Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,240,000; the new one will cost $1,500,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $240,000 after five years. The old computer is being depreciated at a rate of $248,000 per year. It will be completely written off in three years. If we don’t replace it now, we will have to replace it in two years. We can sell it now for $360,000; in two years, it will probably be worth $114,000. The new machine will save us $284,000 per year in operating costs. The tax rate is 40 percent, and the discount rate is 11 percent.

a.	Calculate the EAC for the old computer and the new computer.
b.	What is the NPV of the decision to replace the computer now?

Answer 1

Use spreadsheet for the ease in computations. Enter values and formulas in the spreadsheet as shown in the image below.

|_ D E 1 Answer - a. Calculation of equated annual cost (EAC) of new computer. 2 Initial investment 1500000 3 Life of equipment 4 Annual depreciation =B2/B3 5 Salvage value 250000 6 Annual cost savings 284000 7 Tax rate 10.4 8 Discount rate 0.11 9 After-tax salvage value =B5*(1-B7) F G Answer - a. Calculation of equated annual cost (EAC) of old computer. Initial cost 1240000 Salvage value 114000 Life of equipment After tax salvage value =J2+(H4-J2)*J5 Annual depreciation 248000 Annual cost savings 10 Remaining life Tax rate 0.4 Current book value =H4*H5 Discount rate 0.11 Current market value 360000 After tax current value of=H7+(H6-H7) *J5 10 11 Year 12 Annual cost savings 13 Less: Depreciation 14 Earnings before taxes 15 Less: Tax 16 Earnings after taxes 17 Add: Depreciation 18 Add: Changes in value of equipment 19 Net operating cash flows 20 Present value factor 21 Present value of cash flows 1 to 4 =B6 =B6 =B4 =B4 =C12-C13 =D12-D13 =C14*B7 =D14*B7 =C14-C15 =D14-D15 =B4 =B4 =B9 =C16+C17 =D16+D17+D18 =-PVB8,4,1,0,0) =-PV(B8.5.0.1,0) =C19*C20 =D19*D20 Year Annual cost savings Less: Depreciation Earnings before taxes Less: Tax Earnings after taxes Add: Depreciation Add: Changes in value o=-H8 Net operating cash flows=H17 Present value factor =1/(1+J6) H10 Present value of cash flo =H18*H19 =J4 =H4 =111-112 =113*J5 =113-114 =H4 =J4 =H4 =J11-J12 =J13*J5 =J13-J14 =H4 =J3 =J15+J16+J17 =1/(1+J6J10 =J18*J19 =-B2 =B18 A110 =115+116 1=1/(1+J6) 110 =118*119 =B19*B20 22 23 Net present value 24 Present value factor 25 EAC >> =SUM(B21:D21) =-PV(B8.B3,1,0,0) =B23/B24 Net present value Present value factor EAC >> =SUM(H20:J20) =-PV(J6,2,1,0,0) =H22/H23 26 27 Answer - b. Calculation of net present value of decision of replacing old computer now. 28 Year 29 Net operating cash flows of new computer =B19 =C19 =C29 =D29 =E29 =D19 30 Less: Net operating cash flows of old computer =H18 =118 =J18 31 Net incremental cash flows =B29-B30 =C29-C30 =D29-D30 =E29-E30 |=F29-F30 1=G29-G30 32 Net present value =NPVBS.C31:G31)+B31

The obtained result is provided below.

E Initial cost F G H I T I J Answer - a. Calculation of equated annual cost (EAC) of old computer. $ 1,240,000 Salvage value S 114.000 Life of equipment After tax salvage value $ 167,600 Annual depreciation $ 248,000.00 Annual cost savings Remaining life Tax rate 40% Current book value $ 744,000.00 Discount rate 11% Current market value $360,000 After tax current value of old computer $513.600 SO | 0 Α I B C D 1 Answer - a. Calculation of equated annual cost (EAC) of new computer. 2 Initial investment $ 1,500,000.00 3 Life of equipment 4 Annual depreciation $ 300,000.00 5 Salvage value $ 250,000 6 Annual cost savings $ 284,000 7 Tax rate 40% 8 Discount rate 11% 9 After-tax salvage value $ 150,000.00 10 11 Year 1 to 4 12 Annual cost savings $ 284,000.00 $ 284,000.00 13 Less: Depreciation $ 300,000.00 $ 300,000.00 14 Earnings before taxes -$ 16,000.00 - 16.000.00 15 Less: Tax -$ 6,400.00 -$ 6,400.00 16 Earnings after taxes | -S 9.600.00 -S 9.600.00 17 Add: Depreciation $ 300,000.00 $ 300,000.00 18 Add: Changes in value of equipment -$ 1.500,000.00 $ 150,000.00 19 Net operating cash flows -S 1,500,000.00 $ 290,400.00 S 440,400.00 20 Present value factor 1.00000000 3.10244569 0.59345133 21 Present value of cash flows -$ 1,500,000.00 $ 900,950.23 S 261,355.96 22 23 Net present value -$ 337.693.81 24 Present value factor ue factor 3.69589702 25 EAC >> -$ 91,369.92 Year Annual cost savings Less: Depreciation Earnings before taxes Less: Tax Earnings after taxes Add: Depreciation Add: Changes in value of equipment Net operating cash flows Present value factor Present value of cash flows $ 0.00 $ 248,000.00 -$ 248,000.00 -$ 99.200.00 -$ 148,800.00 S 248,000.00 $ 0.00 $ 248,000.00 -S 248.000.00 -S 99200.00 - 148,800.00 $ 248.000.00 $ 167,600.00 $ 266,800.00 0.81162243 $ 216,540.87 -$ 513,600.00 -$ 513,600.00 1.00000000 -$ 513,600.00 $ 99,200.00 0.90090090 $ 89,369.37 Net present value Present value factor EAC >> -$ 207,689.77 1.71252333 -$ 121.277.04 26 $ 440,400.00 27 Answer - b. Calculation of net present value of decision of replacing old computer now. 28 Year 0 2 3 29 Net operating cash flows of new computer -S 1,500,000.00 $ 290,400.00 $ 290,400.00 $ 290,400.00 $ 290,400.00 30 Less: Net operating cash flows of old computer -S 513,600.00 $ 99,200.00 $ 266,800.00 31 Net incremental cash flows -$ 986,400.00 $ 191,200.00 $ 23,600.00 $ 290,400.00 $ 290.400.00 32 Net present value -$ 130,004.04 $ 440.400.00