Chapter 5: Essential Formulae in Project Appraisal

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Chapter 5 Essential Formulae in Project Appraisal

• A Coverage of the Formulae and Symbols Used to
  Evaluate Investment Projects

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Fundamentals in Financial Evaluation

• Money has a time value a or or today, is
  worth more than a or or next year.
• A risk free interest rate may represent the time
  value of money.
• Inflation too can create a difference in money
  value over time. It is NOT the time value of
  money. It is a decline in monetary purchasing
  power.

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Moving Money Through Time

• Investment projects are long lived, so we usually
  use annual interest rates.
• With compound interest rates, money moved forward
  in time is compounded, whilst money moved
  backward in time is discounted.

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Financial Calculations

• Time value calculations in capital budgeting
  usually assume that interest is annually
  compounded.
• Money in investment projects is known as cash
  flows the symbol is
• Ct Cash flow at end of period t.

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Financial Calculations

• The present value of a single sum is
• PV FV (1 r)-t
• - the present value of a dollar to be received
  at the end of period t, using a discount rate of
  r.

• The present value of series of cash flows is

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Financial Calculations Cash Flow Series

• A payment series in which cash flows are Equally
  sized And Equally timed
• is known as an annuity.
• There are four types
• Ordinary annuities the cash flows occur at the
  end of each time period.
• 2. Annuities due the cash flows occur at the
  start of each time period.

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Financial Calculations Cash Flow Series
Annuities types 3 and 4.
3. Deferred annuities the first cash flow
occurs later than one time period into the future
4. Perpetuities the cash flows begin at the end
of the first period, and go on forever.
a
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Evaluation of Project Cash Flows.

• Cash flows occurring within investment projects
  are assumed to occur regularly, at the end of
  each year.
• Since they are unlikely to be equal, they will
  not be annuities.
• Annuity calculations apply more to loans and
  other types of financing.
• All future flows are discounted to calculate a
  Net Present Value, NPV or an Internal Rate of
  Return, IRR.

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Decision Making With Cash Flow Evaluations

• If the Net Present Value is positive, then the
  project should be accepted. The project will
  increase the present wealth of the firm by the
  NPV amount.

• If the IRR is greater than the required rate of
  return, then the project should be accepted. The
  IRR is a relative measure, and does not measure
  an increase in the firms wealth.

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Calculating NPV and IRR With Excel -- Basics.

• Ensure that the cash flows are recorded with the
  correct signs -, , -, etc.
• Make sure that the cash flows are evenly timed
  usually at the end of each year.
• Enter the discount rate as a percentage, not as a
  decimal e.g. 15.6, not 0.156.
• Check your calculations with a hand held
  calculator to ensure that the formulae have been
  correctly set up.

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Calculating NPV and IRR With Excel -- The Excel
Worksheet.
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Calculating MIRR and PB With Excel.

• Modified Internal Rate of Return the cash flow
  cell range is the same as in the IRR, but both
  the required rate of return, and the
  re-investment rate, are entered into the
  formula MIRR( B6E6, B13, B14)

• Payback there is no Excel formula . The
  payback year can be found by inspection of
  accumulated annual cash flows.

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ARR and Other Evaluations With Excel.

• Accounting Rate of Return there is no Excel
  formula. Average the annual accounting income by
  using the AVERAGE function, and divide by the
  chosen asset base.

• Other financial calculations use Excel Help
  to find the appropriate function. Read the help
  information carefully, and apply the function to
  a known problem before relying on it in a live
  worksheet.

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Calculating Financial Functions With Excel --
Worksheet Errors.

• Common worksheet errors are
• Cash flow cell range wrongly specified.
• Incorrect entry of interest rates.
• Wrong NPV, IRR and MIRR formulae.
• Incorrect cell referencing.
• Mistyped data values.
• No worksheet protection.

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Calculating Financial Functions With Excel --
Error Control.

• Methods to reduce errors
• Use Excel audit and tracking tools.
• Test the worksheet with known data.
• Confirm computations by calculator.
• Visually inspect the coding.
• Use a team to audit the spreadsheet.

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Essential Formulae -- Summary
1.The Time Value of Money is a cornerstone of
finance.
2. The amount, direction and timing of cash
flows, and relevant interest rates, must be
carefully specified.
3. Knowledge of financial formulae is

essential for project evaluation.
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Essential Formulae -- Summary

• 4. NPV and IRR are the primary investment
  evaluation critertia.

5. Most financial functions can be automated
within Excel.
6. Spreadsheet errors are common. Error controls
should be employed.
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Essential Formulae -- Summary
7. To reduce spreadsheet errors -document all
spreadsheets, keep a list of authors and a
history of changes, use comments to guide later
users and operators.
8. Financial formulae and spreadsheet operation
can be demanding. Seek help when in doubt.