1) A lumber company that cuts fine woods for cabinetry is evaluating whether it
ID: 350485 • Letter: 1
Question
1) A lumber company that cuts fine woods for cabinetry is evaluating whether it should retain the current bleaching system or replace it with a new one. The relevant costs for each system are known or estimated. Use an interest rate of 10% per year to (a)perform the replacement analysis and (b) determine the minimum resale price needed to make the challenger replacement choice now. Is this a reasonable amount to expect for the current system?
Current
New
System
System
First cost 7 years ago, $
–450,000
First cost, $
–700,000
Remaining life, years
5
10
Current market value, $
50,000
AOC, $ per year
–160,000
–150,000
Future salvage, $
0
50,000
Current
New
System
System
First cost 7 years ago, $
–450,000
First cost, $
–700,000
Remaining life, years
5
10
Current market value, $
50,000
AOC, $ per year
–160,000
–150,000
Future salvage, $
0
50,000
Explanation / Answer
(a) Replacement analysis
Compound interest factors,
(P/A,10%,5) = ((1+10%)5-1)/(10%*(1+10%)5) = 3.791
(P/A,10%,10) = ((1+10%)10-1)/(10%*(1+10%)10) = 6.145
(A/P,10%,5) = 10%*(1+10%)5/((1+10%)5-1) = 0.2638
(A/P,10%,10) = 10%*(1+10%)10/((1+10%)10-1) = 0.1627
(P/F,10%,10) = 1/(1+10%)10 = 0.3855
Annual Worth (AW) of current system = -160000
Annual Worth (AW) of New system = (-700000+50000)*(A/P,10%,10) - 150000 + 50000*(P/F,10%,10)*(A/P,10%,10) =
= (-700000+50000)*0.1627 - 150000 + 50000*0.3855*0.1627 = -252619
AW of Current system is better, therefore, the current system should not be replaced by the new system
(b) The minimum resale price needed to make the challenger replacement choice = (-160000+150000-50000*0.3855*0.1627)/0.1627+700000 = $ 619,262
This is a very high amount and therefore, not reasonable to expect for the current system.
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