Chapter 5: Essential Formulae in Project Appraisal
A Coverage of the Formulae and Symbols Used to Evaluate
Trang 2Fundamentals 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.
Trang 3Moving 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
Trang 4Financial 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.
Trang 5Financial Calculations
The present value of a single sum is:
PV = FV (1 + r)-t
- the present value of a dollar to be received at
Trang 6Financial 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:
1.Ordinary annuities; the cash flows
occur at the end of each time period.
2 Annuities due; the cash flows occur at
Trang 7Financial Calculations: Cash Flow Series
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
Annuities: types 3 and 4.
Trang 8Evaluation 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.
Trang 9Decision 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.
Trang 10Calculating NPV and IRR With Excel Basics.
1.Ensure that the cash flows are recorded with the correct signs: -$, +$, -$, +$ etc.
2.Make sure that the cash flows are evenly
timed: usually at the end of each year.
3.Enter the discount rate as a percentage, not as a decimal: e.g 15.6%, not 0.156.
4.Check your calculations with a hand held
Trang 12Calculating 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)
Trang 13ARR 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
Trang 14Calculating 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.
Trang 15Calculating 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.
Trang 16Essential Formulae Summary1.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
Trang 17Essential 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
Trang 18Essential Formulae Summary7 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.
$ % $ % $ % $ % $ % $ % $ % $ % $ %$