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Although we use the term “cash flow”, the dollar values used might not be the same as the actual cash amounts. In some instances, actual ‘market prices’ do not reflect the true value of the project’s input or output. | © Harry Campbell & Richard Brown School of Economics The University of Queensland BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets Ch. 3: Decision Rules Applied Investment Appraisal Conceptualizing an investment as: a net benefit stream over time, or, “cash flow”; giving up some consumption benefits today in anticipation of gaining more in the future. + _ time $ A project as a cash-flow: Although we use the term “cash flow”, the dollar values used might not be the same as the actual cash amounts. In some instances, actual ‘market prices’ do not reflect the true value of the project’s input or output. In other instances there may be no market price at all. We use the term ‘shadow price’ or ‘accounting price’ when market prices are adjusted to reflect true values. Three processes in any cash-flow analysis identification valuation comparison Conventions in Representing Cash Flows Initial or ‘present’ period is always year ‘0’ Year 1 is one year from . | © Harry Campbell & Richard Brown School of Economics The University of Queensland BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets Ch. 3: Decision Rules Applied Investment Appraisal Conceptualizing an investment as: a net benefit stream over time, or, “cash flow”; giving up some consumption benefits today in anticipation of gaining more in the future. + _ time $ A project as a cash-flow: Although we use the term “cash flow”, the dollar values used might not be the same as the actual cash amounts. In some instances, actual ‘market prices’ do not reflect the true value of the project’s input or output. In other instances there may be no market price at all. We use the term ‘shadow price’ or ‘accounting price’ when market prices are adjusted to reflect true values. Three processes in any cash-flow analysis identification valuation comparison Conventions in Representing Cash Flows Initial or ‘present’ period is always year ‘0’ Year 1 is one year from present year, and so on All amounts accruing during a period are assumed to fall on last day of period B1 B2 0 1 2 year + _ Graphical Representation of Cash Flow Convention Figure 2.4 We cannot compare dollar values that accrue at different points in time To compare costs and benefits over time we use the concept “discounting” The reason is that $1 today is worth more than $1 tomorrow WHY? Comparing Costs and Benefits Discounting a Net Benefit Stream Year 0 1 2 3 Project A -100 +50 +40 +30 Project B -100 +30 +45 +50 WHICH PROJECT ? Deriving Discount Factors Discounting is reverse of compounding FV = PV(1 + i)n PV = FV x 1/ (1 + i)n 1/ (1 + i)n is the Discount Factor Using Discount Factors If i = 10% then year 1 DF = 1/(1+0.1)1 = 0.909 PV of $50 in year 1 = $50 x 0.909 = $45.45 What about year 2 and beyond? PV of $40 in year 2 = $40 x 0.909 x 0.909 = $40 x 0.826 = $33.05 PV = $30 in year 3 = $30 x 0.9093 = $30 x 0.751 = $22.53 Calculating Net Present Value Net present value (NPV) is found by
