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Date Created: 02/17/15
FIN302 Chapter 4 Introduction to Valuation The Time Value of Money I First thoughts preference for current consumption 0 Sooner rather than later 0 Money ability to store and exchange value 0 Allow specialization I Timeshifting value and wealth creation 0 Key principle time affects value so we cannot directly compare money received at different times The value of a dollar today is not the same as a dollar in the future I These investments all have things in common 0 Pay a certain amount now for an uncertain future series of cash ows 0 Is value gt cost I Periods must be identical in the length I Periods in time vs points in time 0 Time affects value 0 In ation loss of purchasing power erodes the value of the dollar takes more dollars to buy the same thing appears more costly but really the dollar is going down in value I pizza example 0 Risk uncertainty repayment 0 Liquidity deferred consumption opportunity cost I Don t want to defer consumption what if anther opportunity arises I Creditors and investors must be compensated for these 0 Interest 0 Simple interest interest paid on the original amount earned interest stays the same every year earn of number given interest number doesn t change not very common 0 Compound interest earned interest becomes principal so we earn interest on prior interest the principal balance grows exponentially I Time is not a factor simple vs compound I Interest on interest compound interest will grow faster 0 Three factors that effect compound interest 0 Time non linear exponential curve 0 Interest rate same idea as time higher interest dramatically increases interest over time 0 Compounding frequency 0 Other stuff to know about compounding I Compounding period time it takes for interest earned to become interest bearing added to the principal balance I The shorter the compounding period the greater the compounding frequency 0 How long it takes to get into your account years months days I Period Interest Rate r interest rate earned per compounding period it is NOT an annualized rate unless the compounding period is one year I The periodic rate is stated in terms of the compounding period ie per month or per day 0 The periodic rate and the compounding period MUST correspond I Annual Percentage Rate APR an annualized rate 0 Equals the periodic rate times the number of periods in a year I Make annual so that one can compare to other periods Where r the interest rate per period And m the number of periods per year Example An investment pays 1 monthly What is the APR r 1 the periodic rate m 12 periods per year 1 X 12 12 APR 0 APR is not the true or effective interest rate earned It is simple interest it ignores compounding I m must be the compounding frequency implicit in the APR APR m 0 What is Future Value 0 Tell us how much a present sum of money Will be worth at some point in the future given an interest rate or growth rate I Make a table for simple problems compound year after year Future Value a Example StD D Invested stati5 gnmpnunlgleel Irinunll f This Heginrlrig mun Inwasl Elemml Enid315 Amun l 1491in alum inseam J EBJEDI 1121M tljlil EllIE2 ELM HE IJJE T1153 quotII EIJIE 326E TEES 13 t23 If yuan invested MI trade earning 6 interest what will that investment be wefth in 3 1gi39elziir39si39 airan L39 39 ramr F g umquot Where 39 Fume ranhe FLquot Emiliaquot prefEH Hwa r39 yardager re nes 5 FEE 12 52 decal115 1 39 news5 ur mquot r magiu Eug g39g a as 39quotjnrr e amilfzusa39 a PEEPu jEEE IT39 39L39r Pearm 393939 i39r39u u quot quot r and n NIUD 1 correspond Future Value a Example 1MDlnws I 5 compJuneau annually has Ellaginning annun in url Ending Amum l WEDEU EllPUD l ll HD rli Jil EEJEI HELEN EEKd2 11H1ZIE J HES IJJE quotFLHE quotI iedE THEE1H TEES 133513 If you unrealed i il ted earning 15 nilemail what will mm imaa l39m nl39 he in 3 were er WEth Fug momma 119102 Calculator 0 Time value of money keys 0 N number of compounding periods 0 IY periodic interest rate r 0 PV present value 0 PMT what happens when you have to pay a loan 0 FV future value 0 Format at the bottom 0 Change to show correct number of decimals I 2 format 9 enter 0 Shift PY 1 do not change that number continued 0 FV with NonAnnual Periods 0 The formula doesn t change Simply change r and n to correspond with the compounding frequency 0 NOTE The periodic interest rate r 1 correspond with the compounding period 0 You can substitute growth rate g for the interest rate r as long as the growth rate is constant TVM doesn t apply to money 0 Time Value of Money Present Value and Discounting O The amount of money needed today to replicate a known future sum at a given interest rate I PV tells us what a future sum is worth to us today I How much do we have to invest today to achieve number 0 Depends on how quickly grow interest growth rate 0 Solving for Present Value of a Lump Sum EH13 Tune Value Of This is the general farmule far Money Solving for time n and rates of a m 39 lump return r Remember you can I n I always substitute APRm for r 1 Note the compounding period used here FV n determines the period r used to de ne r 0 Interest rate conversion finding equivalent interest rates use the r formula above Just change the n to be annually semiannually quarterly 0 See example 792 month X 12 95 APR 0 True effective rate of return means 0 The Effective Annual Rate Section 53 0 Unlike the stated APR the EAR is the true annualized rate of return taking all compounding into account I To calculate EAR knowing a periodic rate r I where m is the number of compounding periods in a year corresponding to r the periodic rate I m does not equal 11 I they mean different things m 1 1 m 0 Annual rate to periodic rate r1EHR m 1 AFR ri m 1 EAR 1 FJM 1 APR mm EARJEMH 1 Em 1 prmquot 1 Chapter 5 Multiple Cash Flow and Discounted Cash Flow Valuation Annuities a consecutive equal stream of cash ows 3 types of annuities difference is when annuity starts 0 1 Ordinary annuity A stream of equal consecutive payments that are at the end of the period in arrears or the end of the respective period I Future value occurs at the same time as last payment Present value occurs one period before the rst payment 0 EX Loan payments lease payments 0 2 Annuity due payments are at the beginning of each period borrow money and make immediate payment I Payments are in advance Present value is at the same place at the beginning 0 EX Apartment rental payments pay rent right when you sign 0 3 Deferred annuity posted or deferred for some length of time payment stream doesn t begin for some deferred period Present value occurs one period before the rst payment except for annuity due Present value of ordinary annuity 1 1 1r WDPMT1x F 0 n of payments not the number of periods 0 PV is always one period before the first payment which is not necessarily at time zero What the practical value 0 PV How much must we invest today to replicate the future cash ows there are annuities everywhere The amount owed on any loan is the PV of all future payments due Calculating annuity payment amounts 0 EX Buy first house and borrow 300000 at 8 APR compounded monthly for 30 years I What will be your monthly payment Make sure everything is divided by or multiplied by 12 because monthly Payment 220129 per month I What is the total amount you have to pay back if you keep the loan outstanding for the full 30 years X 360 792464 I What will be the total interest you will pay over the life of the loan 792464 300000 492464 Calculating number of annuity payments 0 EX You owe 4000 on your VISA card which charges 18 APR Make payments of 300 per month how long until the balance is paid off Future value of annuity 1r 1 W PMTl x l39 Annuity Interest Rate 0 EX Lease new car Salesman offers you 48 month lease at 595 per month Car costs 35000 and think it will be worth 20000 in four years What is the implicit interest rate on this lease Assume no down payment if 12 512 APR Annuity Due PV amp FV 0 PV annuity due PV ordinary annuity 1r O FV annuity due FV ordinary annuity 1r 0 Or use BEGIN function but be careful I 2nd BGN 211d SET Perpetuities an annuity that never ends infinite stream of consecutive cash ows an infinite stream of equal payments 0 Payments are in arrears Also if you know the PV you can solve for payment or r Wu PMTl r 0 PV of a Level Perpetuity 0 Ex What is the PV of an infinite stream of 100 annual payments discounted at 5 per 39 V year if the first payment Wu quoti i is one year from todav PV of a Perpetuity in Advance 0 Growing Perpetuities an infinite stream of payments increasing at a constant rate g F l39M IT1 r39Q 0 Types of Loans 0 Discount Loans no interim payments I FV principal accumulated interest 0 InterestOnly Loans no principle amortization I Borrow 10000 pay back 10000 but every period in the middle you pay interest on the 10000 dollars The beginning and repayment are the same number 0 Original loan ending balance 0 PVFV 0 FullyAmortized Loans make interim payments of interest and principal so the loan is paid off over time I Payment principle interest I Ending loan balance 0 The sum of the principal payments original loan Wu I Installment loan fully amortized consumer loan interest and principle included Loan Amortization Schedule shows you how a loan is getting paid off over time Loan Amar zn an Schedule 5315 511me page E1161 FixedPayment Amortiiatiun Enheduie Beginning Total Interest Primipal Ending 11555 3511511155 P5 35m ant 9111 Paid Balance 1 5555 1255 155 555 2 111155 1 255 525 51 1 5255 5 5251 1 255 255 555 2251 1 2251 1 255 255 1552 11 25 1125 1255 155 1125 5 T151515 5522 H 5555l 15525225155552 2515f pay151521115 n 5211155511quot 515521551555 H5511 EJ151155 555 quot H15 quotAMSRTW fum m 511 15515 551155115155 Total interest Total payments Amount borrow 0 Shows over time how loan is getting paid off I First beginning of each period I Calculate payment I Figure out how to split the payment between interest and principal paid I Principle X interest interest I Principle paid total payment interest 0 Interest does not pay down a loan only a principal portion pays off the loan 0 AMORT function 0 Balloon Payment Loans I Incomplete amortization the balloon represents a principal balance due at the end of the loan at the end of the loan you still owe something unpaid balance so future value is some amount that you still owe I The unpaid balance due is called the balloon payment I Why would people do this 0 Very desirable from standpoint of buyer most companies prefer balloon payment loans 0 The bigger the balloon the small the monthly payment preserving cash ow FIN302 Chapter 2 Does not cover 24 cash ows Review 0 Investments are economic assets 0 Value is a function of the future 0 Business invests in economic assets to create wealth I To create wealth value must exceed its costs DCF Discounted Cash Flow Valuation investment valuation method What is a corporation 0 00000 O 0 Legal form of organization Views as a separate legal entity Limited liability to owners Potentially infinite life can be passed along May have a multitude of owners Ownership is easily transferrable stock I Publicly traded very easily in stock market I Partnership and sole proprietorship not easily transferable Double taxation corporations are taxpayers if it s a separate entity it can be taxed separately then the corporation pays you the owner because we are separate entities also getting taxed twice huge disadvantage Representative management agency also an issue representative is the BOD Public versus private ownership Public cs Private Ownership O 0000 0 Listed on a stock exchange and regulated by the SEC I Go through disclosure process I IPO and then can be listed on stock exchange and sold somewhere Easy transfer of ownership of an open market Ease of raising equity capital Initial Public Offering IPO going public Venture capital locked in to a risky long term commitment I Sharktank Private equity firms buy when potential value gt current price Levered buy out LB O taking private risk issue I Use borrowed money to invest in the equity of a company Exit strategy cashing out IPO acquisition MampA Investment Banking FIN302 Chapter 2 Financial Statements Taxes emphasis on analytical understanding 0 Financial Statements 0 Publically owned companies are required to publish financial statements quarterly IO Q and annually IO K and they must be prepared according to US GAAP O In addition to statements annual report has Management Discussion and Analysis Notes to the financial statements and an auditors opinion and a letter to shareholders from the company s chairman I A comment on Accounting 0 Accounting information there are preparers and users non accounting majors 0 Financial Statements 0 1 Balance Sheet I Financial position book values of assets and liabilities as of a point in time I Preparing a balance sheet Assets on left liabilities and equity on the right I Assets are carried at original cost less accumulated depreciation and amortization I CS is not what it is worth today I Net working capital represents a company s net capital investment in current assets Net working capital current assets current liabilities 0 Net working Capital Cash Conversion Cycle How long for a company to take cash and go through buy inventory sell inventory collect cash to cash cycle 0 Illustrates change in net working capital uctuations 0 Order inventory 0 Pay for inventory Pay vendor cash out ow at this point nothing on IS 0 Sell inventory Revenue and expense are booked still no cash 0 Collect revenue End of profit cycle 0 What does the change in net working capital represent 0 Represents a cash in ow or out ow or investment or recovery I 30000 increase in net working capital if sales going up you would expect this to go up if sales have not gone up could have some serious implications not following GAAP bad credits 0 Capital expenditures New property plant equipment 0 Must look at depreciation o 2 Income statement I 1 o f o Resu ts over a perlod o tlme 1ncome 1sn t cas I gt Memorize generic income statement ow Jl im39u I 39u 39 K10 quot 39 39 quot tilvquotth I 1 39 LJI I39 u J3 Nmxcuih EK TEE V w nepregen r39ringgrha quotquot1 L3 quot BEFF JEquotquot39339 3915 iE ni39u p n en139 quot quot 39 loss of useful life WWW m lters j i p a g Edam11 M quot T i Taifab ii Inzsm E quot h l 3939 7 HM Trm pais39 l39 u39Ae39 M353 1 mm 5 r v 1 39 hi 1191 5quot5 3quot i39u Sales COGS Gross Margin Overhead operating expenses other manufacturing costs period fixed cost EBITDA earnings before interest taxes operating expense non cash expense depreciation amortization Depreciation EBIT earnings before interest and tax aka operating income Interest Expense cost of financing EBT earnings before tax not taxable income Tax provision accrual not taxes paid not a cash item Net Income Memo Dividends paid Taxes OOO Hm InEEamaf my GAAP accrual accounting I Timing of revenue recognition I Matching principle Noncash items Depreciation amortization accrual deferral provision allowance all of which are timing differences I So you can t pay your bills with income and profitable companies can go bankrupt Liquidity How readily an asset can be converted into cash without a material loss of value ability to meet one s financial obligations Book Value vs Market Value I Market value the price at which an asset would trade in the open market its true economic worth I Book value an accounting construct based on original cost a proxy for investment 0 The two are unlikely to be the same Liquidation Value point in time sale of the pieces GoingConcern Value includes the value of the organization as a whole significance of future cash ows the first is valued as an economic asset Two sets of books financial records GAAP versus tax code Tax provision used to calculate tax expense vs tax payment Progressive Tax brackets 0 32000 represents Taaalala Iaaama Ta Hat 0 256 represents a 3 5a I 5am 1 15 Lsaa saaaa 1a n E x 25 Egg mama 1ii 250 1 ad a alsaa mama 1 33am 25m x i araa aaaaaa 1 361 325nm 1UE h 35 ja 15naaaaa nasaaaaa 3a 13331334 35 Average vs Marginal TaX I How much did you earn on taX return I The average rate paid on ALL your income 0 Marginal taX rate the taX rate applied to the next dollar of taxable income I Helps make decisions I The rate paid on ADDITIONAL income 0 Marginal income is taxed at the marginal rate Wha f is The liability an Hanan a F imam Rates L Haw mach mara Tax manila yam hava fa if E maah af The maid yaa gal fa hag What manila ha warquot aampanfs aw fatal tax lli abilli39hr it What hamns Ta yaar wiilll ngnasa Ta risk tha the tax rat is inaraasacl 0 of ows 0 4 Statement of retain d earnings
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