
Green Valley Fashion is evaluating a 11-year project that would require an initial investment in equipment of $833,000. The equipment would be depreciated to $89,000 over 8 years using straight-line depreciation. For each year of the project, Green Valley Fashion expects relevant revenue associated with the project to be $529,000 per year. Relevant costs associated with the project are expected to be $386,000 in years 1 and 2, and $457,000 in years 3 and later. The tax rate is 30 percent. What is (X plus Y) if X is the relevant operating cash flow associated with the project expected in year 2 of the project and Y is the relevant operating cash flow associated with the project expected in year 3?

To solve for $ X + Y $, where $ X $ is the relevant operating cash flow (OCF) in year 2 and $ Y $ is the relevant OCF in year 3, let's go through the calculations step by step. The operating cash flow (OCF) for each year can be calculated as follows:

\[
\text{OCF} = (\text{Revenue} - \text{Costs} - \text{Depreciation}) \times (1 - \text{Tax Rate}) + \text{Depreciation}
\]

### Step 1: Determine Depreciation
Since the equipment is depreciated from $833,000 to $89,000 over 8 years using straight-line depreciation:

\[
\text{Annual Depreciation} = \frac{833,000 - 89,000}{8} = \frac{744,000}{8} = 93,000
\]

### Step 2: Calculate OCF in Year 2 (X)

For year 2:
- Revenue = $529,000
- Costs = $386,000
- Depreciation = $93,000
- Tax Rate = 30% (or 0.30)

The formula for OCF becomes:

\[
X = (\text{Revenue} - \text{Costs} - \text{Depreciation}) \times (1 - \text{Tax Rate}) + \text{Depreciation}
\]

Substitute the values:

\[
X = (529,000 - 386,000 - 93,000) \times (1 - 0.30) + 93,000
\]

\[
X = (50,000) \times 0.70 + 93,000
\]

\[
X = 35,000 + 93,000 = 128,000
\]

### Step 3: Calculate OCF in Year 3 (Y)

For year 3, the costs increase to $457,000:
- Revenue = $529,000
- Costs = $457,000
- Depreciation = $93,000
- Tax Rate = 30%

Using the OCF formula:

\[
Y = (529,000 - 457,000 - 93,000) \times (1 - 0.30) + 93,000
\]

\[
Y = (529,000 - 550,000) \times 0.70 + 93,000
\]

\[
Y = (-21,000) \times 0.70 + 93,000
\]

\[
Y = -14,700 + 93,000 = 78,300
\]

### Step 4: Calculate $ X + Y $

Now, add the OCFs for years 2 and 3:

\[
X + Y = 128,000 + 78,300 = 206,300
\]

### Final Answer
The value of $ X + Y $ is **$206,300**.

Would you like further details or have any questions?

---

1. How does the tax rate affect operating cash flows?
2. Why is depreciation added back in the cash flow calculation?
3. How would the cash flow change if the costs differed across years?
4. What happens if the project tax rate changes midway?
5. How does straight-line depreciation influence cash flow consistency?

**Tip:** Depreciation reduces taxable income but doesn't involve an actual cash outflow, which is why it’s added back in cash flow calculations.

Green Valley Fashion is evaluating a 11-year project that would require an initial investment in equipment of $833,000. The equipment would be depreciated to $89,000 over 8 years using straight-line depreciation. For each year of the project, Green Valley Fashion expects relevant revenue associated with the project to be $529,000 per year. Relevant costs associated with the project are expected to be $386,000 in years 1 and 2, and $457,000 in years 3 and later. The tax rate is 30 percent. What is (X plus Y) if X is the relevant operating cash flow associated with the project expected in year 2 of the project and Y is the relevant operating cash flow associated with the project expected in year 3?

Learn how to calculate the relevant operating cash flow (OCF) for a project involving depreciation and taxation. This solution covers the depreciation of equipment, the revenue and costs expected in years 2 and 3, and the effect of taxation on cash flows. The OCF for year 2 and 3 is $128,000 and $78,300, respectively, leading to a total of $206,300.

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