Cash Flow Patterns The “LEGO” blocks of Engineering Economics 1 Future Given Present P is the present value at Time 0 F is the future value at Time n (n periods in the future) i is the effective interest rate F? 0 1 2 3 n P F = P(F/P,i,n) 2 Present Given Future P is the present value at Time 0 F is the future value at Time n (n periods in the future) i is the effective interest rate for each period F 0 1 2 3 n P? P = F(P/F,i,n) 3 Future Given Annual A is the equal annual value over the time period (time period: Time 0 to Time n, 1st flow at Time 1) F is the future value at Time n (n periods in the future) i is the effective interest rate for each period F? 0 1 2 3 n A F = A(F/A,i,n) Note: cash flow A does not have to be annual, just periodic 4 Annual Given Future A is the equal annual value over the time period (time period: Time 0 to Time n, 1st flow at Time 1) F is the future value at Time n (n periods in the future) i is the effective interest rate for each period F 0 1 2 3 n A? A = F(A/F,i,n) Note: cash flow A does not have to be annual, just periodic 5 Present Given Annual A is an equal annual flow over the time period (time period: Time 0 to Time n, 1st flow at Time 1) P is the present value at Time 0 (n periods in the past) i is the effective interest rate for each period P? 0 1 2 3 n A P = A(P/A,i,n) Note: cash flow A does not have to be annual, just periodic 6 Annual Given Present A is the equivalent annual flow over the time period (time period: Time 0 to Time n, 1st flow at Time 1) P is the present value at Time 0 (n periods in the past) i is the effective interest rate for each period P 0 1 2 3 n A? A = P(A/P,i,n) Note: cash flow A does not have to be annual, just periodic 7 Present Given Gradient (Linear) G is the linear gradient over the time period (time period: Time 0 to Time n, 1st flow at Time 2) P is the present value of the flow at Time 0 (n periods in the past) i is the effective interest rate for each period P? 0 1 2 3 n G=$/pd P = G(P/G,i,n) 8 Note: cash flow is periodic, no flow at Time 1, flow of G at Time 2 Future Given Gradient (Linear) G is the linear gradient over the time period (time period: Time 0 to Time n, 1st flow at Time 2) F is the future value of the flow at Time n (n periods in the future) i is the effective interest rate for each period F? 0 1 2 3 n G=$/pd F = G(F/G,i,n) 9 Note: cash flow is periodic, no flow at Time 1, flow of G at Time 2 Annual Given Gradient (Linear) G is the linear gradient over the time period (time period: Time 0 to Time n, 1st flow at Time 2) A is the annual equivalent of the gradient flow (annual flow starts at Time 1, goes through Time n) i is the effective interest rate for each period A? 0 1 2 3 n G=$/pd A = G(A/G,i,n) 10 Note: cash flow of G starts at Time 2, flow of A starts at Time 1 Present Given Gradient (Geometric) g is the geometric gradient over the time period (time period: Time 0 to Time n, 1st flow at Time 1) P is the present value of the flow at Time 0 (n periods in the past) i is the effective interest rate for each period P? 0 1 A1 2 3 g = %/pd P = A1(P/A,g,i,n) n (1 g ) n 1 ( 1 i ) when i g i g ( P / A, g , i , n ) n when i g (1 i ) 11 Note: cash flow starts with A1 at Time 1, increases by constant g% Table Factors Listed (P/F, i, n) Present given Future (P/A, i, n) Present given Annual (P/G, i, n) Present given Gradient (linear) (F/P, i, n) Future given Present (F/A, i, n) Future given Annual (A/P, i, n) Annual given Present (A/F, i, n) Annual given Future (A/G, i, n) Annual given Gradient Note: There is NO P/g. Present given Geometric Gradient is: (P/A, g, i, n) 12