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Identify cash flow sequences that are arithmetic gradients and use financial tables (Appendix C) to convert arithmetic gradient cash flows into their present value and uniform payment equivalents. [Reminder: a $0 cash flow is considered part of the gradient and P/G calculates PV one period prior to the period with that $0 cash flow.]

Arithmetic Gradients Assume an 8% interest rate and find S, T, and X. 1800 1200 800 600 600 400 A 200 0 0E +2 3 (a) S = value at i = 0 (b) T= uniform value for 5 periods 4-52 600 450 300 150 01 (c) X = value at i = 0 For diagrams (a) to (d), compute the present values of the cash flows. Arithmetic Gradient Review: t=0 V= N= 80 0 0 0 4 t=1 t=2 t=3 t=4 t=5 t=6 G= 0 20 40 60 100 20 0 0 0 -10 -20 -30 -10 0 25 50 75 25 Arithmetic gradient: A/G calculates uniform payment for these periods P/G calculates PV equivalent for this period 4 "Creative" conversions: t=0 t=1 500 500 0 t=2 510 500 10 t=3 520 500 20 t=4 530 500 30 Use P/A Use P/G 500 500 0 490 500 -10 480 500 -20 470 500 -30 Use P/A Use P/G PV = 500(P/A,10%,4) -10(P/G,10%,4) A = 500 - 10(A/G,10%,4)