A project requires $10 million dollars in initial investment. The projected revenue is $3 million dollars per year for the next 5 years (from year 1 to 5). If we apply a discount factor of 5%, what is

a) the break-even period? (5 points)

b) the discounted cash-flow and the NPV of the proposed project? (6 points)

c) the IRR of the project? (5 points)

To solve this, let’s calculate step by step:

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### **Given**:
1. **Initial investment** = $10 million
2. **Revenue** = $3 million/year for 5 years
3. **Discount rate** = 5%

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### **Steps**:

#### **a) Break-even period**:
The break-even period is when the cumulative cash flows (including the discounted values) equal the initial investment.

- **Formula for discounted cash flow (DCF)**:
  \[
  \text{DCF} = \frac{\text{Cash Flow}}{(1 + r)^n}
  \]
  where:
  - $ r $ = discount rate (5% = 0.05)
  - $ n $ = year number

We calculate the cumulative discounted cash flow year by year to determine when the total equals $10 million.

---

#### **b) Discounted Cash Flow (DCF) and NPV**:
The NPV (Net Present Value) is the sum of the discounted cash flows over the project life minus the initial investment.

\[
\text{NPV} = \sum_{n=1}^{5} \frac{\text{Cash Flow}}{(1 + r)^n} - \text{Initial Investment}
\]

---

#### **c) IRR (Internal Rate of Return)**:
The IRR is the discount rate at which the NPV equals zero. Mathematically, solve for $ r $ in the equation:
\[
0

A project requires $10 million dollars in initial investment. The projected revenue is $3 million dollars per year for the next 5 years (from year 1 to 5). If we apply a discount factor of 5%, what is
a) the break-even period? (5 points)
b) the discounted cash-flow and the NPV of the proposed project? (6 points)
c) the IRR of the project? (5 points)

Learn how to calculate the break-even period, discounted cash flow (DCF), NPV, and IRR for a $10 million investment with a projected revenue of $3 million per year over 5 years and a 5% discount rate. This guide includes detailed formulas and step-by-step solutions for finance and math students.

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