Proprietorship- unincorporated, owned by one individual. Easy to set up. Inexpensive. Few government regulations. No corp tax (personal taxable income only). Difficult to obtain funding for growth. Unlimited
personal liability from debts (debts can exceed money invested). Limited to life of the founder. Partnership- two+ persons to conduct a noncorporate business for profit. May run informal (oral communication) to
formal (filed with secretary for state). Limited partnership can only lose what one invested, have no control, returns are limited (ie: real estate, oil, equipment-leasing, and venture capital). General partners have
unlimited liability. Distributes profits equally, file on personal taxes. Limited liability partnership (LLP)/ Limited liability company (LLC)- tax advantage of a partnership with the limited liability advantage
corporation. Corporation- legal entity created under state laws, separate and distinct from its owners and managers. Advantages: unlimited life, easy transfer of ownership interests- shares of stock transferred
easily, limited liability—losses are limited to actual funds invested. Disadvantages: earnings subject to double taxation, must have charter, bylaws, filing federal and state reports. Owner gives up some control to
board of directors. Charter- legal doc that is filed with the state to incorporate a company. Includes: name of corp, types of activities, capital stock, number of directors, names and address of directors. Must be
filed with secretary of state to be official existence. Bylaws- rules drawn up by the founders of the corp. to include (1) how directors are to be elected, (2) whether the existing stockholders will have the first right
to buy any new shares, (3) procedures for changing the bylaws. Professional Corp (PC)/ Professional Association (PA)- most of the benefits of incorporation but the participants are not relieved of professional
malpractice liability. S Corp- businesses who meet requirements (size and number of stockholders) to be taxed as a proprietorship. Close Held Stock- stock is not actively traded and is owned by only a few
people, usually the company’s managers. Closely Held Corp- refers to companies that are so small that their common stocks are not actively traded. Securities and Exchange Commission (SEC)- government
agency which regulates the sales of new securities exchanges. Helps ensure stable markets, sound brokerage firms, and absence of stock manipulation. Protectus- summarizes info about a new security issue and
the issuing company. Brokerage firm- company that buys and sell stock on behalf of clients. Brokers- registered with the SEC to buy and sell stocks on behalf of clients. Free Cash Flow- available for distribution
to a company’s investors, creditors, and stockholders. A financial asset is considered to have value only if it can generate positive cash flows. FCF= SALES REV – OP COSTS – OP TAXES – REQUIRED
INVEST IN NEW OP CAPITAL. Fundamental value (intrinsic value)- value of company or financial security that incorporates all relevant info regarding expected future cash flows and risk. True value of the
stock or bond based on flows and risk. The value perceived by stock market investors determines the market price of a stock. A stock trading at a price below its intrinsic value is undervalued. A stock trading at a
price above its intrinsic value is overvalued. The primary objective of the corp mngmt team is to maximize the shareholders’ wealth by maximizing the fundamental price of the company’s stock over the long run.
Benefit Corporation (B-Corp)- corp form that expands directors’ fiduciary responsibilities to include other interests than shareholders. Individuals are net providers (savers), nonfinancial corps are net users
(borrowers), governments are net users, financial corps are net users. Direct Transfers- business sells directly to providers for cash. Example: firm has each partner transfer $ to help company make payroll for
next 3 months. Grandfather loans son $ to start small business. Investment Bank Transfers- business sells to investment bank and investment bank sells the securities (stocks, bonds, etc.) to the providers/savers.
IE: Business wants to issue IPO, hires investment bank to underwrite. Financially Intermediary Transfer- FI obtains funds from providers in exchange for its own securities or ownership of savings account. FI
used the money to purchase the business securities. IE: individual provide dollars to bank, bank lends to a small business, business promises to repay loan. IE: Person invests $ by purchasing shares of other
businesses through a mutual fund company. Financial securities are documents and contractual provisions that entitle their owners to specific rights and claims on specific cash flows or values. Debt instrumentspayments over maturity (time). If term longer than 1 yr= capital market security. If less than 1 yr called money market security. Derivatives- securities whose values depend on, or have derived from, the values of
some sort of traded assets (IE: option futures, forward contracts). Hybrid- mix of debt, equity, and derivatives (both debt-like and option-like features). Municipal bonds- Issued by a state, municipality, or a
county, state and local government bonds are debt securities to fund such expenditures as the construction of highways, bridges, schools, and canals. State and local government bonds are exempt from most state
and local taxes, especially if you are a taxpayer in the same state. Bankers’ acceptances- Firms issue a draft payable at a specific future time, under certain conditions. Time drafts are drawn and endorsed by a
bank, which means that the issuing bank will pay the acceptance value when they mature. Commonly used in international trade, they are shielded from potential default from the parties involved and other risk
because the bank guarantees them. Money market mutual funds- invest in financial instruments (T-bills, T-notes, CDs, & commercial paper)—that have high liquidity and short maturities. Less risky. Common
stocks are thus considered to be the riskiest class of ownership, stockholders have voting rights and often get higher returns for the risks that they take. Required Rate of Return- rate of return that fairly
compensates an investor for purchasing or holding a particular investment after considering its production opportunities, risk, timing, expected inflation, and the returns available on other similar investments.
Interest- price of using debt; price paid to borrow funds. Higher risk = higher interest rate. Higher inflation = higher interest rates. Federal reserve policy, federal budget deficit or surplus, level of business
activity, and international factors affect the rate of return. Investment Banks- help companies raise capital and underwrite the capital by advising corps regarding the design and pricing of new securities, buy these
securities from the issuing corp, and resell them to investors. Act as facilitators, consult and advise such as M&A, and brokerage services. Savings and Loan Associates (S&Ls)- accepts deposits from many small
savers and then lend this money to buyers and consumers. Mutual savings banks (MSBs)- like S&LS but operate in northeastern states. Credit Unions- cooperative associations whose members have common
bond (employees of same firm or living in same geographic area). Members savings are loaned only to other members, often the cheapest source of funds for individuals. Commercial Banks- raise funds from
depositors by issuing stock and bonds to investors. Highly regulated. Federal Deposit Insurance Corp (FDIC)- insures up to $250,000 per depositer. Hedge Funds- private limited partnerships whose purpose is to
raise money from investors and engage in a variety of investment activities. Relatively small number of high-net worth individuals, less regulated. Private Equity Funds- like hedge fund, but PE funds own stock
(equity) in other companies and often control those companies. Typically purchases the entire company. Staples, Inc. traded on the NASDAQ stock market until Sycamore Partners purchased in 2017. Physical
Asset Markets- tangible or real (wheat, auto, real estate, computers, machinery). Financial Asset Markets- stocks, bonds, notes, mortgages, derivatives, and other financial instruments. Spot Markets- assets being
bought or sold for “on the spot” delivery (within a few days). Future Markets- assets delivered at some future date, 6 months or year into future. Mortgage Markets- loans on residential, ag, commercial, and
industrial real estate. Consumer Credit Markets- loans on auto, appliances, edu, vacations, etc. Private Markets- worked out directly between two parties and structured in any manner that appeals to them. IE:
Bank loans and private placements of debt with insurance companies. Securities are more tailor-made, less liquid. Private Placements- the sale of stock to only one or a few investors, usually institutional
investors. Advantages of private placements are lower flotation costs and greater speed, since the shares issued are not subject to securities and exchange commission registration. Public Markets- standardized
contracts are traded on organized exchanges, held by large number of individuals, standard contractual features. Primary Markets- corps raise new capital. IE: selling common stock to raise capital. Secondary
Markets- existing, already outstanding securities are traded among investors. Annual Report- issued once a year by a corp and contains basic financial statements and an analysis of past performance and future
prospects. Balance Sheets- snapshot at a point in time, summarizes a company’s assets, liabilities, and stockholders’ equity at a specific point in time. Statement of Cash Flows- Aggregates all cash inflows,
which the company received from its ongoing activities and investment sources, and all cash outflows. How much cash is a firm generating through operating, investing, and financing activities. Statement of
Stockholders Equity- explain the changes in a company’s retained earnings over accounting period. Assets are things a company owns and listed in order of liquidity. Accounts payable due within 30 days,
Notes payable due within 90 days, Bondholders due for 20+ years. Accounts receivable are payments expected from customers (has not yet been paid by customers). Accounts Payable- purchase of supplies
that doesn’t require immediate payment. FIFO (first in, first out) Inventory- accounting method that estimates production costs and the value of remaining inventory by assuming that the first items placed in
inventory are the first ones used in production. LIFO Inventory- most recent inventory, first used in production. Income Statement- prepared monthly, quarterly, or annually and reflects performance during the
period. Depreciation (tangible ie: plant, equip) and amortization (intangible; copyright, patents, trademarks, goodwill) are estimated costs of assets that wear out in producing goods and services. Goodwill- An
accounting intangible asset created when a company acquires another company but pays more than the assets are worth. Operating activities are day-to-day actions needed to conduct business, affect a firm’s
cash position (inflows: cash sales, inventory sales, collections from accounts receivable, royalties, and commission; outflows: payments, disbursements for salaries, bonuses, taxes, purchasing inventory and
supplies, servicing short-term financing, and other operating-related expenses.) IE: company reduces raw materials from previous year, company earns revenue from its royalties. Investing activities are related to
the purchase or sale of investments by a firm are called. IE: Expenditures on capital assets, plant and equipment, purchasing marketing rights, short- and long-term investments in equity or bonds and marketable
securities. Financing activities refers to all cash inflows or outflows made to obtain or repay capital, such as equity and long-term debt. IE: raising capital through initial public offerings, distributing dividends,
repurchasing stock, retiring debt, and all other borrowing and related payments… (-) FCF, (-) NOPAT = operating issues… (+) FCF, (-) NOPAT = high growth phase… (-) FCF, (+) ROIC = growth positive…EVA
measures the amount a shareholder wealth that the firm’s management have generated during a specified time period. (-) EVA indicated reduced firm value. EVA helps analysts and investors determine if the
company’s profits exceed or fall short of the cost of capital in any one period, which is also a reflection of the managers’ performance. MVA helps analysts and investors evaluate if managers are performing their
primary task. If MVA is a positive number, the company has increased its shareholders’ wealth; a negative number indicates that shareholder wealth has been diminished. AMT law must pick the higher of the two
taxes, created to prevent income earners using tax shelters to reduce their tax liability. 2017 provision is 21% flat rate.
NOPAT
(NET OP PROFIT AFTER TAXES)
NOWC
(NET OP WORKING CAPITAL)
NET OPERATING CAPITAL
=EBIT (1 – Tax Rate)
= Op Current Assets - Op Current Liabilities
OR
= (Cash + Acct Rcv + Inventories) – (Acct Payables
+ Accruals)
= NOWC + Operating Long-Term Assets
TOTAL INVESTOR SUPPLIED
OPERATING CAPITAL
EVA
(ECONOMIC VALUE ADDED)
MVA
(MARKET VALUE ADDED)
TOTAL INVESTOR SUPPLIED CAPITAL
= Notes Payable + Long-term Bonds + Preferred
Stock + Common Equity
TOTAL ASSETS TURNOVER RATIO
FCF
= NOPAT – Net Investment in Total Operating
Capital
OR
= NOPAT – Gross Investment in Fixed Assets –
Investment in NOWC
NOPAT / Operating Capital
GROSS PROFIT MARGIN
ROIC
(RETURN ON INVESTED CAPITAL)
OP
(OP PROFITABILITY)
CR
(CAPITAL REQUIREMENT RATIO)
DSO (DAYS SALES OUTSTANDING)
FIXED ASSETS TURNOVER RATIO
NOPAT / Sales
INVENTORY TURNOVER RATIO
CURRENT RATIO
Total Net Operating Capital / Sales
QUICK RATIO
= Receivables / (Annual Sales/365)
DEBT-T0-ASSETS RATIO
= Sales / Net Fixed Assets
DUPONT
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NET PROFIT MARGIN
= Net Income Available to Common Shareholders /
Sales
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MARKET DEBT RATIO
=Total Investor Supplied Capital – Short-term investments
= Net Operating Profit After Taxes - After Tax Dollar Cost
of Capital used to Support Ops
OR
= NOPAT – (Total Net Operating Capital)(WACC)
IN TERMS OF ROIC
=(Total Net Op Capital)(ROIC-WACC)
= Market Value of Stock – Equity capital Supplied by
Shareholders
OR
= (Shares)(Stock Price) – Total Common Equity
= Sales / Total Assets
= (Sales- COGS w/ Depreciation) / Sales
COGS / Inventories
Current Assets / Current Liabilities
(Current Assets – Inventories) / Current Liabilities
Total Debt / Total Assets
*total debt = notes payable + long-term bonds
= Profit Margin * Total Asset Turnover * Equity Multiplier
= (NI/Sales)(Sales/Total Assets)(Total Assets/Common
Equity)
= Total Debt / (Total Debt + Market Value of Equity)
OPERATING PROFIT MARGIN
BEP
(BASIC EARING POWER)
ROA
(RETURN ON ASSETS)
ROE
(RETURN ON COMMON EQUITY)
P/FCF RATIO
= EBIT / Sales
= EBIT / Total Assets
=Net Income Available to Common Stockholders /
Total Assets
=Net Income Available to Common Stockholders /
Common Equity
= Price per Share / FCF per Share
BOOK VALUE PER SHARE
= Total Common Equity / Shares Outstanding
DEBT-TO-EQUITY RATIO
Total Equity / Total Common Equity
LIABILITIES TO ASSET RATIO
EQUITY MULTIPLIER
TIE
(TIMES-INTEREST-EARNED RATIO)
EBITDA COVERAGE RATIO
P/E RATIO
(PRICE/EARNINGS RATIO)
M/B RATIO
(MARKET/BOOK RATIO)
MARKET CAPITALIZATION
= Total Liabilities / Total Assets
= ROE / ROA
= (Net Income / Common Equity) / (Net Income / Total
Assets)
=Total Assets / Common Equity
=EBIT / Interest Expense
= EBITDA + Lease Payments / (Interest + Principal
Payment + Lease Payments)
Price per Share / Earnings per Share
*earnings per share = NI / # of shares
= Market Value per Share / Book Value per Share
= (Price per Share)(Total number of Shares)
Profitability Ratios- Ratios that show the combined effects of liquidity, asset management, and debt on operating and financial results. Gross Profit Margin- gross profit per dollar of sales before other expenses
are deducted. Asset Management Ratios- measure how effectively a firm is managing assets. AKA efficiency ratios. Excessive investment in assets = high operating capital= reduction in free cash flow and stock
price. Not enough assets = loss in sales= hurt on profit, free cash flow, and stock price. Must have right amount invested in assets. Total assets turnover ratio measures the dollars in sales that are generated for
each dollar that is tied up in assets. Fixed assets turnover ratio measures how effectively the firm uses its plant and equipment. Days Sales Outstanding (DSO)-appraises accounts receivable, average length of
time that the firm waits after making a sale before receiving cash. Current Ratio- best single indicator of the extent to which the claims of short-term creditors are covered by assets that are expected to be
converted to cash quickly, most used to measure short-term solvency. Assets: cash, marketable securities, accounts receivable, and inventories. Liabilities: accounts payable, short-term notes payable, current
maturities of long-term debt, accrued taxes, and other accrued expenses. If looking to extend credit, want higher than average number. If liabilities rise faster than assets, means trouble. If stockholder, higher ratio
could mean company has lot of money tied up in nonproductive assets like cash or marketable securities. Or higher ratio could indicate large inventory holdings. No right or wrong to be higher or lower than
average. Red flag is when current ratio is FAR from the average. Liquid Asset- one that trades in an active market, so it can be converted quickly to cash at the going market price. Financial LeverageImplications: (1) stockholders can control a firm with smaller investments of their own equity if they finance part of the firm with debt. (2) if the firm’s assets generate a high pre-tax return on the interest rate on
debt, then the shareholders’ returns are magnified, or “leveraged.” Conversely, shareholders’ losses are also magnified if assets generate a pre-tax return less than the interest rate. (3) if a company has high
leverage, even a small decline in performance might cause the firm’s value to fall below the amount it owes to creditors. Higher leverage = higher risk for creditors. Debt Management Ratios/Leverage Ratios
identify a firm’s use of debt relative to equity and its ability to pay interest and principle. Debt-to-Assets Ratio (Debt Ratio)- measures the % of funds provided by investors other than preferred or common
shareholders. % of assets are financed with debt. Debt-to-Equity Ratio- shows amount of debt per dollar of equity. Market Debt Ratio- ratio of the market value of total debt provided by investor to the total
market value of debt and equity. If market value of debt is not available, then analysists use the book value of debt as reported on the financial statements. Market value of equity of the stock price X number of
shares. Liabilities-to-Assets Ratio- extent to which a firm’s assets are not supported by equity. Equity Multiplier- if the factor by which the return on assets is multiplied to determine the return on equity,
defined as the total assets to common equity ratio. Times-Interest-Earned (TIE) Ratio- measures the extent to which operating income can decline before the firms is unable to meet its annual interest costs.
More for long-term bondholders. Downfall of TIE is that interest is not only fixed financial charge and EBIT does not represent all the cash flow available to service debt. EBITDA coverage ratio considers all of
the “cash” earnings. More for banks and short-term loans. Market Value Ratios- related a firm’s stock price to its earnings, cash flow, and book value per share. Measures the value of a company’s stock relative
to that of another. P/E Ratio- shows how much investors are willing to pay per dollar of reported profits. P/FCF Ratio -shows how much investors are willing to pay per dollar of FCF. Price/EBITDA Ratiobetter measure of operating performance, incorporating nonoperating items. (M/B) Ratio- shows how much current shareholders value the firm relative to the total cumulative amount of cash the firm has raised
from shareholders either directly through stock issuances or indirectly by reinvesting net income rather than paying it all out as dividends. Market Capitalization- total market value of s firm’s stock. Common
Size Analysis- all income statement items are divided by sales (show % of sales), and all balance sheet items are divided by total assets (show % of total assets). Percentage Change Analysis- growth rates are
calculated relative to a base year. Benchmarking- when a firm compares its ratios to other leading companies in the same industry. Potential problems with ratio analysis include many firms operating in different
industries, best to benchmark on industry leaders, not average, inflation, seasonal effects, window dressings, and accounting practices and distort comparisons. Time Value of Money (TVM) aka Discounted Cash
Flow (DCF) Analysis- the method of determining today’s value of cash flow to be received in the future. Because a dollar in the future is worth less than a dollar today. Time Line- a graphical rep used to show the timing of cash
flows. Compounding- process of finding FV of a single payment or series of payments. Based on periodic interest rates unless using continuous compounding. Compound Interest- interest earned on prior periods.
Simple/Regular Interest- interest earned on principal. Opportunity Cost-rate of return you would earn on an alternative investment of similar risk if you don’t invest in the security under consideration. Discounting- process of
finding the present value of a single payment or series of payments. Reverse of compounding. Perpetuity- a series of payments of a fixed amount that continue indefinitely. Annuity- series of payments of a fixed amount for a
specified number of periods (auto loans, mortgages). Deferred (Ordinary) Annuity- An annuity with a fixed number of equal payments occurring at the end of each period (auto loans, mortgages, student loans). Annuity Duemade at beginning of each period (rental leases, life insurance premiums, lottery payoffs). Uneven/Irregular Cash Flow Streams- stream of cash flows that cannot be represented by an annuity. Annual Compounding- %
compounded once a year. Semiannual Compounding- % compounded every 6 months. Nominal (or Quoted) Rate INOM -Rate quoted by banks, brokers, and other financial institutes. To be meaningful must also include
compounding periods. Periodic Rate IPER -Rate charged by a lender or paid by a borrower each period. Can be annually, semiannually, per quarter, month, day, or any other time interval. Effective (or Equivalent) Annual Rate
(EAR or EFF%)- The annual rate that produced the same results as compounding at the periodic rate for M times per year. Future value and EFF% increase as the frequency of compounding increases. Annual Percentage
Rates (APR)-Nominal annual rates charged on loans. Add-on Interest- interest is calculated over the life of the loan as the product of the initial amount borrowed, the number of years until full repayment, and the annual rate on
the loan. This total interest is added to the loan amount to get the total amount of payments. The total amount of payments is divided by the number of payment periods to get equal installment payment each period. This raises the
effective cost of loan. Amortized Loans- A loan that is repaid in equal periodic amounts (or “killed off”) over time. IE: auto loans, mortgages, student loans, etc. Growing Annuity- a series of payments that grow at a constant
rate. Although an annuity payment is constant, the expression “growing annuity” is widely used.
SIMPLE INTEREST
=PV + (PV * I)(N)
N
COMPOUND INTEREST
=PV(1+I)
FUTURE VALUE (FV) EXCEL
EXAMPLE: $100, 3 YR, 5%
PRESENT VALUE (PV) EXCEL
FINDING INTEREST RATE EXCEL
=FV(I,N,PMT,PV)
=FV(0.05,3,0,-100) =115.76
=PV(I,N,PMT,FV)
=PV(0.05,3,0,115.76) = -100
=RATE(N,PMT,-PV,FV)
FINDING NUMBER OF PERIODS
=NPER(I,PMT,PV,FV)
PV of PERPETUITY
= PMT / I
IF INTEREST RISE, PV FALLS. IF INTEREST FALLS,
PV RISES.
=FVAN=PMT(1+I)N-1 + PMT(1+I)N-2 + PMT(1+I)N-3
=FV(I,N,PMT,PV)
=FV(0.05,3,-100,0)
FVADUE= FVAORDINARY (1+I)
FUTURE VALUE OF ORDINARY ANNUITY
EXCEL
FUTURE VALUE OF ANNUITY DUE
EXCEL, USE TYPE 1
SOLVING FOR INTEREST WITH IRREGULAR
CASH FLOWS
NOMINAL RATE
FRACTIONAL PERIODS
EXAMPLE: DEPOSIT $100, 10%, HOW MUCH
AFTER 9 MONTHS?
MORTGAGE MONTHLY PAYMENT
EXAMPLE: 30 YRS, $250,000, 6% APR
INTEREST PAID IN FIRST YEAR
=FV(I,N,PMT,PV,TYPE)
=FV(0.05,3,-100,0,1) = 331.01
=IRR(MUST USE CELL REF)
=IRR(B546:G546) =12.55%
AKA INOM
=DEPOSIT(1+I)M
=0.10 / 365 = 0.000273973
=(9/12)(365)= 273.75 DAYS = 274
=100(1.000273973)274 = $107.79
=PMT((I/12),N,PV,FV)
=PMT((0.06/12),360,250000,0)=1498.88
= (MONTHLY PAYMENT * # OF PAYMENTS) –
TOTAL PRINCIPAL PAYMENTS
PRESENT VALUE OF ORDINARY ANNUITY
EXCEL
PRESENT VALUE OF ANNUITY DUE EXCEL
(USE TYPE 1)
FINDING ORDINARY ANNUNITY PAYMENT
EXAMPLE: $10,000 AVAILABLE IN 5 YRS WITH 6%
FINDING ANNUNITY DUE PAYMENT
EXAMPLE: $10,000 AVAILABLE IN 5 YRS WITH 6%
FINDING NUMBER OF PERIODS
EXAMPLE: CAN ONLY SAE $1200, 6%, HOW LONG
TO SAVE $10,000?
FINDING INTEREST RATE
EXAMPLE: CAN SAVE $1200 ANNUALLY, NEED
$10,000 IN 5 YEARS. WHAT INTEREST RATE?
ANNUITY PLUS FINAL PAYMENT
EXAMPLE: 5 YRS, 12%, $100 ORDINARY ANNUITY
+ FINAL PAYMENT OF $1000
IRRGEGULAR CASH FLOW STREAM
DO NOT INCLUDE PERIOD 0
FUTURE VALUE OF AN UNEVEN CASH FLOW
=PV(I,N,PMT,FV)
=PV(0.05,3,-100,0) = 272.32
=PV(I,N,PMT,FV,TYPE)
=PV(0.05,3,-100,0,1) = 285.94
=PMT(I,N,PV,FV,TYPE)
=PMT(0.06,5,0,10000) = -1,773.96
=PMT(I,N,PV,FV,TYPE)
=PMT(0.06,5,0,10000,1) = -1,673.55
=NPER(I,PMT,PV,FV,TYPE)
=NPER(0.06,-1200,0,10000) = 6.96
=RATE(N,PMT,PV,FV,TYPE)
=RATE(5,-1200,0,10000) = 0.2578 = 25.78%
=PV(I,N,PMT,FV)
=PV(0.12,5,100,1000)= -927.90
=NPV(I,CASH FLOWS)
=NPV(0.12,100,300,300,300,500) = 1016.36
=FV(I,N,PMT,-NPV)
=FV(0.12,5,0,-1016.35) = 1791.15
IPER (PERIODIC)
= INOM / M
EFFECTIVE ANNUAL RATE (EFF%)
AMORTIZED LOAN PAYMENT
EXAMPLE: BORROW $100K, 5 EQUAL PAYMENTS,
6% AT BEGINNING OF EACH YR.
(1+ IPER)M -1.0
=PMT(I,N,PV,FV)
=PMT (0.06,5,100000,0) = -23,739.64
REMAINING BALANCE
EXAMPLE: 30 YRS, $250,000, 6%, HAVE MADE 12
PAYMENTS.
PRINCIPAL PAID IN FIRST YEAR
=FV((I/12),N,PMT,-PV))
=FV(0.06/12),12,1498.88,-250000) = 246.929.93
= (1498.88 * 12) – 3070.07 = 14,916.49
TOTAL PMT & INTERESET DURING LIFE OF MORTGAGE
=MONTHS(MONTHLY PAYMENT) – AMOUNT BORROWED
EXAMPLE: 30 YR, $250,000
=360(1498.88) = 539,597 (-250,000 = $289,597 INTEREST)
=TOTAL LOAN – REMAINING BALANCE AFTER
12 PAYMENTS
=250,000 – 246,929.93 = 3,070.07
Example: Want to retire, have $1 million nest egg, 6% nominal interest rate, 3% inflation, will live for another 20 years, how much can I withdraw annually?
1st Step: Real rate (rr)= [(1+ rnom)/(1+inflation)] -1
Rr= [1.06/1.03]-1 = 0.029126214 = 2.9126214%
Calculate amount to withdraw IMMEDIATELY: =PMT(0.029126214,20,-1000000,0,1) = $64,786.88
Calculate amount BEGINNING OF YEAR WITHDRAW: =PMT(0.029126214,20,-1000000,0) = $66,673.87
Calculate amount END OF YEAR WITHDRAW (included inflation) = 66,673.87 * 1.03 = $68.674.09
source$100,000
was downloaded
by 100000864771035
from
on of
06-05-2023
-05:00 6% interest, 2% inflation.
Example:This
wantstudy
to accumulate
in 10 years, plan
to make deposit now and
thenCourseHero.com
9 more at the beginning
the follow 9 11:07:58
years (total GMT
of 10 deposits).
Real Rate = Rr= [(1+ rnom)/(1+inflation)] -1
=[1.06/1.02]-1 = 0.0392157 = 3.9215686%
Real Value = 100,000/(1+.02) 10 = 82,034.83
INTIAL DEPOSIT= PMT(.039215686,10,0,82,034.83) =6598.87
FOLOWING DEPOSITS = Previous Deposit * (1+Inflation) =6598.87 * 1.02= 6730.85
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