Cash Flow

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					  Capital Investment Analysis

• Determine whether an investment should
  be undertaken or not
  – Capacity expansion (machines, facilities)
  – Equipment replacement
• Selects between investment opportunities
  (mutually exclusive choices)
• Selects best portfolio of investment
  within a budget
               Basics

• Cash Flow Diagram: the financial
  description of a project
• Time Value of Money: the value of
  money changes with time
• Interest: used to move money through
  time for comparisons
• Measure of Worth: method in which to
  financially evaluate a project
             Cash Flow
• Movement of money (in or out) of a
  project

• Inflows: revenues or receipts
• Outflows: expenses or disbursements
• Net Cash Flow: receipts - disbursements
        Cash Flow Diagram
• Describes type, magnitude and timing of
  cash flows over some horizon
• Used to describe any investment
  opportunity.
• Typical investment:
       Cash Flow Analysis
• Given that any investment opportunity
  can be drawn by a cash flow diagram,
  how can we select the best?
• Transform all cash flow diagrams into
  something similar for comparison.
  – Use a Common Interest Rate
  – Use Time Value of Money Calculations
       Time Value of Money
• Money has value because it gives us
  utility.
• Generally, money is preferred now, as
  opposed to later (same amount)
  – One can spend it now and get utility
  – One can invest it and watch it grow into
    larger sums for greater future utility
  – One can put it under the mattress and watch
    it lose purchasing power
       Time Value of Money
• To describe the same amount of money at
  different periods of time requires the use
  of interest.
• Generally, money grows (compounds)
  into larger future sums.
• Similarly, money is smaller (discounted )
  in the past.
                  Interest
• Cost of Money
  – Rental amount charged by lender for use of money
  – In any transaction, someone “earns” and someone
    pays
• Savings Account:

• Home/Auto Loan:
                 Definitions
• Principal: P
   – Amount invested or loaned
• Interest Rate: i
   – Rental charge for money defined as a percentage
     of principal per time period
• Compounding Period
   – Defines how often interest is calculated (may not
     be paid, however)
• Length of loan/investment: n periods
           Simple Interest
• Interest earned/paid is directly
  proportional to capital involved.
        Compound Interest
• Interest is paid on both the capital and
  accrued interest.
Compound Interest and
 Cash Flow Diagrams
     Effective Interest Rates
• Rate of interest charged for a given
  period
• i % per period
     Compound Interest and
      Cash Flow Diagrams
• To perform any analysis, cash flow
  diagrams and interest rate must use same
  measure of a period (i.e. years, months,
  days, etc.)
• Match cash flows and interest rate by
  converting rate to proper period.
Converting Effective Interest Rates
 • Cash flows occur every month. Given
   annual interest rate of 12 %.




 • Cash flows occur every year. Given
   quarterly interest rate of 4 %.
Nominal Interest Rates or APRs
• Annual interest rate that does not
  incorporate the effects of compounding
• r % per year compounded periodically
• r % compounded periodically
• Nominal interest rate: r
Converting Nominal Interest Rates to
      Effective Interest Rates
  • First, convert to compounding period
  • Then convert to required period
   Nominal to Effective Rates
• Nominal Rate: r% compounded
  periodically (m)
• Effective Rate: i% = r%/m

• Example:   12% compounded quarterly

• Example:   14% compounded monthly
   Effective to Nominal Rates
• Effective Rate: i% per period
• Nominal rate: r% = i% * number of
  compounding periods in a year

• Example:    2% per month

• Example:    4% per quarter
Nominal vs. Effective Interest Rates
 • For comparison: compare effective
   interest rates over common period
 • Auto Loan:
   – Bank:       12% compounded quarterly
   – Dealer:     1.5% per month
 • Which is better?
       Cash Flow Evaluation

• With interest, ready to move money through
  time.
• Common calculations:
  – Convert all cash flows to time zero (present value)
  – Convert all cash flows to time n (future value)
  – Convert all cash flows to a set of n equal cash
    flows from time 1 through n (annual equivalent)
• Can learn formulas or use spreadsheets.
       After-Tax Cash Flows

• Need to calculate after-tax cash flows for
  analysis.
• Income Taxes -- paid on profits from
  operations and profitable sale of assets
• Capital Gains Taxes -- paid on the profitable
  sale of assets (greater than purchase price)
• Tax Credits -- received due to loss from
  operations or sales and possibly for
  investments
             Income Taxes

    Revenue
  - Expense
  = Income

     Taxes Paid = Income * Tax Rate

=> Expenses actually reduce our taxable
 income!
                    Expenses

•   Labor
•   Materials
•   Operations...
•   Interest
•   Depreciation
             Depreciation

• Buying an asset does not constitute an
  “expense” in the government’s eyes.
• When you purchase an asset (depreciable), you
  may “expense” it over time. The depreciation
  in a given year is the amount of expense.
• Depreciation is an expense, but NOT a cash
  flow.
                Depreciation
• Effect on income taxes:
  – Depreciation is an expense and therefore reduces
    the before-tax income.
• Effect on sales of assets:
  – The total depreciation accumulated over time by
    an asset determines its book value. The difference
    between the sale price of an asset and its book
    value determines whether the sale is a gain or loss.
• Calculation
  – Requires depreciation method and number of
    periods allowed
                   Book Value

• Depreciation:
  – Dt in time t
• Book value at the end of time n:
  – Initial book value B0 is generally the purchase
    price
  – Bn = B0 -  Dt
        Current Law: MACRS
• Asset Classes and Methods
  – Personal property (equipment, etc. -- not buildings
    or land)
     • 3, 5, 7, 10-year properties: 200% DB to SL
     • 15, 20 -year properties: 150% DB to SL
  – Real property (buildings, bridges, parking
    facilities, etc. -- not personal property or land)
     • 27.5, 31.5 -years -- Alternative SL
• No Salvage Value
• 1/2 year convention (years 1 and n+1)
• Asset sold before year n, 1/2 depreciation
       MACRS Percentages
• 3-year Class
  Year       %
  1        33.33%
  2        44.44%
  3        14.81%
  4        7.41%
             Sales of Assets
• If you sell your asset (at any time) for a value
  SV, you calculate the gain or loss as :
      SV - BVt
• If SV - BV > 0, gain
• If SV - BV < 0, loss
• Note, if sold before year “n”, only half
  depreciation is received.
• Tax Paid = Income Tax Rate * (SV - BV)
       After-Tax Cash Flows
• Once we calculate taxes and subtract them
  from our profits, we still have to
  CALCULATE the after-tax cash flow.
• After-Tax Cash Flow Calculation:




• Reason to use spreadsheets
      Single Project Evaluation
• Goal: Determine if an investment project is
  worth doing.
• Answer the following question: Will it make
  money?
• Better question: Will it make enough money?
• Assume
  – Cash flows (value and timing) are known
  – Interest rate and compounding periods are known
  – Decision is to accept or reject project
       Selecting an Interest Rate

• Generally specified by management
• MARR: Minimum Attractive Rate of Return,
  defines minimum amount you are willing to
  make on an investment
• Assume you can ALWAYS make the interest
  rate -- so your project must beat it to be worth
  the investment.
• PW is a measure of worth above the baseline
Present Worth Analysis
            Project Evaluation

• Present and Future Worth and Annual
  Equivalent
  – Require knowledge of cash flows and MARR
  – Equivalent measures of worth -- same decision
• MARR represents your baseline
  – Only invest in project if you can beat it
  – PW(MARR) > 0 means you make profit above the
    MARR
  – Think of PW as “discounted” profit
         Internal Rate of Return
• Interest rate i* where PW(i*) = 0
• The periodic rate at which your investment earns
  money
   Internal Rate of Return Pitfalls
• More than one rate?
                   Example
• Purchase piece of equipment for $30,000. It is
  expected to bring in revenues of $15,000 per
  year against $1,000 of operating expenses.
  Assume alternative straight-line depreciation
  and a tax rate of 34% per year. At the end of
  three years, the equipment is discarded at no
  cost (or revenue). The asset is a 5-year class
  asset. The interest rate is 12%. Should you
  consider this investment?
Inputs:           MARR:
                                      Cash Flows
                                         12.00% Depreciation:               2 Method:                        3
                  Tax Rate:              34.00% Life:                       5 Principal:
                  Periods:                    3 Salvage:               $0.00 Interest:
                  Policy:                     2                               Periods:

                                n:
Revenues          Inflation %                  0              1             2              3 Totals
   Inflow 1:           0.00%                        $15,000.00    $15,000.00     $15,000.00         $45,000.00
   Inflow 2:           0.00%                             $0.00         $0.00          $0.00              $0.00
   Inflow 3:           0.00%                             $0.00         $0.00          $0.00              $0.00
   Inflow 4:           0.00%                             $0.00         $0.00          $0.00              $0.00
Total Inflows:                                      $15,000.00    $15,000.00     $15,000.00         $45,000.00

Expenses
    Outflow 1:        0.00%                         ($1,000.00)   ($1,000.00)    ($1,000.00)       ($3,000.00)
    Outflow 2:        0.00%                              $0.00         $0.00          $0.00             $0.00
    Outflow 3:        0.00%                              $0.00         $0.00          $0.00             $0.00
  Interest:                                              $0.00         $0.00          $0.00             $0.00
Depreciation:                                       ($3,000.00)   ($6,000.00)    ($3,000.00)      ($12,000.00)
Total Expenses:                                     ($4,000.00)   ($7,000.00)    ($4,000.00)      ($15,000.00)

Taxable Income:                                     $11,000.00     $8,000.00     $11,000.00        $30,000.00

Income Tax:                                         ($3,740.00)   ($2,720.00)    ($3,740.00)      ($10,200.00)

Profit A/T:                                          $7,260.00     $5,280.00      $7,260.00        $19,800.00

Loan Principal:                           $0.00          $0.00         $0.00           $0.00            $0.00

Purchase:                            ($30,000.00)                                                 ($30,000.00)

Cash Flow A/T:                       ($30,000.00)   $10,260.00    $11,280.00     $10,260.00         $1,800.00
                              Analysis
            Cash Flow PW:                                               ($4,544.07)
            Cash Flow AE:                                               ($1,891.92)
            Cash Flow FW:                                               ($6,384.10)
            IRR:                                                             2.97%


            $5,000.00

                $0.00
                          0




                                                          0.4




                                                                                             0.8
                              0.08
                                     0.16
                                            0.24
                                                   0.32


                                                                 0.48
                                                                        0.56
                                                                               0.64
                                                                                      0.72


                                                                                                   0.88
                                                                                                          0.96
            ($5,000.00)
PV(MARR)




           ($10,000.00)

           ($15,000.00)

           ($20,000.00)

           ($25,000.00)
                                                                MARR
                   Example
• What if you sold the equipment for $10,000 after
  year three?
                                            Cash Flows
Inputs:              MARR:                    12.00% Depreciation:                2 Method:                              3
                     Tax Rate:                34.00% Lif e:                       5 Principal:
                     Periods:                       3 Salvage:               $0.00 Interest:
                     Policy:                        2                               Periods:

                                    n:
Revenues             Inf lation %                   0               1              2               3 Totals
   Inf low 1:              0.00%                         $15,000.00     $15,000.00      $15,000.00          $45,000.00
   Inf low 2:              0.00%                               $0.00          $0.00           $0.00               $0.00
   Inf low 3:              0.00%                               $0.00          $0.00           $0.00               $0.00
   Inf low 4:              0.00%                               $0.00          $0.00           $0.00               $0.00
Total Inf low s:                                         $15,000.00     $15,000.00      $15,000.00          $45,000.00

Expenses
   Outf low 1:           0.00%                           ($1,000.00)    ($1,000.00)      ($1,000.00)        ($3,000.00)
   Outf low 2:           0.00%                                $0.00          $0.00            $0.00              $0.00
   Outf low 3:           0.00%                                $0.00          $0.00            $0.00              $0.00
 Interest:                                                    $0.00          $0.00            $0.00              $0.00
Depreciation:                                            ($3,000.00)    ($6,000.00)      ($3,000.00)       ($12,000.00)
Total Expenses:                                          ($4,000.00)    ($7,000.00)      ($4,000.00)       ($15,000.00)

Taxable Income:                                          $11,000.00      $8,000.00      $11,000.00          $30,000.00

Income Tax:                                              ($3,740.00)    ($2,720.00)      ($3,740.00)       ($10,200.00)

Prof it A/T:                                              $7,260.00      $5,280.00       $7,260.00          $19,800.00

Loan Principal:                                $0.00          $0.00          $0.00               $0.00           $0.00

Purchase/Sale:                           ($30,000.00)                                   $10,000.00         ($30,000.00)
Tax on Asset Sale:                                                                       $2,720.00
Cash Flow A/T:                           ($30,000.00)    $10,260.00     $11,280.00      $22,980.00          $14,520.00
                              Analysis
            Cash Flow PW:                                               $4,566.71
            Cash Flow AE:                                               $1,901.35
            Cash Flow FW:                                               $6,415.90
            IRR:                                                           19.50%


           $20,000.00
           $15,000.00
           $10,000.00
            $5,000.00
PV(MARR)




                $0.00
                          0




                                                          0.4




                                                                                             0.8
                              0.08
                                     0.16
                                            0.24
                                                   0.32


                                                                 0.48
                                                                        0.56
                                                                               0.64
                                                                                      0.72


                                                                                                   0.88
                                                                                                          0.96
            ($5,000.00)
           ($10,000.00)
           ($15,000.00)
           ($20,000.00)
           ($25,000.00)
                                                                MARR
                 Next Steps
• Multiple Projects
• Capital Budgets
• Uncertainty
             Payback Period
• Answers the question: How many periods does
  it take us to earn back our investment?
                  Example
• Invest $50,000 in a machine at time zero. It
  brings in income (revenues - expenses) of
  $10,000 in year 1, growing by $10,000 per year
  for 4 years. What is n*?
  Payback Period Characteristics
• Bad
  –   Does not include time-value-of money
  –   Does not consider cash flows past time period n*
  –   Does not provide a measure of worth or return
  –   May deter investment in potentially worthy projects
• Good
  – Gives some measure of “risk” of a project
  – Determines “breakeven point” for an investment
  – Can be used to “enhance” evaluation of a project
    with a traditional measure of worth
              Project Balance
• Evaluates a project at each period of its
  estimated life.
• Calculate the FW(MARR) at each period.
                  Example
• Invest $50,000 in a machine at time zero. It
  brings in income (revenues - expenses) of
  $10,000 in year 1, growing by $10,000 per year
  for 4 years.
Visualizing PB
  Project Balance Characteristics
• PB=FW of a project at each period
• PBn = FW of a project
   – PB provides same investment decision as FW
• Graph of PB defines payback period with interest
   – Point when PB graph crosses over time axis
• Graph defines “good” investments
   –   Low payback period with interest
   –   Large positive area under graph
   –   Small negative area under graph
   –   High FW
           Sensitivity Analysis

• Allows one to consider errors in parameter
  estimates
  – Helps determine which parameters values are critical
    (most sensitive)
  – Also determines which parameters are NOT critical
• Provides ranges of estimates where projects are
  acceptable

				
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