Question

Figure 14-10.

Present value of $1

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

Present value of an Annuity of $1

Periods	4%	6%	8%	10%	12%	14%
1	0.962	0.943	0.926	0.909	0.893	0.877
2	1.886	1.833	1.783	1.736	1.690	1.647
3	2.775	2.673	2.577	2.487	2.402	2.322
4	3.630	3.465	3.312	3.170	3.037	2.914
5	4.452	4.212	3.993	3.791	3.605	3.433
6	5.242	4.917	4.623	4.355	4.111	3.889
7	6.002	5.582	5.206	4.868	4.564	4.288
8	6.733	6.210	5.747	5.335	4.968	4.639
9	7.435	6.802	6.247	5.759	5.328	4.946
10	8.111	7.360	6.710	6.145	5.650	5.216

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:

Cost	$12,000
Salvage value at the end of five years	1,000
Useful life, in years	5
Annual operating cost	4,000

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:

Additional years of use	5
Annual operating costs	$9,000
Remaining book value	12,000
Current salvage value	3,000
Cost of capital	12%

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?

Answer 1

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

Conclusion

Since the Net present value of new computer is positive, billing office services should buy the new computers Note 1 Salvage value of old computer after 5 years Current salvage value            3,000 PV factor at 12% for 5 years 0.567 Salvage value after 5 years            1,701 *Note 2 I have taken the discounting factors for 12% as the cost of capital is 12%. Present value Annuity table has been used where we have calculated directly for 5 years, and when calculation is made for each year individually, Present value table is used. Note 3 Cost incurred has been written in negative and cost savings have been stated as positive, hence all positive numbers indicate cost savings on installation of new machine