Question

Production planning of a small quarry having 3 years of life is shown in the figure. The following information of revenue and cost data are available. 

Selling price of ore = Rs. 1500/tonne 
Ore mining cost = Rs. 500/tonne 
Waste mining cost = Rs. 500/m\(^3\) 
Initial capital = Rs. 1000 million 
Discount rate = 10% 
By neglecting depreciation, salvage value and corporate tax, the NPV of the mining project, in million Rs., is \(\underline{\hspace{2cm}}\). [round off to 2 decimal places]

Hint:

NPV is calculated by discounting future cash flows to the present value using the discount rate.

Answer 1

Correct Answer: 35.5

To calculate the Net Present Value (NPV), we need the cash flows for each year:
Year 1:
Revenue = \( 3.0 \, \text{million tonnes} \times 1500 \, \text{Rs/tonne} = 4500 \, \text{million Rs} \)
Ore mining cost = \( 3.0 \, \text{million tonnes} \times 500 \, \text{Rs/tonne} = 1500 \, \text{million Rs} \)
Waste mining cost = \( 5.0 \, \text{million m}^3 \times 500 \, \text{Rs/m}^3 = 2500 \, \text{million Rs} \)
Cash Flow (Year 1) = \( 4500 - 1500 - 2500 = 500 \, \text{million Rs} \)
Year 2:
Revenue = \( 3.0 \, \text{million tonnes} \times 1500 \, \text{Rs/tonne} = 4500 \, \text{million Rs} \)
Ore mining cost = \( 3.0 \, \text{million tonnes} \times 500 \, \text{Rs/tonne} = 1500 \, \text{million Rs} \)
Waste mining cost = \( 5.5 \, \text{million m}^3 \times 500 \, \text{Rs/m}^3 = 2750 \, \text{million Rs} \)
Cash Flow (Year 2) = \( 4500 - 1500 - 2750 = 250 \, \text{million Rs} \)
Year 3:
Revenue = \( 3.0 \, \text{million tonnes} \times 1500 \, \text{Rs/tonne} = 4500 \, \text{million Rs} \)
Ore mining cost = \( 3.0 \, \text{million tonnes} \times 500 \, \text{Rs/tonne} = 1500 \, \text{million Rs} \)
Waste mining cost = \( 5.0 \, \text{million m}^3 \times 500 \, \text{Rs/m}^3 = 2500 \, \text{million Rs} \)
Cash Flow (Year 3) = \( 4500 - 1500 - 2500 = 500 \, \text{million Rs} \)
The NPV formula is:
\[ NPV = \sum \frac{CF_t}{(1 + r)^t} \] where \( r = 10% \) is the discount rate, and \( t \) is the year number.
\[ NPV = \frac{500}{(1 + 0.1)^1} + \frac{250}{(1 + 0.1)^2} + \frac{500}{(1 + 0.1)^3} \] \[ NPV = \frac{500}{1.1} + \frac{250}{1.21} + \frac{500}{1.331} \] \[ NPV = 454.55 + 206.61 + 375.38 = 1036.54 \, \text{million Rs} \] Thus, the NPV of the mining project is \( \boxed{1036.54} \, \text{million Rs} \).