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:

  1. 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.

  2. Discount the adjusted cash flows to the present at the required rate of return (9.2%).

Step-by-Step Solution:

  1. Initial Investment:
    C0=39,500C_0 = -39,500

  2. Year 1 Cash Flow (Blocked and Reinvested):
    C1=22,600×(1+0.028)=22,600×1.028=23,232.8C_1 = 22,600 \times (1 + 0.028) = 22,600 \times 1.028 = 23,232.8

  3. Year 2 Cash Flow (Blocked and Reinvested):
    C2=28,800×(1+0.028)=28,800×1.028=29,606.4C_2 = 28,800 \times (1 + 0.028) = 28,800 \times 1.028 = 29,606.4

  4. Year 3 Cash Flow (No Blocking):
    C3=29,100C_3 = 29,100 (no reinvestment, as it's received at the end of the project).

  5. Discounting to Present Value:
    The formula for discounting is:
    PV=FV(1+r)tPV = \frac{FV}{(1 + r)^t}
    Where rr is the required return (9.2% or 0.092), and tt is the time in years.

    • For Year 1: PV1=23,232.8(1+0.092)2=23,232.8(1.092)2=23,232.81.19246419,487.8PV_1 = \frac{23,232.8}{(1 + 0.092)^2} = \frac{23,232.8}{(1.092)^2} = \frac{23,232.8}{1.192464} \approx 19,487.8

    • For Year 2: PV2=29,606.4(1+0.092)3=29,606.4(1.092)3=29,606.41.29412222,860.6PV_2 = \frac{29,606.4}{(1 + 0.092)^3} = \frac{29,606.4}{(1.092)^3} = \frac{29,606.4}{1.294122} \approx 22,860.6

    • For Year 3: PV3=29,100(1+0.092)3=29,1001.29412222,481.3PV_3 = \frac{29,100}{(1 + 0.092)^3} = \frac{29,100}{1.294122} \approx 22,481.3

  6. Summing the Present Values:
    NPV=PV1+PV2+PV3+C0NPV = PV_1 + PV_2 + PV_3 + C_0 Substituting the values:
    NPV=19,487.8+22,860.6+22,481.339,500NPV = 19,487.8 + 22,860.6 + 22,481.3 - 39,500 NPV25,329.7NPV \approx 25,329.7

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:

  1. How does reinvestment at a blocked rate affect project evaluation?
  2. How would the NPV change if the required return were higher or lower?
  3. What is the impact of reinvestment interest being lower than the required return?
  4. How does the timing of cash flows influence the NPV?
  5. 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