Fundamentals of Investment Appraisal Martina Röhrich ISBN: © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen Abbildungsübersicht / List of Figures Tabellenübersicht / List of Tables

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 2 Table 1-1 Characteristics of the methods of investment appraisal

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 3 Figure 2-1 Average capital employed

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 4 Table 2-1 Comparison of alternatives by the cost comparison method

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 5 Table 2-2 Comparison of alternatives by the cost comparison method with salvage values

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 6 Table 2-3 Basic data for the calculation of critical values

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 7 Figure 2-2 Critical activity quantity by the cost comparison method

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 8 Table 2-4 Basic data for the new vehicle

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 9 Table 2-5 Relevant costs with regard to the replacement decision

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 10 Table 2-6 Replacement decision by the cost comparison method

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 11 Table 2-7 Check for the replacement decision by the cost comparison method

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 12 Table 2-8 Replacement decision by the cost comparison method with salvage values

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 13 Table 2-9 Comparison of alternatives by the profit comparison method

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 14 Table 2-10 Comparison of alternatives by the profit comparison method with salvage values

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 15 Table 2-11 Decision about the replacement of the HL Securitas by the profit comparison method

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 16 Table 2-12 Decision about the replacement of the BMC Minerva by the profit comparison method

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 17 Table 2-13 Comparison of alternatives by the accounting rate of return method

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 18 Table 2-14 Comparison of alternatives by the accounting rate of return method with salvage values

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 19 Table 2-15 Replacement decision by the accounting rate of return method

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 20 Table 2-16 Calculation of non-discounting payback through average annual cash flow

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 21 Table 2-17 Calculation of non-discounting payback through average annual profit

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 22 Table 2-18 Calculation of non-discounting payback through average annual cash flow with salvage values

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 23 Table 2-19 Calculation of non-discounting payback through average annual profit with salvage values

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 24 Table 2-20 Replacement decision by the non-discounting payback

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 25 Table 2-21 Results from the non-discounting methods of investment appraisal

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 26 Table 3-1 Basic example of the time value of money

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 27 Table 3-2 Cost comparison for the basic example

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 28 Table 3-3 Symbols for the discounting methods of investment appraisal (Continued)

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 29 Table 3-3 Symbols for the discounting methods of investment appraisal

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 30 Table 3-4 Investment’s payments within the example

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 31 Table 3-5 Calculation of present values within the example

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 32 Figure 3-1 Time line illustration of a net present value

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 33 Table 3-6 Complete financial plan, investment of € 70,000 on the capital market

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 34 Table 3-7 Complete financial plan, transaction of the investment, financing with equity

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 35 Table 3-8 Complete financial plan, Transaction of the investment, financing with debt at 100 % and repayment at the end of the time period in a single sum

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 36 Table 3-9 Complete financial plan, Transaction of the investment, financing with debt at 100 % and repayment at the best possible rate

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 37 Table 3-10 Calculation of the net present value for Investment 1

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 38 Table 3-11 Calculation of the net present value for Investment 2

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 39 Table 3-12 Net present value method and differential investments

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 40 Figure 3-2 Net present value profile

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 41 Table 3-13 Basic data for the comparison of alternatives by the net present value method

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 42 Table 3-14 Calculation of current cash outflow for the comparison of alternatives by the net present value method

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 43 Table 3-15 Calculation of net present values for the comparison of alternatives without cash inflow

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 44 Table 3-16 Calculation of net present values for the comparison of alternatives with cash inflows

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 45 Table 3-17 Basic data for the CSA Toutatis

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 46 Table 3-18 Marginal cash flows of new car purchase

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 47 Table 3-19 Equivalent annuity as annualised net present value

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 48 Table 3-20 Comparison of Alternatives by the annuity method

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 49 Table 3-21 Calculation of equivalent annuities for the replacement decision

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 50 Table 3-22 Basic data for graphical and arithmetic approximation of the internal rate of return

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 51 Figure 3-3 Graphical estimate of the internal rate of return

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 52 Table 3-23 Calculation of internal rates of return by Excel

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 53 Table 3-24 Illustration of investment desirability ranking conflicts

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 54 Figure 3-4 Net present value profiles for the HL Securitas and the BMC Minerva

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 55 Table 3-25 Calculation of the discounted cumulative cash flow of the HL Securitas

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 56 Table 3-26 Calculation of the discounted cumulative cash flow of the BMC Minerva

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 57 Table 3-27 Results from non-discounting and discounting payback method

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 58 Table 4-1: Correction of the input variables

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 59 Table 4-2 Initial data for the comparison of alternatives

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 60 Table 4-3 Net present values for the comparison of alternatives using the correction method

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 61 Table 4-4 Data basis for the comparison of alternatives

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 62 Table 4-5: Rise of cash flow by 10 % within the sensitivity analysis

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 63 Table 4-6: Reduction of cash flow by 10 % within the sensitivity analysis

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 64 Table 4-7: Synopsis of the results of the band width analysis

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 65 Table 4-8 Identifying the BMC Minerva’s sensitive input variables

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 66 Table 4-9 Definition of the uncertain input variables

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 67 Table 4-10 Probability distributions of the uncertain input variables

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 68 Table 4-11 Allocation of random numbers to the uncertain input data

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 69 Figure 4-1 Monte Carlo Simulation to incorporate probability distributions of cash flows and economic life

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 70 Table 4-12 Generated random numbers for the uncertain input data

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 71 Table 4-13 Net present values for the iterations

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 72 Table 4-14: Results of the risk analysis

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 73 Figure 4-2 Risk profile

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 74 Table 4-15 Initial data for the comparison of alternatives using the fixed planning

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 75 Figure 4-3 Probability tree

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 76 Table 4-16 Current value of cash flows from the investment depending on the state of the economy

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 77 Table 4-17 Discounted cash flows from the investment project depending on the state of the economy

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 78 Figure 4-4 Decision tree – fixed planning

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 79 Table 4-18 Net present values and weighted net present values in the outcome nodes of period 2 using the fixed planning approach

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 80 Table 4-19 Discounted cash flows from the investment project depending on the state of the economy

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 81 Figure 4-5 Decision tree – flexible planning

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 82 Table 4-20 Explanation of the way to the results in period 2

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 83 Table 4-21 Net present values in the final nodes in period 2 within the flexible planning approach

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 84 Table 4-22 Overview of the decision nodes in period 1

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 85 Table 4-23 Calculation of the expected net present value for the action ‘no reaction’

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 86 Table 4-24 Calculation of the expected net present value for the action ‘advertising’

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 87 Table 4-25 Summary of the expected net present values for the decision nodes in period 1

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 88 Table 4-26 Summary of useful decisions in the decision nodes of period 1

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 89 Table 4-27 Probability distributions of the uncertain input variable

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 90 Table 4-28 Allocation of random numbers to the uncertain input variable

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 91 Table 4-29 Generated random numbers for the uncertain input variable ‘sales revenues’

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 92 Table 5-1: Calculation of the net present value without and with taxes

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 93 Table 5-2 Derivation of the project’s after tax cash flow

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 94 Table 5-3 Basic data for the calculation of the net present values without taxes

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 95 Table 5-4 Calculation of net present values after tax

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 96 Table 5-5 Comparison of alternatives based on net present values after tax

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 97 Table 5-6 Basic data for the calculation of the net present values without inflation

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 98 Table 5-7 Basic data to set up a complete financial plan

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 99 Table 5-8 Complete financial plan for the BMC Minerva at a discount rate of 5 %

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 100 Table 5-9 Complete financial plan for the BMC Minerva with a debit interest rate of 6 % and a credit interest rate of 5 %

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 101 Table 5-10 Contributions of the assessment criterion ‘Eco Friendliness’

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 102 Table 5-11 Partial values of benefit for the alternatives under consideration

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 103 Table 5-12 Total values for the alternatives considered

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 104 Table 5-13 Basic data for the macroeconomic net present value method

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 105 Table 5-14 Calculation of the macroeconomic net present value

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 106 Future Value Factor

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 107 Annuity Future Value Factor

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 108 Sinking Fund Factor

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 109 Annual Equivalent Factor

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 110 Present Value Factor

Fundamentals of Investment Appraisal, Martina Röhrich ISBN © 2014 Oldenbourg Wissenschaftsverlag GmbH, Mu ̈ nchen 111 Annuity Present Value Factor