1 Chapter 5: Essential Formulae in Project Appraisal A Coverage of the Formulae and Symbols Used to Evaluate Investment Projects

2 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.

3 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’.

4 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: C t Cash flow at end of period t.

5 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:

6 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: 1. 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.

7 Financial 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. α

8 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.

9 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.

10 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 Check your calculations with a hand held calculator to ensure that the formulae have been correctly set up.

11 Calculating NPV and IRR With Excel -- The Excel Worksheet.

12 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.

13 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.

14 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.

15 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.

16 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.

17 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.

18 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. $ % $ % $ % $ % $ % $ % $ % $ % $ %$ %