What is the expected after-tax cash flow from selling a piece of equipment if Silver Mountain Health purchases the equipment today for $414,000, the tax rate is 35 percent, the equipment would be sold in 14 years for $85,000, and the equipment would be depreciated to $62,000 over 11 years using straight-line depreciation?

 

Input instructions: Round your answer to the nearest dollar.

To calculate the expected after-tax cash flow from selling the equipment, we’ll follow these steps:

1. **Calculate the annual depreciation** using straight-line depreciation.
2. **Determine the book value** of the equipment at the end of 14 years.
3. **Calculate the gain or loss** on the sale of the equipment.
4. **Compute the after-tax impact** of this gain or loss.
5. **Determine the after-tax cash flow** from the sale.

### Step 1: Calculate Annual Depreciation

The initial purchase price of the equipment is $414,000, and it will be depreciated to $62,000 over 11 years using straight-line depreciation.

\[
\text{Annual Depreciation} = \frac{\text{Purchase Price} - \text{Salvage Value}}{\text{Useful Life}}
\]
\[
\text{Annual Depreciation} = \frac{414,000 - 62,000}{11} = \frac{352,000}{11} = 32,000
\]

### Step 2: Determine the Book Value at the End of 14 Years

Since the equipment will be fully depreciated by 11 years, the book value after 11 years will be $62,000, and this will remain unchanged for years 12 through 14.

So, at the end of 14 years:
\[
\text{Book Value} = 62,000
\]

### Step 3: Calculate the Gain or Loss on the Sale

The equipment is sold for $85,000, and its book value at that time is $62,000. Therefore, there is a gain of:

\[
\text{Gain} = \text{Sale Price} - \text{Book Value}
\]
\[
\text{Gain} = 85,000 - 62,000 = 23,000
\]

### Step 4: Compute the After-Tax Impact of the Gain

The tax rate is 35%, so we calculate the tax on the gain:

\[
\text{Tax on Gain} = \text{Gain} \times \text{Tax Rate}
\]
\[
\text{Tax on Gain} = 23,000 \times 0.35 = 8,050
\]

### Step 5: Determine the After-Tax Cash Flow from the Sale

The after-tax cash flow from the sale is the sale price minus the tax on the gain:

\[
\text{After-Tax Cash Flow} = \text{Sale Price} - \text{Tax on Gain}
\]
\[
\text{After-Tax Cash Flow} = 85,000 - 8,050 = 76,950
\]

### Answer

The expected after-tax cash flow from selling the equipment is:

\[
\boxed{76,950}
\]

Would you like a further breakdown or have any questions?

---

Here are five related questions that expand on this topic:
1. How would changes in the tax rate affect the after-tax cash flow?
2. What is the effect of extending the depreciation period on the after-tax cash flow?
3. How would an accelerated depreciation method impact this calculation?
4. What would the after-tax cash flow be if the equipment sold for less than its book value?
5. How would including maintenance costs in the analysis affect the overall calculation?

**Tip:** For capital assets, remember that the choice of depreciation method can significantly impact cash flows due to the timing of tax savings.

What is the expected after-tax cash flow from selling a piece of equipment if Silver Mountain Health purchases the equipment today for $414,000, the tax rate is 35 percent, the equipment would be sold in 14 years for $85,000, and the equipment would be depreciated to $62,000 over 11 years using straight-line depreciation?

Learn how to calculate the expected after-tax cash flow from selling equipment with depreciation and tax impact. This example uses straight-line depreciation and provides a step-by-step guide to determine the impact of a 35% tax rate on a $414,000 equipment purchase. The expected after-tax cash flow is $76,950.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation