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)
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Discount each block's economic value back to the present using its own extraction year, then add all nine discounted values.
Instead of discounting each of the nine blocks one at a time, it's cleaner to first group the blocks by which year they get mined, add up the values within each year, and only then discount each year's total once.
Step 1: Group the blocks by extraction year. Reading the model, year 1 has two blocks worth +1 and +1. Year 2 has three blocks worth -1, -1 and +2. Year 3 has three blocks worth -1, -1 and +1. Year 4 has one block worth +2.
Step 2: Add up the value scheduled for each year.
Year 1 total: $1 + 1 = 2$ lakhs.
Year 2 total: $-1 - 1 + 2 = 0$ lakhs.
Year 3 total: $-1 - 1 + 1 = -1$ lakh.
Year 4 total: $+2$ lakhs.
Step 3: Discount each year's total back to the present at 10% and add. The discount factor for year $t$ is $1/(1.1)^t$.
Year 1: $2/(1.1)^1 = 2 \times 0.9091 = 1.8182$
Year 2: $0/(1.1)^2 = 0$
Year 3: $-1/(1.1)^3 = -1 \times 0.7513 = -0.7513$
Year 4: $2/(1.1)^4 = 2 \times 0.6830 = 1.3660$
$NPV = 1.8182 + 0 - 0.7513 + 1.3660 = 2.4329$, which rounds to 2.43 lakhs. This matches discounting all nine blocks separately, since addition and discounting can be reordered freely, grouping by year first is just a shortcut that avoids repeating the same discount factor many times.
Let's summarize:
Grouping blocks by year gives net cash flows of +2, 0, -1 and +2 lakhs for years 1 through 4.
Discounting each year's net flow at 10% and adding gives the total NPV.
The result is Rs. 2.43 lakhs.
So the net present value of the block extraction sequence is Rs. 2.43 lakhs.
