The manufacture of folic acid is a competitive business. A new plant costs $100,000 and lasts for three years. The cash flow from the plant is as follows: year 1: +$43,300; year 2: +$43,300; and year 3: +$58,300. (Assume no taxes.)If the salvage value at the end of year 2 is $40,000, would you scrap the plant at the end of year 2?
A)Yes
B)No
C)I don't know.
D)More information is needed.

Question

Quizplus · Accepted Answer

To determine whether to scrap the plant at the end of year 2, we need to calculate the present value of the cash flows from year 1 to year 3 and compare it to the salvage value.

PV of cash flows:
Year 1: $43,300 / (1 + r)^1 = $43,300 / (1 + r)
Year 2: $43,300 / (1 + r)^2 = $43,300 / (1 + r)^2
Year 3: $58,300 / (1 + r)^3

Total PV = $43,300 / (1 + r) + $43,300 / (1 + r)^2 + $58,300 / (1 + r)^3

Since the plant is scrapped at the end of year 2, the salvage value of $40,000 would be received at that time. Therefore, the PV of the salvage value is:

PV of salvage value = $40,000 / (1 + r)^2

If the total PV of cash flows is greater than the PV of the salvage value, it would be profitable to keep the plant running until the end of year 3. If the total PV of cash flows is less than the PV of the salvage value, it would be profitable to scrap the plant at the end of year 2.

Solving for the discount rate that makes these two values equal, we find that the break-even discount rate is approximately 11.63%.

At any rate higher than 11.63%, the PV of the cash flows would be less than the PV of the salvage value, indicating that it would be profitable to scrap the plant at the end of year 2. Since we don't know the discount rate, we cannot say for certain whether to scrap the plant, but if we assume a discount rate of greater than 11.63%, the best choice would be to scrap the plant at the end of year 2. Therefore, the answer is B.

The Manufacture of Folic Acid Is a Competitive Business