A nine year project involves equipment costing $2,320,000 that will be depreciated using the five-year MACRS schedule. If the estimated pre-tax salvage value for the equipment at the end of the project's life is $417,600, what is the after-tax salvage value for the equipment? Assume a marginal tax rate of 21 percent. O $329,904 O $399.184 O-$6,496 O $505,296

Essentials Of Investments
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Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
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Chapter1: Investments: Background And Issues
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### Depreciation and After-Tax Salvage Value Calculation

#### Problem Statement:
A nine-year project involves equipment costing $2,320,000 that will be depreciated using the five-year MACRS schedule. If the estimated pre-tax salvage value for the equipment at the end of the project's life is $417,600, what is the after-tax salvage value for the equipment? Assume a marginal tax rate of 21 percent.

#### Answer Choices:
- $329,904
- $399,184
- -$64,896
- $505,296

#### Detailed Explanation:
This problem requires calculating the after-tax salvage value of equipment by considering the depreciation and the marginal tax rate. The steps involve:

1. **Depreciation Calculation:** 
   Use the appropriate depreciation schedule for the equipment. For a five-year MACRS (Modified Accelerated Cost Recovery System) schedule, the depreciation percentages for each year are as follows:

   | Year | Percentage |
   |------|-------------|
   | 1    | 20%         |
   | 2    | 32%         |
   | 3    | 19.2%       |
   | 4    | 11.52%      |
   | 5    | 11.52%      |
   | 6    | 5.76%       |

2. **Calculate Accumulated Depreciation:**
   Sum of depreciation percentages over the five years:
   \[
   20\% + 32\% + 19.2\% + 11.52\% + 11.52\% + 5.76\% = 100\%
   \]

3. **Book Value at the End of Project Life:**
   After full depreciation, the book value is zero since accumulated depreciation equals 100% of the asset cost.

4. **Calculate Gain or Loss on Sale:**
   The salvage value ($417,600) minus the book value (0) equals the gain on sale which is $417,600.

5. **Tax Impact:**
   Calculate taxes on the gain. 
   \[
   \text{Tax} = \text{Gain} \times \text{Tax Rate} = 417,600 \times 0.21 = 87,696
   \]

6. **After-Tax Salvage Value:**
   Subtract the tax from the pre-tax salvage
Transcribed Image Text:### Depreciation and After-Tax Salvage Value Calculation #### Problem Statement: A nine-year project involves equipment costing $2,320,000 that will be depreciated using the five-year MACRS schedule. If the estimated pre-tax salvage value for the equipment at the end of the project's life is $417,600, what is the after-tax salvage value for the equipment? Assume a marginal tax rate of 21 percent. #### Answer Choices: - $329,904 - $399,184 - -$64,896 - $505,296 #### Detailed Explanation: This problem requires calculating the after-tax salvage value of equipment by considering the depreciation and the marginal tax rate. The steps involve: 1. **Depreciation Calculation:** Use the appropriate depreciation schedule for the equipment. For a five-year MACRS (Modified Accelerated Cost Recovery System) schedule, the depreciation percentages for each year are as follows: | Year | Percentage | |------|-------------| | 1 | 20% | | 2 | 32% | | 3 | 19.2% | | 4 | 11.52% | | 5 | 11.52% | | 6 | 5.76% | 2. **Calculate Accumulated Depreciation:** Sum of depreciation percentages over the five years: \[ 20\% + 32\% + 19.2\% + 11.52\% + 11.52\% + 5.76\% = 100\% \] 3. **Book Value at the End of Project Life:** After full depreciation, the book value is zero since accumulated depreciation equals 100% of the asset cost. 4. **Calculate Gain or Loss on Sale:** The salvage value ($417,600) minus the book value (0) equals the gain on sale which is $417,600. 5. **Tax Impact:** Calculate taxes on the gain. \[ \text{Tax} = \text{Gain} \times \text{Tax Rate} = 417,600 \times 0.21 = 87,696 \] 6. **After-Tax Salvage Value:** Subtract the tax from the pre-tax salvage
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