1. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Chapter 10: Comparing Monetary Returns Over Time

2. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Objectives Find the payback time for a project Understand the concept of time value of money Calculate a net present value for a project Criticise the process Discuss the selection of discount factors

3. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Costs & Benefits Costs usually come at the beginning of a project Their level is often known with some certainty Benefits come over some future time period They are open to considerable variation They are also uncertain

4. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Payback This method only takes into account how long it will take to pay back the initial investment in nominal terms If we invest £1,000 and get back £500 in year 1 and £500 in year 2 Then it takes 2 years to payback If the money back were £750 in year 1 And £750 in year 2 Then it would take one and a third years to pay back

5. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Interest Calculations Interest is earned on a sum of money invested over a period of time The amount of interest depends upon the interest rate and the time period, But also on the method of interest accumulation SIMPLE INTEREST:Here the same amount is earned each year So if you invest £100 at 10% you get £10 interest in year 1 £10 interest in year 2 and so on ……….. So the total interest is (the amount)x(interest rate)x(number of years)

6. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Compound Interest With compound interest, the money earned is left invested from year to year And hence you get interest on interest If you invest £100 at 10%, you get £10 interest at the end of year 1 In year 2, you get £10 interest on your £100 plus £1 interest on the £10 A formula has been developed to help work out the total amount: A 0 (1+r) n Where A 0 is the initial amount, r is the decimal interest rate and n is the number of years

7. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Time-value of Money Money which we get in the future will not buy as much as the same amount received now. One reason is inflation. To work out the present value of a sum of money, we need to assume a rate of interest. We can then use the formula: A 0 - start year A t - in t years time This is just a manipulation of the compound interest formula

8. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Tables You could work out the values of the present value formula: by hand, or you could use a spreadsheet, or you could use tables To find the figure for 4% And 6 years You get

9. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Present Value For example: How much would you need to invest now at 10% interest, to have £242 in two years time? A t = £242r =0.1 = 242 * 0.826446 = £200 So invest £200 to get £242 two years from now

10. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Choosing between Opportunities You are offered a choice between two deals The first gives you £700 in 4 years time The second gives £850 in 6 years time The rate of interest is set at 8% Option 1: Option 2: = 700 * 0.735 = £514.50 =850 * 0.6302 =£535.67 CHOICE?

11. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Investment Appraisal Businesses often have several competing uses for their funds They need to find a way of objectively comparing them This needs to take account of the time value of money Net Present Value calculations meet these criteria Method:For each project or use of funds we need to determine 1.Initial cost 2.Income in each year 3.Costs in each year 4.An interest rate to be used 5.The projected life of the project or asset

12. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Example - 1 A company needs to invest in new manufacturing capacity and can buy either two Xenion Producers at £50,000 each or one Yeoming Producer at £120,000 The Xenion Producer will need to be upgraded in year two at a cost of £20,000 per machine There are no expected future costs with the Yeoming Producer during its lifetime All Producers are expected to last for 6 years and have zero scrap value Expected revenues are given in the table A 8% interest rate is used

13. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Example - 2 YrXY 0 00 1 2500020000 2 3000025000 3 3000040000 4 3500040000 5 2500030000 6 1500020000 Expected RevenuesExpected Costs XY -100000-120000 -40000 Net Revenues XY -100000-120000 2500020000 -1000025000 3000040000 3500040000 2500030000 1500020000 R - C

14. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Tables 2 To help answer this problem we need six years of present value factors

15. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Example - 3 CHOICE -£9,418.15 £14,124.50 Net Revenue times Present Value Factor Total Net Present Value

16. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Choosing r No-one publishes a specific value of r to use There are a range of alternatives: The rate of inflation The rate used in the past The rate of return on capital (from the accounts) The rate available on the stock market The rate currently paid on the bond market A rate to reflect the riskiness of the project

17. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Ranges of Benefits We already know that the future is uncertain But the future expected income may possibly be labelled By the likelihood of it happening And then we could assign probabilities to the sets of outcomes The next example considers this situation

18. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Ranges 2 A company is assessing a project and has 3 sets of projections of contribution. These are shown in the table below. Year PessimisticGeneralOptimistic Cost £100,000 Expected Contribution, Year 1 £10,000£12,000£20,000 Expected Contribution, Year 2 £20,000£25,000£40,000 Expected Contribution, Year 3 £40,000£50,000£70,000 Expected Contribution, Year 4 £25,000£40,000£60,000 Expected Contribution, Year 5 £10,000£20,000£30,000 The company uses a discount rate of 12% and you have determined the probabilities of the three scenarios as 0.2, 0.7 and 0.1 respectively.

19. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Ranges 3 £100,000 - £100,00 0 £10,000 £12,00 0£20,000 0.89285 7£8,929£10,714£17,857 £20,000 £25,00 0£40,000 0.79719 4£15,944£19,930£31,888 £40,000 £50,00 0£70,0000.71178£28,471£35,589£49,825 £25,000 £40,00 0£60,000 0.63551 8£15,888£25,421£38,131 £10,000 £20,00 0£30,000 0.56742 7 NPV-£25,094£3,002£54,723 Year Pessimist ic Gener al Optimisti c PV1PV2PV3 Cost Expected Contribution, Year 1 Expected Contribution, Year 2 Expected Contribution, Year 3 Expected Contribution, Year 4 Expected Contribution, Year 5 £5,674£11,349£17,023 The first step is to find NPV’s in the normal way

20. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Expected NPV (-£25,094 x 0.2) + (£3,002 x 0.7) + (£54,723 x 0.1) = £2,555.20 You then take each NPV and multiply it by the appropriate probability Where there are several projects competing for the same funds, this method suggests that you choose the one with the highest expected NPV

21. Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Thomson Learning 2004 Jon Curwin and Roger Slater, QUANTITATIVE METHODS: A SHORT COURSE ISBN 1-86152-991-0 © Cengage Conclusions Net Present Value takes account of the time value of money Other methods are available: Discounted Cash FlowLooks for the rate of return on the investment which gives zero NPV Internal Rate of ReturnAccounting ratio Payback period Ignores time value of money Just counts up income until total equals the cost