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Sagot :
To evaluate the proposed acquisition of the special-purpose truck, we need to calculate the cash flows for the project over the three-year period. Here's the step-by-step solution:
### Step 1: Initial Investment (Year 0)
At Year 0, the cash outflow includes the cost of the truck and the increase in net working capital (NWC):
- Cost of truck: \[tex]$60,000 - Increase in NWC: \$[/tex]2,300
The total initial cash outflow is:
[tex]\[ \text{Year 0: } -(60,000 + 2,300) = -\$62,300 \][/tex]
### Step 2: Depreciation (Years 1 to 3)
The truck falls into the MACRS 3-year class. The MACRS depreciation percentages for the 3-year class are:
[tex]\[ 33.33\%, 44.45\%, 14.81\%, \text{ and } 7.41\% \][/tex]
Using these percentages, the depreciation expenses are calculated as follows:
- Year 1: [tex]\( 60,000 \times 0.3333 = \$19,998 \)[/tex]
- Year 2: [tex]\( 60,000 \times 0.4445 = \$26,670 \)[/tex]
- Year 3: [tex]\( 60,000 \times 0.1481 = \$8,886 \)[/tex]
### Step 3: After-Tax Savings on Operating Costs
The truck saves the firm \[tex]$20,100 per year in before-tax operating costs. After accounting for the tax rate (21%), the annual after-tax savings are: \[ \text{After-tax savings} = 20,100 \times (1 - 0.21) = 20,100 \times 0.79 = \$[/tex]15,879 \]
### Step 4: Cash Flow Calculation for Each Year
#### Year 1:
[tex]\[ \text{Year 1 cash flow} = \text{after-tax savings} + \text{depreciation} = 15,879 + 19,998 = \$35,877 \][/tex]
#### Year 2:
[tex]\[ \text{Year 2 cash flow} = \text{after-tax savings} + \text{depreciation} = 15,879 + 26,670 = \$42,549 \][/tex]
#### Year 3:
- After-tax salvage value: The truck is sold for \[tex]$20,300. Considering the tax on the salvage value, the after-tax salvage value is: \[ \text{After-tax salvage value} = 20,300 \times (1 - 0.21) = 20,300 \times 0.79 = \$[/tex]16,037 \]
- Net Working Capital recovery: Recover NWC of \[tex]$2,300 at the end of the project. \[ \text{Year 3 cash flow} = \text{after-tax savings} + \text{depreciation} + \text{after-tax salvage value} + \text{NWC recovery} = 15,879 + 8,886 + 16,037 + 2,300 = \$[/tex]43,102 \]
### Summary of Cash Flows:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \text{Year} & \text{0} & \text{1} & \text{2} & \text{3} \\ \hline \text{FCF} & -62,300.00 & 35,877.00 & 42,549.00 & 43,102.00 \\ \hline \end{array} \][/tex]
Therefore, the cash flows for this project will be as shown in the table.
### Step 1: Initial Investment (Year 0)
At Year 0, the cash outflow includes the cost of the truck and the increase in net working capital (NWC):
- Cost of truck: \[tex]$60,000 - Increase in NWC: \$[/tex]2,300
The total initial cash outflow is:
[tex]\[ \text{Year 0: } -(60,000 + 2,300) = -\$62,300 \][/tex]
### Step 2: Depreciation (Years 1 to 3)
The truck falls into the MACRS 3-year class. The MACRS depreciation percentages for the 3-year class are:
[tex]\[ 33.33\%, 44.45\%, 14.81\%, \text{ and } 7.41\% \][/tex]
Using these percentages, the depreciation expenses are calculated as follows:
- Year 1: [tex]\( 60,000 \times 0.3333 = \$19,998 \)[/tex]
- Year 2: [tex]\( 60,000 \times 0.4445 = \$26,670 \)[/tex]
- Year 3: [tex]\( 60,000 \times 0.1481 = \$8,886 \)[/tex]
### Step 3: After-Tax Savings on Operating Costs
The truck saves the firm \[tex]$20,100 per year in before-tax operating costs. After accounting for the tax rate (21%), the annual after-tax savings are: \[ \text{After-tax savings} = 20,100 \times (1 - 0.21) = 20,100 \times 0.79 = \$[/tex]15,879 \]
### Step 4: Cash Flow Calculation for Each Year
#### Year 1:
[tex]\[ \text{Year 1 cash flow} = \text{after-tax savings} + \text{depreciation} = 15,879 + 19,998 = \$35,877 \][/tex]
#### Year 2:
[tex]\[ \text{Year 2 cash flow} = \text{after-tax savings} + \text{depreciation} = 15,879 + 26,670 = \$42,549 \][/tex]
#### Year 3:
- After-tax salvage value: The truck is sold for \[tex]$20,300. Considering the tax on the salvage value, the after-tax salvage value is: \[ \text{After-tax salvage value} = 20,300 \times (1 - 0.21) = 20,300 \times 0.79 = \$[/tex]16,037 \]
- Net Working Capital recovery: Recover NWC of \[tex]$2,300 at the end of the project. \[ \text{Year 3 cash flow} = \text{after-tax savings} + \text{depreciation} + \text{after-tax salvage value} + \text{NWC recovery} = 15,879 + 8,886 + 16,037 + 2,300 = \$[/tex]43,102 \]
### Summary of Cash Flows:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \text{Year} & \text{0} & \text{1} & \text{2} & \text{3} \\ \hline \text{FCF} & -62,300.00 & 35,877.00 & 42,549.00 & 43,102.00 \\ \hline \end{array} \][/tex]
Therefore, the cash flows for this project will be as shown in the table.
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