What value of X makes these two cash flows equivalent assuming an interest rate of 10%? 150 150 100 100 100 100 X 2 3 4 1 2 3 4 200

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
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**Title: Understanding Cash Flow Equivalence with Interest Rates**

**Introduction**

In financial analysis, understanding the equivalence of cash flows is crucial. This example demonstrates how to determine the value of a cash flow so that two sets of cash flows are equivalent, given an interest rate. 

**Problem Statement**

"What value of X makes these two cash flows equivalent assuming an interest rate of 10%?"

**Cash Flows Overview**

1. **Cash Flow Diagram on the Left**
    - At time 0: $100
    - At time 1: $100
    - At time 2: $100
    - At time 3: $150
    - At time 4: $100
    - At time 5: $150

2. **Cash Flow Diagram on the Right**
    - At time 0: $100
    - At time 1: $100
    - At time 3: X
    - At time 4: $200 (negative cash flow, indicated by a downward arrow)
    - At time 5: X

**Objective**

Determine the value of X that makes these two cash flows equivalent under a 10% interest rate. 

**Approach**

To solve this, each series of cash flows needs to be evaluated for their present value (PV), using the formula for the present value of future cash flows, and then set them equal to solve for X. 

**Conclusion**

This example helps in understanding how to match cash flows to achieve equivalence at a specific interest rate, a valuable skill in financial planning and analysis.
Transcribed Image Text:**Title: Understanding Cash Flow Equivalence with Interest Rates** **Introduction** In financial analysis, understanding the equivalence of cash flows is crucial. This example demonstrates how to determine the value of a cash flow so that two sets of cash flows are equivalent, given an interest rate. **Problem Statement** "What value of X makes these two cash flows equivalent assuming an interest rate of 10%?" **Cash Flows Overview** 1. **Cash Flow Diagram on the Left** - At time 0: $100 - At time 1: $100 - At time 2: $100 - At time 3: $150 - At time 4: $100 - At time 5: $150 2. **Cash Flow Diagram on the Right** - At time 0: $100 - At time 1: $100 - At time 3: X - At time 4: $200 (negative cash flow, indicated by a downward arrow) - At time 5: X **Objective** Determine the value of X that makes these two cash flows equivalent under a 10% interest rate. **Approach** To solve this, each series of cash flows needs to be evaluated for their present value (PV), using the formula for the present value of future cash flows, and then set them equal to solve for X. **Conclusion** This example helps in understanding how to match cash flows to achieve equivalence at a specific interest rate, a valuable skill in financial planning and analysis.
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