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

Study objectives

 After studying this chapter the reader should be able to:

 Apply a discounting rate to cash flows occurring at different points

in time to translate them into a common measure of value

 Calculate present value, net present value (NPV) and internal rate

of return (IRR) from a given cash flow series

 Calculate monthly loan (mortgage) repayments, their interest and principal components and the loan balance of a mortgage loan

 Understand the financial mathematics involved in the discounted cash flow techniques (such as NPV and IRR) and mortgage loans

 Apply the relevant annuity formulae for project appraisal

Internal rate of return

 The internal rate of return is an alternative

measure for evaluating projects

 It is the calculated rate of return (or discount rate)

r at which the NPV will be equal to zero.

 In project evaluation this rate has to be equal to or greater than the required rate of return for the

project to be acceptable

 It is calculated manually by trial and error, or by a special routine in computerized spreadsheets

Internal Rate of Return: IRR

IRR is the discount rate that forces

PV inflows = cost This is the same

as forcing NPV = 0.

1  .

0

NPV r

CF

t t n





NPV: Enter r, solve for NPV.

IRR: Enter NPV = 0, solve for IRR.

Internal Rate of Return: IRR

 Arriving at the IRR solution will involve a number of iterations, so where there are more than two cash flows, a computer package (such as Excel) or a financial calculator (with an IRR function) is

recommended

Internal Rate of Return: IRR

 In the NPV model, the NPV is clearly defined

 In the IRR equation, however, it is difficult to

define IRR in its own terms, because it

effectively means something like: ‘the rate of

return at which all funds, if borrowed at the IRR, could be repaid from the project, without the firm having to make any cash contribution’.

 The IRR criterion does not measure the project’s contribution to the firm’s value.

Internal Rate of Return: IRR

annum.

What is the IRR?

Internal Rate of Return: IRR

 IRR = 133.76%

What is the payback period?

The number of years required to recover a project’s cost,

or how long does it take to get the business’s money back?

Payback for Project N’s

(Long: Most CFs in out years)

2.4

=Project M’s (Short: CFs come quickly)

Strengths of Payback:

1 Provides an indication of a

project’s risk and liquidity.

2 Easy to calculate and understand.

Weaknesses of Payback:

1 Ignores the TVM.

2 Ignores CFs occurring after the

payback period.

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.

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.

rate of return, then the project should

be accepted The IRR is a relative

measure, and does not measure an

Calculating 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.

calculator to ensure that the formulae

Calculating NPV and IRR With Excel The Excel Worksheet

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.

ARR and Other Evaluations

 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

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.

Calculating Financial Functions With Excel Error Control.

Methods to reduce errors:

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.

Essential Formulae Summary

4 NPV and IRR are the primary

investment evaluation criteria.

5 Most financial functions can be

automated within Excel.

6 Spreadsheet errors are common Error

controls should be employed.

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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