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Introduction To Corporate Finance Corporate Finance and the Financial Manager Forms of Business Organization The Goal of Financial Management The Agency Problem and Control of the Corporation Financial Markets and the Corporation Corporate Finance Some important questions that are answered using finance What longterm investments should the rm take on Capital budgeting Where will we get the longterm financing to pay for the investment Capital structure How will we manage the everyday financial activities of the firm Working capital management Financial Management Decisions Capital budgeting What longterm investments or projects should the business take on Capital structure How should we pay for our assets Should we use debt or equity Working capital management How do we manage the daytoday nances of the rm Financial Manager Financial managers try to answer some or all of these ques ons The top financial manager within a firm is usually the Chief Financial Officer CFO Treasurer oversees cash management credit management capital expenditures and financial planning Controller oversees taxes cost accounting financial accounting and data processing An Organizational Chart Forms of Business Organization Three major forms in the United States Sole proprietorship A business owned by one person Partnership two or more owners General unlimited joint liability Limited a limited partner who does not actively participate in the business operations Corporation a legal person separate from its owners Articles of incorporation and bylaws Goal Of Financial Management What should be the goal of a corporation Maximize profit Minimize costs Maximize market share Problem It is not clear they are in the company s stockholders best interests Answer Maximize the current value of the company s stock More general maximize the market value of the existing owner s equity The Agency Problem Agency relationship Principal hires an agent to represent hisher interests Stockholders principals hire managers agents to run the company Agency problem Conflict of interest between principal and agent Management goals and agency costs Financial Markets Primary markets the original sale of securities by governments and corporations Public offering supervised by Security and Exchange Commission SEC Private placement Secondary markets Auction markets eg NYSE AMX brokers Dealer markets overthecounter eg NASDAQ dealers International financial markets TSE LSE NYSE NASDAQ National Association of Securities Dealers Automated Quotations Chapter 5 Introduction to Valuation The Time Value of Money Future Value and Compounding Present Value and Discounting More on Present and Future Values Basic De nitions Time value of money a dollar in hand today is worth more than a dollar promised at some time in the future Future Value the amount an investment is worth after one or more periods later money on a tIme line Present Value the current value of future cash flows discounted at the appropriate discount rate earlier money on a time line Interest rate exchange rate between earlier money and later money Future Value Example 1 Suppose you invest 1000 for one year at 5 per year What is the future value in one year Interest 100005 50 Value in one year principal interest 1000 50 1050 Future Value FV 10001 05 1050 Suppose you leave the money in for another year How much will you have two years from now FV 100010510510001052 110250 Future Values General Formula FV PV1 rt FV future value PV present value r period interest rate expressed as a decimal t number of periods Future value interest factor 1 rt or FVFr t 1 rt Effects of Compounding Simple interest Compound interest Consider the previous example FV with simple interest FV with compound interest What does the difference stands for Calculator Keys Texas Instruments BA ll Plus 4 l I fill i i lit N number of periods IN period interest rate PY must equal 1 for the IN to be the period rate Interest is entered as number of percent not a decimal PMT annuity cash flow FV future value PV present value Remember to clear the registers CLR TVM after each problem Other calculators are similar in format Future Values Example 2 Suppose you invest the 1000 from the previous example for 5 years at 5 interest rate How much would you have at the end of year 5 Formula FV1000155 Calculator 5 N 5 IN 1000 PV CPT FV 127628 What is the effect of compounding The effect of compounding is small for a small number of periods but increases as the number of periods increases compare the difference between simple interest and compound interest for example 1 and 2 Future Values Example 3 Suppose you had a relative deposit 10 at 55 interest 200 years ago How much would the investment be worth today Formula Calculator What is the effect of compounding Present Values How much do I have to invest today to have some amount in the future FV PV1 rt Rearrange to solve for PV FV 1 rt Present value interest factor 1 1 rt or PVFr t 1 1 rt When we talk about discounting we mean finding the present value of some future amount Present Value Example 1 Suppose you need 10000 in one year for the down payment on a new car If you can earn 7 annually how much do you need to invest today Formula PV 10000 1071 934579 Calculator 1 N 7 IN 10000 FV CPT PV 934579 Present Values Example 2 You want to begin saving for your daughter s college education and you estimate that she will need 150000 in 17 years If you feel confident that you can earn 8 per year how much do you need to invest today Formula Calculator Present Values Example 3 Your parents set up a trust fund for you 10 years ago that is now worth 1967151 Ifthe fund earned 7 per year how much did your parents invest Formula Calculator Present Value Important Relationship I For a given interest rate the longer the time period the lower the present value What is the present value of 500 to be received in 5 years 10 years The discount rate is 10 5 years N 5 IN 10 FV 500 CPT PV 31046 10 years N 10 Y 10 FV 500 CPT PV 49277 Present Value Important Relationship 11 For a given time period the higher the interest rate the smaller the present value What is the present value of 500 received in 5 years if the interest rate is 10 15 Rate 10 N 5 W 10 FV 500 CPT PV 31046 Rate 15 N 5 W 15 FV 500 CPT PV 24859 The Basic PV Equation Refresher PV FV1 rt There are four parts to this equation PV FV r andt If we know any three we can solve for the fourth If you are using a financial calculator be sure and remember the sign convention put negative sign before PV or you will receive an error or a nonsense answer when solving for r or t Discount Rate Often we will want to know what the implied interest rate is on an investment Rearrange the basic PV equation and solve for r FV PV1 rt r FV PV1t 1 If you are using formulas you will want to make use of both the yX and the 1x keys Discount Rate Example 1 You are looking at an investment that will pay 1200 in 5 years if you invest 1000 today What is the implied rate of interest Formula r 12001OOO15 1 03714 3714 Calculator the sign convention matters N 5 PV 1000 you pay 1000 today FV 1200 you receive 1200 in 5 years CPT W 3714 Discount Rate Example 2 Suppose you are offered an investment that will allow you to double your money in 6 years You have 10000 to invest What is the implied rate of interest Formula Calculator Discount Rate Example 3 Suppose you have a 1year old son and you want to provide 75000 in 17 years towards his college education You currently have 5000 to invest What interest rate must you earn to have the 75000 when you need it Formula Calculator Finding the Number of Periods Start with basic equation and solve fort FV PV1 rt t nFV PV n1 r You can use the financial keys on the calculator as well just remember the sign convention Number of Periods Example 1 You want to purchase a new car and you are willing to pay 20000 If you can invest at 10 per year and you currently have 15000 how long will it be before you have enough money to pay cash for the car Formula Calculator Number of Periods Example 2 Suppose you want to buy a new house You currently have 15000 and you figure you need to have a 10 down payment plus an additional 5 of the loan amount for closing costs Assume the type of house you want will cost about 150000 and you can earn 75 per year How long will it be before you have enough money for the down payment and closing costs Table 54 PV Present value whai future cash ows are worth today m qum valu what cash laws are warm in the futura r Intareal rate rate of return m discount rate per period typically but nm always one year t Number 01 Mods typically but not always the number 91 years 0 Gash amount Emails E cxn f me term 1 isqalled39 rp39 mm w iua fhcron m E mmmm Bmazmrm PV 2 cm r39 The arm 1 m n is called the present value factor quot M r avmggm39 22 Chapter 6 Discounted Cash Flow Valuation Future and Present Values of Multiple Cash Flows Valuing Level Cash Flows Annuities and Perpetuities Comparing Rates The Effect of Compounding Loan Types Multiple Cash Flows FV Example You think you will be able to deposit 4000 at the end of each of the next three years in a bank account paying 8 percent interest You currently have 7000 in the account How much will you have in three years In four years Find the value at year 3 of each cash flow and add them together FV3 7000 18 A3 400018quot2 400018quot1 881798 48 488580 4320 4000 2180358 Value at year 4 1 Multiple Cash Flows PV Example 1 You are offered an investment that will pay you 200 in one year 400 in two years 600 in three years and 800 in four years You can earn 12 percent on very similar investments How much is this investment worth today PV Example 1 Timeline O 1 2 3 4 200 400 600 800 17857 31888 42707 50841 143293 Multiple Uneven Cash Flows Using the Calculator Another way to use the financial calculator for uneven cash flows is to use the cash flow keys Press CF and enter the cash flows beginning with year 0 You have to press the Enter key for each cash flow Use the down arrow key to move to the next cash flow The F is the number of times a given cash flow occurs in consecutive periods Use the NPV key to compute the present value by entering the interest rate for I pressing the down arrow and then computing the answer Clear the cash flow worksheet by pressing CF and then 2nol CLR Work Multiple Cash Flows PV Example 2 You are offered the opportunity to put some money away for retirement You will receive five annual payments of 25000 each beginning in 40 years How much would you be willing to invest today if you desire an interest rate of 12 Formula Calculator Multiple Cash Flows PV Example 2 Timeline 39 40 41 42 43 44 2 0 0 0 0 25K 25K 25K 25K 25K 1 l l 0 Notice that the year 0 cash ow 0 CF0 0 The cash ows years 1 39 are 0 C01 0 F01 39 The cash ows years 40 44 are 25000 C02 25000 F02 5 Annuities and Perpetuities De ned Annuity finite series of equal payments that occur at regular intervals If the first payment occurs at the end of the period it is called an ordinary annuity If the first payment occurs at the beginning of the period it is called an annuity due Perpetuity infinite series of equal payments Annuities and Perpetuities Formulas Perpetuity PV C r Annuities 739 I 1 1 PV 2 C 1rt Cx1 PVIFrt FVC1rt 1Cgtlt FVIFrt 1j 739 739 Annuities Calculator You can use the PMT key on the calculator for the equal payment Use period interest rate The sign convention still holds Annuity Example 1 After carefully going over your budget you have determined you can afford to pay 632 per month towards a new sports car You call up your local bank and find out that the going rate is 1 percent per month for 48 months How much can you borrow Formula Calculator Annuity Example 2 Suppose you win the Publishers Clearinghouse 10 million sweepstakes The money is paid in equal annual endof year installments of 33333333 over 30 years Ifthe appropriate discount rate is 5 how much is the sweepstakes actually worth today Formula Calculator Annuity Application You are ready to buy a house and you have 20000 for a down payment and closing costs Closing costs are estimated to be 4 of the loan value You have an annual salary of 36000 and the bank is willing to allow your monthly mortgage payment to be equal to 28 of your monthly income The interest rate on the loan is 6 per year with monthly compounding 5 per month for a 30year fixed rate loan How much money will the bank loan you How much can you offer for the house Finding the Payment Suppose you want to borrow 20000 for a new car You can borrow at 8 per year compounded monthly 812 66667 per month If you take a 4year loan what is your monthly payment Finding the Number of Payments You ran a little short on your spring break vacation so you put 1000 on your credit card You can only afford to make the minimum payment of 20 per month The interest rate on the credit card is 15 percent per month How long will you need to pay off the 1000 Finding the Rate Suppose you borrow 10000 from your parents to buy a car You agree to pay 20758 per month for 60 months What is the monthly interest rate Annuity Finding the Rate Without a Financial Calculator Trial and Error Process Choose an interest rate and compute the PV of the payments based on this rate Compare the computed PV with the actual loan amount If the computed PV gt loan amount then the interest rate is too low If the computed PV lt loan amount then the interest rate is too high Adjust the rate and repeat the process until the computed PV and the loan amount are equal Future Values for Annuities Suppose you begin saving for your retirement by depositing 2000 per year in an IRA Ifthe interest rate is 75 how much will you have in 40 years Formula Calculator Perpetuity Example Perpetuity formula PV C r Example Suppose the Fellini Co wants to sell preferred stock at 100 per share A very similar issue of preferred stock already outstanding has a price of 40 per share and offers a dividend of 1 every quarter What dividend will Fellini have to offer if the preferred stock is going to sell Summary Table 62 PV Present va ue what futme cash flaws are With today FV Future value what cash ows ave worm in the tmure r Interest rate rate El f return or discount rate per pe odtypicalm but nut always one year t Number of periods typically but not always the numbar of yams C Cash amount IuwaEfizx bis E7131 t t 39 bifify i iif i i m 39Fwacuu An39v11xr A seriaabfjdao w cash ws39ifs39calf adan enmity and ma temp In 39 r 1m is called mg mnmmmtm dm cw 39 The term 1 1m d1 is called the annuity present varue factor A Bl I 3939 IF 5 6 A pmia m y has39thesama ca h ow forever Effective Annual Rate EAR This is the actual rate paid or received after accounting for compounding that occurs during the year If you want to compare two alternative investments with different compounding periods you need to compute the EAR and use that for comparison Annual Percentage Rate This is the annual rate that is quoted by law By definition APR period rate times the number of periods per year Consequently to get the period rate we rearrange the APR equation Period rate APR number of periods per year You should NEVER divide the effective rate by the number of periods per year it will NOT give you the period rate Computing APRs What is the APR if the monthly rate is 5 What is the APR if the semiannual rate is 5 What is the monthly rate if the APR is 12 with monthly compounding Computing EARS Example 1 Suppose you can earn 1 per month on 1 invested today What is the APR How much are you effectively earning Suppose if you put it in another account you earn 3 per quarter What is the APR How much are you effectively earning the APR is the same in either case but your effective rate is different EAR Formula APR m III EAR 1 1 Remember that the APR is the quoted rate m is the number of compounding periods per year EARExample 2 You are looking at two savings accounts One pays 525 with daily compounding The other pays 53 with semiannual compounding Which account should you use First account Second account Computing APRS from EARS If you have an effective rate how can you compute the APR Rearrange the EAR equation and you get APR 2 m 1 EAR1 1 APR Example Suppose you want to earn an effective rate of 12 and you are looking at an account that compounds on a monthly basis What APR must they pay Continuous Compounding Sometimes investments or loans are figured based on continuous compounding EAR eq 1 The e is a special function on the calculator normally denoted by ex Example What is the effective annual rate of 7 compounded continuously