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Cash Flow Patterns

Cash Flow Patterns. The “LEGO” blocks of Engineering Economics. 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). Present Given Future.

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Cash Flow Patterns

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  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 F ? 0 1 2 3 n P 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 F 0 1 2 3 n P ? 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 F ? 0 1 2 3 n A 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 F 0 1 2 3 n A ? 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 P ? 0 1 2 3 n A 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 P 0 1 2 3 n A ? 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 P ? 0 1 2 3 n G=$/pd P = G(P/G,i,n)

  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 F ? 0 1 2 3 n G=$/pd F = G(F/G,i,n)

  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 A ? 0 1 2 3 n G=$/pd A = G(A/G,i,n)

  11. P ? 0 1 2 3 n A1 P = A1(P/A,g,i,n) 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 A1 at Time 1, increases by constant g% 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 NOP/g. Present given Geometric Gradient is: (P/A, g, i, n)

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