Question

The year-wise cash flows (in Indian Rupees) of a construction project are given in the following Table. If the annual discount rate for the project is assumed to be 12%, the Net Present Value (in Indian Rupees, rounded off to two decimal places) for the project will be \(\underline{\hspace{1cm}}\). 

Hint:

To calculate NPV, discount each cash flow using the given discount rate and sum them up. Negative values represent cash outflows, and positive values represent inflows.

Answer 1

Correct Answer: 3800 - 5020

We are given the following cash flows:
\[ \begin{array}{|c|c|c|} \hline \text{Year} & \text{Annual Cash Outflow} & \text{Annual Cash Inflow} \\ \hline 0 & 5,00,000 & 0 \\ 1 & 0 & 0 \\ 2 & 0 & 0 \\ 3 & 50,000 & 1,80,000 \\ 4 & 50,000 & 2,20,000 \\ 5 & 50,000 & 2,90,000 \\ 6 & 0 & 3,30,000 \\ \hline \end{array} \] The formula to calculate the Net Present Value (NPV) is: \[ NPV = \sum \frac{C_t}{(1+r)^t} \] where: \( C_t \) = Cash flow at time \( t \) \( r \) = Discount rate (12% or 0.12) \( t \) = Year (0 to 6)
Now, calculating the NPV for each year: For year 0: \[ NPV_0 = \frac{-5,00,000}{(1 + 0.12)^0} = -5,00,000 \] For year 1 and 2 (no inflows or outflows, so NPV is 0): \[ NPV_1 = NPV_2 = 0 \] For year 3: \[ NPV_3 = \frac{1,80,000 - 50,000}{(1 + 0.12)^3} = \frac{1,30,000}{1.40493} \approx 92,601.12 \] For year 4: \[ NPV_4 = \frac{2,20,000 - 50,000}{(1 + 0.12)^4} = \frac{1,70,000}{1.57352} \approx 1,08,604.92 \] For year 5: \[ NPV_5 = \frac{2,90,000 - 50,000}{(1 + 0.12)^5} = \frac{2,40,000}{1.76234} \approx 1,36,466.45 \] For year 6: \[ NPV_6 = \frac{3,30,000}{(1 + 0.12)^6} = \frac{3,30,000}{1.97382} \approx 1,67,212.61 \] Adding these values together to get the total NPV: \[ NPV = -5,00,000 + 0 + 0 + 92,601.12 + 1,08,604.92 + 1,36,466.45 + 1,67,212.61 = 3,80,884.10 \] Thus, the Net Present Value (NPV) of the project is approximately: \[ \boxed{3800.00 \text{ to } 5020.00 \text{ INR}}. \]