The lining of a plating tank must be replaced every three years at the cost of...

The lining of a plating tank must be replaced every three years at the cost of approximately $2,000. A new lining material has been developed that is more resistant to the corrosive effects of the plating liquid and will cost approximately $4,000. If the required rate of return is 20% and annual property taxes and insurance amount to about 4% of the initial investment, how long must the new lining last to be more economical than the present one? Please answer in terms of years.

Solutions

Expert Solution

The Annual Capital Charge for the machine = PV of all cost / Annuity Factor for n years of Required Return

Therefore, for Existing Machine :

Investment Cost = $ 2000

Annual Insurance Cost = $2,000 x 4% = $ 80

PV of Annual Insurance Cost = 80 x PVAF(20%,3)

= 80 x 2.1064

= $ 168.512

PV of all costs net of Insurance Cost = 2000 - 168.512

= $ 1,831.488

Hence, Annual Capital Charge (ACC) = 1,831.488 / PVAF (20%,3)

= 1,831.488 / 2.1064

= $ 869.4873

Now, the new machinery has a cost of $4,000. To be more economical than the present Machine, the new lining must last till the ACC is less than $ 911.51.

So,

Investment Cost = $ 4000

Annual Insurance Cost = $4,000 x 4% = $ 160

PV of Annual Insurance Cost = 160 x PVAF(20%,3)

= 160 x 2.1064

= $ 337.024

PV of all costs net of Insurance Cost = 4000 - 337.024

= $ 3,662.976

Annual Capital Charge (ACC) = $ 869.4873

869.4873 = 3,662.976 / PVAF (20%,n)

PVAF (20%,n) = 3,662.976 / 869.4873

PVAF (20%,n) = 4.2128

So, therefore n = 10.33 years (approx)

Answer : The new lining has to for approximately 10.33 years to be more economical than the present one.

jeff jeffy answered 2 years ago

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