Question:medium
A customer has made a lumpsum investment of INR 2,00,000 with a bank. The discount rate is 15% per year. The investment enables the customer to receive a payout of INR 1,00,000 yearly for next three consecutive years.
The net present value (NPV) of his/her investment is INR ______ (rounded off to the nearest integer).
A customer has made a lumpsum investment of INR 2,00,000 with a bank. The discount rate is 15% per year. The investment enables the customer to receive a payout of INR 1,00,000 yearly for next three consecutive years.
The net present value (NPV) of his/her investment is INR ______ (rounded off to the nearest integer).
The net present value (NPV) of his/her investment is INR ______ (rounded off to the nearest integer).
Show Hint
Discount each year's INR 1,00,000 payout back to present value at 15% (or use the annuity present value formula), sum them, then subtract the initial INR 2,00,000 investment.
Updated On: Aug 5, 2026
Show Solution
Correct Answer: 28323
Solution and Explanation
Step 1: Understanding the Concept:
NPV compares money received in the future with money paid today by bringing every cash flow back to its present day worth.
Here the customer invests INR 2,00,000 now and receives INR 1,00,000 at the end of year 1, year 2 and year 3.
We discount each of the three payouts separately at 15% per year and then subtract the initial outflow.
Step 2: Key Formula or Approach:
\[ NPV = -C_0 + \sum_{t=1}^{n} \frac{C_t}{(1+r)^t} \]
where $C_0$ is the initial investment, $C_t$ is the cash inflow in year $t$, and $r$ is the discount rate.
Step 3: Detailed Explanation:
Year 1 present value: $\frac{1,00,000}{(1.15)^1} = 86,956.52$
Year 2 present value: $\frac{1,00,000}{(1.15)^2} = \frac{1,00,000}{1.3225} = 75,614.37$
Year 3 present value: $\frac{1,00,000}{(1.15)^3} = \frac{1,00,000}{1.520875} = 65,751.62$
Adding these three:
\[ Total\ PV = 86,956.52 + 75,614.37 + 65,751.62 = 2,28,322.51 \]
Now subtract the original investment:
\[ NPV = 2,28,322.51 - 2,00,000 = 28,322.51 \]
Final Answer:
Rounded to the nearest integer, the NPV of the investment is INR 28,323. \[ \boxed{28323} \]
NPV compares money received in the future with money paid today by bringing every cash flow back to its present day worth.
Here the customer invests INR 2,00,000 now and receives INR 1,00,000 at the end of year 1, year 2 and year 3.
We discount each of the three payouts separately at 15% per year and then subtract the initial outflow.
Step 2: Key Formula or Approach:
\[ NPV = -C_0 + \sum_{t=1}^{n} \frac{C_t}{(1+r)^t} \]
where $C_0$ is the initial investment, $C_t$ is the cash inflow in year $t$, and $r$ is the discount rate.
Step 3: Detailed Explanation:
Year 1 present value: $\frac{1,00,000}{(1.15)^1} = 86,956.52$
Year 2 present value: $\frac{1,00,000}{(1.15)^2} = \frac{1,00,000}{1.3225} = 75,614.37$
Year 3 present value: $\frac{1,00,000}{(1.15)^3} = \frac{1,00,000}{1.520875} = 65,751.62$
Adding these three:
\[ Total\ PV = 86,956.52 + 75,614.37 + 65,751.62 = 2,28,322.51 \]
Now subtract the original investment:
\[ NPV = 2,28,322.51 - 2,00,000 = 28,322.51 \]
Final Answer:
Rounded to the nearest integer, the NPV of the investment is INR 28,323. \[ \boxed{28323} \]
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