FIN 345 1nd EditionExam # 3 Study GuideChapter 91. Objectivesa. Identify various types of cash flow patterns (streams) that are observed in businessb. Compute (a) the future values and (b) the present values of different cash flow streams and explain the resultsc. Compute the return (interest rate) and the present values of different cash flowstreams and explain the resultsd. Explain the difference between the annual percentage rate and the effective annual rate and explain when each is more appropriate to usee. Describe an amortized loan and compute amortized loan payments and the balance on an amortized loan at a specific point during its life2. Time value of moneya. The principles and computations used to revalue cash payoffs at different timesso they are stated in dollars of the same time periodb. The most important concept in finance used in nearly every financial decisioni. Business and personal finance decisions3. Cash flow patternsa. Lump sum amount: a single payment paid or received in the current period or some future periodb. Annuity: a series of equal payments that occur at equal time intervalsc. Uneven cash flow stream: multiple payments that are not equal, do not occur at equal intervals, or both conditions exist4. Cash flow timelines: graphical representations used to show timing of cash flows5. Future value: the amount to which a cash flow or series of cash flows will grow over a period of time when compounded at a given interest ratea. How much would you have at the end of one year if you deposit $700 in a bankaccount that pays 10% interest each year?i. FVn=FV1=PV + INTii. =PV+PV( r )iii. =PV (1 + r)iv. =$700(1+0.10)=$100(1.10)=$7706. Three ways to solve time value of money problemsa. Use equationsb. Use financial calculatorc. Use electronic spreadsheet7. Numerical equationa. FVn=PV(1+r)^nThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.i. Already programmed in financial calculatorPV (present value) n (number of years)i/r (interest rate) PMT (amount of periodic payments) FV (future value)1. Cash flow patternsa. Lump Sumi. Example A: What will $1,000 invested today at 8% be worth in 12 years?1. FV - Calculate future valueii. Example B: You expect to receive $20,000 in 6 years. What is this amount today assuming an interest rate of 5%?1. PV - Calculate present valueiii. You invest $15,000 today for a home down payment. How many years will it take to be worth $20,000 if it earns 7% annually?1. N – number (of years)iv. Example D: You invest $15,000 today for a home down payment. What rate of return will you have to earn for the account to be worth $20,000 in 3 years?1. i/r - Interest rateb. Annuitiesi. Example A: If I save $500 per month what will my account be worth at the end of 7 years if I earn 4% annually? If I earn 7% annually? (84 months = 7 years x 12)1. FVii. Example B: If I want to have $20,000 at the end of 5 years, what amountdo I need to save each month if I earn 6% annually?1. PMT – Paymentiii. Example C: I want to accumulate $20,000 for a home down payment. If Iearn 6% on my investment, how long will it take to reach my goal of $20,000 if I begin saving $500 each month?1. N (of months)iv.c. Uneven Cash Flows2. Worked out example: Suppose you have $1,000 to invest for a period of 5 years at an interest rate of 10% per year. How much will you have accumulated at the end of this time period?a. Use financial calculatori. On TI-84 Calculator, click “apps,” press enter on 1. Finance, press enter on 1.TVM Solver… under CALCii. PV= -1,000iii. N= 5 yearsiv. i/r= 10v. PMT= 0vi. FV= _______ calculated automatically after entering the above informationvii. Answer = $1,610.511. Future value of an annuitya. Annuity: a series of payments of equal amounts at equal intervals for a specified number of periodsb. Ordinary (deferred) annuity): an annuity whose payments occur at the end of each periodc. Annuity Due: an annuity whose payments occur at the beginning of each period2. Present value: the value today of a future cash flow or series of cash flowsa. Discounting: the process of finding the present value of a future cash flow or series of future cash flows; it is the reverse of compoundingb. PVAn=the present value of an annuity with n paymentsc. Each payment is discounted, and the sum of the discounted payments is the present value of the annuity3. Uneven cash flow streamsa. A series of cash flows in which the amt varies from one period to the nexti. Payment PMT designates constant cash flows – an annuity streamii. Cash flow CF designates cash flows in general, both constant cash flows and uneven cash flows4. Semiannual and other compounding periodsa. Annual compounding is the process of determining the future (present) value of a cash flow or series of cash flows when interest is added (computed) once a yearb. Semiannual compounding is the process of determining the future (present) value of a cash flow or series of cash flows when interest is added (computed) twice a year5. Compoundinga. Will the FV of a lump sum be larger or smaller if we compound more often, holding the stated r constant?i. If compounding is more frequent than once per year – for example, semiannually, quarterly, or daily – interest is earned on interest.Because interest is compounded more often, the future value will be larger6. Amortized Loansa. A loan that is repaid in equal payments over its life; payment includes both principal repayment and interestb. Amortization tables are widely used to determine how much of each payment represents principal repayment and how much represents interestc. Financial calculators and spreadsheets can be used to set up amortization tables7. How are dollars from different time periods compared when making financial decisions?a. Dollars from different time periods must be stated in the same Time Value before they can be comparedb. Dollars can be translated into the same time period by computing either present value or future