Question

Suppose we are thinking about replacing an old computer with a new one. The old one cost us $1,620,000; the new one will cost, $1,949,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about $405,000 after five years.

The old computer is being depreciated at a rate of $336,000 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 $531,000; in two years, it will probably be worth $153,000. The new machine will save us $363,000 per year in operating costs. The tax rate is 23 percent, and the discount rate is 10 percent.

a-1.	Calculate the EAC for the the old computer and the new computer. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
a-2.	What is the NPV of the decision to replace the computer now? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) a-1. Old computer EAC ? New computer EAC ? a-2. NPV ?

Answer 1

the operating cash flow for new computer, x1 =[ savings in operating cost*(1-tax rate) ] + [ (cost of new computer/useful life of new computer )*(tax rate)]

= [363,000*(1-0.23)] +[(1949000/5)*0.23] = 279,510 + 89654 = 369,164

after tax salvage value, s1 = salvage value*(1-tax rate) = 405,000*(1-0.23) = $311,850

discount rate = r = 10% = 0.10

NPV of new computer = n1 = -cost of new computer + (x1*PVIFA) + (s1/(1+r)⁵ )

where PVIFA = present value interest rate factor of annuity

PVIFA(10%,5 years ) =[ (1+r)ⁿ -1]/((1+r)ⁿ *r)

= [ (1.10)⁵ -1]/((1.10)⁵ *0.10) = 3.7907868

n1 = -1949000 + (369,164*3.7907868) + (311,850/(1.10)⁵ )

= -1949000 + 1399422.006942 + 193634.314596 = -355,943.678462 or -355,943.68

EAC of new computer = n1/PVIFA

= -355,943.68/3.7907868= -93,897.05

operating cash flow for old computer , x2 = depreciation per year * tax rate = 336,000*0.23 = 77,280

after tax salvage value of old computer , s2 = amount it can be sold for now + (( depreciation value for 3 years - amount it can be sold for now )*tax rate

= 531,000 + (((336,000*3)-531,000)*0.23) = 421,290

after tax salvage value in two years = s3 = worth of old computer after 2 years + ( (depreciation - worth of old computer after 2 years)*tax rate)

= 153,000 + (( 336,000 - 153,000)*0.23) = 195,090

NPV of old computer , n2 = -s2 +( x2/(1+r)) + ((x2+s3)/(1+r)² )

n2 = -421,290 + (77,280/(1.10)) + ((77,280+195,090 )/(1.10)² )

= -421,290 + 70,254.5455 + 225,099.1736 = -125,936.2809

EAC of old computer = n2/PVIFA

PVIFA = [ (1+r)ⁿ -1]/((1+r)ⁿ *r)

= [ (1.10)² -1]/((1.10)² *0.10) = 1.73553719

EAC of old computer = n2/PVIFA = -125,936.2809/1.73553719 = -72,563.29

NPV of decision to replace the computer = n1 - n2 = -355,943.68 - (-125,936.28 ) = -355,943.68 +125,936.28 = -230,007.4