In: Finance
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.
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.