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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 CF0 Cost CF1 CF2 Inflows CF3 IRR is the discount rate that forces PV inflows = cost This is the same as forcing NPV = NPV: Enter r, solve for NPV n CFt = NPV ∑ t t = (1 + r ) IRR: Enter NPV = 0, solve for IRR CFt ∑ t = t = (1 + IRR) n What’s Project N’s IRR? IRR = ? -100.00 PV1 PV2 PV3 = NPV 10 60 80 Enter CFs in CFLO, then press IRR: IRRN = 18.13% 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 Example 5.14 Net cash inflows of a project are estimated as: EOY $3,000; EOY $4,000; and EOY $8,000 Capital outlays for the project will occur during the first and second years and they are estimated as $2,000 and $1,500, respectively They are assumed to occur at the beginning of each period The timing notation for the correct discounting of these will be: EOY $2,000; and EOY $1,500 The discount rate is 10% per annum What is the IRR? Internal Rate of Return: IRR 10 IRR = 133.76% What is the payback period? The number of years required to recover a project’s cost, or how long does it take to get the business’s money back? 11 Payback for Project N’s (Long: Most CFs in out years) CFt -100 Cumulative -100 PaybackL 12 = 2 10 -90 + 30/80 2.4 60 100 -30 80 50 = 2.375 years Project M’s (Short: CFs come quickly) CFt -100 Cumulative -100 PaybackS 13 1.6 70 100 50 20 -30 40 20 = + 30/50 = 1.6 years Strengths of Payback: Provides an indication of a project’s risk and liquidity Easy to calculate and understand Weaknesses of Payback: Ignores the TVM Ignores CFs occurring after the payback period 14 Evaluation of Project Cash Flows 15 Cash flows occurring within investment projects are assumed to occur regularly, at the end of each year Since they are unlikely to be equal, they will not be annuities Annuity calculations apply more to loans and other types of financing All future flows are discounted to calculate a Net Present Value, NPV; or an Internal Rate of Return, IRR Decision Making With Cash Flow Evaluations If the Net Present Value is positive, then the project should be accepted The project will increase the present wealth of the firm by the NPV amount If the IRR is greater than the required rate of return, then the project should be accepted The IRR is a relative measure, and does not measure an increase in the firm’s wealth 16 Calculating NPV and IRR With Excel Basics 17 Ensure that the cash flows are recorded with the correct signs: -$, +$, -$, +$ 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 Calculating NPV and IRR With Excel The Excel Worksheet 18 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 19 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 20 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 21 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 22 Essential Formulae Summary 1.The Time Value of Money is a cornerstone of finance The amount, direction and timing of cash flows, and relevant interest rates, must be carefully specified Knowledge of financial formulae is essential for project evaluation 23 Essential Formulae Summary NPV and IRR are the primary investment evaluation criteria Most financial functions can be automated within Excel Spreadsheet errors are common Error controls should be employed 24 Essential Formulae Summary 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 Financial formulae and spreadsheet operation can be demanding Seek help when in doubt $ % $ % $ % $ % $ % $ % $ % $ % $ %$ % 25 ... of finance The amount, direction and timing of cash flows, and relevant interest rates, must be carefully specified Knowledge of financial formulae is essential for project evaluation 23 Essential. .. occurring after the payback period 14 Evaluation of Project Cash Flows 15 Cash flows occurring within investment projects are assumed to occur regularly, at the end of each year Since... 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