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Chapter 5: Essential Formulae in Project Appraisal. A Coverage of the Formulae and Symbols Used to Evaluate Investment Projects . Fundamentals in Financial Evaluation. Money has a time value: a $ or £ or € today, is worth more than a $ or £ or € next year.

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Chapter 5: Essential Formulae in Project Appraisal

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Chapter 5 essential formulae in project appraisal l.jpg

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.

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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 firm’s 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( B6:E6, 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.

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