1. Engineering Economics - Introduction
4/28/2019
Cash Flow Patterns
The “LEGO” blocks of Engineering Economics
Copyright (C) , D. H. Jensen

2. Engineering Economics - Introduction
4/28/2019
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
i=?
F ? 1 2 3 n P
F = P(F/P,i,n)
Copyright (C) , D. H. Jensen

3. Engineering Economics - Introduction
4/28/2019
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
i=? F 1 2 3 n
P ?
P = F(P/F,i,n)
Copyright (C) , D. H. Jensen

4. Engineering Economics - Introduction
4/28/2019
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
i=?
F ? 1 2 3 n A
F = A(F/A,i,n)
Copyright (C) , D. H. Jensen

5. Engineering Economics - Introduction
4/28/2019
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
i=? 1 2 3 n
A ?
A = F(A/F,i,n)
Copyright (C) , D. H. Jensen

6. Engineering Economics - Introduction
4/28/2019
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 ?
i=? 1 2 3 n A
P = A(P/A,i,n)
Copyright (C) , D. H. Jensen

7. Engineering Economics - Introduction
4/28/2019
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
i=? 1 2 3 n
A ?
A = P(A/P,i,n)
Copyright (C) , D. H. Jensen

8. Present Given Gradient (Linear)
Engineering Economics - Introduction
4/28/2019
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 ?
i=? 1 2 3 n
G=$/pd
P = G(P/G,i,n)
Copyright (C) , D. H. Jensen

9. Future Given Gradient (Linear)
Engineering Economics - Introduction
4/28/2019
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
i=?
F ? 1 2 3 n
G=$/pd
F = G(F/G,i,n)
Copyright (C) , D. H. Jensen

10. Annual Given Gradient (Linear)
Engineering Economics - Introduction
4/28/2019
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
i=?
A ? 1 2 3 n
G=$/pd
A = G(A/G,i,n)
Copyright (C) , D. H. Jensen

11. Present Given Gradient (Geometric)
Engineering Economics - Introduction
4/28/2019
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% n A1
P ? 1 2 3
P = A1(P/A,g,i,n)
i=?
g = %/pd
Copyright (C) , D. H. Jensen

12. Engineering Economics - Introduction
4/28/2019
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)
Copyright (C) , D. H. Jensen

13. CASH FLOW DIAGRAM
Yes -- you do need the Sticks!!