# Mathematics of Investing How you can bring appreciable growth to assets over time ? Wilson B. Gräb Forsyth Technical CC Winston-Salem, NC

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Mathematics of Investing How you can bring appreciable growth to assets over time ? Wilson B. Gräb Forsyth Technical CC Winston-Salem, NC wgrab@forsythtech.edu

2 Key to Investing “Buy Quality and Diversify” John Woodard Woodard & Company

Why Invest ? 3 Inflation Rate – 1.7% Money Market Rate – 1.0% Savings Rate – 0.75% Losing Purchasing Power at Rate of 0.7% per Year

Why Invest ? To grow your assets over a specified period of time To provide for your retirement To provide for your children's education To participate in future product development To protect and preserve items of interest to you – historic sites, etc. 4

Where to Invest 5 Real Estate Domestic Stock Market (Stocks – Bonds – Securities) International Stock Market (Stocks – Bonds – Securities) Antiques - Collectables Automobiles Education (Self or Others) Whatever is of interest to you

6 Markets Served Depending on the item selected from the previous slide, one needs to understand the applicable market and its cycles, drivers, risk and reward potential, and volatility. One also needs to consider Market Segmentation – Are there sub-markets that should be considered as being separate from the Main Market – Antiques – Glassware – Frackturs - Coins

7 Basic Terms and Definitions Stock – ownership in a company Bond – loan to a company Mutual Fund – grouping of stocks, bonds or both Growth Stock – Stock whose earnings are expected to grow above average rate Dividend Stock – Stock that pays a dividend but whose growth is less than a growth stock

8 Basic Terms and Definitions cont’d Large Cap Stock - market capitalization value of more than \$10 billion Mid Cap Stock -market capitalization between \$2 and \$10 billion Small Cap Stock - market capitalization of between \$300 million and \$2 billion Penny Stock - stock that trades at a relatively low price and market capitalization, outside major market exchanges. Extremely HIGH Risk

9 Basic Terms and Definitions cont’d Mutual Funds - No Load - A mutual fund in which shares are sold without a commission or sales charge Mutual Fund – Loaded - A mutual fund that comes with a sales charge or commission. The load is either paid up front at the time of purchase (front-end load), when the shares are sold (back- end load), or as long as the fund is held by the investor (level-load).

10 Basic Terms and Definitions cont’d Municipal Bonds -A debt security issued by a state, municipality or county to finance its capital expenditures, usually triple tax free Junk Bonds - Term for a high-yield or non-investment grade bond, fixed- income instruments that carry a low rating because of their higher default risk in relation to investment-grade bonds.

11 Basic Terms and Definitions cont’d Dividends - Dividend per share (DPS) is the total dividends paid out over an entire year (including interim dividends but not including special dividends) divided by the number of outstanding ordinary shares issued. Can be expressed as a % or a figure

12 Basic Terms and Definitions cont’d DPS can be calculated by using the following formula: DPS = (D – SD)/S D - Sum of dividends over a period (usually 1 year) SD - Special, one time dividends S - Shares outstanding for the period

13 Basic Terms and Definitions cont’d EPS – Earnings per Share - The portion of a company's profit allocated to each outstanding share of common stock. Earnings per share serves as an indicator of a company's profitability.

14 Basic Terms and Definitions cont’d EPS = (Net Income – Dividends on Preferred Stock)/Average Outstanding Shares When calculating, it is more accurate to use a weighted average number of shares outstanding over the reporting term, because the number of shares outstanding can change over time.

15 Dividend Performance Item1 YR 3YR 5YR 10YR Item A15% 10% 10%8% Item B5% 4% 3%2% Item C2% 3% 4%5%

16 52 Week Performance 52 Week High\$80.00/S hare 52 Week Low\$40.00/Share Current Price A\$60/Share Current Price B\$50/Share Current Price C\$70/Share

17 Growth Rate For Specific Stock Industry Growth Rate Historical – you select the time period Projected – Based on analyst or company estimates Contributing Factors – Laws, economy, resources, etc. Use Excel for Regression Analysis, Graphing, and R 2 Value

18 Bond Basics and Types Government Bonds Municipal Bonds Corporate Bonds Zero Coupon Bonds

19 Bond Basics and Types Face Value/Par Value The face value (also known as the par value or principal) is the amount of money a holder will get back once a bond matures.par value When a bond trades at a price above the face value, it is said to be selling at a premium. When a bond sells below face value, it is said to be selling at a discount.premium discount

20 Bond Basics and Types Maturity The maturity date is the date in the future on which the investor's principal will be repaid. Issuer The issuer of a bond is a crucial factor to consider, as the issuer's stability is your main assurance of getting paid back.

21 Bond Basics and Types The bond rating system helps investors determine a company's credit risk. Think of a bond rating as the report card for a company's credit rating.bond rating Bond Rating GradeRisk Moody\'sS&P/ Fitch AaaAAAInvestment Highest Quality AaAAInvestmentHigh Quality AAInvestmentStrong BaaBBBInvestment Medium Grade Ba, BBB, BJunkSpeculative Caa/Ca/CCCC/CC/CJunk Highly Speculative CDJunkIn Default

22 Morningstar Ratings - Mutual Funds Is a descriptive, backward-looking measure of historical performance Is strictly quantitative--there is no analyst input or opinion Combines return and risk (volatility) Is calculated once per month

23 Morningstar Ratings - Mutual Funds Compares funds with their peers in specific investment categories Has a fixed distribution of stars--10% of funds within each category receive 5 stars, 22.5% receive 4 stars, 35% receive 3 stars, 22.5% receive 2 stars, and 10% receive 1 star

24 Morningstar Ratings - Stocks Is a measure of whether or not the stock is over- or undervalued based on forward-looking estimates Is risk adjusted Is based on both quantitative and subjective inputs--it includes analysts' opinions, which are embedded in their estimates of future cash flows

25 Morningstar Ratings - Stocks Is calculated daily Does not divide stocks into comparison groups, nor does it have a fixed distribution of stars--the percentage of stocks receiving 5 stars will fluctuate daily.

26 Math Tools Utilized For Evaluation Regression Analysis – evaluate trends Ratios – Proportions Probability Statistics – Mean – Median Allocation

27 Free Internet Links www.Fidelity.com www.Morningstar.com www.Pimco.com www.putnam.com www.Scottrade.com www.thestreet.com www.transamerica.com www.TRowePrice.com www.Vanguard.com www.TDAmeriTrade.com

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