 25 250 BBB 4000 20000 X 20 400 CCC 6000 20000 X 16 480 DDD 8000 20000 X 10 400 total 20000 Exp return 1530 35 What is the CAPM An equilibrium model specifying the relationship between and required return on assets held in diversi ed portfolios It says that the return on any asset is equal to the riskfree return plus a riskpremium The riskpremium equals the asset s beta times the riskpremium for the market portfolio 36 What is the market risk premium Additional return over the riskfree rate needed to compensate investors for assuming an average amount of risk Its size depends on the perceived risk of the stock market and investors degree of risk aversion Varies from year to year but most estimates suggest that it ranges between 4 and 8 per year 37 Since by forming welldiversified portfolios we can eliminate company specific risk we need a risk measure that only considers market risk Beta is that risk measure Beta measures the risk of an asset relative to the market Beta shows how risky a stock is if the stock is held in a welldiversified portfolio 38 How are betas calculated Run a regression of past returns on Stockiversus returns on the market The slope of the regression line is defined as the beta coefficient 39 f beta 10 average stock f beta gt 10 stock riskierthan average f beta lt 10 stock less risky than average Most stocks have betas in the range of 05 to 15 40 Security Market Line SML ki kRF kM kRFbi kRF riskfree return kM return on market portfolio bi beta for asseti ki return on asset i 41 SML ki 8 15 8 bi k SML 2 Risk bi 42 Factors that change the SML What if investors raise inflation expectations by 3 what would happen to the SML k SMLZ Risk pi 43 Factors that change the SML What if investors risk aversion increased causing the market risk premium to increase by 3 what would happen to the SML k W SML2 18 SML1 15 11 8 Portfolio beta The beta for a portfolio is the weighted average of the betas for all stocks in the portfolio A n bp 1wi bi portfolio beta wi fraction of funds invested in asset i bi beta for ith asset 45 Beta for a Portfolio Riskfree rate 5 Market return 13 Asset Invested Beta AAA 2000 20000 X 30 030 BBB 4000 20000 X 25 050 CCC 6000 20000 X 16 048 DDD 8000 20000 X 12 048 total 20000 Beta port 176 46 Expected Return for a Portfolio Now use the calculated Beta for the portfolio to calculate the expected return forthe portfolio I ki 5 17613 5 1908 47 Has the CAPM been verified through empirical tests Not completely Those statistical tests have problems that make verification almost impossible 48 Investors seem to be concerned with both market risk and total risk Therefore the SML may not produce a correct estimate of ki ki kRF kM kRFbi 49 Also CAPMSML concepts are based on expectations yet betas are calculated using historical data A company s historical data may not reflect investors expectations about future riskiness 50 HP 10BII Tutorial By default the HP 10B displays only two decimal places At most you will usually need four decimal places To change the display press the second function key usually orange or gold in color then DISP and then the number 4 The HP 10B also has periods per year set equal to 12 You can change the periods per year for each problem but the solutions in the lecture supplement are based on the periods per year being set to one To change the setting press the number 1 then the second function key and then P YR The C key is the clear key that clears the display To clear the time value function keys press the second function key and then C ALL You should get into the habit of clearing the time value function keys before starting a new problem Note that the calculator treats PV as negative numbers cash out ows Therefore it is good to enter all PV s as negative numbers To make a number negative be sure to enter the number first and then press the key Do not use the subtraction key You will use the time value keys at the top of the calculator to solve lump sum and annuity future and present value problems To enter values simply type the number first and then press the associated time value key For example if you want n8 press the number 8 and then press the N key EXAMPLES A calculate PV What is the present value of 2000 received 10 years from now if the interest rate you could have received is 7 First enter the information that is given 1 7 PV PMT 0 FV 2000 To solve the problem press the PV key Answer 101670 The answer will appear with a negative sign B calculate FV What is the future value 10 years from now of 2000 deposited today in an account which has a quoted annual interest rate of 10 with quarterly compounding of interest First enter the information that is given Note For the calculated values be sure to hit the key before pressing the time value key N 10X4 This indicates 10 years times 4 interest payments per year 1 104 This indicates 25 per quarter PV 2000 The negative sign is a result of the calculator s default programming PMT 0 FV To solve the problem press the FV key Answer 537013 C calculate i What annual interest rate must you earn if you plan to deposit 10000 in the bank today and you want it to grow to be 1762342 in 5 years First enter the information that is given N 5 1 PV 10000 The negative sign is due to the calculator s default programming PMT 0 FV 1762342 To solve the problem press the 1YR key Answer 12 D calculate n If you deposit 5000 in an account which earns 9 per year how many years will it take for the investment to grow to be worth 10000 First enter the information that is given N 1 9 PV 5000 The negative sign is a result of the calculator s default programming PMT 0 FV 10000 To solve the problem press the N key Answer 80432 years Your calculator allows you to solve for the various items for an ordinary annuity 01 an annuity due You must make sure the calculator is in the correct quotmodequot for the type of annuity you are considering The calculator has two annuities modes END and BEGIN The quotBEGINquot mode is used for an annuity due begin means the payments are at the beginning of the period The quotENDquot mode is used for ordinary annuities end means the payments are at the end of the period The BEGEND key changes the payment mode of the calculator To change modes press the second function key and then the BEG END key If you are in the begin mode the word BEGIN will show in the display To change to the end mode do the same again EXAMPLE You are offered an investment that will pay you 5000 per year for the next 10 years Each payment will be made at the end of each year If the appropriate discount rate is 9 per year what is the present value of the annuity Note Payments are at the end of each year so be sure you are in the end mode Enter the information that is given 1 9 PV PMT 5000 FV 0 To solve the problem press the PV key Answer 3208829 EXAMPLE You are offered an investment that will pay you 8000 per year for the next 20 years Each payment will be made at the beginning of each year If you expect to earn an annual return of 7 per year what is the future value of the annuity at the end of the 20 years Note Payments are at the beginning of each year so make sure you are in the begin mode Enter the information that is given 1 7 PV 0 PMT 8000 FV To solve the problem press the FV key Answer 35092141 Uneven Cash Flows The calculator will calculate the present value of an uneven stream of cash ows using the NPV function You enter the cash ows in the order they occur starting with any cash ow that occurs now cash flow zero To enter the cash ows press the number first and then press the CFj key After you enter all cash ows enter the interest rate by pressing the number and then the IYR key To solve the problem press the second function key and then the NPV key Example Suppose that you are offered an investment which will pay 100 at the end of the first year 200 at the end of the second year 300 at the end of the third year 400 at the end of the fourth year and 500 at the end of the fifth year How much are the cash ows worth in today s dollars if your annual required rate of return is 12 To solve the problem first enter the cash ows Remember you must start with cash ow zero Since nothing happens now in the problem cash ow zero equals 0 Press 0 then CFj Press 100 then CFj TI 83 and TI 83 Plus Tutorial By default the TI 83 displays only two decimal places To change the display press the Mode key then the down arrow key to the Float line Next use the right arrow key to highlight the number of decimal places desired 4 is a good choice and press Enter Finally press 2nd and Quit to eXit the menu Before entering data for any type of nancial problem you must go to the nance functions page For the TI83 press 2nd then FINANCE On the TI 83 Plus press the Apps button and then choose the Finance menu To solve a lump sum or annuity problem you choose 1 TVM Solver from the finance function menu Either highlight lTVM Solver and then press Enter or just enter 1 You will now see in your screen a series of items you are able to enter N 1 PV PMT FV P Y CY All lump sum and annuity problems require that you enter the data given by using the arrow keys to place the cursor next to the items you know and typing the value Make sure all items that are not used in the problem are set equal to zero After entering the data you are given move the cursor to the item you wish to solve and press Alpha and then Enter NOTES 1 The calculators by default treat PV as a negative number cash out ow Therefore it is a good idea to enter all PV s as negative numbers On theses calculators you enter a negative number by first pressing the sign change key and entering the number value 2 Make sure the values for P Y and CY are set equal to l EXAMPLES A calculate PV What is the present value of 2000 received 10 years from now if the interest rate you could have received is 7 First enter the information that is given 1 7 PV PMT 0 FV 2000 To solve the problem place the cursor beside PV and press Alpha and then solve Answer 101670 The answer will appear with a negative sign 227 B calculate FV What is the future value 10 years from now of 2000 deposited today in an account which has a quoted annual interest rate of 10 with quarterly compounding of interest First enter the information that is given For the calculated values be sure to press the enter key so the answer is calculated N 10X4 This indicates 10 years times 4 interest payments per year 1 104 This indicates 25 per quarter PV 2000 The negative sign is a result of the calculator s default programming PMT 0 FV To solve the problem place the cursor beside FV and press Alpha and then solve Answer 537013 C calculate i What annual interest rate must you earn if you plan to deposit 10000 in the bank today and you want it to grow to be 1762342 in 5 years First enter the information that is given 1 PV 10000 The negative sign is a result of the calculator s default programming PMT 0 FV 1762342 To solve the problem place the cursor beside 1 and press Alpha and then solve Answer 12 D calculate n If you deposit 5000 in an account which earns 9 per year how many years will it take for the investment to grow to be worth 10000 First enter the information that is given 1 9 PV 5000 The negative sign is a result of the calculator s default programming PMT 0 FV 10000 To solve the problem place the cursor beside N and press Alpha and then solve Answer 80432 years 228 Your calculator allows you to solve for the various items for an ordinary annuity or an annuity due You must make sure the calculator is in the correct quotmodequot for the type of annuity you are considering The calculator has two annuities modes END and BEGIN The quotBEGINquot mode is used for an annuity due begin means the payments are at the beginning of the period The quotENDquot mode is used for ordinary annuities end means the payments are at the end of the period The calculator is using the mode that is highlighted To change modes use the arrow keys to highlight the correct mode and then press enter EXAMPLE You are offered an investment that will pay you 5000 per year for the next 10 years Each payment will be made at the end of each year If the appropriate discount rate is 9 per year what is the present value of the annuity First enter the information that is given 1 9 PV PMT 5000 FV 0 NOTE Make sure you are in the END mode To solve the problem place the cursor beside PV and press Alpha and then solve Answer 3208829 EXAMPLE You are offered an investment that will pay you 8000 per year for the next 20 years Each payment will be made at the beginning of each year If you expect to earn an annual return of 7 per year what is the future value of the annuity at the end of the 20 years First enter the information that is given N 20 1 7 PV 0 PMT 8000 FV NOTE Make sure you are in the BEGIN mode To solve the problem place the cursor beside FV and press Alpha and then solve Answer 35092141 229

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