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KADS, Incorporated has spent [tex]\$410,000[/tex] on research to develop a new computer game. The firm is planning to spend [tex]\$210,000[/tex] on a machine to produce the new game. Shipping and installation costs of the machine will be capitalized and depreciated using bonus depreciation; they total [tex]\$51,000[/tex]. The machine has an expected life of three years, a [tex]\$76,000[/tex] estimated resale value, and falls under the MACRS seven-year class life. Revenue from the new game is expected to be [tex]\[tex]$610,000[/tex] per year, with costs of [tex]\$[/tex]260,000[/tex] per year. The firm has a tax rate of 21 percent, has an opportunity cost of capital of 11 percent, and expects net working capital to increase by [tex]\$105,000[/tex] at the beginning of the project.

What will the cash flows for this project be?

Note: Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.

\begin{tabular}{|l|l|l|l|l|}
\hline
Year & 0 & 1 & 2 & 3 \\
\hline
FCF & & & & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
To determine the cash flows (FCF) for this project, we'll need to go through a series of steps to calculate the values for each year of the project. Here's the step-by-step solution:

### Step 1: Initial Investment (Year 0)
1. Machine Cost: [tex]$210,000 2. Shipping and Installation Costs: $[/tex]51,000
3. Increase in Net Working Capital: [tex]$105,000 The total initial investment (Year 0 FCF) is: \[ \text{Initial Investment} = 210,000 + 51,000 + 105,000 = 366,000 \] Since this is an outflow, it will be recorded as a negative amount: \[ \text{Year 0 FCF} = -366,000 \] ### Step 2: Depreciation The machine will be depreciated using the MACRS seven-year class life. The applicable MACRS depreciation rates for the first three years are 14.29%, 24.49%, and 17.49%. ### Step 3: Yearly Cash Flows (Years 1, 2, 3) For each year, we need to calculate: - Revenue - Costs - Depreciation - Taxable Income - Taxes - Net Income - Cash Flow - Free Cash Flow (FCF) We are given: - Annual Revenue: $[/tex]610,000
- Annual Costs (excluding depreciation): [tex]$260,000 - Tax Rate: 21% #### Year 1: 1. Depreciation: \( 51,000 \times 0.1429 = 7,287.9 \) 2. Revenue: $[/tex]610,000
3. Costs: [tex]$260,000 4. Total Costs (including depreciation): \( 260,000 + 7,287.9 = 267,287.9 \) 5. Taxable Income: \(610,000 - 267,287.9 = 342,712.1 \) 6. Taxes: \(342,712.1 \times 0.21 = 71,969.541 \) 7. Net Income: \(342,712.1 - 71,969.541 = 270,742.559 \) 8. Cash Flow (Net Income + Depreciation): \(270,742.559 + 7,287.9 = 278,030.459 \) 9. Free Cash Flow (Yearly Cash Flow): \(278,030.459 \) #### Year 2: 1. Depreciation: \( 51,000 \times 0.2449 = 12,499.9 \) 2. Revenue: $[/tex]610,000
3. Costs: [tex]$260,000 4. Total Costs (including depreciation): \( 260,000 + 12,499.9 = 272,499.9 \) 5. Taxable Income: \(610,000 - 272,499.9 = 337,500.1 \) 6. Taxes: \(337,500.1 \times 0.21 = 70,875.021 \) 7. Net Income: \(337,500.1 - 70,875.021 = 266,625.079 \) 8. Cash Flow (Net Income + Depreciation): \(266,625.079 + 12,499.9 = 279,124.979 \) 9. Free Cash Flow (Yearly Cash Flow): \(279,122.879 \) (rounded) #### Year 3: 1. Depreciation: \( 51,000 \times 0.1749 = 8,914.9 \) 2. Revenue: $[/tex]610,000
3. Costs: $260,000
4. Total Costs (including depreciation): [tex]\( 260,000 + 8,914.9 = 268,914.9 \)[/tex]
5. Taxable Income: [tex]\(610,000 - 268,914.9 = 341,085.1 \)[/tex]
6. Taxes: [tex]\(341,085.1 \times 0.21 = 71,627.871 \)[/tex]
7. Net Income: [tex]\(341,085.1 - 71,627.871 = 269,457.229 \)[/tex]
8. Cash Flow (Net Income + Depreciation): [tex]\(269,457.229 + 8,914.9 = 278,372.129 \)[/tex]
9. Free Cash Flow (Yearly Cash Flow + Machine Resale Value - Release of Working Capital): [tex]\( 278,372.129 + 76,000 - 105,000 = 249,372.129 \)[/tex] (rounded)

### Final Cash Flows
[tex]\[ \begin{tabular}{|l|l|l|l|l|} \hline \text{Year} & \text{0} & \text{1} & \text{2} & \text{3} \\ \hline \text{FCF} & -366,000 & 278,030.46 & 279,122.88 & 249,373.18 \\ \hline \end{tabular} \][/tex]

Thus, the Free Cash Flows (FCF) for the project are as follows (in dollars, rounded to 2 decimal places):
- Year 0: -366,000
- Year 1: 278,030.46
- Year 2: 279,122.88
- Year 3: 249,373.18

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