Sorry that the math stuff did not work in the Chapter 4 post. I do not have time to fix it so refrenced the book for the material folks. I tried an experiment with an editor that let me do math stuff but blogger does not seem to like it...

Chapter 4 - Risk and Return: The Basics

1. Investment Returns
   

   One way to express the return on an investment is how much of a dollar
   return you have made.

   
   

   Dollar Return = Amount received - Amount invested

   
   

   The problem with this is that It does not tell you how long the money
   was held nor how much money it took to get that return. In its place we
   can use a Rate of Return

   
   

   Rate of Return = (Amount received - Amount invested)/Amount
   Invested

   
   

   This resolves the problem by giving us a percentage of the original
   investment. If we then can express this across the years that the
   security is held then we can get the interest as an annual rate of
   return.

   
   


2. Stand Alone Risk
   

   Stand alone risk is defined as an exposure to loss or injury. In any
   security purchased one will be exposed to a chance that their will not be
   a payback of the money invested as well as any extra payback. This is the
   risk taken to invest in the security.

   
   

   One can look at these risks in two ways. The stand alone risk is where
   the security is the only one owned. If you had one security that was
   fairly secure in its return (a treasury bill for example) then it would
   be considered risk free. On the
   other hand, something moth return the same rate of return but have a
   chance of loosing your money, this is would be highly risky. How you
   invest would be a consideration of if you feel you can handle risk or
   not. In no case should you invest if your expected rate of return is not
   high enough to compensate for the perceived risk of the investment.

   
   

   One good/bad think about risky assets is they rarely return their
   expected rate of return. It is usually much higher (good) or much lower
   (bad).

   
   
   
   
   1. Probability Distributions
      

      This is defined as the chance that an event may occur. In
      investing we can say that a particular security could have a chance
      of returning a certain amount on its investment. This can even be
      broken down to the chance being strong, normal and weak, or even more
      shades as well as the percentages that they will happen with them.
      This becomes the probability distribution.

      
      
   
   
   2. Expected Rate of Return
      

      Multiply the possible outcomes by the probability that they will
      occur. Then take them and sum them up. This is the weighted average
      of outcomes. This is also know as the expected rate of return. It is
      named in formulas as r with a ^ symbol over it (called r-hat). Many
      securities can wind up with the same Expected Rate of Return even
      though they are widely varied in the chance they will succeed.
      Obviously we need another tool.

      
      
   
   
   3. Measuring Stand-Alone Risk: The Standard Deviation
      

      If we graph the probability distribution in a continuous curve we
      can see that some securities will have a tighter graph than others
      will. The tighter the graph, the smaller the risk is for the
      security. We measure this tightness by using a 'standard deviation',
      the symbol being σ and pronounced sigma. To find the standard
      deviation we do 4 steps:

      
      
      
      
      1. Calculate the expected rate of return
         

         Expected rate of return = r-hat = $$
         
         ∑
         
         i
         =
         1
         
         n
         
         P_ir_i

         
         
      
      
      2. Subtract the expected rate of return (r-hat) from each possible
         outcome (r_i) to get a set of deviations.
         

         Deviation = r_i - r-hat

         
         
      
      
      3. Square the deviation and multiple it by the chance that it
         might occur and then sum them to get the variance.
         

         Variance = σ² = $$
         
         ∑
         
         i
         =
         1
         
         n
         
         (r_i - r-hat)²P_i

         
         
      
      
      4. Finally do a square root of the Variance to find the standard
         deviation.
         

         The lower this standard deviation is, the tighter the graph it
         would produce and the less risk that it has. All things being
         normal, you can expect the actual return will be within one
         standard deviation of the expected rate of return.

         
         
      
      
      
      
   
   
   4. Using Historical Data to Measure Risk
      

      We have assumed to this point that we have a known probability
      distribution. If we have some sample return data form past periods we
      can figure out standard deviation as well.

      
      

      Estimated σ = S =$$
      
      
      
      
      ∑
      
      r
      =
      1
      
      n
      
      
      (
      
      rbar
      t
      
      
      −
      
      rbar
      Avg
      
      
      )
      
      
      
      2
      
      
      
      
      n
      −
      1
      
      
      
      

      
      

      Historic sigma is often an indicator of future sigma.

      
      
   
   
   5. Measuring Stand -Alone Risk: The Coefficient of Variation
      

      Given a choice, we will tend to choose the investment with the
      less risk, so will choose between two investments with the same
      expected returns the one with the lowest standard deviation. If two
      had the same standard deviation but one a higher expected return we
      would go for it. What do you do if neither has one that is the same.
      The coefficient of variation (CV devides the standard deviation by
      the expected return.

      
      

      CV = $$
      
      σ
      rhat
      
      

      
      

      This shows the risk per a unit of return so that they can be
      compared better. The lower this number is, the better the chance that
      it will bring a good return.

      
      
   
   
   6. Risk Aversion and Required Returns
      

      Most people will choose the less risky return on investment and
      therefore we could say that they have risk aversion. While this is
      not bad in itself, it can have influence on things that get invested
      in. If you had two stocks, one was less riskier, that sold for the
      same price, most would go for the less riskier one. Since there would
      be more demand for it, the price would go up and the return would go
      down. Likewise those who own the risker one would sell causing its
      price to drop, changing its risk and return. The differences in the
      start and finish price is known as the risk premium (RP).

      
      
   
   
   
   


3. Risk in a Portfolio Context
   

   By adding stocks together in a portfolio, the risks of one stock can
   offset the risks of other stocks. In fact many stocks can be up while
   others are down and this can balance out the portfolio.

   
   
   
   
   1. Portfolio Returns
      

      To get the expected return on a portfolio add together the
      weighted averages of all the members of the portfolios.

      
      

      rbar_p = $$
      
      ∑
      
      i
      =
      1
      
      n
      
      
      w
      i
      
      
      rbar
      i
      
      

      
      
   
   
   2. Portfolio Risk
      

      The risk of the portfolio will almost always be smaller than the
      weighted average of the asset's σ. One thing should be noted
      about stocks that are up when others are down. If we had ones that
      has a perfect correlation (one was at the exact opposite point of th
      other), they would cancel each other out and have no risk. In truth
      it is not possible to get stocks in perfect alignment like this so we
      measure the correlation coefficient (noted as ρ (pronounced
      rho)). ρ can range from -1 (if exact opposites) to +1 (if exactly
      the same). For that reason, in order to diversify we must find stocks
      that have ρ that cancel each other out. In general you would want
      to have investments in tow or more separate industries instead of
      just all in one. If they are all in one industry type, the problem is
      that when that industry goes into a slump so will all the investments
      that you own in it.

      
      
   
   
   3. Diversifiable Risk versus Market Risk
      

      It is not impossible to find stocks that are negatively correlated
      as they tend to work with the economy as a whole. So there is risk in
      any investment but not as much if all is held in one stock. A market
      portfolio, all the stocks combined, should have a standard deviation
      of about 20.1 %. By research it is found that 40 or more stocks in
      diversified industries should diversify out most risk involved. The
      risk involved in a stock that moves with the market itself is called
      Market Risk, the part that deals with the stock itself and how
      lawsuits, strikes, etc. can affect it is called diversifable risk.
      Market risk can not be diversified out, diversifiable risks can.
      Capital Asset Pricing Model (CAPM), is used to analyze the
      relationship between risk and rate of return.

      
      
   
   
   4. The Concept of Beta
      

      The relevant risk of an individual stock is called its beta
      coefficient. and is defined under CPAM as the amount of risk that the
      stock contributes to a portfolio.

      
      

      $$
      
      b
      i
      
      =
      
      (
      
      
      σ
      i
      
      
      σ
      M
      
      
      )
      
      
      ρ
      iM
      
      

      
      

      A stock with a high standard deviation ($$
      
      σ
      i
      
      ) will have a high beta. It is possible to use a calculator or
      a spreadsheet to do the job. You can also take a graph and plot the
      stock as its return on the y and the market portfolio as the x, we
      could plot the graph of the graph of expectations by setting another
      point by using the slope with the various beta possibilities (2.0
      high, 1.0 average, .5 low) then we can figure out the , then we could
      see volatility possibilities.

      
      
   
   
   
   


4. Calculating Beta Coefficients
   

   Different organizations calculate Betas in different way so other than
   sticking with a beta from one organization it is a good idea to calculate
   your own. The first step is to compile the data for the company you want
   plus a standard to go by (say the S & P 500 Index). Second is to
   convert the data to rates of return (change from previous month/this
   month value) for both the stock and the standard. Plot on a graph the
   returns of the company against the standard and run a line through them
   to show the regression (Spreadsheets may make this easier). The slope of
   the line would be the beta.

   
   


5. The Relationship Between Risk and Rates of Returns
   

   The Market Risk Premium ($$
   
   RP
   M
   
   ) is the premium that people want for bearing the risk of the
   average stock. It would be the current market risk minus the risk free
   premium. We can use this to calculate our required return

   
   

   Required return = Riskfree return + premium for risk .

   
   


6. This leads to the Security Market Line (SML)
   

   $$
   
   r
   i
   
   =
   
   r
   RF
   
   +
   
   (
   
   r
   M
   
   −
   
   r
   RF
   
   )
   
   b
   i
   
   
   

   
   
   
   
   1. The Impact of Inflation
   
   
   2. Changes in Risk Aversion
      

      The slope of the SML reflects the averseness to risk of the
      investor.

      
      
   
   
   3. Changes in a Stock's Beta Coefficient
      

      A firm can influence its own beta by the assets it has and the use
      of it's debt. Other external factors can influence it as well.

      
      
   
   
   
   


7. Projects versus Securities
   

   Only by analyzing these situations can we begin to understand
   comparing projects in a business environment

   
   


8. Some Concerns About Beta and the CAPM
   

   There are some problems with CAPM. The size of a firm and it's
   market/book ratio can affect the CAPM but have no real effect on the
   beta.

   
   


9. Volatility versus Risk
   

   Volatility and risk are not the same thing. A company can have wild
   fluctuation and still be very profitable. Rule to follow, earnings
   volatility does not necessarily mean risk but stock price volatility
   does.

   
   

Chapter 3 - Financial Statements, Cash Flows, and Taxes

1. Financial Statements and Reports
   
   Annual reports contain a narrative on how company is going. It also
   contains four financial statements (Balance sheet, income statement,
   statement of retained earnings, and statement of cash flows), to show
   what is really happening. These both work together to tell us about the
   company.


2. The Balance Sheet.
   
   A balance sheet is a snapshot of a company, usually on the last day of
   business for the year but can be done at any time. It will be different
   for what ever day it is run.
   
   The left side lists Assets (money or things that can be converted to cash
   within a year). The right side will be liabilities and equity (money we
   owe to others).
   
   
   
   
   
   1. Assets
      
      
      
      
      
      • Money
      
      
      • Quickly converted securities
      
      
      • account receivable
      
      
      • Inventories (LIFO and FIFO methods of accounting can affect the
        numbers)
      
      
      • Depreciation of plant and equipment
      
      
      
      
   
   
   2. Liabilities
      
      
      
      • Accounts Payable
      
      
      • Notes Payable
      
      
      • Long Term Bonds
      
      
      • Preferred Stock Dividends
      
      
      • Common Stock Dividends
      
      
      • Retained Earnings
      
      
      
      

      Total liabilities should be equal to total assets.

      
      
   
   
   
   


3. The Income Statement
   

   Income statement shows numbers over the year. It will start with Net
   Sales and will subtract form the the operating costs. This gives us
   Earnings Before Interest, Taxes, Depreciation, and Amortization (EBITDA).
   After this, things are listed and removed from the EBITDA that will
   affect tax payments (Depreciation and amortization). This is followed by
   Interest and then Taxes. Preceded and then common dividends follow.
   Lastly, information about per share numbers are posted.

   
   


4. Statement of Retained Earnings
   

   This statement starts with what a company started with last year and
   then adds in income for the year. It then subtracts dividends to give us
   retained earnings for the year.

   
   


5. Net Cash Flow
   

   Net Cash Flows are figured by the information from statements.

   
   

   Net Cash Flow = Net Income - Noncash revenues + Noncash charges

   
   

   Noncash charges would be depreciation and amortization. Noncash
   revenues often net out as $0 so a good rewrite on the equation would
   be

   
   

   Net Cash Flow = Net Income + Depreciation and Amortization

   
   

   Depreciation takes the cost of a machine and expenses it over the life
   of the machine instead of just the year that it is purchased. It must be
   added back here so that we can get a true net income.

   
   


6. Statement of Cash Flows
   

   This statement summarizes where cash went throughout the year. It
   contains:

   
   
   
   
   • Operating Activities
   
   
   • Investing Activities
   
   
   • Financing Activities
   
   
   
   

   Profits can be doctored in many ways but it would be difficult to do
   so and have the statement of earnings still look good.

   
   


7. Modifying Accounting Data for Managerial Decisions
   
   
   
   1. Operating Assets and Total Net Operating Capital
      

      Because two firms, or even two divisions in a company can use
      different accounting methods, it is necessary to find ways to compare
      them. To do so we compare operating income and operating assets.
      First we need to modify total assets. It becomes Operating Assets
      (necessary to run business) and non-operating assets (cash and short
      term inventory above what is needed to run company).

      
      

      Operating Assets are then further divided to operating current
      assets (inventory) and long term operating assets (plans and
      equipment) We will also have operating current liabilities (accrued
      wages and taxes) so that:

      
      

      Net Operating Working Capital = Operating Current Assets -
      Operating Current Liabilities

      
      

      We also have:

      
      

      Total Net Operating Capital = Net Operating Working Capital - Long
      Term Assets.

      
      
   
   
   2. Net Operating Profit After Taxes (NOPAT)
      

      NOPAT = EBIT * (1 - Tax Rate)

      
      

      EBIT is from the Income Statement (tax rate is listed there as
      well).

      
      
   
   
   3. Free Cash Flows
      

      Free Cash Flows (FCF) is cash flow actually available for
      distribution to investors after investment in fixed
      assets and working capital necessary to sustain operations have been
      taken out.

      
      
   
   
   4. Calculating Free Cash Flows
      

      FCF = NOPAT - Net investment in operating capital

      
      

      Gross Investment in Operating Capital = Net Investment +
      Depreciation

      
      

      FCF = (NOPAT + Depreciation) - Gross Investment in Operating
      Capital

      
      
   
   
   5. The Uses of FCF
      
      
      
      • Pay Interest to debt holders
      
      
      • Repay Debt holders (pay off debt)
      
      
      • Pay dividends to stockholders
      
      
      • Purchase Stock from shareholders
      
      
      • Buy marketable securities or other non-operating assets
      
      
      
      
   
   
   6. FCF and Corporate Value
      

      The value of a firm primarily depends on its expected FCF.

      
      
   
   
   7. Evaluating FCF, NOPAT, and Operating Capital
      

      Negative FCF is not necessarily a bad thing. Staying negative for
      a long rimland letting it continue could be. Negative FCF could be
      due to investing in equipment for growth purposes. Also, if the NOPAT
      and the FCF is both negative, this needs to be a warning. Check the
      Return of Invested Capital (ROIC) to see if it is in the right range
      of what an investor should be looking for, the Weighted Average Cost
      of Capital. If ROIC is above WACC then it is usually a good
      investment.

      
      
   
   
   
   


8. MVA and EVA
   
   
   
   1. Market Value Added (MVA)
      

      MVA = Total Market Value - Total Capital

      
      

      Total Market Value = (Market Value of Stock + Market Value of
      Debt).

      
      
   
   
   2. Economic Value Added (EVA)
      

      EVA = NOPAT - After Tax Dollar Cost of Capital Used to SUpport
      Operations

      
      

      EVA = EBIT * (1 - Tax Rate) - Net Operating Capital /WACC

      
      

      EVA = (Operating Capital) * (ROIC - WACC)

      
      

      EVA is an estimate of a business's true economic profit for the
      year. There is a relationship between MVA and EVA but it is no t a
      direct one. However, if one is either negative or positive, the other
      is usually the same sign.

      
      
   
   
   
   


9. The Federal Tax System
   
   
   
   1. Corporate Income Taxes
      

      Taxes are figured by income time the tax percentage charged by the
      government.

      
      
      
      
      1. Interest and Dividend Income Received by a Corporation
         

         A company can take 70% of income that it receives as a
         dividend of another corporation and not have to pay taxes on it.
         

         
         

         Also if a company pays out dividends to shareholders, those
         share holders have to pay taxes on them on top of the taxes the
         company paid. For that reason it may be worthwhile to invest in
         another corporation and get a tax break and an income as well.
         

         
         
      
      
      2. Interest and Dividends Paid by a Corporation
         

         Because debt reduces income before taxes, $1 paid to debt does
         not equal $1 paid out as dividends, it is better to pay off debt
         that to pay out dividends.

         
         
      
      
      3. Corporate Capital Gains
         

         Laws used to be in favor of these but are now not longer that
         way.

         
         
      
      
      4. Corporate Loss, Carry-Back and Carry-Forward
         

         If a company takes a loss one year, then the losses can be
         claimed against the previous two years (and get a refund from
         them), and then what is left can be claimed on future taxes up
         till 20 years from now.

         
         
      
      
      5. Inappropriate Accumulation to Avoid Payment of Dividends
         

         The IRS does not want corporations to hold what would be paid
         out in dividends. They set a limit of what could be held at
         $250,000 unless a company has a good reason for doing so.

         
         
      
      
      6. Consolidated Corporate Tax Returns
         

         When a company owns 80% of another company, the companies can
         file taxes jointly so that losses from one company can help out
         the more prosperous company.

         
         
      
      
      
      
   
   
   2. Taxation of Small Business Corporations
      

      Small business that meet IRS rules may incorporate for protection
      as an S corporation but still have the income distributed to the
      owners at a pro-rated rate to ownership.

      
      
   
   
   3. Personal Taxes
      

      This section deals with various taxes that must be paid and how
      they affect personal income.

      
      
   
   
   
   

Managerial Finance Chapter 2 - Time Value of Money

1. Time Lines
   Time lines are used to make the problem clear. You would lay out a line with tic marks on it above which would be the time periods in numerical order. Between the tic marks would be the Interest Rates, (if they do not vary only listing it once would be enough). Below the ticks would be the cash flows, real or calculated.
2. Future Value
   To know what money is going to be worth in the future, we must be able to calculate it. The following are commonly used.
   
   PV is Present value
   
   i is set as interest rate, what the money will earn. It can also be noted as I or r (mostly used in financial literature)
   
   INT is the dollars of Interest earned. INT = Beginning amount X i
   
   FV_n is the amount that you have earned at the end of n amount of periods.
   
   n is the number of periods that we are calculating for.
   
   We could calculate each period by using the formula FV = PV + INT which can be broken down to FV = PV(1+i). By extension, we could say FV_n = PV(I + i)ⁿ
   This process is called compounding.
   
   These and all other problems can be solved by using a regular calculator, a financial calculator or a spreadsheet program. What works best for you is what you should use.
   
3. Present Value
   In previous example we figured out what our amount would be worth in the future. We can also calculate for what the value of a future amount of money would be worth now. This is defined as Present Value (PV). To figure it out you need to follow a procedure called discounting. Like before, a time line would be the best way to see what is going on visually. Using the formula from before we can extrapolate a formula to figure PV
   
   PV = FV_n (1/1+i)ⁿ
   
   Again, several ways to solve, chose your best way.
4. Solving for Interest Rate and Time
   FV_n = PV(I + i)ⁿ is a handy formula to know. If we want to solve for interest (i), we must know the other values, likewise for time (n).
5. Future Value of An Annuity
   An annuity is a series of equal payments made at fixed intervals for a specific number of periods. They can be Ordinary or Due.
   
   1. Ordinary Annuities
      In an ordinary Annuity, the payments are made at the end of a time period. An example would be an deposit into a savings account of 100 each year, what would it be worth at each time point. Unlike the FV problem, We keep putting money into the account on a regular basis. This now creates a series of FV problems that must be added together.
   2. annuities Due
      The difference between this and Ordinary Annuities is that payments are made at the beginning of the periods not at the end. This changes the problem slightly but it is still a series of FV problems.
6. Present Value of an Annuity
   No notes taken from book. Mostly how to do on various methods.
7. annuities: Solving for Interest Rate, Number of Periods, or Payment
   No notes taken from book. Mostly how to do on various methods.
8. perpetuites
   Most annuities call for the payments to be made over time, but, a perpetuities is an amount paid regularly for an indefinite period of time. To find the PV you would use:
   
   PV = PMT/i
   
   This winds up being different at different interest rates.
9. Uneven Cash Flow Streams
   Our book will use PMT (Payment ) for annuity situations and CF (Cash Flow) for uneven cash flows. We will use this for when situations develop that income does not come in as steady as it would in an annuities.
   1. Present Value of an Uneven Cash Flow Stream
      Like an annuity, this becomes a series of PV problems with each amount being calculated back to the 0 year and the sums being added together. Spreadsheets are good for this as are Financial calculators that have a CF register in them.
   2. Future Value of an Uneven Cash Flow Stream
      Live the above, we now calculate the other way and again sum things up.
   3. Solving for i with Uneven Cash Flow Streams
      This will really need to be done with a spreadsheet or financial calculator. Attempting it with a regular calculator is a hit or miss way of doing things.
10. Growing Annuities
    No notes taken from book. Mostly how to do on various methods.
11. Semiannual and Other Compounding Periods
    If an interest rate is compounded once a year that would be called annual compounding, twice a year is semiannual compounding. For problems we do we must know what type of periods we are doing and if the interest is per that period or annual. It may need to be changed to deal with a solution to the problem.
    1. Types of Interest Rates
       
       1. Nominal or quoted rate: Often called the Annual Percentage Rate (APR) is the value that is most often quoted but as noted above, it must be taken into account with the times that the rate will have interest charged.
       2. Periodic rate: This is the rate charged per a period. You would use it with time lines and with calculations.
       3. Effective (or equivalent) annual rate (EAR) - annual rate that produces the same results as if we had compounded at a given periodic rate m times a year.
    2. The Result of Frequent Compounding
       Because you earn interest on interest, frequent compounding will result in increased income.
12. Fractional Time Periods No notes taken from book. Mostly how to do on various methods.
13. Amortized Loans
    amortized loans include interest as well as principal payments back to the lender. It is necessary to us tools to figure out these breakdowns as to what is payment and what is interest.