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### System Engineering & Economy Analysis

Lecturer

Maha Muhaisen

College ofApplied Engineering& Urban Planning

Cash flow

- Cash flow diagram (CFD) summarized the cost and benefit of the project occur over time.
- CFD is created by first drawing a segmented time – based horizontal line, divided onto appropriate time units.
- At each time at which cash flow will occur a vertical arrow is added. Pointing down for cost , pointing up for revenues or benefit.

Key Concepts

- Cash Flow Diagram: the financial description (visual) of a project
- Time Value of Money: the value of money changes with time
- Money provides utility (value) when spent
- Value of money grows if invested
- Value of money decreases due to inflation
- Interest: used to move money through time for comparisons

Cash Flow

- Movement of money in (out) of a project
- Inflows: revenues or receipts
- Outflows: expenses or disbursements
- Net Cash Flow: receipts - disbursements

Cash Flows

- Discrete: Movement of cash to or from a project at a specific point in time.
- Continuous: Rate of cash moving from or to a project over some period of time.

Cash Flow Diagram

- Financial representation of a project.
- Describes type, magnitude and timing of cash flows over some horizon.

Cash Flow Diagram

- Describes type, magnitude and timing of cash flows over some horizon

0

1

2

3

4

5

Time Periods over the Horizon

Cash Flow Diagram

- Describes type, magnitude and timing of cash flows over some horizon

0

1

2

3

4

5

50$

100$

500$

Discrete Cash Outflow (Disbursement, Expense)

Note the direction of the arrow!

Cash Flow Diagram

- Describes type, magnitude and timing of cash flows over some horizon

500$

200$

200$

200$

0

1

2

3

4

5

Discrete Cash Inflow (Revenue)

Cash Flow Diagram

- Describes type, magnitude and timing of cash flows over some horizon

500$

200$

200$

200$

0

1

2

3

4

5

50$

100$

500$

Cash Flow Diagram

- Net cash flows add expenses and disbursements at same point in time.

500K

200K

200K

200K

0

1

2

3

4

5

50K

100K

Can write as net cash flow

500K

Cash Flow Diagram

- Net cash flows add expenses and disbursements at same point in time.

500$

200$

200$

100$

0

1

2

3

4

5

50$

500$

Cash Flow Diagram

- Continuous cash flows define a rate of movement of cash over time.

500$

200$

200$

0

1

2

3

4

5

Continuous Cash Inflow (Revenue)

200$ Rate of Flow per unit time

500$

Cash Flow Diagram

- Continuous cash flows define a rate of movement of cash over time.
- While good for analysis, not used often.

500$

200$

200$

0

1

2

3

4

5

Continuous Cash Inflow (Revenue)

200$ Rate of Flow per unit time

500$

Cash Flow Diagram

- Can describe any investment opportunity.
- Typical investment:

Cash Flow Diagram

- Can describe any investment opportunity.
- Typical investment:

0

P

Make an initial investment (purchase)

Cash Flow Diagram

- Can describe any investment opportunity.
- Typical investment:

0

1

2

3

N

P

Receive revenues over time.

Cash Flow Diagram

- Can describe any investment opportunity.
- Typical investment:

0

1

2

3

N

P

Pay expenses over time.

Cash Flow Diagram

- Can describe any investment opportunity.
- Typical investment:

Receive salvage value at time N.

F

0

1

2

3

N

P

Cash Flow Diagram

- Can describe any investment opportunity.
- Typical investment:

AN

A3

A2

0

1

2

3

N

A1

P

Write as a NET cash flow in each period.

Example (Nothing to Sneeze At!)

- Tissue paper company Svenska Cellulosa announced an investment of $490 million for a new tissue machine at its Valls, Spain plant to expand capacity by 60,000 tons/year. Most product is for retail private labels.
- Assume: Investment in 2006 with operations beginning in 2007. The machine has a service life of 10 years and a salvage value of $25M. Fixed O&M costs are $10 million in year 1, increase 8% per year. Revenues are $6,400/ton against costs of $4,600/ton.
- Draw the cash flow diagram.

Cash Flow Diagram

- Individual cash flows: Fixed Costs

384M

384M

384M

384M

0

1

2

3

10

276M

276M

276M

276M

10M

10.8M

11.7M

20M

490M

Cash Flow Diagram

- Individual cash flows: Salvage Value

25M

384M

384M

384M

384M

0

1

2

3

10

276M

276M

276M

276M

10M

10.8M

11.7M

20M

490M

Cash Flow Diagram

- Net Cash Flow Diagram

113M

98.0M

97.2M

96.4M

89.5M

0

1

2

3

9

10

This is a “typical” investment.

(Invest at zero, returns later.)

490M

Cash Flow Diagram

- Net Cash Flow Diagram

113M

98.0M

97.2M

96.4M

89.5M

0

1

2

3

9

10

This is a “typical” investment.

(Invest at zero, returns later.)

Can also use a spreadsheet!

490M

Spreadsheet Basics

Sheet defined by rows and columns of cells.

Spreadsheet Basics

Can enter the following into a cell:

- Data: Input that is fixed.
- Variables: Input that can change.
- Accomplished by references.
- Absolute references are fixed when copied.
- Relative references change when copied.
- Functions: Accept input (arguments) and return pre-defined output.
- Combinations: Data, Variables, and Functions.
- Labels: Formatting that makes it easy to read!

Good Spreadsheet Form

- Give your spreadsheet a title.
- Put data in a “data center” and reference it (so you can change it easily).
- Label units, scales, time, etc.
- Use formatting to make it easy to read.

Good Spreadsheet Form

- Give your spreadsheet a title.
- Put data in a “data center” and reference it (so you can change it easily).
- Label units, scales, time, etc.
- Use formatting to make it easy to read.

If you don’t, you will just end up doing it again!

Return to our Example

Data Center with Data

Return to our Example

Relative Reference: A13: Copies relative distance between cell and

copied cell to the new cell.

Absolute Reference: $G$4: Copies the cell reference exactly (fixed).

Return to our Example

Function Call: SUM(argument1, argument2,…) = argument1+argument2…

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