We have been assuming that if your income stream is Y1,Y2, your consumption stream must be the same. And if you invest, your consumption stream must be C1,C2. However, by lending or borrowing at the market rate of interest, you can choose any point on the net present value line through A (if you don’t invest), or through B (if you do invest). | © Harry Campbell & Richard Brown School of Economics The University of Queensland BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets Ch. 2: Investment Appraisal - Principles Review of basic concepts used in investment appraisal interest rate discount factor net present value internal rate of return marginal productivity of capital benefit/cost ratio net benefit stream annuities perpetuities cost of capital depreciation inflation real and nominal (money) rates of interest risk premium How do we appraise this proposed investment? Compare: the world with the investment (represented by point B, with consumption C1 and C2); and the world without the investment (represented by point A, with consumption Y1 and Y2). Which do you prefer? Point A or point B? We can’t simply compare Y1+Y2 with C1+C2 because of the time value of money (represented by the interest rate). Calculate present values: PV(Y1,Y2) = F; PV(C1,C2) = E; E>F, hence, prefer E – . undertake the | © Harry Campbell & Richard Brown School of Economics The University of Queensland BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets Ch. 2: Investment Appraisal - Principles Review of basic concepts used in investment appraisal interest rate discount factor net present value internal rate of return marginal productivity of capital benefit/cost ratio net benefit stream annuities perpetuities cost of capital depreciation inflation real and nominal (money) rates of interest risk premium How do we appraise this proposed investment? Compare: the world with the investment (represented by point B, with consumption C1 and C2); and the world without the investment (represented by point A, with consumption Y1 and Y2). Which do you prefer? Point A or point B? We can’t simply compare Y1+Y2 with C1+C2 because of the time value of money (represented by the interest rate). Calculate present values: PV(Y1,Y2) = F; PV(C1,C2) = E; E>F, hence, prefer E – . undertake the investment Lending and Borrowing We have been assuming that if your income stream is Y1,Y2, your consumption stream must be the same. And if you invest, your consumption stream must be C1,C2. However, by lending or borrowing at the market rate of interest, you can choose any point on the net present value line through A (if you don’t invest), or through B (if you do invest). For example, if you do invest (B) you could borrow in period 1 to finance the consumption combination represented by point G. Note that G represents more of both commodities (dollars now and dollars next year) than A. Applying Investment Decision Rules NPV = BC[1/(1+r)] - AC > 0, hence undertake project. The relation BC[1/(1+r)] - AC > 0 can be rearranged in various ways to yield equivalent decision rules: Benefit/Cost Ratio, BCR = BC[1/(1+r)]/AC > 1, hence undertake the project; Marginal Productivity of Capital, MPK = BC/AC > (1+r), hence undertake the project; Internal Rate of Return, IRR = MPK - 1 = [BC/AC] > r,
