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Chapter 10: Comparing Monetary Returns Over Time

Chapter 10: Comparing Monetary Returns Over Time. 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. Costs & Benefits.

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Chapter 10: Comparing Monetary Returns Over Time

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  1. Chapter 10: Comparing Monetary Returns Over Time

  2. 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. 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. 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. 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. 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: A0(1+r)n Where A0is the initial amount,ris the decimal interest rate andnis the number of years

  7. 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 thepresent valueof a sum of money, we need to assume a rate of interest. We can then use the formula: A0 - start year At - in t years time This is just a manipulation of the compound interest formula

  8. 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. Present Value For example: How much would you need to invest now at 10% interest, to have £242 in two years time? At = £242 r =0.1 = 242 * 0.826446 = £200 So invest £200 to get £242 two years from now

  10. 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: = 700 * 0.735 = £514.50 Option 2: =850 * 0.6302 =£535.67 CHOICE?

  11. 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 Valuecalculations meet these criteria Method: For each project or use of funds we need to determine • Initial cost • Income in each year • Costs in each year • An interest rate to be used • The projected life of the project or asset

  12. 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. R - C Example - 2 Expected Revenues Expected Costs Net Revenues

  14. Tables 2 To help answer this problem we need six years of present value factors

  15. Net Revenue times Present Value Factor Example - 3 -£9,418.15 £14,124.50 CHOICE Total Net Present Value

  16. 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. 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. Year Pessimistic General Optimistic Cost £100,000 £100,000 £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 Ranges 2 A company is assessing a project and has 3 sets of projections of contribution. These are shown in the table below. 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. Year Pessimistic General Optimistic PV1 PV2 PV3 Cost £100,000 £100,000 £100,000 -£100,000 -£100,000 -£100,000 Expected Contribution, Year 1 £10,000 £12,000 £20,000 0.892857 £8,929 £10,714 £17,857 Expected Contribution, Year 2 £20,000 £25,000 £40,000 0.797194 £15,944 £19,930 £31,888 Expected Contribution, Year 3 £40,000 £50,000 £70,000 0.71178 £28,471 £35,589 £49,825 Expected Contribution, Year 4 £25,000 £40,000 £60,000 0.635518 £15,888 £25,421 £38,131 Expected Contribution, Year 5 £10,000 £20,000 £30,000 0.567427 £5,674 £11,349 £17,023 NPV -£25,094 £3,002 £54,723 Ranges 3 The first step is to find NPV’s in the normal way

  20. Expected NPV You then take each NPV and multiply it by the appropriate probability (-£25,094 x 0.2) + (£3,002 x 0.7) + (£54,723 x 0.1) = £2,555.20 Where there are several projects competing for the same funds, this method suggests that you choose the one with the highest expected NPV

  21. Conclusions Net Present Value takes account of the time value of money Other methods are available: Discounted Cash Flow Looks for the rate of return on the investment which gives zero NPV Internal Rate of Return Accounting ratio Payback period Just counts up income until total equals the cost Ignores time value of money

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