Exam 1 Fin 221 Lecture Notes PDF

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Module 1 Lecture Notes What is Finance  Finance is about making investment decisions while considering the value of these investments (time value of money and risk/return)  Goal of the firm: maximize owner’s wealth o The stockholders are the owners of a corporation. This means maximizing shareholder wealth by maximizing long-run intrinsic stock value. o The intrinsic value is the present value of the stocks future expected cash flows which is dependent upon the size, timing, and riskiness of these expected cash flows  Sole proprietorships o Easy to form, single owner, owner and manager are the same, business earnings taxed at the owner’s individual tax rate  Partnerships o Same characteristics as sole proprietorships: all owners have unlimited liability o Limited partnerships  Run by managing or general partners who have unlimited liability  Limited partners are passive investors who have limited liability: can only lose up to the amount of their investment  Corporations o Advantages  Easy access to capital markets (sell stocks/bonds to public or take loans)  Infinite life unless go bankrupt or merged by others  Owners have limited liability  Liquid corporate ownership (can easily transfer business rights) o Disadvantages  Shareholders are exposed to double taxation  Costs of running a corporation is relatively high  Most difficult (and costly) to form a corporation  Corporations suffer from potentially serious governance problems  Conflicts: Managers and Stockholders o Managers are naturally inclined to act in their own best interests (not always the same as stockholders). These factors impact managerial behavior  Managerial compensation packages  Tie their pay to the price of stocks, so their interest aligns  Direct intervention by shareholders  The threat of firing or takeover  Conflicts: Bondholders and Stockholders o Stockholders prefer riskier projects because they receive more of the upside if it’s a success. Bondholders receiving fixed payments are more interest in limiting risk o Bondholders are concerned about the use of additional debt o Bondholders attempt to protect themselves by including covenants in bond agreements that limit the use of additional debt and constrain mangers’ actions

Module 2 Lecture notes Future Value of a Single Cash  Future value: the amount to which an investment will grow after earning interest  Compound interest: interest earned on interest  Simple Interest: interest earned only on the original investment  Ex: $100 invested at 10% for 3 years o Simple interest gives us $10 each year and we end with FV: $130 o Compound gives us (100 * 1.1) + (110 * 1.1) + (121 * 1.1) = $133.10  Future value of a single cash flow o FV = PV x (1+r)n Futurama Value  Fry is in the year 2000 with $0.93 in his account that pays 2.25% compounded annually. How much does he have in his account when he is in the year 3000? o FV = 0.93 x (1+0.0225)1000 = $4,283,508,450 Future Value Relationships  There is a positive relationship between future value and time money is invested  There is a positive relationship between future value and the interest rate (high r) Present Value of a Single Cash Flow Example  Flip the equation for Present value o PV = (FVn) / ((1+r)n)  Ex: You want to send your child to a 2-year MBA program when the baby is 25. You estimated future cost to be $133,000 for year 1 and $138,000 for year 2. What do you need to deposit in an account paying 5% interested compounded annually today? o PVyear1= 133,000 / (1+0.05)25 = $39,275 o PVyear2 = 138,000 / (1+0.05)26 = $38,811 o Total deposit = $78,086 Present Value Relationships  The image on the right shows the power of high discount rates  Inverse relationship between time and present value  Inverse relationship between interest rate and present value (higher r = lower PV) Finding a Rate of Return or Interest Rate  Ex: a broker offers you an investment that pays you $1000, 10 years from now for the cost of $640 today. What is your annual rate of return? o 1000 = 640 x (1+r)10 o 1.5625(1/10) = 1+r o r = 4.564%

Time Value of Annuity Concepts  Annuities: a sequence of equal cash flows, occurring at the end of each period. This is known as ordinary annuity  Future Value of Ordinary annuity (FVAn) END – calculator o FVAn = PMT x (((1+r)n – 1) / r)  Examples of ordinary annuities o If you buy a bond, you will receive equal semi-annual coupon interest payments over the life of the bond o If you borrow money to buy a house/car, you will repay the loan with a stream of equal payment  Annuity due: a sequence of periodic cash flows occurring at the beginning of each period o Examples: case lease payments, cable and internet bills, monthly rent payments that are due at the beginning of each month Comparison of Annuity Types and Time Value Techniques  What is the difference between ordinary annuity and an annuity due   Future value of annuity due (FVA(DUE)n) BGN – calculator o PVA(DUE)n = PMT x (((1- (1/r)n ) / r) x (1+r) ) o FVA(DUE)n = PMT x (((1+r)n - 1) / r) x (1+r)  How to calculate time value annuities o 1. Use the algebraic formulas o 2. Use excel functions  Ordinary: =FV(rate, nper, pmt, pv, blank or 0)  Du e :=PV( r a t e , n p e r ,p mt , f v , 1 ) o 3 . Us efin a nc i a lc a l c u l a t et i mev a l ueo fmo n e yf u n c t i o n s  Toc h a n g et oBGN, p r e s st h ef o l l o wi n gk e y s . 2 ND, PMT( 2 ND&PMT= BGN) , 2 ND, ENTER( 2 ND&ENTER=SET) . SETf un c t i o na c t sl i k e t o g g l es wi t c ht oc h a n g eb a c ka n df o r t hf r o mENDt oBGNmo de . J us tp r e s s CE\ Cb u t t ona f t e ry o uh a v et h emo d es e t . IRA Example  Example 1: How much would you have at age 65 if you deposit $4000 at the end of each year in an IRA with 8% expected annual return starting at… (end of year = ordinary) o Age 55? (n=10)  FVAn= 4000 x (((1+0.08)10 – 1) / 0.08) = $57,946.25 o Age 22? (n=43)  FVAn= 4000 x (((1+0.08)43 – 1) / 0.08) = $1,318,332.02  Example 2: Let’s assume the 55-year-old accumulated $600,000 in the IRA. How much would they have to deposit annually at 8% expected annual return to catch up with the 22y-o and be a millionaire at 65? o Want the FV to be $1,318,332.02  600000(1.08)10 + PMT(FVA at 8%)10 = $1,318,332.02

 PMT(FVA at 8%)10 = $1,318,332.02 – 1,295,355  PMT (FVA at 8%)10 = $22,977  PMT = 1586 o On the calculator  I /Y: 8 N: 10 PV: -600,000 FV: 1,318,332  CPT  PMT Winning Mega Millions Example  Mega Millions prize was $162 million. Reported prices are the sum total of future annual payments. In this case, 26 beginning on the year annuity payments that will be paid to the prize winner. For the current prize: annual annuity payment = $162 million / 26 = $6.23 million. The winner can elect the cash option of $98 millions today instead of the 26-year annuity. Which option would you choose if you demanded a 4% annual return? o 1. PV (cash option) = $98 million o 2. PV (26-year annuity due) – shift calculate to Begin (BGN) mode  N: 26 PMT: 6.23 I/Y: 4 FV: 0  CPT  PV = 103.56 million  Algebra: 6.23 x ((1-(1/1.04)26)/0.04) x (1.04) = 103.56 million o Looking at the choices, option 2 is better  Continue the scenario above. Assume the winner elects for the cash option of $98 millions today. What is the implied interest rate of the annuity due vs $98 million cash option? Imagine investing or paying the cash option amount in order to get the annuity. o 1. BGN mode PV: -98 PMT: 6.23 N: 26 FV: 0  Compute for interest rate CPT I/Y = 4.56% Mr. Burns Retirement Planning  Mr. Burns, 85, wants to retire at 100 so he can steal candy from baby’s full time. Once he retires, he wants to withdraw $100 million at the beginning of each year for 10 years from an account that pays 20% annually. In order to fund his retirement, Mr. Burns will make 15 equal end-of-the year deposits in this same special account that will pay 20% annually. How large of an annual deposit must be made to fund Burns retirement plans? o FV(deposits) = PV (retirement benefits) o PV of retirement benefits  PMT: 100 N:10 I/Y: 20 FV: 0  BGN mode CMT PV = 503.09 million o FV of 15 deposits  PV = FV = 503.09 million  END mode  FV: 503.09 I/Y: 20 N:15 PV:0  CPT PMT = 6.98 million Module 3 Lecture notes Perpetuities  A fixed payment every period (month, year…) forever  Present Value (PV) = PMT / r o PMT = periodic cash payment r = interest rate

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Ex: you want to create an endowment to fund a football scholarship, which pays $20,000 per year, forever, how much money must be set aside today if the rate of interest is 5%? o PV = 20000/0.05 = 400,000

Time Value of Uneven Cash Flows  What is the PV of the uneven cash flow shown on the image to the right? o The PV of $100 after 1 year is $90.91 … o Adding all of the PV’s, you get 530.08 o How to do this on the Fin calc  CF  2nd Clear  down arrow  enter the cash flow for year 1  Enter  down arrow  enter frequency of cash flow 1 (how many 100 cash flows do u have? We only have 1 so we put 1 and move on)  down arrow  enter cash flow 2  down arrow  enter frequency (hit enter if u change the number)  enter more cash flows and frequencies  NPV  put in interest rate and hit Enter  down arrow  CPT (compute)  What is the FV at year 4 for this uneven cash flow stream at 10%? o FV = PV x (1+r) n o = 530.09 (1.1)4 = 776.10 Nominal, Periodic, & Effective Interest Rates  Nominal annual or simple rate (APR): an annual rate that ignores compounding effects o Written as rNOM or rSIMPLE  Periodic rate (rPER): amount of interest charged each period (monthly or quarterly)  rPER = rNOM / M o M is the number of compounding periods per year (M=4 for quarterly and M=12 for monthly)  Effective (or equivalent) annual rate (EAR = EFF%): the annual rate of interest actually being earned, accounting for compounding o EFF% for 10% semiannual investment  EFF% = (1 + (rNOM / M)) M – 1  = (1 + (0.10 / 2))2 -1 = 10.25%  Why is it important to consider effective rates of return? o Investments with different compounding intervals provide different effective returns o To compare investments with different compounding intervals, you must look at their effective returns (EFF% or EAR) o See how the effective return varies between investments with the same nominal rate, but different compounding intervals  Non-annual interest compounding o FV and PV with non-annual interest compounding  n = number of years  m = number of times interest is paid per year  rNOM = states nominal annual or simple rate (APR)  rNOM / M = periodic rate

o PV and FV with non-annual interest compounding  Single cash flow (CF):  FV = PV(1 + (rNOM / M)) MN  PV = FV / (1 + (rNOM / M)) MN o Annuities  Use periodic rate and number of annuity payment and compounding periods if interest compounding period and annuity payment period are the same. Otherwise, need to find effective interest rate for each annuity payment period Futurama example  I ma g i n eFr ykn e wi na d v a n c et h a th ewo ul db ef r o z e nf o r1 0 0 0y e a r sa n dwa nt e dt oh a v e $9 , 0 00 , 0 00 , 0 00wh e nh et ha wso u t . Ho wmu c hwo u l dFr yn e e dt od e p o s i ti nh i sa c c o u n t pa y i n g2% APRc o mp o u n d e dq ua r t e r l yb e f o r ef a l l i n gi n t ot h ec r y o g e ni cf r e e z e r ?  FV = 9B n = 1000 m=4 r = 0.02  PV = 9,000,000,000 / (1+ (0.02 / 4))4x1000 = $19.50 Finding Loan Payments  Most car and home mortgage loans are amortized loans where each periodic equal loan payment pays interest and principle on the loan  The loan amount is the present value of the annuity of periodic payments that will be made to repay the loan  Loan Amount = PMT x PVAFapr/m, mn  Apr/m = periodic interest rate = rNOM / m 

EX:Pr o f . Fi n a n c ewa n t st or e fin a nc eh i sc u r r e n t3 0 -y e a rmo r t g a g eb a l a n c eo f$ 1 4 5, 0 0 0 i n t oa1 5 y e a rmo r t g a g ewi t hafix e dr a t eo f3. 2 % APR. Wh a twi l lb ePr o f . Fi n a n c e ’ s mo n t h l ymo r t g a g ep a y me n ti fh ed e c i d e st or e fin a n c ewi t ht h e1 5 y e a rmo r t g a g e ? o N = 15 m = 12 r = 0.032 apr/m = 0.032/12 = 0.00267 o nm = 180 PV = 145,000 FV = 0 o On the financial calculator  I/Y = 2.667 N = 180 PV = 145000 FV = 0  CPT PMT  PMT = 1,015.35...