Question

A firm can purchase a centrifugal separator​ (5-year MACRS​ property) for

​$21,000.

The estimated salvage value is

​$2,500

after a useful life of six years. Operating and maintenance​ (O&M) costs for the first year are expected to be

​$2,100.

These​ O&M costs are projected to increase by

​$500

per year each year thereafter. The income tax rate is

25​%

and the MARR is

11​%

after taxes. What must the uniform annual benefits be for the purchase of the centrifugal separator to be economical on an​ after-tax basis?

Year 1 2 3 4 5 6 GDS Recovery Rates (r) for the Six Personal Property Classes Recovery Period (and Property Class) 3-year 5-year" 7-year" 10-year 15-year 0.3333 0.2000 0.1429 0.1000 0.0500 0.4445 0.3200 0.2449 0.1800 0.0950 0.1481 0.1920 0.1749 0.1440 0.0855 0.0741 0.1152 0.1249 0.1152 0.0770 0.1152 0.0893 0.0922 0.0693 0.0576 0.0892 0.0737 0.0623 0.0893 0.0655 0.0590 0.0446 0.0655 0.0590 0.0656 0.0591 0.0655 0.0590 0.0328 0.0591 0.0590 0.0591 0.0590 0.0591 0.0295 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 20-year 0.0375 0.0722 0.0668 0.0618 0.0571 0.0528 0.0489 0.0452 0.0447 0.0447 0.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0446 0.0223 Print Done Clear All

Answer 1

Solution :-

A1 Solution :- B C D F G H T 1 Solution : 2 3 MACRS Dep Schedule Year 1 2 3 4 5 5 Rate 6 Cost 0.2 $21,000 $4,200 0.32 $21,000 $6,720 0.192 $21,000 $4,032 0.1152 $21,000 $2,419 0.1152 $21,000 $2,419 0.0576) $21,000 $1,210 7 Depreciation 8 2 3 4 5 9 Year 0 10 Initial Cost ($21,000) 11 Operating Cost 12 Depreciation 13 Total Exps 14 Less :- Tax Saving @ 25% 15 Net Exps 16 Add :- Depreciation 17 After tax Salvage value 18 19 Net Cash flows ($21,000) 20 PVF @ 11% 21 Present Value ($21,000) 22 23 Net Present Value of Cash Outflows ($2,100) ($4,200) ($6,300) ($1,575.00) ($4,725.00) $4,200 ($2,600) ($6,720) ($9,320) ($2,330.00) ($6,990.00) $6,720 ($3,100) ($4,032) ($7,132) ($1,783.00) ($5,349.00) $4,032 ($3,600) ($2,419) ($6,019) ($1,504.80) ($4,514.40) $2,419 ($4,100) ($2,419) ($6,519) ($1,629.80) ($4,889.40) $2,419 ($4,600) ($1,210) ($5,810) ($1,452.40) ($4,357.20) $1,210 $1,875 1 ($525.00) 0.901 ($473) ($270.00) 0.812 ($219) ($1,317.00) 0.731 ($963) ($2,095.20) 0.659 ($1,380) ($2,470.20) 0.593 ($1,466) ($1,272.60) 0.535 ($680) ($26,181.59) 24

А B C D E F G H 1 3 4 5 6 1 Solution :- 2 3 MACRS Dep Schedule 4 Year 5 Rate 6 Cost 7 Depreciation 8 2 0.32 0.2 21000 =C5*C6 0.192 21000 =E5*E6 0.1152 21000 =F5F6 0.1152 21000 21000 =D5*D6 0.0576 21000 =G5 G6 =H5*H6 0 1 2 3 4 5 6 -21000 =C11-500 =F11-500 --G7 =G11+G12 -2100 --C7 =C11+C12 =C13*0.25 =C13-C14 =C7 =D11-500 =-E7 =E11+E12 =E13*0.25 =E13-E14 --D7 =D11+D12 =D13*0.25 =D13-D14 =D7 9 Year 10 Initial Cost 11 Operating cost 12 Depreciation 13 Total Exps 14 Less :- Tax Saving @ 25% 15 Net Exps 16 Add :- Depreciation 17 After tax Salvage value 18 19 Net Cash flows 20 PVF @ 11% 21 Present Value 22 23 Net Present Value of Cash Outflows =E11-500 =-F7 =F11+F12 =F13*0.25 =F13-F14 =F7 =G11-500 --H7 =H11+H12 =H13*0.25 =H13-H14 =G13*0.25 =G13-G14 =G7 =E7 =H7 =2500*(1-0.25) =B10 =C15+C16 =G15+G16 1 =B20/1.11 =D15+D16 =C20/1.11 =D19*D20 =E15+E16 =D20/1.11 =E19*E20 F15+F16 =E20/1.11 =F19*F20 =F20/1.11 =G19*G20 =SUM(H15:H17) =G20/1.11 =H19*H20 =B19*B20 =C19*C20 =SUM(B21:H21)
Now Expected Uniform Annual Benefits Required = Net Present Value of Cash Outflows / PVAF ( r, n )

= $26,181.59 / PVAF ( 11% , 6 )

= $26,181.59 / 4.231

= $6,188.71

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