Figure 14-10. Present value of $1 Present value of an Annuity of $1 Problem 14-3

Question

Figure 14-10.

Present value of $1

Present value of an Annuity of $1

Problem 14-3

Refer to Figure 14-10. Billings Office Services is considering the purchase of a new computer system to replace the one in operation. Data on the new computer system are:

If the existing computer system is kept and used, it would require the purchase of additional hardware a year from now costing $2,000. After using the system for five years, the salvage value would be $300. Additional information on the existing system is:

The company uses the straight-line method of depreciation.

Required:

Compute the net present value of the new computer system. $

Should the new system be purchased?

Periods 4% 6% 8% 10% 12% 14% 1 0.962 0.943 0.926 0.909 0.893 0.877 2 0.925 0.890 0.857 0.826 0.797 0.769 3 0.889 0.840 0.794 0.751 0.712 0.675 4 0.855 0.792 0.735 0.683 0.636 0.592 5 0.822 0.747 0.681 0.621 0.567 0.519 6 0.790 0.705 0.630 0.564 0.507 0.456 7 0.760 0.665 0.583 0.513 0.452 0.400 8 0.731 0.627 0.540 0.467 0.404 0.351 9 0.703 0.592 0.500 0.424 0.361 0.308 10 0.676 0.558 0.463 0.386 0.322 0.270

Explanation / Answer

Since the Net present value of new computer is positive, billing office services should buy the new computers

Billing Office Services Calculation of present value of new computer Year Particulars Amount Discounting factor at 12%* Net Amount (A) (B) C=A*B Year 1 Cost of purchase        -12,000 1        -12,000 Year 1 - 5 Savings in annual operating cost            5,000 3.605          18,025 (Operating cost of old machine - operating cost of new machine) (9,000-4,000) Year 1 - 5 Depreciation on old computer            2,060 3.605            7,426 (This will also be a saving as we will not have to depreciate the old asset on purchase of new asset) (remaining book value - salvage value after 5 years(note 2)/5 (12000-1701)/5 Year 1 Salvage value of old computer (This is also savings as we will receive this)            3,000 1            3,000 Year 1 - 5 Depreciation on new computers           -2,200 3.605          -7,931 ((Cost-salvage value)/useful life)) (12000-1000/5) Year 2 Hardware purchase cost saved            2,000 0.797            1,594 Year 2 Depreciation on hardware 340 0.797 271 (Saving as we will not have to incur this in case of purchase of new computer) (2000-300)/5 Year 3 Depreciation on hardware 340 0.712 242 Year 4 Depreciation on hardware 340 0.636 216 Year 5 Depreciation on hardware 340 0.567 193 Year 5 Salvage value of old computer           -3,000 0.567          -1,701 (This would have been received, if old computer was used. Now it will not be received and hence is a cost) Year 5 Salvage value of new computer            1,000 0.567 567 Year 6 Depreciation on hardware 340 0.507 172 Year 6 Salvage value of hardware              -300 0.507              -152 (This would have been received, if old computer was used. Now it will not be received and hence is a cost) Net Present value            9,922

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