BASIC FORMULAE & DEFINITIONS FOR AN INTRODUCTORY COURSE IN BUSINESS MATHEMATICS INTEREST Amount required to cover operating expenses and make a profit • cost of goods is what the retailer pays the supplier or manufacturer for goods • selling price of goods is what the customer pays the retailer for goods (i.e., the buyer's purchasing price) • cost + markup = selling price • markup (or margin) = selling price - cost • percent markup on cost = markup + cost • percent markup on cost = percent markup on selling price + (I - percent markup on selling price) • percent markup on selling price = markup + selling price • percent markup on selling price = percent markup on cost + (1 + percent markup on cost) • markdown = original selling price - marked-down price • markdown percent = markdown + original selling price • markdown = markdown percent X original selling price • selling price per unit = [total cost of all units - percent markup on cost (total cost of all units)] + [total units - total spoiled units] DISCOUNTS Discounts: Reduction to a basic price Trade Discounts: Discounts given to partners in the distribution channel of goods; also called functional discounts, and are given to distribution channel members to perform specific tasks • net price = list price - trade discount amount r - ~ Exact Number of Days: Interest is calculated over a time period, from when a loan is given to the end date; day the loan is due mayor may not be included in the period • To determine loan period, the actual number of days ill each month should be known Tip: 30 days hath September, April, June, and November; all the rest have 31, excepting February alone, which hath but 28, in fine, till leap year gives it 29 • Leap years are divisible by 4, which is why 2004 was a leap year and also why an extra day is added to February in every leap year Simple Interest: Time is expressed in the same units as the rate; if r is an annual rate, then t is in years • simple interest (i) = principal (p) x rate in percent (r) x time (t) • maturity value = principal + interest • p is principal of the loan (or borrowed) amount or invested amount (face value); i is the amount of interest paid for the loan or earned on the investment; r is the percent rate of interest paid for the use of someone else's money or earned for lending the money • exact interest: time = t = exact number of days 365 • ordinary interest (Banker's Rule): _ _ exact number of days tIme - t 360 Cash Discount: Discounts given to customers for paying with cash; cash discount is also called sales discount by seller or purchase discount by buyer • cash discount = selling price (or invoice amount) x cash discount rate • amount buyer pays = selling price - cash discount Partial Payment Rule: Any partial loan payment is first used to pay the interest that has accrued (total interest to date), and the remainder is used to reduce the principal of the loan Terms: Cash discount rate is usually stated in credit terms; credit term 2/10 on an invoice means that a 2% cash discount is allowed if the payment is made within 10 days of the date of the invoice; cash discount period can a/so begin when the buyer receives the goods (ROG = receipt of goods) DEPRECIATION PAYROLL Pay Based on Hourly Wages: Pay is based on hours of work done • gross pay = (number of regular hours x regular hourly rate) + (number of overtime hours x overtime hourly rate) Pay Based on Piece Work: Pay is based on acceptable pieces of work produced • gross pay = total number of acceptable pieces produced x piece work rate Pay Based on Commission: Commission is a percentage of sales; usually paid to the person generating the sales • gross pay = commission = sales x commission rate Depreciation: Loss in value of tangible business assets or property (excluding land) over its useful life due to deterioration, obsolescence, etc.; also called depreciation expense; periodically charged to operating expenses; total depreciation limited to cost of property • accumulated depreciation = total amount of depreciation to date • cost of asset = cost paid for asset, including freight • book value of asset = cost of asset - accumulated depreciation Compound Int erest: Interest that C is paid on both the principal and the interest accumulated from past periods; interest gained is added to " the original investment • maturity value = p x (I + i)n • wherc p = principal; i = interest rate in , percent per period; n = number of periods • alternative formula: maturity value (future value) = p x (I + rln)nt • where t = time in years; II = number of periods per year; r = interest rate in percent per year compounding period is interest is calculated every n annual quarter IDGIIdl day day 365 Present & Future Value • present value (PV) = value of the , loan or investment today • future value (FV) or maturity value = final amount of the loan or investment at the end of the last ~ period II I C l Simple Interest Future Value • FV = PV x (I + (i x n)] • where i = interest rate per period; n = , number of periods Compound Interest Future Value • FV = PV x ( I + i )" • where i = interest rate in percent per period; n = number of periods Interest Earned = FV - PV • residual value (or salvage value, scrap value) = cash value of asset at end of useful life Straight line Method: Depreciation expense is equal over eaeh year of its useful life • depreciation expense per year = (asset cost - residual value) estimated useful life of asset in years • partial-year depreciation expense = depreciation expense per year x number of months of useful life in the year 12 Units of Production Method: Depreciation expense based on the usage of the asset • depreciation rate per unit = (asset cost - residual value) estimated total number of units produced over useful life of asset ~ C III II i , • depreciation expense per year = depreciation rate per unit X number of units produced per year Service Hours Method: Depreciation expense based on hours of useful service • depreciation rate per service hour = (asset cost - residual value) estimated total number of hours of useful service over useful life of asset • depreciation expense per year = depreciation rate per service hour x number of service hours per year Sum of Years-Digits Method: Depreciation expense is greater for earlier years than for later years • sum of years-digits = sum of the digits representing year of useful life OR sum of years-digits = N (~ +1), where N is the number of years of useful life • for an asset with six years of useful life, sum of years-digits = + + + + + = 21, or 6(;+1) =4{=21 • depreciation expense per year = (asset cost - residual value) remaining useful life in years sum of years-digits x Declining Balance Method: Depreciation expense declines steadily over the useful life of the asset • depreciation rate for double declining balance method = (100% estimated number of years of useful life of the asset) x • depreciation expense per year = book value of asset at the beginning of the year x depreciation rate • book value of asset at the beginning of a year = book value of asset at the end of the previous year • book va~ue at the end of a year = asset cost x (1 - depreciation rate)n; n = estimated number of years of useful life of the asset Cost of Goods Sold • cost of goods sold = cost of goods available for sale - cost of ending inventory Weighted Average Method: Used to calculate cost of ending inventory when the goods available for sale were purchased at different costs at different points in time cost of goods available for sale • weIghted average cost per umt = number of units available for sale • cost of ending inventory = units in ending inventory x weighted average cost per unit First In-First Out (FIFO) Method: Used to calculate cost of ending inventory when the goods available for sale were purchased at different costs and at different points in time; assumption is that goods purchased earliest into inventory are the ones that are sold first; goods in ending inventOlY are those that were purchased most recent~v • cost o f ending inventory = units in ending inventory X their corresponding costs Last In-First Out (LIFO) Method: Used to calculate cost of ending inventory when the goods available for sale were purchased at different costs and at different points in time; assumption is that goods purchased most recently into inventory are the ones that are sold first; goods in ending inventory are those that were purchased the earliest • cost o f ending inventory = units in ending inventory x their corresponding costs Inventory Turnover: How often a business sells and replaces its inventory; usually over a year • inventory turnover at retail = net sales average IOventory at retaIl • average inventory at retail = beginning inventory at retail + ending inventory at retail cost of goods sold • mventory turnover at cost = average IOven t orya t cos t • average inventory at cost = beginning inventory at cost + ending inventory at cost BASIC FINANCIAt REPORTS Inco me St ateme nt (Profit and Loss [P & L! Statement): A financial report of a business that shows net profit or loss for a specific period by reporting revenue and expense items during that period of operations Sales Tax: Tax paid on purchase of most goods and services, though some are exempt from sales tax; it is applied to the net price (selling price - trade discounts) but not to shipping charges; sales tax varies between states; collected by the business and paid to the state government • sales tax = net price x sales tax rate • purchase price = net price (1 + sales tax rate) • actual sales = total sales 1+ sales tax rate Excise Tax: Tax paid on specific goods and services, such as luxury automobiles, gasoline and air travel • excise tax = net price x excise tax rate Property Tax: Levied on the assessed value of property by local government to pay for services such as schools, fire and police services; assessed value is a fraction of actual market value of the property that is used for tax purposes • property tax rate = estimated revenue from tax total taxable assessed value OR budgeted need of local government property tax rate = total taxable assessed value • assessed value = market value x assessment rate • property tax = assessed value x property tax rate • mill rate: a mill is 1/1000 of a dollar or 0.001 dollar; tax rate in mills is the tax per $1,000.00 of assessed value Income St atement Items • revenue from sales (or revenues, sales, income, turnover) • sales = number of items x Oist price - trade discount) • net sales = sales - sales discount or cash discount • cost o f goods sold COGS (or cost of sales) is the amount a product cost to produce • COGS = net purchase price + cost of acquiring, preparing and placement of goods for sale • gross profit on sales (or gross profit) = net sales - cost of goods sold gross profit • gross margm percent = net sales x 100 • operating expenses (including general and administrative expenses IG & AI) = expenses to manage the business, and include salaries, legal and professional fees, utilities, insurance, stationery supplies, property and payroll taxes • sales and marketing expenses = expenses needed to sell products, and include sales, salaries and commissions, advertising, freight and shipping • R&D expenses = expenses incurred in research and development • operating expense = G & A expense + sales & marketing expense + R&D expense • earnings before interest, taxes, depreciation and amortization (EBITDA) OR operating income = gross profit - operating expense • operating margins percent = ;!IJa?:S x 100 • earnings before interest and taxes (EBIT) = EBITDA - depreciation and amortization expenses • earning before taxes (EBT) or pretax net income = EBIT - interest expenses • taxes include federal, state and local government taxes on income • net income (or earnings) = EBT - taxes Series of periodic payments usually made in equal amounts; payments computed by compound interest methods; payments made at equal intervals oftime • profit margin = net income x 100 net sales payment dates Balance Sheet • assets - liabilities = owner's equity or shareholder's equity • assets are items on a company's books that have a positive monetary value; they typically include items of obvious value, such as cash or equivalent investments (treasuries, CDs, money market), accounts receivable, prepaid expenses, inventory of finished goods that are ready for sale, depreciated real estate and equipment, and other intangibles, such as goodwill, copyrights, trademarks and patents • liabilities are monies owed; they typically include accounts payable, bank and bond short-term debt (to be paid off within a year), and long-term debt Basic Financi al St at ement Ratio s • liquidity ratios: measures of ability jilr a business to meet short-term obligations • current ratio = current assets -;- current liabilities • quick ratio = cash + accounts receivable -;- current liabilities • activity ratios: measures ofefficiency in generating sales with assets • days inventory 365 lOventory turnover = • collection period = acco~nts receivable credIt sales per day cost of goods sold • mventory turnover = average lOven t ory • asset turnover net sales total assets • profitabili!y ratios: measures ofreturns = return on sales = net income net sales return on assets (ROA) = net income total assets • return on equity (ROE) = net in~ome eqUIty earnings available to common stockholders • earnings per share = -=-n~u=-=-m~b-"'e':":r =o"-f:;;=sh;="'a-"'re-"s~o"'f';C' -common stock outstanding • price to earnings (P/E) ratio = price per share of common stock earnings per share LIFE INSURANCE Life Insurance: Insurance that pays a specified sum to the policyholder's beneficiary at the time of the policyholder's death • insured: person covered by policy • policyholder/policy owner: person who owns policy • premium: periodic payments made for insurance coverage • face amount: proceeds received on the death o(the insured • beneficiary(ies): person(s) who receivers) the face amount Types of Life Insurance • term life is life insurance coverage for a specified period oftime; can be at a guaranteed rate or a guaranteed rate for a period of time and then a projected rate; no cash value except face amount in event of death of insured within the period of the insurance • whole life is life insurance that has a guaranteed level premium (i.e., no increases in premium) and a guaranteed cash value; also called straight life or ordinary life • universal life is life insurance that is permanent; premiums are not guaranteed (i.e., may go up or down) Period of time between two successive Time between the beginning ofthe first payment period and the end of the last payment period Future dollar amount of a series of annuity payments and the accrued interest • annuity certain: term of annuity begins and ends on definite dates; has a specified number of payments • contingent annuity: term of annuity begins on a definite date, but ending date is dependent on a future or uncertain event; no fixed number of payments • perpetual annuity: term of annuity begins on a definite date, but has no ending date; length of term is infinite D • ordinary annuity: periodic payments are made at the end of each payment period • deferred annuity: periodic payments are made at the end of each payment period, but the term of the annuity begins after a specified period of time • annuity due: periodic payments are made at the beginning of each payment period Je of an Ordinary Annuity • using annuity tables • future value of ordinary annuity = annuity payment per period x ordinary annuity table factor • using formula • future value of ordinary annuity = annuity payment amount per period x [ ... • liquidity ratios: measures of ability jilr a business to meet short-term obligations • current ratio = current assets -;- current liabilities • quick ratio = cash + accounts receivable -;- current... data is called a frequency distribution US $5.95 CAN $8,95 Author: Ravi Behara, PhD, NOTE: This QuickStudy" guide is intended for infonnational purposes only, Due to its condensed fonnat, this guide... trade discounts) but not to shipping charges; sales tax varies between states; collected by the business and paid to the state government • sales tax = net price x sales tax rate • purchase price