4-53For diagrams (a) to (d), compute the present values of the cash flows. ### Cash Flow Diagrams#### Diagram (a): Interest Rate (i) = 10%This diagram represents a cash flow scenario at an interest rate of 10%. The timeline on the horizontal axis spans from year 0 to year 4.- At year 0, there is no cash flow.- At year 1, there is an inflow of 125.- At year 2, there is an inflow of 150.- At year 3, there is an inflow of 175.- At year 4, there is an inflow of 200.#### Diagram (b): Interest Rate (i) = 10%This diagram shows a cash flow scenario at a 10% interest rate, spanning from year 0 to year 3.- At year 0, there is no cash flow.- At year 1, there is no cash flow.- At year 2, there is an inflow of 3000.- At year 3, there is an inflow of 2000.- At year 3, there is an additional inflow of 1000.#### Diagram (c): Interest Rate (i) = 10%This diagram presents another cash flow scenario with the same interest rate of 10%, over a timeline from year 0 to year 5.- At year 0, there is no cash flow.- At year 1, there is no cash flow.- At year 2, there is an inflow of 1000.- At year 3, there is an inflow of 2000.- At year 4, there is no cash flow.- At year 5, there is an inflow of 3000.### ExplanationEach vertical arrow represents a cash inflow at the specified time. The diagrams effectively illustrate the time value of money, where different cash inflows occur at different times and amounts under a consistent interest rate of 10%. These scenarios can help in understanding the financial principle of discounting future cash flows to their present values.

(a) The present value of cash flow is calculated as mentioned below: Present value = 125(P/F,i,1) +…

Answered: 3000 200 175 2000 150 1000 125 0- -3-…

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3000 200 175 2000 150 1000 125 0- -3- 0- -3 (a) i = 10% (b) i = 10% 3000 2000 1000 0-1-2-3- (c) i = 10% 4,

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Concept explainers

Cash Flow in Engineering Economics (Interest and Equivalence)

The cash flows of a firm are of two categories such as cash inflows and cash outflows. Cash inflow is the money or income entering a firm during a specific period whereas cash outflow is the money exiting a firm during a specific period in the form of the expenses incurred by the firm. In other words, we can say that cash flow is a series of expenses and credits that run over the project over the lifetime it existed whereas cash inflows are all the income and gains the company earns as a result of its operations.

Question

4-53

For diagrams (a) to (d), compute the present values of the cash flows.

### Cash Flow Diagrams

#### Diagram (a): Interest Rate (i) = 10%

This diagram represents a cash flow scenario at an interest rate of 10%. The timeline on the horizontal axis spans from year 0 to year 4.

- At year 0, there is no cash flow.
- At year 1, there is an inflow of 125.
- At year 2, there is an inflow of 150.
- At year 3, there is an inflow of 175.
- At year 4, there is an inflow of 200.

#### Diagram (b): Interest Rate (i) = 10%

This diagram shows a cash flow scenario at a 10% interest rate, spanning from year 0 to year 3.

- At year 0, there is no cash flow.
- At year 1, there is no cash flow.
- At year 2, there is an inflow of 3000.
- At year 3, there is an inflow of 2000.
- At year 3, there is an additional inflow of 1000.

#### Diagram (c): Interest Rate (i) = 10%

This diagram presents another cash flow scenario with the same interest rate of 10%, over a timeline from year 0 to year 5.

- At year 0, there is no cash flow.
- At year 1, there is no cash flow.
- At year 2, there is an inflow of 1000.
- At year 3, there is an inflow of 2000.
- At year 4, there is no cash flow.
- At year 5, there is an inflow of 3000.

### Explanation

Each vertical arrow represents a cash inflow at the specified time. The diagrams effectively illustrate the time value of money, where different cash inflows occur at different times and amounts under a consistent interest rate of 10%. These scenarios can help in understanding the financial principle of discounting future cash flows to their present values.

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