Math Problem Statement
Maud'Dib Intergalactic has a new project available on Arrakis. The cost of the project is $39,500 and it will provide cash flows of $22,600, $28,800, and $29,100 over each of the next three years, respectively. Any cash earned in Arrakis is "blocked" and must be reinvested in the country for one year at an interest of 2.8 percent. The project has a required return of 9.2 percent. What is the project's NPV?
Solution
To compute the Net Present Value (NPV) of this project, we need to account for the reinvestment constraint. Here's the process:
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Determine the effective cash flows considering the blocked reinvestment rate.
Each cash flow earned will need to be reinvested for one year at 2.8%. Thus, the cash flows must be adjusted to reflect the reinvested amount before they are discounted. -
Discount the adjusted cash flows to the present at the required rate of return (9.2%).
Step-by-Step Solution:
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Initial Investment:
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Year 1 Cash Flow (Blocked and Reinvested):
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Year 2 Cash Flow (Blocked and Reinvested):
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Year 3 Cash Flow (No Blocking):
(no reinvestment, as it's received at the end of the project). -
Discounting to Present Value:
The formula for discounting is:
Where is the required return (9.2% or 0.092), and is the time in years.-
For Year 1:
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For Year 2:
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For Year 3:
-
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Summing the Present Values:
Substituting the values:
Final Answer:
The Net Present Value (NPV) of the project is approximately $25,329.70.
Do you want more details or need help understanding any part?
Here are 5 related questions to expand your understanding:
- How does reinvestment at a blocked rate affect project evaluation?
- How would the NPV change if the required return were higher or lower?
- What is the impact of reinvestment interest being lower than the required return?
- How does the timing of cash flows influence the NPV?
- What alternatives exist for evaluating blocked cash flows in international projects?
Tip: Always confirm the assumptions in cash flow projections when working with reinvestment constraints or country-specific regulations.
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Math Problem Analysis
Mathematical Concepts
Finance
Net Present Value (NPV)
Cash Flow Discounting
Reinvestment Rates
Formulas
NPV = PV_1 + PV_2 + PV_3 + C_0
PV = FV / (1 + r)^t
Adjusted Cash Flow = Cash Flow × (1 + reinvestment rate)
Theorems
Time Value of Money
Discounting of Cash Flows
Suitable Grade Level
Grades 11-12, College-Level Finance
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