Question

A distillation column has a purchase cost of ₹ 10 lakhs with an installation factor \(5.8\). The installed capital is annualized over \(6\) years at \(5%\) per annum, compounded annually. Find the annual cost (in lakhs of rupees) of the installed capital.

Hint:

Annualizing a capital cost uses \(A=C_0 \times \text{CRF}\) with \(\text{CRF}=\dfrac{i(1+i)^n}{(1+i)^n-1}\).
Installation factor converts purchase price to total installed cost before annualization.

Answer 1

Correct Answer: 11

Step 1: Installed capital: \[ C_0=10\times 5.8=58\ \text{lakhs}. \] Step 2: Use capital recovery factor (CRF): \[ \text{CRF}=\frac{i(1+i)^n}{(1+i)^n-1},\quad i=0.05,\; n=6. \] \[ (1+i)^n=1.05^6=1.3401,\; \text{CRF}=\frac{0.05\times 1.3401}{1.3401-1}=0.1971. \] Step 3: Annual cost: \[ A=C_0\times \text{CRF}=58\times 0.1971=11.42\ \text{lakhs}\approx \boxed{11.4}. \]