1 Cash Flow Patterns The “LEGO” blocks of Engineering Economics

2 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 0n P F ? 123 F = P(F/P,i,n)

3 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 0n P ? F 123 P = F(P/F,i,n)

4 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  Note: cash flow A does not have to be annual, just periodic 0n A F ? 123 F = A(F/A,i,n)

5 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  Note: cash flow A does not have to be annual, just periodic 0n A ? F 123 A = F(A/F,i,n)

6 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  Note: cash flow A does not have to be annual, just periodic 0n A P ? 123 P = A(P/A,i,n)

7 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  Note: cash flow A does not have to be annual, just periodic 0n A ? P 123 A = P(A/P,i,n)

8 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  Note: cash flow is periodic, no flow at Time 1, flow of G at Time 2 0n P ? 123 P = G(P/G,i,n) G=$/pd

9 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  Note: cash flow is periodic, no flow at Time 1, flow of G at Time 2 0n F ? 123 F = G(F/G,i,n) G=$/pd

10 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  Note: cash flow of G starts at Time 2, flow of A starts at Time 1 0n A ? 123 A = G(A/G,i,n) G=$/pd

11 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 Note: cash flow starts with A 1 at Time 1, increases by constant g% 0n A1A1 P ? 123 P = A 1 (P/A,g,i,n) g = %/pd

12 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)