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# FI305 Lecture Notes #1 (1)

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FIN305 Survey of Finance Lecture Notes 1 pring 2015 Someone is sitting in the shade today because someone planted a tree a long time ago Warren E Buffett Chapter 1 Financial Management What is Finance The art and science of managing wealth Using financial data to make sound decisions gt wealth creation Is it accounting Financial management the activities that create or preserve the economic value of the assets of either an individual or corporation Areas of Finance 1 Corporate Finance set of financial activities that support the operations of a business its use of money and those decisions that affect the wealth of its owners 2 Investments buying and selling of both real assets amp nancial assets stocks amp bonds placing a proper valuation on them 3 Financial Institutions amp Markets the intermediaries which facilitate the cycle of money markets are where this occurs Purpose of Financial Markets to allocate capital from investors wishing to save to rms wanting to invest Financial S Intermediaries S Investors Businesses Lenders Borrowers If You Win the Mega Millions Jackpot Don39t Take the Annuity Business Insider July 2012 Chipotle Raises Prices America Orders More Burritos Bloomberg Businessweek July 2014 Dollar General sweetens bid to buy Family Dollar to 80share Fortune Sept 2014 Designer Shoe Warehouse Opens New Store in Maryland April 2014 Course Breakdown 1 Tools amp Analysis Financial Statement Analysis Time Value of Money 2 Valuation Valuing the financial securities of companies stocks amp bonds How will the company finance its operations 3 Capital Budgeting Evaluation and selection of the projects in which the company will invest How will the company allocate its capital Objectives of Sound Financial Management Allocating the firm s capital toward high return investments l Maximize profits and cash flow of the company i Maximizes the value of the firm quotA lot of people love OREOs So their manufacturer is making lots of money That means more dividends for 2 shareholdersquot Maria Bartiromo Chapter 2 Financial Statements Where to nd Company Financial Statements quotDo you know the one thing that gives me pleasure It s to see my dividends coming inquot JD Rockefeller SEC Website httpwwwsecgovedgarsearchedgarcompanysearchhtml YahooFinance wwwfinanceyahoocom Components of the Annual ReportIOK Financial Statements STATEMENT OF OPERATIONS For the period ending December 31 2014 I l STATEMENT OF CASH FLOWS For the period ending gt December 31 2014 BALANCE SHEET December 31 2013 STATEMENT OF SHAREHOLDERS EQUITY BALANCE SHEET December 31 2014 Balance Sheet Assets Liabilities Equity Ij lili 39r EtlslitiniIr I il 39 39Lii39tS ayl E E ii l tEi i T i Im azmart Amueij liaisil iti ES A Ui t receivl E irt term lat quotIL Fire y lent IEEJELII mam Ether Itiii itEi39iT39l a ets Ttal Ttal U ili Sdthlrs39 uiw What can the Balance Sheet tell us Balance Sheet for the quotAverage American Householdquot Jill 1a 11 1 E TUE lJ39Ebili EE 5 5 533 urce JEFFES make quotTrackii gthe Hnuaehnl cl al a ce Eheet39 ThE Baaelirae Ear15m L Feb 155 What happened between 2004 and 2009 to cause such a drop in personal net worth Noticeable items How do families fund their asset purchases Let s rearrange the balance sheet accounts to think about the company in a slightly different way laments e Quart term rte i i iti ee grimterm generate reeeiee e her art term ate e I l I e il l 3 Fr el e eeui errert 2terrr1 deer her 39 terrr1 te r i ea Hetei heel eemi r1 Tetel Tetal Uebilitiee Er Steekheldare39 EQin Terminology Net Working Capital refers to the current assets and current liabilities of the firm needed to run the day today operations primarily cash receivables and inventory offset by accounts payables and accrued liabilities firms often seek bank loans to finance their working capital needs NWC Current Assets Current Liabilities Fixed Capital generally refers to the amount of Fixedlong term Assets the firm has Financial Capital represents the amount of capital the firm needs to fund its NWC and Fixed Capital amounts Net Operating Assets generally speaking equals Total assets current liabilities JFFEWt EE IEE CaEh Iii 1 Eli Halal e I 131 migratory r11119 D Ether CLr rant 35533 3 513 EDS Fl 15563 r1133 33 Tint ME 5 511 mrrmt IJ abi iti E mayam e 81 E cmma liabili es 115 123 Wearawtliabili ea 13 Emitterm 213231 2 i 1519 lg l burg Tarn 12 112 13539 Equity ED 241 T td ljetiiliti c dd da g SEE g EA nancial capital mrra t aa Darrth abilitig we Work Hg Cram tal FIHEZl Camital 39Iherefrjre rmth Fl namial Capital Eiih rmr r dt nameitself Which company finances its current assets most efficiently How does each company finance its remaining assets Income Statement A typical Income Statement will look like this iii1 r r illi 0H5 EEIEE 1 ii EDS Di EDECiEECid 7 ii GCEEFirD t CperatirigEmenaea rati 1 J Ii ii39TEfE 39i iii i Intereat Iii438F193 Ii ii39T39Ef Ea r39ii r1 Baf e TEHEE TEEES JI39Earr i I TERMINOLOGY a Top Line b Bottom Line c Margins Gross margin Operating margin Net margin d Tax rate A Word about Depreciation amp Amortization Expense Remember depreciation is a noncash expense 8 If not stated separately on the Income Statement you have to nd it on the Statement of Cash Flows discussed later Analysts are constantly using the depreciation gures when calculating cash ow numbers Another way to look at it so as to separate out the Depreciation lm Player 1amp5 El e S that of 330 31421 DEE Firij t Eell itquotl General a d r1i grime Earner 5amp5 Eami e jre Intereat Teratea redatitjn m tmationl l Genre Hio mrtizati rr1 Ea i efore IF ItEFEEt rTEIEGEE El U El II E rati A J I mme Intere Ema 1E EEI T39Ii HABe ijre TarE5 al e TEEGE e I me Tame Net I mmef F39I l l 2 TERMINOLOGY EB IT EB ITDA Is Net income the same as Cash Flow calculating Operating Cash FIOW use this way when doing your homework Net Income EBIT Plus Depreciation Plus Depreciation Plus Interest EXpense Less Taxes Operating Cash Flow Operating Cash Flow Another more technically correct method of calculating Operating Cash Flow Net operating income after taX NOPAT Operating income 1 taX rate Operating cash ow NOPAT Depreciation 10 Statement of Retained Earnings The Statement of Retained Earnings is simply a rollforward of the retained earnings account for the year It is affected by the profitability of the firm net income and the amount of profits paid out to the shareholders dividends Profits accrue to the owners of the firm The shareholders and management decide what to do with profits Profits can be paid out to shareholders in the form of a dividend 0 or they can be retained by the firm to finance the purchase of new assets We use the Statement of Retained Earnings to find the amount of dividends paid out by the firm Statement of Retained Earnings Retained earnings beginning of the period Plus Net income Less Dividends paid to shareholders Retained earnings end of the period Dividend payout ratio refers to the percentage of net income which gets paid out to the shareholders in the form of a dividend Dividend payout ratio dividends paid net income IV Statement of Cash Flows Skim Section 22 in book but don t spend a lot of time on it Purpose Measures the amount of cash generatedused by a business in a given year Details the sources and uses of cash that a company has Simply answers the question What caused the cash balance to go updown Re ects activity from both the Balance Sheet and Income Statement There are three sections of the Statement of Cash Flows Operating Activities Details the amount of cash generated by the operations of the company along with changes in working capital levels Net Income Usually a source of cash Plus Depreciation Source of cash 11 PlusMinus various operating items Source or use of cash or PlusMinus Changes in Working Capital Accounts Source or use of cash or Cash Provided by Operating Activities Usually a source of cash You add back depreciation since it was a noncash eXpense on the Income Statement Changes in Net Working Capital 0 negative change in net working capital increase in cash source of cash 0 positive change in net working capital decrease in cash use of cash 0 If inventory goes up it was a use of cash as you built inventory levels 0 If receivables go down it was a source of cash as that money was collected 0 If payables go down it was a use of cash as you paid your bills down Investing Activities Details the amounts invested in property plant and equipment capital expenditures along with any proceeds from the sale of assets Capital eXpenditures Use of cash Proceeds from the sale of assets Source of cash Cash Used by Investing Activities Usually a use of cash 0 Almost all companies have some reinvestment into the business in the form of capital expenditures 0 Pay attention to the level of capeX relative to the level of depreciation being added back 0 Investing activities is almost always a negative number unless the company divested of something sizable Financing Activities Details amounts borrowed or repaid on debts dividends paid and amounts receivedpaid by issuingbuying back company stock Proceeds from issuing new debt Source of cash Repayments made on debt Use of cash Dividends paid to shareholders Use of cash Proceeds from issuing new common stock Source of cash Purchase of common stock in the marketplace Use of cash Cash ProvidedUsed by Financing Activities Can be either a source or use of cash 12 0 When old debt gets paid off by issuing new debt refinancing the two cancel each other out 0 This section is usually a negative for successful companies as they pass out the cash operations has generated to their shareholders or by paying off debt 0 Will be positive for companies still growing fast need additional financing to grow the business since the cash generated by the operations isn t sufficient to fund all of needs Here is a real life Statement of Cash Flows for Panera Bread FY2011 Iii 3931 ii i r i iiiu n I39 ii 139 J Flues fre39n Emelij Net I cer re 155555I eer39eeietier39i er39iel er r ner39tizeti er391 31mg efer39r39eel ir39ieer r e texee LE1 efer39r39eel rer39it El l her i ter e 13151 e me i F et we ei g Eleni tel ecceuet leel emcee Heeeieelelee frer freriehieeee 16355 Imer iteri ee EH1 Preeeiel exeer ie ee 1323 cee Lmte peggelel e 551 eel exeer39ie ee 153 IDFHe eaeew Flm39i ddi tier15 te ereeertveriel eeLii erreel in l l i ieuiei tier15 elf ether eerrpe iee all31252 Llsmm lm irg iii 15213 ll Hm 39 n ra reg x e ti e geei Le gter mnelelet Reeur39cheee ef terreerw39e CDFFFFDF I eten 555335 i39eieri eue etheriter r e 531 Usaiin 51351 EH Em iminm EEJEQE CESl IJEIEglFIFIlFIngDEFl eel Celel39i er39iel ef eerieel 2221mm 13 llicgyr I Eer E l g Net i ricer r e JEi Debreci eti DH 512i Cher1amp5 ir391 wedj g Eleni tel cmurlte receivable Elli miter1m r H cmurlte beyebl e 3 cmed liebi liti ee Ei Cepi tel eme eli turee E233 Net breeeede fmmtbe eele bf eeeete 35h Llsmw lm i i2 Ftebey r e t bf debt ii leeuer39lce bf HEW debt leeuer39lce at New St ck Ir Dieielerwde beiel tb eber39ebbl eler39e E15 Gash E31 5 Celeb beler lce beg39 bbi gbftbeberi eel 2 ash Hate Hid the ex 5 Is the company s operations generating cash How did net working capital change during the period How much did the company invest in new assets How did the company s financing change during the year Did the company pay dividends during the year 14 CALCULATING FREE CASH FLOW Free Cash Flow FCF Cash Flow from Operations Capital Expenditures OR Operating cash ow Capital expenditures Change in NWC Defined as the amount of cash left to payback its owners or creditors Metric often used in valuing a business Comprehensive Problem Using the condensed balance sheet and income statement below along with the Statement of Cash Flows from page 14 for Panera FY2011 calculate Fi ll arrawtaaaaza 325 593 N t W rkln It Dtha aaaaE E DlJEQ e 0 9 cap a Tatal aaaaza LDEEEEE Garraat i alai iti E 238334 aura Lawatamliaailiug Baal NEt Operat39ng Assets T tal i abilitiE FEE 15 aarahzal aaa amitf EEDEE T tal Uabili ag uw 1321322 EZEIZEITIEIT Gross margin F ll Trial Salea 1U53EE ad a f 1 12d and aaaa Ma a dEd lril Daaanarw 115330 Gawaral ar aar 39 Hauauva aaziaaaaa 113383 Net margin Dazraaiatiaaar E Crtha aE a a naa ana Di 39ati E 1 EEDEEE m m I T Operating Cash Flow Inta sEtam a a a2 Crtha F39EIJ HEIiFFElfamp EWSEit TE MISSquot Earni Ea ara Taaaa 21aaaa NOPAT Taaaa 33351 Hat inam39ra 135E352 EBITDA 15 Free cash ow FCF Chapter 14 Financial Ratios and Firm Performance Uses of Financial Statements Managers use financial statements to review and monitor the firm s performance and overall financial health Lenders use the financial statements to determine the firm s creditworthiness Stockholders and securities analysts use the financial statements to determine a firm s value to predict future performance and to analyze the stock s attractiveness as an investment Financial statement analysis is generally conducted at two levels 1 1 Comparing one firm s performance with other firms often in the same industry LDllIE39S E Home llmpmvemem Warehouse l 2 Identifying trends in the firm s financial position over time The two most common tools used in financial statement analysis are 1 2 l Commonsizing the Balance Sheet and Income statement 1 2 Calculating Financial Ratios 16 First a lesson on calculating Growth Rates Chipotle Mexican Grill Fiscal Year of stores 2010 1084 2011 1230 2012 1410 2013 1595 2014 1770 CommonSizing Financial Statements What is the growth rate in stores from 2013 to 2014 What is the compound annual growth rate CAGR over the period 2010 to 2014 17 I mua 5 l i Int Earn an data 1 lm ma Ema is Aasats C h ElamTam Imi39astmerta Hawaii a Na Ma39ckardi Crtker TIEIEI Cer39E t Pet Inf Centred ati cur1 Ether F i T tal Liabilitias E amhnl ers Equity LiEbiliti i ElamTam Matu ti asnfLTDEht Payabl E Crtker Uabil itiES TIEIEI Cer39E t IJ Ebi Iiti as LinnTerm Debt t 39 t EfilT Ether LimaTerm Liabilities Tate Uabilitiea EhEI EIF IDIIEEFSI Snub Tutsi Uabil itiESEq E aemlmra39 Equ39ty I mEEE rmI i r Int Gun suli ated El t 39l nt f Er nings NE SEES C03 cf ES GEES Prc t Ellir q Email ampAd ni r i xative ITEM DE 39Etj ati m ElmHaj ml mee T I t 39 Ear39r39i ET EES Mme TEEE Primi 539 cm we Fquotiquotr 2 13 1 15 312 533 13335 3214 1 an 32F32 I 6 43 5 433 52 SEE L 131EEE 1 31 11 3 3232 FquotiIr REE 5341 34341 1346 12355 5 511 1 4 145i 4E 1I 12mm mun E E 113 El 53 El 32 1 31 3145 E3 65 4 34 l EFJ E 113 El 15 1533 1343 312 3331 5 33 E33 353 l Elam mun E E 1m Ema mam 3459 E4IE 13333 2 34 E was a was a x 2 name 4 H39s393 What can we learn from common sized financials Ratio Analysis 18 Liquidity Ratios Current ratio Current assets Current liabilities Quick ratio Acid Test Current assets inventory Current liabilities Cash ratio Cash Current liabilities Purpose Gives an indication of the company s ability to meet its shortterm obligations Interpretation The higher the current ratio the more liquid is the company the more able to pay its bills but a wellrun company likes to keep its current ratio in the range of 10 15 as too high a number may mean they have excess assetscapital lying around Solvency Financial Leverage Ratios Debt ratio Total liabilities Total assets Debttoequity ratio Total liabilities Stockholders equity Financial leverage also equity multiplier Total assets Stockholders equity Times interest earned ratio EBIT Interest eXpense Cash coverage ratio EBIT depreciation Interest eXpense Purpose Indicates how leveraged the company is how much debt does the company have Measures whether the company can meet its longterm debt obligations interest expense Interpretation Debt ratio normally 4060 above 60 considered more risky below 30 very safe Financial leverage usually between 15 20 Close to 30 considered more risky Profitability Ratios Gross profit margin Gross pro t Sales Operating profit margin Operating profit Sales Net profit margin Net income Sales Return on assets ROA Net income Total assets Return on equity ROE Net income Stockholders equity Purpose Measures the profitability of the firm Measures how efficiently a company turns its assets and sales into profits Gross profit margin tells you how much a company marks up its product Formula for calculating markup Markup Revenue Cost of Sales 1 Operating margin tells you how much the operations of the business are earning before taX 0 When comparing companies this is the ratio which you should use applestoapples 0 Is unaffected by the firm s capital structure or taX situation Net margin tells you the ultimate profitability of the company 0 However it is greatly affected by the capital structure of the firm interest costs and taxes Company Ticker Gross Operating Return on margin margin Assets Caseys gas CASY Caseys grocery CASY Colgate CL Microsoft MSFT Lowes LOW Zales ZLC Chipotle CMG Briggs amp Stratton BGG 20 Southwest LUV Airlines Apple AAPL Whole Foods WFMI M a rket Waste WM M a n a g e me nt Starbucks SBUX Dupont Analysis Purpose To better understand a firm s performance by breaking down the Returnonequity ROE calculation into its three components Operating e iciency as measured by its net profit margin Asset management e iciency as measured by asset turnover Financial leverage as measured by the nancial leverage Net Income Sales Net Income Return on Assets ROA X Sales Total Assets Total Assets Net Pro t margin Asset turnover Net Income Sales Total Assets Net Income Return on X X Equity ROE Total Sales Total Assets Total Equity equity 21 Net pro t margin Asset turnover Financial leverage Comparison of Returns across various companies Net X Asset Return on X Financial Return on Margin Turnover Assets Leverage Equity Franklin Electric 86 095 817 182 149 Whole Foods Mkt Cerner Lowes 43 163 701 254 178 Home Depot Target 27 157 424 283 120 Walmart Chipotle 102 175 1785 132 236 Starbucks Panera Bread Interpretation 22 These ratios help measure how efficiently a company manages its assets Asset Management Activity Ratios Inventory turnover Cost of goods sold Inventory Days sales in inventory 365 Inventory turnover Receivables turnover Sales Receivables Days sales in receivables 365 Receivables turnover Total asset turnover Sales Total assets Inventory Turnover indicates how many times the company s inventory is turned each year 0 it costs money to have inventory sitting on the shelf ie car dealer jewelry store 0 every time you sell an inventory item you presumably make a profit Thus the higher the number of turns the better Days in inventory the number of days inventory is on hand until it is turned Days in Company Inventory Cabelas Kroger McDonalds DSW 23 Lowes Zales Costco Receivables Turnover conceptually hard to comprehend Days in Receivables indicates how long on average it takes to collect a receivable 0 remember you re financing your client s purchases from you 0 sooner collected the better as default risk looms 0 those never collected are direct hits to the company s bottom line 0 need to use Credit Sales if company splits it out for you Asset Turnover answers the question How much sales are generated by our asset base PerStore calculations can be interesting as well of stores 394 Revenue 2231000000 Cost of sales 1120400000 Inventory 55 305849000 of pairs of shoes per store 24000 DESIiGNI lRHE WAREHUSE a Calculate the average annual Revenueperstore b Calculate the average Inventoryperstore c Calculate the average cost per pair of shoes d Calculate the average markup which DSW enjoys 24 e Calculate the average selling price per pair of shoes f How many pairs of shoes does DSW sell in a store each day on average of stores 1595 Revenue 3214000000 Avg ticket price per customer a Calculate the average annual Revenue per store b How much Revenue does the average store make in a day c Then how many customers are going through a Chipotle each day on average Does it make sense Chapter 13 Working Capital Management Section 131 132 only Terminology Current assets Cash and assets that convert into cash within a one year time period Current liabilities Obligations that must be paid within one year this includes ST Debt Current ratio Current assets Current liabilities Working capital generally refers to a company s current assets cash NR inventory Net working capital Current assets Current liabilities The Working Capital Cycle Jan 15 Buy Inventory on Account Cash Effect Inventory 100 Accounts payable 100 25 Feb 15 Sell the Inventory to a customer who charges it Accounts Receivable 150 Sales 150 Cost of goods sold 100 Inventory 100 Feb 15 Pay your accounts payable balance Accounts Payable 100 Cash 100 Mar 315 Collect your accounts receivable Cash 150 Accounts Receivable Jan Mar Production Cycle Collection Cycle V V V Payables cycle Cash Conversion Cycle the length of time between actual cash expenditures used to pay for productive resources ie materials and labor and actual cash receipts from the sale of products or services Cash Average Average 26 Conversion Production Collection Payment Cycle Cycle Cycle Cycle V of days to convert of days to convert of days until purchases inventory into sales sales into cash must be paid V ii 365 365 365 Inventory Receivables Payables turnover turnover turnover NOTE Use Average Balances in denominator when calculating turnovers for homework Example 27 e i5 Inc 11 l H It 1 arr12 Fltrn 31381 Baal 1 EJi El n rts eiyable E l Imenta eg 3234 fin rtapayatle and aedliajilitieg EEE Fltrn Wilm t Ed ea 4253 Eta E31 macdam d Calculate the Average Production Cycle l 13855 115423 BEBE Calculate the Average Collection Cycle Cash Conversion Cycle Calculate the Average Payment Cycle 28 Comparison with other companies Eagle h h39 1 Materials Zales Payless S oes C 1pm e Avg Production Cycle Avg Collection Cycle Avg Payment Cycle Cash Conversion Cycle Things to do to improve your cash conversion cycle 1 Speed up receivables collection 2 Slow down payments to suppliers 3 Improve inventory management Evaluating Payment Policies When a company issues credit to its customers it then must decide credit terms when the company requires payment and what reductions to the bill are available in return for early payment Invoice Credit Terms 210 net 60 for a 1000 invoice Translation 2 discount if paid within 10 days otherwise full amount is due in 60 days from the invoice date L r T i 10 days 60 days 980 1000 Options pay 980 within 10 days or pay 1000 in 60 days Decision Calculate the implied interest rate you re being charged if you pay later 29 So would this cause you to pay early Chapters 3 amp 4 Time Value of Money TVM Compounding going from Present Value to Future Value I money grows in value over time I therefore a dollar today is worth more than a dollar tomorrow I earning interest on your interest compounding is the foundation of TVM Single period What is the value of 1000 invested at 10 for one year N 1 year l 1000 Future Value FV Mathematical Formula FV PV 1 r 0 Five Components of Time Value of Money Calculations Present Value PV Interest Discount Rate r or IY 30 Number of Periods N Future Value FV Payment PMT Multiperiod What is the value of 1000 invested at 10 compounded annually for three years N 3 years l cm L 1000 Future Value Mathematical Formula FV PV 1 r A 11 Compound interest the interest you earn in subsequent periods is on the interest already received in previous periods 31 Beginlniln1 Belenee eetumuleted Interest lllnterestt an Primeipam Interest e01 Interest Ending Belenee 11000 1 10000 0 00 11000 Year 2 11000 1000 1000 100 12100 Year 3 12100 1 2100 1000 210 13310 Year 0 13310 3310 10 331 14001 Veer 1041 1000 404 10L05 Veer 10105 5105 1000 011 12210 Year 1711 15 1000 EN 04 8 Year 8 10402 048 1000 000 21 Veer 21030 11213E 1000 1103 23570 What is the value of a 20000 investment in a bank CD earning 8 compounded annually at the end of 5 years N 5 years 20000 Solving problems with a financial calculator T11 Celeuleter Keys Exeell Spreadsheet 0000010 Names Variable Number 0f periods N Nper W 10011 ual rate Rate 11001110010 rate Interest rate Present 103111113 PM 00 Payment PIMT Pmt Future value F0 F0 32 Example You want to know how much money you will have accumulated in your bank account after 4 years if you deposit all 5000 of your high school graduation gifts into an account that pays a fixed interest rate of 5 compounded annually You leave the money untouched for all four of your college years Inputs to your Calculator El III Solve E D Inputs for solving with a calculator 33 Solve using Excel spreadsheet Nr 4 5 REE El 393 P t El El FEE Example You have seen your dream house which is currently listed at 300000 but unfortunately you are not in a position to buy it right away and will have to wait at least another 5 years before you will be able to afford it If house values are appreciating at the average annual rate of in ation of 5 how much will a similar house cost after 5 years El III Solve E D Computational Practice Calculator a Future value of 10000 invested at 5 compounded annually for 5 years 34 b Future value of 10000 invested at10 compounded annually for 5 years c Future value of 10000 invested at 10 compounded annually for 20 years d Future value of 20000 invested at 10 compounded annually for 20 years Present Value Interest Rate Time Period Future Value III El IIZI 10000 5 5 10000 10 5 10000 10 20 20000 10 20 Discounting going from Future Value back to Present Value I Bringing an amount of money in the future back to its present day value Single period How much money do I need to invest today in order to have 5000 at the end of one year assuming I earn 7 interest compounded annually 11 1 year Present Value 5000 Mathematical Formula PV FV1r 35 Multiperiod How much money do you need to invest today in order to have 20000 in 3 years assuming you can earn 8 interest compounded yearly N 3 years l l Present Value 20000 Mathematical Formula PV FV1r A N Example Let s say you just won a jackpot of 50000 at the casino and would like to save a portion of it so as to have 40000 to put down on a house after 5 years Your bank pays a 6 rate of interest compounded annually How much money will you have to set aside from the jackpot Winnings in order to achieve your 40000 goal in 5 years El III Solve E D 36 Computational Practice Calculator a Present value of 80000 assuming annual interest rate of 5 over 5 year period b Present value of 80000 assuming annual interest rate of 10 over 5 year period c Present value of 80000 assuming annual interest rate of 10 over 10 year period d Present value of 160000 assuming annual interest rate of 10 over 10 year period Present Value Interest Rate Time Period Future Value IQ El Cl 5 5 80000 10 5 80000 10 10 80000 10 10 160000 SemiAnnual and other Compounding Periods see Ch 5 section 52 pg 118122 All of the examples up to this point have involved the annual compounding of interest In the real world interest rates are often compounded more often than once per year By convention interest rates are quoted on an annual basis An interest rate quoted on an annual basis which is compounded more often than once per year is called a nominal rate stated rate quoted rate or annual percentage rate APR What do you do when the problem involves semi Annual or another compounding period r r110m m where 0 r the rate per period 0 r110m the nominal rate or stated or annual percentage rate and 37 0 m the number of compounding periods per year Thus 0 a 12 nominal rate compounded monthly a periodic rate of 1 per month 0 a 6 nominal rate compounded quarterly a periodic rate of 15 per quarter 0 a 10 nominal rate compounded semi annually a periodic rate of 5 per half year 0 Three of the TVM variables PMT N IY must all re ect the same periodic value Thus if the interest is compounded at semi annual intervals N must re ect the number of semi annual periods in the payment stream and IY must re ect the semi annual rate of interest called the periodic rate Compounding Annual Nominal Periodic Rate Time Periods What if 3 year Interval Rate in lyr E time frame E Annual 12 SemiAnnual 12 Quarterly 12 Monthly 12 Example You want to know how much money you will have accumulated in your bank account after 4 years if you deposit all 5000 of your high school graduation gifts into an account that pays a fixed interest rate of 5 compounded semiannually You leave the money untouched for all four of your college years Inputs to your Calculator El III Solve E D 38 Example Let s say you just won a jackpot of 50000 at the casino and would like to save a portion of it so as to have 40000 to put down on a house after 5 years Your bank pays a 6 rate of interest compounded quarterly How much money will you have to set aside from the jackpot winnings to reach that goal El III Solve E D Computational Practice Calculator a Future value of 10000 invested at 10 annual percentage rate compounded semiannually for 8 yrs b Present value of 50000 assuming 7 nominal rate compounded quarterly for 10 years c Future value of 25000 invested at 6 nominal rate compounded monthly for 3 years Compounding Annual Interest Rate Years of periods Present Value Future Value Interval Rate a D D Semiannually 10 8 10000 Quarterly 7 10 50000 Monthly 6 3 25000 Series of Payments Time Value of Money Chapter 4 material Up to this point we have been dealing with single lump sum payments However many assets provide a series of cash ows over time annuities and many obligations such as car loans and mortgages require a series of payments to be made Compounding Future Value of an Uneven Series of Payments Example If you were to receive the amounts below at the times specified how much would your account grow to assuming you earned 5 annually on your balance 39 WE 050000 0quot 0 00020000 03000 x 1 0531 V 03530750 a 313000 105Z 1r 139 231525 14022031 Solve for each payment separately and sum up Present Value Interest Rate Time Period Future Value 2000 5 3 3000 5 2 4000 5 1 5000 5 0 Total Compounding Future Value of an Ordinary Annuity Equal Payments What is the future value of a series of 1000 payments for 5 years at 6 compounded annually 40 0000I 01000l L000 1j000l 1000 1l39UU 39U 0000 gtlt 100 100000 quotquot i000 10622 112360 quotquot1 quot7 000001063 01019102 F 2 0000 gtlt 100l 2 563010 Mathematical Formula FV PMT 1rn 1 r Example Jill will be depositing 2000 at the end of each year for the next 10 years into an account that pays 8 compounded annually How much money will she have accumulated in the account Inputs to your Calculator El III Solve E D 41 Discounting Present Value of an Ordinary Annuity Equal Payments Example Depiction of the present value of 250 ordinary annuity for 4 years discounted at 8 TD Ti 52 50 2 5 250 253 1031 L032 1033 LIBS4 23 L4 3 4 1 2 1 433 i l 9846 VETl 336 i if 32303 Mathematical Formula Example John wants to make sure that he has saved up enough money prior to the year in which his daughter begins college Based on current estimates he figures that college expenses will amount to 40000 per year for 4 years ignoring any in ation or tuition increases during the 4 years of college How much money will John need to have accumulated in an account that earns 7 per year just prior to the year that his daughter starts college El III Solve E D Year 1 Year 2 Year 3 Year 4 Beginning balance 42 Earnings 7 Annual college costs 40000 40000 40000 40000 Ending balance One Equation 5 Variables Recognize that all of these Time Value of Money problems involve 5 variables with one being unknown To this point we have been solving for either Present Value PV or Future Value FV But any of the 5 variables could be listed as the unknown in a problem so you need to know how to solve for the unknown using your calculator Sample problems 1 Your parents will retire in 18 years They currently have 250000 and they think they will need 1000000 at retirement What annual interest rate must they earn to reach their goal assuming they don t save any additional funds Present Value Interest Rate Time Period Payment Future Value III El III 2 Martha wants to save up 100000 as soon as possible so that she can use it as a down payment on her dream house She figures that she can easily set aside 8000 per year and earn 8 annually on her deposits How many years will Martha have to wait before she can buy that dream house Present Value Interest Rate Time Period Payment Future Value III El III 3 You want to buy a car and a local bank will lend you 20000 The loan will be fully amortized over 5 years 60 months and the nominal interest rate will be 12 with interest paid monthly What will be the monthly loan payment Present Value Interest Rate Time Period Payment Future Value III El III 43 4 John needs to borrow 10000 to cover certain college expenses The bank will loan him the money with the understanding that John will repay them with a lump sum of 1486414 principal plus accrued interest in five years Given these terms what is the annual interest rate charged on the loan assuming annual compounding Present Value Interest Rate Time Period Payment Future Value III El III 5 You desire a car and can afford a monthly payment of only 400 Your bank will finance the car for 5 years with a nominal interest rate of 600 What is the most eXpensive car you can purchase assume you cannot put any money down on the purchase Present Value Interest Rate Time Period Payment Future Value III El III Perpetuity a neverending annuity pg 92 To calculate the value of a never ending annuity use the following formula PV PMT r Example What is the value of an asset which pays a 225 per year income stream forever if the discount related to such asset is 12 What if the perpetuity is growing PV PMT r g where g annual growth rate 44 Same example with the 225 annuity growing at 3 per year Annuity Due pg 92 An annuity due is when the annuity payments are made at the beginning of each time period whereas with an ordinary annuity the payments are made at the end of each time period A comparison a Ordinary annuity t t t i t 5000 5000 5000 5000 b Annuity due 1 t t t i 5000 5000 5000 5000 PV annuity due PV ordinary annuity 1 r 45 FV annuity due FV ordinary annuity 1 r Financial website httpwwwzenwea1thcomBusinessFinanceOnlineindexhtm 46

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