Question

A reactor, which will contain corrosive liquid, has been design. If the reactor is made of mild steel, the initial installed cost will be $6000, and the useful life period will be 4 years. Since stainless steel is highly resistant to the corrosive action of the liquids, stainless steel, as the material of construction, has been proposed as an alternative to mild steel. the stainless steel reactor would have an initial installed cost of $16000. The scrape value at the end off the useful life would be zero for either type of reactor, and both could be replaced at a cost equal to the original price. On the basis of equal capitalized cost for both types of reactors, what should be the useful life period for the stainless steel reactor if money is ?worth 4 percent compounded annually

Answer 1

For equipment 1:- a Cv- Installed cost of CVF $ 6000 C&F Scrap value Csi= $0 ni = ureful period of mild steel of mild mild steel (4) of mind & teel ($) (years) ni= 4 years i = Annual interest rate = 4.1 I=0.04. 106 K1 = Capalelised Coast of mild 8teel (4) Cast :- KI By definition of coup celeilized cost Cvit cv-CAL (1+i)ni-1 - Ki $ 6000 + ($6000 11.04)+ - Ki $ 6000 +$35 294.118 KI = $41294.1181 → @

2:- Steel CD For Equipment C'V2 = Installed Cost of stainless steel (4) CV2 = $ 16000 C92= Scrap value of steinless C82 = 10 useful period of stainless & feel (years) M2= unknown. Annual interese seite uu 4 =0.04. K2= Capalaliped cost of stainless steel. (&)- On Basis of equal copetalised Cost - Ki = K2 -> K2 = $ 412.94.118 (from ®) nza 100 + K2= CV2t (C2-C82) (1+i) n2-1 412.94.118 = 16000 (16000-0). (1.04n2-1 =) (1.0.4m2 16000 + (41294.118 - 16000) (1.04n2. 0-63256+1 =) (1.0402 1.63 256. taoking en both sides =) n 2* en 1.04) en(1.63256) en (1.63256) 0.48462 en (1.04) 0.03922 - 102= 12.356 years. = n2 s Anqwer.