Math Problem Statement

Anderson International Limited is evaluating a project in Erewhon. The project will create the following cash flows: - Year 0: -$1,340,000 - Year 1: $515,000 - Year 2: $580,000 - Year 3: $475,000 - Year 4: $430,000 The company uses a required return of 15 percent and needs to calculate the Net Present Value (NPV) and Internal Rate of Return (IRR).

Solution

To solve this problem, we need to calculate both the Net Present Value (NPV) and the Internal Rate of Return (IRR) for the project, given the cash flows and the required return rate.

Given Data:

  • Year 0: Cash Flow = $1,340,000-\$1,340,000
  • Year 1: Cash Flow = $515,000\$515,000
  • Year 2: Cash Flow = $580,000\$580,000
  • Year 3: Cash Flow = $475,000\$475,000
  • Year 4: Cash Flow = $430,000\$430,000
  • Required Return = 15%
  • Reinvestment Rate = 4%

Steps to Calculate NPV:

  1. The NPV formula is: NPV=Ct(1+r)t\text{NPV} = \sum \frac{C_t}{(1 + r)^t} where:

    • CtC_t is the cash flow at time tt.
    • rr is the discount rate (required return).
    • tt is the year (time period).
  2. Substitute the values into the NPV formula and calculate.

Steps to Calculate IRR:

  • The IRR is the discount rate that makes the NPV of the project zero: 0=1,340,000+515,000(1+IRR)1+580,000(1+IRR)2+475,000(1+IRR)3+430,000(1+IRR)40 = -1,340,000 + \frac{515,000}{(1 + \text{IRR})^1} + \frac{580,000}{(1 + \text{IRR})^2} + \frac{475,000}{(1 + \text{IRR})^3} + \frac{430,000}{(1 + \text{IRR})^4}
  • We solve this equation iteratively or use a financial calculator/software to find IRR.

Let's calculate these values.

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Math Problem Analysis

Mathematical Concepts

Finance
Net Present Value (NPV)
Internal Rate of Return (IRR)

Formulas

NPV = Σ (Ct / (1 + r)^t) where Ct is the cash flow at time t and r is the discount rate
IRR is the discount rate that makes the NPV of the project zero: NPV = 0

Theorems

Time Value of Money
Present Value Theorem

Suitable Grade Level

University Level (Finance, Accounting, Business Management)