Question

eEgg is considering the purchase of a new distributed network computer system to help handle its warehouse inventories. The system costs $40,000 to purchase and install and $29,000 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 $50,000 per year. The firm’s cost of capital (discount rate) is 9%.

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 27% 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 27% 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.

Answer 1

1.a) Calculation of Net present value Annual cost savings Less: Cost of Operation Annual Cash inflow $50,000 $29,000 $21,000 PV Factor for 9% for 4 years 3.2397 Present value of cash inflow Less :Initial Investment Net Present Value $68,034 $40,000 $28,034 1.b) Calculation of Net present value Annual cost savings Less: Cost of Operation Less: Depreciation Net Taxable income Less: Tax at 27% Profit after Tax Add:Depreciation Annual Cash inflow $50,000 $29,000 $10,000 ($40,000/4 years) $11,000 $2,970 $8,030 $10,000 $18,030 PV Factor for 9% for 4 years 3.2397 Present value of cash inflow Less:Initial Investment Net Present Value $58,412 $40,000 $18,412 1.c) Year DDB Pre-tax cash Depreciation inflows Expense Taxable Income Income tax at 27% After tax - Discount net cash Factor inflow at 9% Present value 0 1 2. $40,000 $21,000 $21,000 $21,000 $21,000 -$20,000 -$10,000 -$5,000 -$5,000 $1,000 $11,000 $16,000 $16,000 -$40,000 1 -$270 $20,730 0.9174 -$2,970 $18,030 0.8417 -$4,320 $16,6801 0.7722) $4,320 $16,680 0.7084 Net Present value -$40,000 $19,018 $15,176 $12,880 $11,816 $18,890 3 4 Year Double Declining balance method- Depreciation calculation Net Book Opening Depreciation Year Depreciation Value (Year Balance Rate end) Year 1 $40,000 50% $20,000 $20,000 Year 2 $20,000 50% $10,000 $10,000 Year 3 $10,000 50% $5,000 $5,000 Year 4 $5,000 $5,000 $0 Depreciation rate DDB Rate 25%|(1/4 years) 50%|(25% X 2) 2 Internal rate of return (IRR) Year o Year 1 Year 2 Year 3 Year 4 Internal Rate of return Cash Flow Cash Outflow Cash Inflow Cash Inflow Cash Inflow Cash Inflow 1 (a) No tax -$40,000 $21,000 $21,000 $21,000 $21,000 38.0% 1(b) 1(c) SLM with tax DDB with tax -$40,000 -$40,000 $18,030 $20,730 $18,030 $18,030 $18,030 $16,680 $18,030 $16,680 28.6% 30.1% In IRR Net present value of cash outflow = Net present value of cash inflow