demand question

Question

In 2010, National Textile installed a new textile machine in one of its factories at a cost of $250,000. The machine is depreciated linearly over 10 years with a scrap value of $10,000.

 

Find the machine's book value in 2014

Value: 

Answer 1

Value at any time  = Original value (1 - rate) ^t

 

r is the rate of depreciation in decimal ;  t is time

 

We need to find r:

 

            $10,000  =  $250,000 ( 1 - r ) ¹⁰

 

10,000/250,000 = ( 1 - r )¹⁰  

 

                  1/25 = ( 1 - r )¹⁰

 

       (1/25)^(1/10) = 1 - r

 

                       r = 1 -  (.04)^.1

 

                       r = .2752

 

Then:

 

       Value (2014) = $250,000 ( 1 - .27522 ) ⁴

 

  Value (2014)  = $68,994.23

 

Sorry, I depreciated mine exponentially at a rate of

27.52% per year;  My mistake, I made the problem

Harder than it was.

Answer 2

The initial cost of the machine is $250,000

The scrap value is $10,000

Therefore, $240,000 will be depreciated, linearly (evenly) over the next 10 years.

This is $24,000 per year.

 

The book value in 2014 will be

 

$250,000 - $24,000(4) = $154,000