Percentage Increase and Decrease Worksheets - Free Printable

To solve the problem, we need to calculate the Net Present Value (NPV) of the project. The NPV is calculated using the formula:

\[
NPV = \sum_{t=0}^{n} \frac{CF_t}{(1 + r)^t}
\]

Where:
- \( CF_t \) is the cash flow in period \( t \)
- \( r \) is the discount rate
- \( t \) is the time period

Step-by-Step Solution:

#### 1. Identify the Cash Flows and Discount Rate
From the image:
- Initial Investment (\( CF_0 \)): $500,000
- Annual Cash Inflows (\( CF_1 \) to \( CF_5 \)):
- Year 1: $200,000
- Year 2: $250,000
- Year 3: $300,000
- Year 4: $350,000
- Year 5: $400,000
- Salvage Value (\( CF_5 \)): $50,000 (added to Year 5 cash flow)
- Discount Rate (\( r \)): 10% or 0.10

#### 2. Calculate the Total Cash Flow for Each Year
- Year 0: Initial Investment = $-500,000
- Year 1: Cash Inflow = $200,000
- Year 2: Cash Inflow = $250,000
- Year 3: Cash Inflow = $300,000
- Year 4: Cash Inflow = $350,000
- Year 5: Cash Inflow = $400,000 + Salvage Value ($50,000) = $450,000

#### 3. Discount Each Cash Flow to Present Value
We use the formula for present value of a cash flow:

\[
PV_t = \frac{CF_t}{(1 + r)^t}
\]

- Year 0:
\[
PV_0 = \frac{-500,000}{(1 + 0.10)^0} = \frac{-500,000}{1} = -500,000
\]

- Year 1:
\[
PV_1 = \frac{200,000}{(1 + 0.10)^1} = \frac{200,000}{1.10} = 181,818.18
\]

- Year 2:
\[
PV_2 = \frac{250,000}{(1 + 0.10)^2} = \frac{250,000}{1.21} = 206,611.57
\]

- Year 3:
\[
PV_3 = \frac{300,000}{(1 + 0.10)^3} = \frac{300,000}{1.331} = 225,394.43
\]

- Year 4:
\[
PV_4 = \frac{350,000}{(1 + 0.10)^4} = \frac{350,000}{1.4641} = 238,958.02
\]

- Year 5:
\[
PV_5 = \frac{450,000}{(1 + 0.10)^5} = \frac{450,000}{1.61051} = 279,432.84
\]

#### 4. Sum the Present Values
Now, sum all the present values to get the NPV:

\[
NPV = PV_0 + PV_1 + PV_2 + PV_3 + PV_4 + PV_5
\]

\[
NPV = -500,000 + 181,818.18 + 206,611.57 + 225,394.43 + 238,958.02 + 279,432.84
\]

\[
NPV = -500,000 + 1,132,215.04
\]

\[
NPV = 632,215.04
\]

Final Answer:

\[
\boxed{632215.04}
\]

Explanation:

The NPV of the project is positive ($632,215.04), indicating that the project is expected to add value to the company. Therefore, based on the NPV criterion, the project should be accepted.