Fox Hollow Franks is looking at a new system with an installed cost of $540,000. This equipment is depreciated at a rate of 20 percent per year (Class 8) over the project’s five-year life, at the end of which the sausage system can be sold for $80,000. The sausage system will save the firm $170,000 per year in pre-tax operating costs, and the system requires an initial investment in net working capital of $29,000. If the tax rate is 34 percent and the discount rate is 10 percent, what is the NPV of this project?
Well, well, well, looks like Fox Hollow Franks is feeling a bit saucy with their new system! Let's crunch the numbers and find out the NPV, shall we?
First, we need to calculate the annual depreciation expense. Since the equipment is depreciated at a rate of 20 percent per year, we can use the straight-line method to find this out. The initial cost is $540,000, so the annual depreciation expense is $540,000 * 20% = $108,000.
Next, let's calculate the annual cash flows. We have the savings in operating costs of $170,000 per year, the depreciation expense of $108,000 per year, and the salvage value of $80,000 at the end of the project's life.
So, the annual cash flows are $170,000 - $108,000 = $62,000. At the end of the project's life, there's an additional inflow from the sale of the system, which is $80,000.
Now, let's calculate the net cash flows each year by subtracting the tax on depreciation. The tax rate is 34 percent, so the tax shield on depreciation is $108,000 * 34% = $36,720.
Year 1: $62,000 - $36,720 = $25,280
Year 2-5: $62,000
Now, let's calculate the NPV using these cash flows and the discount rate of 10 percent.
Year 1: $25,280 / (1 + 10%)^1 = $23,074.55
Year 2-5: $62,000 / (1 + 10%)^2 + $62,000 / (1 + 10%)^3 + $62,000 / (1 + 10%)^4 + $62,000 / (1 + 10%)^5 = $198,983.4711
Salvage Value: $80,000 / (1 + 10%)^5 = $51,441.92
Now, let's sum up the NPV by subtracting the initial investment ($540,000) and adding the net working capital investment ($29,000).
NPV = -$540,000 + $29,000 + $23,074.55 + $198,983.4711 + $198,983.4711 + $198,983.4711 + $198,983.4711 + $51,441.92
After some wacky calculations, we find that the NPV is $361,539.8628.
So, it seems like the project is indeed a winner! Fox Hollow Franks can expect a nice boost to their bottom line with this new system. Just make sure you don't clown around with that money, Fox Hollow Franks!
To calculate the net present value (NPV) of the project, we need to calculate the cash flows for each year and discount them to their present value. Then we add up the present values of the cash flows to find the NPV.
Here are the steps to calculate the NPV:
Step 1: Calculate the annual depreciation expense.
Based on the given information, the equipment is depreciated at a rate of 20 percent per year (Class 8). The initial cost of the equipment is $540,000. So, the annual depreciation expense is:
Annual Depreciation = Initial Cost * Depreciation Rate
Annual Depreciation = $540,000 * 20% = $108,000
Step 2: Calculate the annual after-tax operating cost savings.
The sausage system will save the firm $170,000 per year in pre-tax operating costs. The tax rate is 34 percent. So, the annual after-tax operating cost savings can be calculated as:
Annual After-tax Operating Cost Savings = Pre-tax Operating Cost Savings * (1 - Tax Rate)
Annual After-tax Operating Cost Savings = $170,000 * (1 - 0.34) = $112,200
Step 3: Calculate the net cash flow for each year.
Now we can calculate the net cash flow (NCF) for each year. The NCF is equal to the annual after-tax operating cost savings minus the depreciation expense. For the last year, we also consider the resale value of the equipment.
Year 0:
NCF0 = Initial Investment - Initial Net Working Capital
NCF0 = -$540,000 - $29,000 = -$569,000 (negative due to cash outflow)
Year 1:
NCF1 = Annual After-tax Operating Cost Savings - Depreciation Expense
NCF1 = $112,200 - $108,000 = $4,200
Year 2:
NCF2 = Annual After-tax Operating Cost Savings - Depreciation Expense
NCF2 = $112,200 - $108,000 = $4,200
Year 3:
NCF3 = Annual After-tax Operating Cost Savings - Depreciation Expense
NCF3 = $112,200 - $108,000 = $4,200
Year 4:
NCF4 = Annual After-tax Operating Cost Savings - Depreciation Expense
NCF4 = $112,200 - $108,000 = $4,200
Year 5:
NCF5 = Annual After-tax Operating Cost Savings + Resale Value - Depreciation Expense
NCF5 = $112,200 + $80,000 - $108,000 = $84,200
Step 4: Discount the cash flows to their present value using the discount rate.
Now we need to discount the cash flows to their present value using the discount rate of 10 percent. The present value (PV) of each cash flow is calculated as follows:
PV = Cash Flow / (1 + Discount Rate)^Year
Present Value (PV) calculations:
PV0 = -$569,000 / (1 + 0.10)^0 = -$569,000
PV1 = $4,200 / (1 + 0.10)^1 = $3,818.18
PV2 = $4,200 / (1 + 0.10)^2 = $3,471.08
PV3 = $4,200 / (1 + 0.10)^3 = $3,155.53
PV4 = $4,200 / (1 + 0.10)^4 = $2,868.66
PV5 = $84,200 / (1 + 0.10)^5 = $56,519.59
Step 5: Calculate the NPV by summing up the present values.
Finally, we calculate the NPV by summing up all the present values:
NPV = PV0 + PV1 + PV2 + PV3 + PV4 + PV5
NPV = -$569,000 + $3,818.18 + $3,471.08 + $3,155.53 + $2,868.66 + $56,519.59
NPV = $-496.96 (rounded to the nearest dollar)
Therefore, the NPV of this project is approximately -$496.
To calculate the Net Present Value (NPV) of this project, we need to follow these steps:
1. Calculate the annual depreciation expense: The depreciation expense is determined by multiplying the initial cost of the equipment by the depreciation rate. In this case, the depreciation rate is 20%, and the initial cost is $540,000. So, the annual depreciation expense is $540,000 * 0.2 = $108,000.
2. Calculate the annual cash flows: The annual cash flows include the savings in pre-tax operating costs, the salvage value at the end of the project, and the change in net working capital. In this case, the annual savings in pre-tax operating costs is $170,000, the salvage value is $80,000, and the initial net working capital investment is -$29,000 (negative because it's an outflow). Therefore, the annual cash flows are:
Year 0: -$540,000 (initial cost + net working capital investment)
Year 1: $170,000 - $108,000 = $62,000 (savings - depreciation)
Year 2: $170,000 - $108,000 = $62,000
Year 3: $170,000 - $108,000 = $62,000
Year 4: $170,000 - $108,000 = $62,000
Year 5: $170,000 - $108,000 + $80,000 = $142,000 (savings - depreciation + salvage value)
3. Calculate the present value of each cash flow: To calculate the present value, we need to discount each cash flow to its present value using the discount rate of 10%. The formula for present value is PV = CF / (1 + r)^t, where PV is the present value, CF is the cash flow, r is the discount rate, and t is the time period.
Year 0: -$540,000 / (1 + 0.10)^0 = -$540,000 (no discounting since it's the initial investment)
Year 1: $62,000 / (1 + 0.10)^1 = $56,363.64
Year 2: $62,000 / (1 + 0.10)^2 = $51,330.58
Year 3: $62,000 / (1 + 0.10)^3 = $46,664.16
Year 4: $62,000 / (1 + 0.10)^4 = $42,335.60
Year 5: $142,000 / (1 + 0.10)^5 = $88,549.56
4. Calculate the NPV: The NPV is the sum of all the discounted cash flows, including the initial investment.
NPV = -$540,000 + $56,363.64 + $51,330.58 + $46,664.16 + $42,335.60 + $88,549.56 = $45,243.54
Therefore, the NPV of this project is $45,243.54.