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Classified Balance Sheet (11-14) – snapshot of accts on a particular date
Assets: current assets used within 1 yr e.g. marketable securities, notes receivables, accts receivables, inventories, prepaid expenses
long-term investments longer than 1 yr stocks and bonds held onto; notes receivables and accts receivables which cannot be collected within 1 yr; prepaid expenses that cover more than 1 yr
fixed assets land, equipment, furniture
intangible assets patents, goodwill
Liabilities (12) current less than 1 yr must be paid notes payable: money borrowed under promissory notes due within one yr accts payable accrued liabilities or wages: services already performed unearned revenues: amts which co will have to refund if it does not perform the services
long-term lease; mortgage due in more than 1 yr
liabilities get priority when liquidation occurs, so listed before SH’s equity secured claims: co has pledged one or more assets as collateral comes next during liquidation
SH’s Equity
Income Statement (28) – how much net worth (equity) has changed over a period
gives a summary of earnings or losses btw balance sheet dates Revenues: increase in assets, decrease in liabilities from services central to operations gains: increase in assets, decrease in liabilities from incidental txns not involving investments by owners professional income
Expenses: decrease in assets, increase in liabilities from services central to operations losses: decrease in assets, increase in liabilities from incident txns which do not involve distributions to owners
Net Income = proprietorship
Statement of Changes in Owner’s Equity (49)
Drawings: dividends or distributions SH’s Equity – 3 components (53) – used by accounts capital stock: common stock, preferred stock additional paid in capital/capital surplus: capital contributed in excess of par retained earnings – track all undistributed profits that remain invested in the corp.
SH’s Equity – 3 components (61) – used by attys stated capital capital surplus earned surplus
Legal Capital or Stated Capital (54) stated capital = issued shares X par value e.g. 1000 shares at $1 par but sold for $20 stated capital = $1,000 capital surplus = $19,000
Capital Surplus = the amt of the shares sold that exceeds the stated par value capital surplus is recorded as “additional paid in capital”
stated capital + capital surplus = the total capital that SH’s contribute to a corp. (Look to lawful dividends section for restrictions) treasury shares (repurchases shares) = issued shares – outstanding shares required par value bc ensure investors that all SHs purchased their shares for equivalent amts (cannot purchase for less than par value) but corps don’t have to bear any specified par value (p.56)
can’t distribute when paying dividends more than stated capital very nominal par value minimized the contributed capital that CANNOT be distributed to the SHs.
Shares with Par Value (57) capital stock + add’l paid in capital = corp’s total contributed capital TO FIND ISSUED SHARES – look on balance sheet and also the Capital Stock Footnote (p.59 for e.g.)
No Par Shares (60) stated value = the amt allocated to stated capital with no par amt (directors come up with this number)
Earned Capital (61) reinvested earnings by the co: repurchase shares; pay dividends Retained Earnings/earned surplus: earnings that remain invested in the co. In legal Capital system it is called “Earned surplus”
STATEMENT OF CASH FLOWS (122)
Cash flow: refers to the movement of cash into and out of the enterprise, can det the co’s financial success must have access to cash to meet “recurring expenses” → payroll, rent, pay accts payable, pay outstanding debt
Revenue form operations provide primary source of cash, but some txns not reflected in the income statement (borrowing money, paying cash dividends, purchasing long-lived assets) may significantly increase or decrease cash. a number of txns (borrowing, issuing new stock, or buying capital assets) greatly affect cash but do not appear in the income statement for the period and emerge on the balance sheet at the end of the period. Common Cash Inflows: sales for cash collection of accts receivable short and long-term borrowings sale of property, plant and equipment issuance of stock for cash
Common Cash Outflows: operating expense acquisition of property, plant, equipment or other long-term assets repayment of short and long-term debt distributions to owners
Statement of Cash Flows: reports the changes in cash and cash equivalents during acctg period and explains those changes. Purpose: (listed on p124) assess ability to generate positive future net cash flows ability to mt obligations, pay dividends, needs for external financing reasons for diff btw net income and associated cash receipts and payments asses the effects on co’s financial position of both cash and noncash investing and financing txns during the period
cash and cash equivalents: short-term, highly liquid investments cash equivalents must mt 2 requirments: co msut be able to convert the equivalents to cash readily equivalents orig maturity dates must not exceed 3 months so that changes in interest rates do not threaten to affect adversely their value
e.g. of cash equivalents: US Treasury bills, commercial paper, money mkt funds
must incl defn of cash equivalents in a related disclosure to its statement of cash flows
Classification of Statement of Cash Flows (126) 3 categories: operating activities: acquiring and selling the co’s products and services cash inflows from op activities incl interest and dividends form loans to and ownership investment in other co’s cash outflows incl cash interest payments to lenders and creditors Direct method: report major classes of cash payments and receipts 7 classes listed on p127 acctg stds require that co’s that use the direct method of reporting net cash flows form op to incl an indirect operating section in its financial statements
Indirect method: reconcile net income, prepared under accrual acctg to net cash from operations co’s that use indirect method must also disclose the amts of interests and income taxes paid during that period either on the face of the statements of cash flows or in the notes to the financial statements indirect op section must also report changes in inventory, receivables and payables
investing activities: incl acquiring and disposing of long-term investments and long-lived assets cash expenditures to acquire other co’s through merger or stock acquisition Capital expenditure: manufacturing co’s spend most on property, plan and equipement DOES NOT incl interest and dividends form long-term investments
financing activities incl obtaining of resources form owners and providing them with a return on their investment. issuance and retirement of short and long-term debt from creditors Cash outflows incl cash dividends or other distributions to owners
statement of cash flows must reconcile the total change in cash for the period with beginning and ending balances which appear on the current and prior balance sheets. NONCASH INVESTING AND FINANCING ACTIVITIES (128) does not fall into any of the 3 categories bc does not involve cash transfer e.g. xchange stock for assets of another co, converting debt to equity, acquiring assets by assuming related liabilities, exchanging noncahs assets for other noncash assets
not required to report on the statement of cash flows → but must disclose in the footnotes
DISCLOSURES disclose policy for determining which items are cash equivalent, if change policy and must disclose that
CONSOLIDATED FINANCIAL STATEMENTS (132) defn: aggregate financial data for a parent co and its majority and wholly owned subs as if the parent and subs constitute a sgl acctg entity. SUMMARY on p.136 “intra-family” obligations/liabilities do not belong on the composite picture, an accountant would eliminate any liabilities btw X and Y in the consolidation process by canceling the receivable in one corp’s accts agst the payable on the other corp’s books. (135) retained earnings is the same after txn bc it is the parent’s retained earnings (parent is in effect buying Y’s net assets incl the retained earnings) eliminate parent’s investment in the sub, substituting instead the sub’s assets and liabilities. Also eliminate the sub’s equity accts and any intercompany txns → avoid duplication and premature revenue recognition e.g. must subtract from parent’s cash account (or asset account) the sub’s total assets bc that is how much the parent invested in the sub. On the consolidated balance sheet, an add’l account for “investments” would be added. (133 – look at example) after subtracting from cash account, on the consolidated balance sheet, must once again reflect the sub’s ind cash and plant account and add to parent’s accounts to get net amt.
common stock reflects the common stock of the parent (it does not change) each share of capital stock in a corp is a proportionate interest in the equity of the corp
consolidating financial statements incl not only consolidated financial statements, but also the financial statements of the consolidated group’s ind components in diff columns plus column for any eliminations (p.136) combined financial statements aggregate accts of commonly controlled co.s that do not share a corp parent e.g. an ind may own shares in both X corp and Y corp present no only combined statements but also the sep financial statements for each member of the combined grp plus a sep column for any eliminations
STEPS: subtract investment from cash of parent, then get = Investment – (total assets of sub – liabilities of sub) and add to parent’s cash, also add the cash of sub to get total cash for consolidated balance sheet.
The Need for Accounting Principles (141-146)
So users can compare one enterprise to another, and from successive periods. Managers may not be the most objective reporters of their own performance Indep Auditor: check on underlying facts represented in fin stmts
review of principles applied in portraying the info
SEC has authority to estb acctg principles but has deferred to acctg profession Congress has implicitly retained the power to mandate acctg principles registrant: 500 or more owners and $10M
How do Acctg Principles Become Generally Accepted? (p.167)
GAAP Hierarchy (168) Category a: officially promulgated by a body that the AIPCA Council has designated to establish such principles under Rule 203 of AICPA Code of Professional Conduct SEC’s rules and interpretative release carry similar status for SEC registrants SEC registrants place SABs and EITF here.
e.g. FASB statements, FASB interpretations ARBs that are not superseded. APB Opinions and interpretations that FASB has not superseded CAP
Category b: pronouncements from bodies of expert accountants that deliberate acctg issues in public forums pronouncement must meet two conditions relevant body must have exposed pronouncement for public comment body which qualifies to establish Category a principles (category a organizations) must have cleared the pronouncement category a orgs can’t object
FASB Technical Bulletins AICPA Industry Audit and Acctg Guides
Category c: pronouncements from bodies of expert accountants that category a formed and discuss acctg issues in public forums pronouncements that would otherwise qualify in category b EXCEPT was not exposed to public comment. e.g. EITF consensus positions (is raised to category a status by the SEC – look in book) and AcSEC Practice Bulletins
Category d: knowledgeable application of generally accepted pronouncements to specific circumstances practices that accountants acknowledge as enjoying general acceptance.
Other accounting literature (p.170)
Who Selects Among Generally Accepted Acctg Principles? (173)
Mgmt chooses mgmt selects an indep auditor opinion shopping: mgmt can put pressure on auditor by threatening to fire SEC requires full disclosure of changes in auditors → reduce pressure
Auditor can influence by threatening to issue a qualified opinion. Qualified Opinion: can change a co’s financial status Adverse opinon Clean Opinion: acceptable GAAP stds. but even an unqualified opinion does not guarantee accuracy bc only takes a sample (5% or less of annual txns) bc test sample txns→ observed deviations may indicate larger problems → internal control plays a factor
Generally accepted auditing stds (180) – auditing procedure chosen by the auditor
Overview: Auditing Stds: require an auditor to opine whether the financial statements fairly rep the enterprise’s financial position and results of operations and cash flows in conformity with GAAP. make sure no material misstatements or omissions
Need for audit: Information risk: principle (SH) lack access to info of agents (Mgmt), need indep monitor to reduce info risk if monitoring reduces info risk to principal, then cost of capital drops for the agent bc principal will accept lower return.
various users of financial statements (owners, creditors, potential investors, lenders, regulatory bodies) want assurances
Auditor seeks to verify the underlying txn and events reported in the financial statements to test the application of GAAP SEC has power to estb auditing stds but has only occasionally done so, as a result, acctg profession through the AICPA’s Auditign Stds Board has det
Independent Auditor’s Role (182) can’t audit co if CPA’s firm owns a direct or material indirect financial interest in the registrant auditors can be held personally liable.
The Audit Process (200) audit gathers evid abt 5 categories of assertions made by financial statements reported assets and liabilities exist and that recorded txns occurred during the particular acctg period that financial statement present all tranxns and accounts listed assets represent the enterprise’s rights and the reported liabilities show the business’s obligations appropriate recording of assets, liabilities, revenues, and expenses enterprise has properly classified, described and disclosed the financial statements’ components
3 phases: planning audit and assessing internal control (203) must assess client’s internal control before developing an audit program investigate the client’s business and accounting policies info on conditions in the industry business products and services sales trends major customrs production and mktg techniques characteristics of mgmt, personnel budgeting and acctg systems affiliations with outside influences
will review prior years audit results internal control: means systems, procedures and policies that co employs to help assure that organization proper execution and recording of txns can be administrative controls plan of organization, procedures, records that lead up to mgmt’s aurthorization of txns
or acctg controls plan, procedures and records which co uses to safeguard assets and produce reliable financial records
e.g. cash registers that display prices and totals, that total all txns during a shift to discourage clerks in pocketing money
conduct some compliance tests to det if internal controls function → then decide whether to rely on some to reduce the need to test actual txns VOUCHING: selects a txn recorded in the books to det whether underlying data supports the recorded entry TRACING: choosing a particular item and follow through the accounting books to det whether co has properly recorded and accounted for the data FCPA (Foreign Corrupt Practices Act) – made professional auditing stds an explicit statutory requirment antibribery provision 13b2B: required to maintain internal accounting controls (look on p205 for list of conditions that must be met)
accounting requirements 13b2A: federally mandated minimum record-keeping and internal controls stds for all co.s
1988 amendment: defn reasonable detail
implementing audit program Audit program: plan that sets forth the detailed procedures that auditor will perform to text txns (defn on p215) based on initial info gathered from internal control, auditor makes a prelim materiality judgment and risk assessment which determine the nature, timing, and extent of the procedures TYPICAL AUDIT: verify tangible assets observe business activities confirm account balances e.g. accts receivable: money that customers owe client → might select customers randomly and confirm outstanding balance
check math computations and seek confirmation from mgmt and outside counsel
AUDIT WORKING PAPERS: documentation of procedures and findings e.g. schedules, memos, analyses and corresponding results
reporting the results must have “reasonable basis” to express and opinion report states 4 things: financial statements remain mgmt’s responsibility express an opinion on the financial statements based on audit auditor conducted the audit in accordance with generally accepted auditing stds which require the auditor to plan and perform the audit to obtain reasonable assurance that the financial statements do not contain material misstatements financial statements present fairly in all material respects, the financial position, the results of operations and cash flows in conformity with GAAP.
Incentives for estb strong internal controls (213) Sentencing Guidelines reduced penalties: offers leniency to wrongdoers that can show they have estb a strong internal control
enormous losses due to inadequate internal controls derivatives: financial contracts that base their value on some underlying asset, such as bonds or foreign currencies properly used derivatives offer co.s the ability to manage and transfer risk but at the same time, can provide a recipe for financial disaster
Establishing Generally accepted auditing stds: SEC deferred to acctg profession on auditing stds→ acctg profession turned responsibility to develop and promulgate GAAP to FASB, but the corresponding duty to set auditing stds still lie with the AICPA through the ASB (auditing stds board)
Regulations S-X and S-B (sml business): (220) address accountants qualifications, provide rules regarding the form and content for financial statements can’t audit if CPA or CPA’s firm or member of the firm owns financial interest with co or subsidiaries can impose disciplinary sanctions
GENERALLY ACCEPTED AUDITING STANDARDS (10 statements fall into 3 grps) (225) – very broad stds and does not estb specific procedures General Standards: auditor must possess adequate technical training and proficiency auditor must maintain indep mental attitude in all matters relating to the assignment auditor must exercise due professional care
Standards of Field Work: adequately plan the work and properly supervise any assistants properly study and evaluate the exiting internal controls to assess whether can rely on obtain sufficient competent evid, through inspection, observation, inquiries, or confirmation to form reasonable basis
Reporting Standards: report must express whether comply with GAAP or expln why must disclaim an opinion Change in practice must be reported along with why: report must id circumstances in which the co has not consistently observed those principles in the current period in relation to preceding period profession regards info disclosure in financial statements as reasonably adequate unless the audit report specifically states otherwise express and opinion regarding financial statements as a whole or expln why must disclaim an opinion.
AUDITING PROCEDURES: (226) e.g. reconciling cash amts in ledger with the balances reflected in statements from financial institutions observing physical inventories price testing inventories confirming assets and liabilities txnal testing involving expenses, purchases, sales and payroll performing cut-off tests btw acctg periods reading minutes of SH and director mtgs obtaining representation letters form mgmt and attys
EXPECTATION GAP (227) – diff expectations between what investors and other users of financial statements expect and that which auditors provide auditor assess the risk that errors and fraud may cause the financial statements to contain material misstatements.
auditor must design audit plan that will detect material misstatements
General Rule: → rejected by the SEC however (SEC adopted a case by case analysis) any amt under 5% of income before taxes as immaterial, any amt over 10% of income before taxes as material material has different meaning to different co.s
Qualitative factors to consider when determining “materiality” sml omission could nevertheless qualify as material if: arises from an item capable of precise measurement masks a change in earnings or other trends hides a failure to mt analysts’ consensus expectations for the co changes a loss into income or vice versa list continues (229)
“PRESENT FAIRLY” (230) in addition to complying with GAAP, also requires auditor to assess whether: whether acctg principles selected by mgmt enjoy general acceptance acctg principles are appropriate in the circumtnaces financial statements and related notes provide info abt those matters that may affect their use, understanding and interpretation FS classify and summarize info, neither providing too much detail nor too few specifics FS reflect underlying txns that presents the financial position, results of op and cash flows stated within acceptable limits that co can reasonably attain
IN CASE OF FRAUD AND OTHER ILLEGAL ACTS (231) Private Securities Litigation Reform Act – Reporting requirements if uncover illegal act, auditor must investigate and assess effects on the FS. unless “clearly unconsequential” then auditor must inform mgmt and audit board if mgmt does not take remedial measures and auditor reasonably believes failure to do so would warrant either departure form auditor’s std report or resignation form the audit engagement → then must report to board of directors client/registrant must then notify SEC within one business day and the auditor, if auditor doesn’t receive in one b day then report to SEC
STANDARD AUDIT REPORT (will generally compare present with previous yrs) (234) Components: General Elements: contain a title that includes the word “independent” id a specific addressee auditing firm’s manual or printed signature will appear at the bottom date the report → usually rep the last day that the auditor performed field work
Introductory Paragraph: id the financial statements that the indep auditor examined and states auditor audited those docs state the various parties that are responsible for financial statement (mgmt) and opinion on the statements based on audit (auditor)
Scope Paragraph: state auditor performed in accordance with GAAS state GAAS require the auditor to plan and perform the audit to obtain reasonable assurance that FS don’t contain material misstatements state scope describe an audit and that it includes 3 steps state whether auditor believes the audit provides a rsnble basis for the audit opinion
Opinion Paragraph: whether FS present fairly in all material respects a co’s financial position as of the balance sheet date, plus the results of its op and its cash flows in accordance with GAAP unqualified opinion: yes, FS do present fairly…
4 other kinds of reports: (236) unqualified opinion with explanatory language (necessary in the following circumstances) using another auditor’s work change in acctg principles or in the way application has materially affected the comparability of FS btw acctg periods FS must depart from promulgated acctg principles to avoid misleading presentation
qualified opinion notes exceptions in the FS which do not conform to GAAP EXCEPT (always contain this word) for the effects of the matter to which the qualification relates, the FS present fairly in all material respects, the co’s financial picture prevention of full audit bc lack of acctg records
adverse opinion: that statements do not fairly present the financial position, op results, or cash flows states that FS do not present fairly…in conformity with GAAP should expln the deviations
disclaimer of opinion: opinion that states auditor can not express any opinion e.g. auditor has not performed an exam sufficient in scope to enable to form an opinion bc co. failed to make account of certain things.
ALTERNATIVES TO AUDITS (240) - privately owned co.s do not need to file audited FS with the SEC Two kinds: Review: limited examination by accountant, and limited assurance only give accountant rsnble basis for expressing limited assurance that FS do not require any material changes to conform to GAAP, OR another basis of acctg such as cash method. consists mostly of inquiries with co personnel and analytical procedures applied to financial data → discuss co’s ops with mgmt to det any changes in business does not require accountant to become familiar with the internal controls
Compilation: does not express opinion or assurance, accountant converts info that mgmt has provided in the form of FS accountant takes info that remains representations of the mgmt into the form of FS. accountant prepares FS without expressing any assurance that the statements fairly present the co’s financial condition or accordance with GAAP should have general understanding of business need not be indep, but must disclose if not indep
GAAS do not govern either, AICPA’s Statements on Standards for Attestation Engagements govern these two procedures Other services provided by accountants special report on specific elements
PUBLISHED SOURCES OF GAAP, GAAS (243) GAAP FASB publishes annually “ Original Pronouncements” → contain the most authoritative sources of GAAP FASB also publishes EITF abstracts CCH Inc (Commerce Clearing House) publishes info abt SEC and fed securities laws
GAAS AICPA (American Institute of Certified Pubic Accountants) publishes two sets containing various auditing stds first volume contains US auditing stds incl SASs and related Auditing Interpretations and attestation stds 2nd volume contains the stds applying to reviews and compilations
TIME VALUE OF MONEY (a dollar today is always worth more than a dollar tomorrow)
Overview: For borrower: time value of money refers to the interest expense of borrowing money over a period of time For lender: refers to the interest earned from lending or investing money P: a lawyer rep P should remember to request prejudgment interest D: lawyer rep D in a lawsuit seeking future lost profits, should ask the court to reduce any such award to present value.
INTEREST (276) Overview: formula: interest = rate over a specified period of time Interest = Principal x Rate x Time
Borrowers: pay interest when benefit they receive from spending the money outweighs the interest they pay to borrow Lenders and investors: lend money when they believe that the interest income they will earn in the future outweighs the opportunity cost of spending today.
Factors Determining Interest Rates pure rate of interest: rate which lenders would charge and borrowers would pay if the risks did not exist. (usually btw 2-3% each yr) e.g. US Treasury obligations → risk free interest rate
inflation premium: compensates the lender for inflation expected over the loan’s term inflation risk: general loss in purchasing power that rising prices cause, when inflation increases → interest rates ↑, when price level declines → interest rates ↓
maturity premium: offsets the risks associated with committing funds for longer periods. long term interest rates have exceeded short term interest rates for investments presenting similar risks.
default premium: risk that the borrower will default on the loan and that lender will lose the loan principal and any accrued interest. US Treasury obligations (bonds) do not incl a default premium. e.g. diff rates btw bonds with similar maturities in diff risk categories (US Treasury bonds – high grade corp bonds – below investment grade bonds “junk bonds”) reflect the default premium.
illiquidity premium: compensates the lender for lack of marketability and the resulting price concession that lender may have to grant if unexpected circum force lender to sell the debt instrument
SIMPLE INTEREST CALCULATION (279) Interest = Principal x Rate x Time Interest = dollar amt of interest Principal = amt of money debtor borrows Rate = cost of borrowing $1 per unit of time (interest rate) Time = # of periods, look on table (1049) # of units of time that principal remains unpaid (1 yr = 1 unit)
Simple interest: borrower pays interest on the original principal amt only regardless of any interest that has accrued in the past.
COMPOUND INTERST CALCULATION borrower pays interest on the unpaid interest of past periods as well as the orig principal. Lenders and investors prefer more frequent compounding bc compounding produces higher interest Borrowers prefer simple interest or compound interest with less frequent compounding 2 yr term compounded annually with a principal of 10,000 @ 8% 10,000 x .08 x 1 = 800 after first yr 10,800 x .08 x 1 = 864 after the second yr
APPENDIX B – contains four tables of shortcuts for 4 diff types of compound interest calculations (1049) FV of an amt FV of a series of equal amts PV of an amt PV of a series of equal amts
FUTURE VALUE (FV) defn: sum to which an amt or series of periodic and equal amts will grow at the end of a certain time, invested at a particular compound interest rate. FV = amt which current principal (p) will grow at the end of (n) periods, invested at (i) compound interest rate. FV of a sgl amt compounded interest annually Example 5 (281) 40,000 invested from 1901-2000 @ 5% compounded annually 40,000 x .05 x 99 first find factor for 50 periods = 11.46740, which tells us that one dollar will grow to abt 11.47 if invested at 5% compound interest for 50 yrs → 458,696 40,000 x 11.46740 = 458,696
next find factor for 40 yrs = 7.03999 458,696 x 7.03999 = 3,229215.25 (the 458,696 @ the end of 90 yrs)
finally take the factor for 9 periods = 1.55133 3,229215.25 x 1.55133 = 5,009578.49 after 99 yrs
FV of sgl amt compound semiannually 10,000 @ 8% compounded semiannually, how much at the end of 10 yrs?
in 10 yrs will be compounded 20 times, every six months earn 4% interest find 4% interest for 20 periods = 2.19112 10,000 x 2.19112 = 21,911.20
10,000 @ 8% compounded quarterly, how much at the end of 10 yrs? at end of 10 yrs will have compounded 40 times, every 3 months earn 2% interest find 2% interest for 40 periods using Table I = 2.20804 10,000 x 2.20804 = 22,080.40
Rule of 72s or Doubling an Investment (283) dividing 72 by t.he interest rate gives us the approximate number of yrs in which an investment will dbl at compound interest e.g. if 8%, 72/8 = 9, look at table and it tells you that 8% in 9 periods will = 1.99900 (close to dbl) e.g. for 25 yr old to get 1M by 65 (p.284)
annuity: (285) refers to a sequence of periodic and equal amts at regular time intervals Ordinary annuity (annuity in arrears): investor start making payments at the end rather than at the beginning of the first period e.g. if investor contributes 1,000 at the end of each yr for 4 yrs at 5% compounded annually the first payment will compound 3 times at the end of 4 yrs 2nd payment will compound 2 times 3rd payment will compound once and 4th payment does not earn any interest
Table II (uses future value factors from Table I for sgl amts to calc the FV factors for an ordinary annuity) → shortcut to the above calc bc will give you the same number just by looking at the number of payments and the interest rate. FV of an ordinary annuity (example 8, p287) – look at Table II 2,000 at end of each yr for 15 yrs @ 6% = 2,000 x 23.27597 = 46,551.94
Annuity Due (annuity in advance): investor makes payments at he beginning of each period. one more period than the payment would under an ordinary annuity produce greater amt if pay at the beginning of the yr → one more period of interest accrual Table II does not contain amts for annuity due Formula for Annuities Due using Table II: Future value factor of an annuity due for (n) payments = fv factor of an ordinary annuity for ((n) +1 payments) – 1. n = no of payments for ordinary annuity, then add one add’l payment and find the factor for that
Example 9 2000 at the beginning of each yr for 15 yrs @ 6% compounded annually total of 16 payments to an ordinary annuity
2000 x (25.6725 – 1) = 49,345.06 25.6725 reflects the n +1 payment factor, n would equal 15 in ordinary annuity but must add one payment and find the factor for 16 payments
PRESENT VALUE (PV) (290) –Table III → shows the PV of $1 at the end of (n) periods discounted at (r) compound interest defn: how much a given future sum or annuity is worth today PV = amt that will grow to a larger sum a the end of (n) periods of time in the future at (r) compound interest rate. discounted: bc we start with a larger known amt in the future and det the lower PV
Single amounts: principal that a dollar is worth more today than a dollar tomorrow bc you can invest that dollar today and earn interest tomorrow Example 10 A promised to give D 10000 on his 22 birthday (D is 12). What is the PV discounted at 8% annually? PV = 10000 x .46319 (which is the 8% for 10 yrs) = 4631.90 can verify by using Table I to find FV factor for 10 periods at 8% which is 2.15892, then multiply 4631.90 x 2.16 = 9,999.90
Example 11: PV interest compounded semiannually A promised D 10000 on 22 birthday @ 8% but will compound semiannually. PV = 10000 x .45639 (which is PV factor for 20 yrs since compounded twice a yr at 4%) take half of the orig interest per yr → 4%
Example 12: PV interest compounded quarterly A promised D 10000on 22 b-day @ 8% but will compound quarterly 10 yrs compounded 4 times a yr = 40 periods at 2% each period 10000 x .45289 = 4,528.90
the more frequently we compound interest the lower the present value drops, bc more frequent compounding produces higher effective rate of interest, a higher effective rate of interest means that we can invest less now, which means a lower present value, to arrive at a given sum in the future.
Annuities (292) someone promises to make a series of equal payments Ordinary Annuity: Use Table VI →
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