In order to expand its business, Auto Parts Distributing, Inc., is considering the purchase of four pickup trucks at a total cost of $180,000. The company expects to keep these trucks for four years, then sell them. The company expects these trucks to generate a after tax net cash flow of $95,000 in year 1, $90,000 in year 2, $85,000 in year 3, $80,000 in year 4, and to sell after four years for a total price of $30,000 non-taxable. The company’s marginal tax rate is 35% and its cost of capital is 12%.
Calculate:
a. After tax cash flow for each year 1 through 4 (ignore depreciation)
b. Payback period
c. Profitability Index
d. Net Present Value
e. Internal Rate of Return
To calculate the answers to these questions, we need to follow a series of steps. Let's go through each step to find the answers.
Step 1: Calculate the after-tax cash flow for each year.
To calculate the after-tax cash flow for each year, we need to subtract the taxes from the net cash flow. We'll use the marginal tax rate of 35%.
Year 1:
Net cash flow = $95,000
Taxes = 35% of $95,000 = $33,250
After-tax cash flow = Net cash flow - Taxes = $95,000 - $33,250 = $61,750
Year 2:
Net cash flow = $90,000
Taxes = 35% of $90,000 = $31,500
After-tax cash flow = Net cash flow - Taxes = $90,000 - $31,500 = $58,500
Year 3:
Net cash flow = $85,000
Taxes = 35% of $85,000 = $29,750
After-tax cash flow = Net cash flow - Taxes = $85,000 - $29,750 = $55,250
Year 4:
Net cash flow = $80,000
Taxes = 35% of $80,000 = $28,000
After-tax cash flow = Net cash flow - Taxes = $80,000 - $28,000 = $52,000
Note: We don't need to calculate the after-tax cash flow for the sale of the trucks since it is stated as non-taxable.
Step 2: Calculate the payback period.
The payback period is the time it takes for the initial investment to be recovered. To calculate it, we sum up the net cash flow for each year until it exceeds the initial investment.
Initial investment = $180,000
Payback period:
Year 1 cash flow = $61,750
Year 2 cash flow = $58,500
Year 3 cash flow = $55,250
Year 4 cash flow = $52,000
Payback period = Year 4 (since the cumulative cash flow exceeds the initial investment in year 4)
Step 3: Calculate the profitability index.
The profitability index calculates the present value of the future cash flows and compares it to the initial investment. It is calculated by dividing the present value of the future cash flows by the initial investment.
To calculate the profitability index, first, we need to calculate the present value (PV) of the future cash flows for each year using the cost of capital of 12%. Then we sum up the present values.
PV factor for each year:
Year 1 = 1 / (1 + r)^1 = 1 / (1 + 0.12)^1 = 0.8929
Year 2 = 1 / (1 + r)^2 = 1 / (1 + 0.12)^2 = 0.7972
Year 3 = 1 / (1 + r)^3 = 1 / (1 + 0.12)^3 = 0.7118
Year 4 = 1 / (1 + r)^4 = 1 / (1 + 0.12)^4 = 0.6355
Present value of cash flows:
Year 1 = $61,750 * 0.8929 = $55,186.75
Year 2 = $58,500 * 0.7972 = $46,608.60
Year 3 = $55,250 * 0.7118 = $39,269.15
Year 4 = $52,000 * 0.6355 = $33,097.60
Profitability index = (Sum of present values) / Initial investment
Profitability index = ($55,186.75 + $46,608.60 + $39,269.15 + $33,097.60) / $180,000
Step 4: Calculate the net present value.
The net present value calculates the present value of the future cash flows and subtracts the initial investment from it. It uses the cost of capital of 12% to discount the cash flows.
To calculate the net present value, we subtract the initial investment from the sum of the present values of the cash flows.
Net present value = ($55,186.75 + $46,608.60 + $39,269.15 + $33,097.60) - $180,000
Step 5: Calculate the internal rate of return.
The internal rate of return is the discount rate at which the net present value becomes zero. It is the rate that makes the present value of the future cash flows equal to the initial investment.
We can use an Excel or financial calculator to find this rate.