Question

An economic block model along with extraction sequence is shown. The numbers given at the centre of the block represent the year of extraction, and that at the corners represent the block economic value in Rs. (lakhs). If the discount rate is 10%, the net present value (NPV), in lakhs, is Rs. . (rounded off to two decimal place)

Hint:

Discount each block's economic value back to the present using its own extraction year, then add all nine discounted values.

Answer 1

Correct Answer: 2.43

Step 1: Read the value and extraction year of every block.
The block model has 9 blocks in three rows. Each block carries two numbers: the small corner number is its economic value in lakhs (positive or negative), and the large centre number is the year it gets mined out.
Top row (left to right): (-1, year 3), (-1, year 2), (+1, year 1), (+1, year 1), (-1, year 2).
Middle row (left to right): (-1, year 3), (+2, year 2), (+1, year 3).
Bottom row: (+2, year 4).

Step 2: Recall the NPV formula for a sequenced block model.
Each block's value is received (or paid, if negative) in the year it is extracted, so it must be discounted back to the present by that many years before adding it to the total.
\[ NPV = \sum_{i} \frac{V_i}{(1+r)^{t_i}} \]
where \(V_i\) is the block's economic value, \(t_i\) is its extraction year, and \(r = 0.10\) is the discount rate.

Step 3: Discount each block and add them up.
\[ \begin{array}{lll} -1/(1.1)^3 = -0.7513 & -1/(1.1)^2 = -0.8264 & +1/(1.1)^1 = +0.9091 \\ +1/(1.1)^1 = +0.9091 & -1/(1.1)^2 = -0.8264 & -1/(1.1)^3 = -0.7513 \\ +2/(1.1)^2 = +1.6529 & +1/(1.1)^3 = +0.7513 & +2/(1.1)^4 = +1.3660 \end{array} \]
Adding all nine discounted values:
\[ NPV = -0.7513-0.8264+0.9091+0.9091-0.8264-0.7513+1.6529+0.7513+1.3660 = 2.43 \]

Final Answer:
The net present value of the block sequence is about Rs. 2.43 lakhs. \[ \boxed{Rs.\ 2.43 \text{ lakhs}} \]