Question

eEgg is considering the purchase of a new distributed network computer system to help handle its warehouse inventories. The system costs $41,000 to purchase and install and $25,000 to operate each year. The system is estimated to be useful for 4 years. Management expects the new system to reduce the cost of managing inventories by $46,000 per year. The firm’s cost of capital (discount rate) is 11%.

Required:

1. What is the net present value (NPV) of the proposed investment under each of the following independent situations? (Use the appropriate present value factors from Appendix C, TABLE 1 and Appendix C, TABLE 2.)

1a. The firm is not yet profitable and therefore pays no income taxes.

1b. The firm is in the 21% income tax bracket and uses straight-line (SLN) depreciation with no salvage value. Assume MACRS rules do not apply.

1c. The firm is in the 21% income tax bracket and uses double-declining-balance (DDB) depreciation with no salvage value. Given a four-year life, the DDB depreciation rate is 50% (i.e., 2 × 25%). In year four, record depreciation expense as the net book value (NBV) of the asset at the start of the year.

2. What is the internal rate of return (IRR) of the proposed investment for situations in requirement 1, parts (a) through (c)? Use the IRR builit-in function in Excel to compute the IRR.

The firm is in the 21% income tax bracket and uses double-declining-balance (DDB) depreciation with no salvage value. Given a four-year life, the DDB depreciation rate is 50% (i.e., 2 × 25%). In year four, record depreciation expense as the net book value (NBV) of the asset at the start of the year. (Negative amounts should be indicated by a minus sign. Round discount factor to 3 decimal places and other answers to the nearest whole dollar amount.)

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	Year Pre-Tax Cash Inflows DDB Depreciation Expense Taxable Income Income Taxes After-tax Net Cash Inflow Discount Factor Present Values 0 $(41,000) $(41,000) $(41,000) 1 2 3 4 Net present value (NPV) = $(41,000)

Answer 1

1. Calculation of NPV

(a)

Annual Cost savings	$46,000
Less: Cost of operation	($25,000)
Annual cash inflow	$21,000
PVF@11%,4 years	3.1024
PV of cash inflow	65,150.4
Less: Initial Investment	(41,000)
Net present value (NPV)	$24,150.4

(b)

Annual Cost savings	46,000
Less: Cost of operation	(25,000)
Less: Depreciation (41,000/4)	(10,250)
Net taxable income	10,750
Less: Tax@21%	(2257.5)
Profit after tax	8492.5
Add: Depreciation	10250
Annual Cash inflow	18742.5
PVF@11%, 4years	3.1024
PV of Cash inflow	58,146.73
Less:Intial investment	($41,000)
Net Present Value	17,146.73

(c) Calculation of NPV

	Year 1	Year 2	Year 3	Year 4	Total
Annual cost savings	46,000	46,000	46,000	46,000
Annual operation cost	25000	25000	25000	25000
Depreciation	20,500	10,250	5125	5125
Net taxable income	500	10,750	15,875	15875
Tax@21%	105	2257.5	3333.75	3333.75
Income after taxes	395	8492.5	12,541.25	12,541.25
Add depreciation	20500	10250	5125	5125
Annual cash inflow	20,895	18,742.5	17,666.25	17,666.25
PVF@11%	0.9009	0.8116	0.7312	0.6587
PV of cash inflow	18,824.31	15,211.41	12,917.56	11,636.76	58,590.04

Total PV of cash inflow. $58,590.04

Less: Initial investment ($41,000)

Net present value. $17,590.04

Depreciation calculation under DDB Method

Year	Opening Balance	Depreciation rate	Depreciation	Net Book Value(Year end)
1	41,000	50%	20,500	20,500
2	20,500	50%	10,250	10,250
3	10,250	50%	5125	5125
4	5125		5125	-

(2) calculation of IRR

		1(a)	1(b)	1(c)
	Cash flow	no tax	SLM with tax	DDB with tax
Year 0	cash OF	($41,000)	($41,000)	($41,000)
Year 1	Cash IF	21,000	18,742.5	20,895
Year 2	cash IF	21,000	18,742.5	18,742.5
Year 3	Cash IF	21,000	18,742.5	17,666.25
Year 4	Cash IF	21,000	18,742.5	17,666.25
IRR(Using IRR formula)		36.44%	29.42%	30.59%