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?

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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.