X Company is planning to drop a department that has shown a loss over the past f
ID: 2462815 • Letter: X
Question
X Company is planning to drop a department that has shown a loss over the past few years. Its accountant estimates that the savings from dropping the department will be $27,500 a year for the next 7 years. The accountant also believes that the company will be able to immediately sell some equipment that was used in the department for $10,000. Assuming a discount rate of 5%, what is the net present value of dropping the department?
Present Value of $1.00
Period 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 1 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 2 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 0.812 0.797 3 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.731 0.712 4 0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683 0.659 0.636 5 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.593 0.567 6 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.535 0.507 7 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 0.482 0.452 8 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467 0.434 0.404 9 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 0.391 0.361 10 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.352 0.322Explanation / Answer
NPV in the given case is the present value of cash flows. The net present value of cash values can be calculated with the use of following formula:
Net Present Value of Cash Flows = Cash Flow from Sale of Equipment + Annual Savings*PVIFA(Years,Discount Rate) where PVIFA is Present Value Interest Factor for An Annuity
________
We will have to sum the present value interest factor for 5% from Year 1 to Year 7 to determine the PVIFA. The same has been calculated below:
PVIFA(7Years,5%) = .952 + .907 + .864 + .823 + .784 + .746 + .711 = 5.787
Now, we can calculated the NPV as follows:
NPV = 10,000 + 27,500*5.787 = $169,142.50 or $169,143 (answer)
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