Question

Dog Up! Franks is looking at a new sausage system with an installed cost of $740,000. This cost will be depreciated straight-line to zero over the project's 7 -year life, at the end of which the sausage system can be scrapped for $102,000. The sausage system will save the firm $217,000 per year in pretax operating costs, and the system requires an initial investment in net working capital of $69,000. If the tax rate is 22 percent and the discount rate is 9 percent, what is the NPV of this project? Note: Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.

Answer 1

To calculate the NPV of the project, determine the annual cash flows and discount them to their present value using the discount rate. Then, sum up all the present values and subtract the initial investment.

Step-by-step explanation:

To calculate the NPV of the project, we need to sum up the present value of all cash flows associated with the project. The initial investment in the project is $740,000, which will be depreciated straight-line over 7 years. The salvage value of the sausage system at the end of the project's life is $102,000. The net working capital investment is $69,000. The annual pretax operating cost savings is $217,000.

To calculate the NPV, we first need to calculate the annual cash flows. The annual cash flow is equal to the pretax operating cost savings minus the depreciation expense. In the first year, the cash flow is $217,000 - ($740,000 / 7) - $69,000. In the second year, the cash flow is $217,000 - ($740,000 / 7) - $69,000, and so on, until the seventh year.

Using the formula for NPV, we discount each cash flow to its present value using the discount rate of 9 percent. Then, we sum up all the present values to calculate the NPV.

The NPV of the project is the sum of all the present values of cash flows minus the initial investment. In this case, the NPV is $8,158.63.

Answer 2

The NPV of the project is $657,789.26.

Step-by-step explanation:

To calculate the NPV of the project, we need to discount the cash flows to the present value. The initial investment of $740,000 and the net working capital investment of $69,000 are both cash outflows, so we need to discount them. The annual savings of $217,000 in pretax operating costs is a cash inflow, so we also need to discount it. The salvage value of $102,000 at the end of the project's life is a cash inflow, but it is not discounted.

To calculate the NPV, we calculate the present value of each cash flow and sum them all up. The present value of the initial investment and the net working capital investment can be calculated using the discount rate and the number of years. The present value of the annual savings can be calculated using the discount rate and the number of years. The NPV is the sum of the present values minus the initial investment.

Using the given information:

Initial Investment = $740,000

Net Working Capital Investment = $69,000

Annual Savings = $217,000

Salvage Value = $102,000

Tax Rate = 22%

Discount Rate = 9%

Project Life = 7 years

Step 1: Calculate the present value of the initial investment and the net working capital investment:

PV of Initial Investment = Initial Investment / (1 + Discount Rate)^Project Life = $740,000 / (1 + 0.09)^7 = $740,000 / 1.71701 = $430,395.99

PV of Net Working Capital Investment = Net Working Capital Investment / (1 + Discount Rate)^Project Life = $69,000 / (1 + 0.09)^7 = $69,000 / 1.71701 = $40,172.40

Step 2: Calculate the present value of the annual savings:

PV of Annual Savings = Annual Savings * (1 - Tax Rate) * ((1 - (1 + Discount Rate)^(-Project Life)) / Discount Rate) = $217,000 * (1 - 0.22) * ((1 - (1 + 0.09)^(-7)) / 0.09) = $217,000 * 0.78 * (1 - (1 + 0.09)^(-7)) / 0.09 = $217,000 * 0.78 * 0.487605 = $85,221.87

Step 3: Calculate the NPV:

NPV = PV of Initial Investment + PV of Net Working Capital Investment + PV of Annual Savings + Salvage Value = $430,395.99 + $40,172.40 + $85,221.87 + $102,000 = $657,789.26

Therefore, the NPV of this project is $657,789.26.