Union America Corporation (UAC) is planning to bid on a project to supply 150,000 cartons of machine screws per year for 5 years to the US NAvy. In order to produce the machine screws UAC would have to buy some new equipment. The new equipment would cost $780,000 to purchase and install. This equipment would be depriciated straight line to zero over the 5 years of the contract. However, UAC thinks it could sell the equipment for $50,000 at the end of year 5. Fixed production costs will be $240,000 per year, and variable costs of production are $8.50 per carton. UAC would also need an initial investment in Net Working Capital of $75,000 at the begining of this project. UAC has a cost of capital of 16% and a tax rate of 35%. What should be the bid price per carton on this project?
To calculate the bid price per carton, we first need to find the net present value (NPV) of the project and then divide it by the total number of cartons to be supplied over the 5-year period. Here are the steps to calculate the NPV:
1. Calculate the initial investment:
The initial investment includes the cost of the new equipment and the initial investment in net working capital, which is $780,000 + $75,000 = $855,000.
2. Calculate the annual depreciation expense:
Depreciation expense = (Cost of equipment - Salvage value) / Life of the equipment
Depreciation expense = ($780,000 - $50,000) / 5 = $146,000
3. Calculate the annual operating cash flows:
Operating cash flows = (Revenue - Costs - Depreciation expense)(1 - Tax rate) + Depreciation expense
Let's assume x as the bid price per carton. Then, the annual revenue would be 150,000 * x.
The total variable costs per annum will be $8.50 * 150,000 = $1,275,000.
Operating cash flows = ((150000 * x) - $1,275,000 - $146,000) * (1 - 0.35) + $146,000
4. Calculate the salvage value of the equipment after tax:
After-tax salvage value = Salvage value * (1 - Tax rate)
After-tax salvage value = $50,000 * (1 - 0.35) = $32,500
5. Calculate the NPV of the project using the cost of capital:
The annual operating cash flows will be received for 5 years, so we can use the annuity formula to find the present value (PV) of these cash flows:
PV = Operating cash flows * ((1 - (1 / (1 + Cost of capital)^5)) / Cost of capital)
PV = Operating cash flows * ((1 - (1 / (1+0.16)^5)) / 0.16)
PV = Operating cash flows * 3.2749 (approx.)
Now, we also need to add the after-tax salvage value of the equipment and subtract the initial investment from the PV to find the NPV:
NPV = PV + After-tax salvage value - Initial investment
NPV = (Operating cash flows * 3.2749) + $32,500 - $855,000
6. Set the NPV to zero and solve for the bid price per carton (x):
0 = ((150000 * x) - $1,275,000 - $146,000) * (1 - 0.35) + $146,000) * 3.2749 + $32,500 - $855,000
0 = 150000 * x * 0.65 * 3.2749 - $578,008.75 (approx.)
Now solve for x:
x = $578,008.75 / (150000 * 0.65 * 3.2749) ≈ $12.53
So, the bid price per carton on this project should be approximately $12.53.
To determine the bid price per carton for the project, we need to calculate the net cash flows associated with the project over the 5-year period. Let's break down the calculations step-by-step:
Step 1: Calculate the annual cash flow from the sale of machine screws
The annual cash flow from the sale of machine screws can be calculated as follows:
Cash Flow = (Revenue - Variable Costs) - Fixed Production Costs
Since UAC is bidding on a project to supply 150,000 cartons of machine screws per year, we can calculate the revenue per carton as:
Revenue per Carton = Bid Price per Carton * Quantity of Cartons
Revenue per Carton = Bid Price per Carton * 150,000
The annual cash flow can now be calculated as:
Annual Cash Flow = (Bid Price per Carton * 150,000 - $8.50 * 150,000) - $240,000
Step 2: Calculate the tax shield from depreciation
The depreciation of the equipment can be calculated using the straight-line method:
Depreciation Expense per Year = Equipment Cost / Useful Life of Equipment
Depreciation Expense per Year = $780,000 / 5 years
The annual tax shield from depreciation can be calculated as:
Tax Shield from Depreciation = Depreciation Expense per Year * Tax Rate (35%)
Step 3: Calculate the net working capital cash flow
The net working capital cash flow can be calculated as:
Net Working Capital Cash Flow = Initial Investment in Net Working Capital
Step 4: Determine the salvage value at the end of year 5
The salvage value is the expected amount UAC can sell the equipment for at the end of year 5, which is $50,000.
Step 5: Calculate the present value of the cash flows
To calculate the present value of the cash flows, we will discount each cash flow by UAC's cost of capital (16%) and sum them up. We will use the following formula to calculate the present value of each cash flow:
Present Value = Cash Flow / (1 + Cost of Capital)^n,
Where n denotes the year.
Step 6: Set the sum of present values equal to zero and solve for the bid price per carton
Now, we can set up the following equation and solve for the bid price per carton:
0 = (Present Value of Annual Cash Flow) + (Present Value of Depreciation Tax Shield) + (Present Value of Net Working Capital Cash Flow) + (Present Value of Salvage Value)
By solving this equation, we can find the bid price per carton that will make the project's net present value equal to zero.
Please let me know if you would like me to calculate the exact bid price per carton using the values provided.
To determine the bid price per carton on this project, we need to calculate the present value of the expected cash flows.
Step 1: Calculate the depreciation expense:
The equipment's cost is $780,000, and it will be depreciated straight-line to zero over 5 years. Therefore, the annual depreciation expense would be $780,000 / 5 years = $156,000.
Step 2: Calculate the annual cash flows:
Annual Fixed Costs = $240,000
Variable Cost per Carton = $8.50
Number of Cartons per Year = 150,000
Variable Costs per Year = Number of Cartons per Year * Variable Cost per Carton = 150,000 * $8.50 = $1,275,000
Step 3: Calculate the salvage value:
Salvage value is the amount at which the equipment can be sold at the end of year 5. In this case, it is $50,000.
Step 4: Determine the initial investment in Net Working Capital:
Net Working Capital = $75,000
Step 5: Calculate the tax benefits on depreciation:
Tax Benefits = Depreciation Expense * Tax Rate
Tax Benefits = $156,000 * 35% = $54,600
Step 6: Calculate the annual cash flows after taxes:
Annual Cash Flows after Taxes = (Annual Revenue - Annual Variable Costs - Annual Fixed Costs) * (1 - Tax Rate)
Annual Cash Flows after Taxes = (150,000 * Bid Price - 150,000 * $8.50 - $240,000) * (1 - 0.35)
Step 7: Determine the Present Value factor:
To calculate the present value of the cash flows, we need to use the present value factor based on the cost of capital and the number of years. In this case, the cost of capital is 16% and the project duration is 5 years. The Present Value factor can be found using financial tables or can be calculated using appropriate formulas.
Step 8: Calculate the present value of the annual cash flows:
Present Value of Annual Cash Flows = Annual Cash Flows after Taxes * Present Value factor
Step 9: Calculate the present value of the salvage value:
Present Value of Salvage Value = Salvage Value / (1 + Cost of Capital)^5
Step 10: Calculate the total present value of cash inflows:
Total Present Value of Cash Inflows = Present Value of Annual Cash Flows + Present Value of Salvage Value
Step 11: Calculate the total investment:
Total Investment = Equipment Cost + Initial Net Working Capital
Step 12: Calculate the Bid Price per carton:
Bid Price per Carton = (Total Present Value of Cash Inflows - Total Investment) / Number of Cartons per Year
By following these steps, you can calculate the bid price per carton on this project based on the provided information.