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.
