Jackson Company invests in a new piece of equipment costing $40,000. The equipment is expected to yield the following amounts per year for the equipment's four-year useful life:
Cash revenues $ 60,000
Cash expenses (32,000)
Depreciation expenses (straight-line) (10,000)
Income provided from equipment $ 18,000
Cost of capital 14%
What is the net present value of this investment in equipment, assuming no taxes are paid?
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To calculate the net present value (NPV) of the investment in equipment, we need to discount the cash flows from the equipment's four-year useful life to present value using the cost of capital.
Step 1: Calculate the present value of each year's cash flows.
Year 1: $60,000 - $32,000 - $10,000 = $18,000
Year 2: $18,000
Year 3: $18,000
Year 4: $18,000
Step 2: Determine the discount factor for each year.
Using the cost of capital of 14%, we can calculate the discount factor for each year.
Year 1: 1 / (1 + 0.14)^1 = 0.8772
Year 2: 1 / (1 + 0.14)^2 = 0.7695
Year 3: 1 / (1 + 0.14)^3 = 0.6750
Year 4: 1 / (1 + 0.14)^4 = 0.5921
Step 3: Calculate the present value of each year's cash flows by multiplying the cash flow by the discount factor.
Year 1: $18,000 * 0.8772 = $15,789.60
Year 2: $18,000 * 0.7695 = $13,851.00
Year 3: $18,000 * 0.6750 = $12,150.00
Year 4: $18,000 * 0.5921 = $10,657.80
Step 4: Calculate the net present value by summing up the present values and subtracting the initial investment cost.
NPV = ($15,789.60 + $13,851.00 + $12,150.00 + $10,657.80) - $40,000
NPV = $52,448.40 - $40,000
NPV = $12,448.40
Therefore, the net present value of this investment in equipment is $12,448.40.
To calculate the net present value (NPV) of the investment in equipment, we need to discount the cash flows to their present value and then subtract the initial cost.
1. Calculate the cash flows for each year:
Year 1: $60,000 (Cash revenues) - $32,000 (Cash expenses) - $10,000 (Depreciation expenses) = $18,000 (Income provided from equipment)
Year 2: $18,000 (Income provided from equipment)
Year 3: $18,000 (Income provided from equipment)
Year 4: $18,000 (Income provided from equipment)
2. Determine the present value factor for each year. The present value factor is calculated using the cost of capital (14%) and the number of years. We can use the formula:
Present value factor = 1 / (1 + cost of capital)^number of years
Year 1: Present value factor = 1 / (1 + 0.14)^1 = 1 / 1.14 = 0.877
Year 2: Present value factor = 1 / (1 + 0.14)^2 = 1 / 1.2996 = 0.770
Year 3: Present value factor = 1 / (1 + 0.14)^3 = 1 / 1.4833 = 0.674
Year 4: Present value factor = 1 / (1 + 0.14)^4 = 1 / 1.6909 = 0.592
3. Calculate the present value of each cash flow by multiplying the cash flow for each year by the present value factor for that year:
Year 1: $18,000 * 0.877 = $15,786
Year 2: $18,000 * 0.770 = $13,860
Year 3: $18,000 * 0.674 = $12,132
Year 4: $18,000 * 0.592 = $10,656
4. Calculate the net present value (NPV) by summing up the present values of each cash flow and subtracting the initial cost of the equipment:
NPV = ($15,786 + $13,860 + $12,132 + $10,656) - $40,000 = $52,434 - $40,000 = $12,434
Therefore, the net present value (NPV) of this investment in equipment is $12,434.