Calculating the Net Present Value
In this assignment, you will be required to calculate the net present value. The Woodruff Corporation purchased a piece of equipment three years ago for $230,000. It has an asset depreciation range (ADR) midpoint of eight years. The old equipment can be sold for $90,000.
A new piece of equipment can be purchased for $320,000. It also has an ADR of eight years. Assume the old and new equipment would provide the following operating gains (or losses) over the next six years:
Ye New Equipment Old Equipment Year
1 $80,000 $25,000 1
2 76,000 16,000 2
3 70,000 9,000 3
4 60,000 8,000 4
5 50,000 6,000 5
6 45,000 (7,000) 6
Question: The firm has a 25 percent tax rate and a 9 percent cost of capital. Should the new equipment be purchased to replace the old equipment? Explain your answer.
To answer this question, we need to calculate the net present value (NPV) of the cash flows for each option, and then compare them. The NPV is calculated by discounting each year’s cash flow to its present value using the cost of capital.
First, let’s calculate the depreciation expense for the old equipment. The ADR midpoint is 8 years, so the annual depreciation expense is $230,000 / 8 = $28,750. Using the straight-line method, the book value of the old equipment at the end of year 3 is $230,000 – $28,750 * 3 = $144,750. The book value at the end of year 6 is $230,000 – $28,750 * 6 = $86,250. Since the old equipment can be sold for $90,000, there will be a gain of $3,750 at the end of year 6.
Next, let’s calculate the cash flows for each option. For the old equipment, the cash flows are:
Year 1: $25,000 Year 2: $16,000 Year 3: $9,000 Year 4: $8,000 Year 5: $6,000 Year 6: $3,750 (gain on sale)
To calculate the present value of these cash flows, we need to discount each cash flow to its present value using the cost of capital. The present value factors are:
Year 1: 1 / (1 + 0.09) = 0.9174 Year 2: 1 / (1 + 0.09)^2 = 0.8424 Year 3: 1 / (1 + 0.09)^3 = 0.7722 Year 4: 1 / (1 + 0.09)^4 = 0.7084 Year 5: 1 / (1 + 0.09)^5 = 0.6505 Year 6: 1 / (1 + 0.09)^6 = 0.5987
Using these present value factors, we can calculate the present value of the cash flows for the old equipment:
PV = $25,000 * 0.9174 + $16,000 * 0.8424 + $9,000 * 0.7722 + $8,000 * 0.7084 + $6,000 * 0.6505 + $3,750 * 0.5987 = $44,271
For the new equipment, the cash flows are:
Year 1: $80,000 Year 2: $76,000 Year 3: $70,000 Year 4: $60,000 Year 5: $50,000 Year 6: ($45,000)
The cash flow in year 6 is negative because the new equipment has a salvage value of zero. To calculate the present value of these cash flows, we use the same present value factors as before:
PV = $80,000 * 0.9174 + $76,000 * 0.8424 + $70,000 * 0.7722 + $60,000 * 0.7084 + $50,000 * 0.6505 – $45,000 * 0.5987 = $189,035
Now we can calculate the net present value of each option:
NPV(old equipment) = $44,271 – $230,000 + $86,250 + $90,000 = $-9,479 NPV(new equipment) = $189
