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# I have problem when solving this exercise, can anyone break it into step by step for me to follow. Thank you so much

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You are working on a bid to build a bridge per year for the next three years. This project requires the purchase of \$1,000,000 of equipment that will be depreciated using straight-line depreciation to a zero-book value over the project's life. Ignore bonus depreciation. The equipment can be sold at the end of the project for \$400,000. You will also need \$250,000 in net working capital over the life of the project. The fixed costs will be \$500,000 per year and the variable costs will be \$3,000,000 per bridge. Your required rate of return is 20 percent for this project and your tax rate is 10 percent. What is the minimal amount, rounded to the nearest \$100, you should bid per bridge?

Note: 3 years annuity factors of 20% required return = 2.106

Jun 5, 2024

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Here's how to calculate the minimal amount you should bid per bridge for this three-year project:

1. Consider the Equipment:

Equipment cost: \$1,000,000

Salvage value (selling price after 3 years): \$400,000

Depreciation: Straight-line over 3 years

Annual depreciation expense: (\$1,000,000 - \$400,000) / 3 years = \$200,000/year

2. Factor in Working Capital:

Net working capital needed: \$250,000 (constant throughout the project)

3. Analyze Costs and Taxes:

Fixed cost per year: \$500,000

Variable cost per bridge: \$3,000,000

Required rate of return: 20%

Tax rate: 10%

4. Calculate After-Tax Cash Flow per Year:

We'll consider one year at a time. Let's denote the year as "Y":

Revenue from the bridge (unknown yet - this is what we're solving for): "Bid amount (X)"

Total cost: Fixed cost + Variable cost - Depreciation expense

Taxable income before depreciation: Bid amount (X) - Total cost

Depreciation tax shield: Annual depreciation expense * Tax rate = \$200,000 * 10% = \$20,000

Taxable income: Taxable income before depreciation - Depreciation tax shield

Taxes (at 10% rate): Taxable income * Tax rate

After-tax cash flow (Y): Bid amount (X) - Total cost - Taxes + Depreciation expense + Net working capital

5. Apply Annuity Factor for Present Value:

We're considering a three-year project, so we need to find the present value of the after-tax cash flow for each year. Since the cash flow happens at the end of each year (annuity due), we'll use an annuity factor (considering the required rate of return of 20%).

Annuity factor for 3 years at 20% interest: 2.106 (given)

6. Solve for the Minimum Bid (X):

We want the project's Net Present Value (NPV) to be zero at the minimum acceptable bid. NPV is the sum of the present values of all future cash flows.

Net Present Value (NPV) Equation:

NPV = After-tax cash flow (Year 1) + After-tax cash flow (Year 2) + After-tax cash flow (Year 3) - Initial equipment cost + Salvage value = 0

We can rewrite the above equation with the annuity factor and solve for X (the minimum bid amount).

After rearranging and substituting the after-tax cash flow formula from step 4:

X * (1 - (1 + Required return)^(-Project life)) / Required return = (Total cost - Depreciation expense + Net working capital) * Annuity factor + Equipment cost - Salvage value

Plugging in the numbers:

X * (1 - (1 + 0.2)^(-3)) / 0.2 = (\$500,000 + \$3,000,000 - \$200,000 + \$250,000) * 2.106 + \$1,000,000 - \$400,000

X * (1 - 0.512) / 0.2 = \$3,856,000 * 2.106 + \$600,000

X * 0.488 = \$8,038,16 + \$600,000

X = (\$8,038,16 + \$600,000) / 0.488 ≈ \$8,647,764

Minimum Bid amount rounded to nearest \$100: \$8,647,800

Therefore, the minimum amount you should bid per bridge to achieve a zero Net Present Value for this three-year project is approximately \$8,647,800.

Jun 5, 2024