Given below are the cash flows of a project. Find out the net present value of the project. Cost of capital is 18% and initial investment is Rs. 2,00,000.
Year Cash Flows (lakhs)
1. 40
2. 45
3. 60
4. 60
5. 75
Well, well, well! Let's calculate the net present value (NPV) of this project, shall we?
To calculate the NPV, we need to discount each cash flow back to its present value. We'll use a discount rate of 18%, just as you mentioned.
Here's how it goes:
1. In Year 1, we have a cash flow of Rs. 40,000.
2. In Year 2, the cash flow is Rs. 45,000.
3. In Year 3, it's Rs. 60,000.
4. In Year 4, it's Rs. 60,000 again.
5. Finally, in Year 5, we have Rs. 75,000.
Now, to discount these cash flows, we divide each one by (1 + 0.18) raised to the power of the respective year.
After discounting all the cash flows and summing them up, we find the NPV of the project is approximately Rs. 46,168.
So, it seems like this project has a positive NPV. Grab your party hat and enjoy the success!
To calculate the net present value (NPV) of the project, we need to discount each cash flow to its present value and then sum them up.
The formula to calculate the present value of a cash flow is:
PV = CF / (1 + r)^n
Where PV is the present value, CF is the cash flow, r is the discount rate (cost of capital), and n is the number of years.
Given:
Cost of capital (discount rate): 18%
Initial investment: Rs. 2,00,000
Using the formula, we can calculate the present value of each cash flow:
Year 1: PV1 = 40 / (1 + 0.18)^1 = 33.90 lakhs
Year 2: PV2 = 45 / (1 + 0.18)^2 = 33.13 lakhs
Year 3: PV3 = 60 / (1 + 0.18)^3 = 38.89 lakhs
Year 4: PV4 = 60 / (1 + 0.18)^4 = 31.39 lakhs
Year 5: PV5 = 75 / (1 + 0.18)^5 = 40.46 lakhs
Next, we sum up the present values of the cash flows:
NPV = PV1 + PV2 + PV3 + PV4 + PV5 - Initial Investment
NPV = 33.90 + 33.13 + 38.89 + 31.39 + 40.46 - 2.00
NPV = 175.77 - 2.00
NPV = 173.77 lakhs
Therefore, the net present value (NPV) of the project is Rs. 173.77 lakhs.
To find the net present value (NPV) of the project, we need to discount each cash flow to its present value by using the cost of capital. Then, we sum up all the present values and subtract the initial investment.
Here's how you can calculate the NPV step by step:
Step 1: Determine the discount rate
The discount rate is given as 18%.
Step 2: Calculate the present value of each cash flow
For Year 1:
PV1 = Cash Flow1 / (1 + Discount Rate)^1
= 40 / (1 + 0.18)^1
= 40 / 1.18
= 33.90 (rounded to the nearest two decimals)
For Year 2:
PV2 = Cash Flow2 / (1 + Discount Rate)^2
= 45 / (1 + 0.18)^2
= 45 / 1.3924
= 32.35 (rounded to the nearest two decimals)
For Year 3:
PV3 = Cash Flow3 / (1 + Discount Rate)^3
= 60 / (1 + 0.18)^3
= 60 / 1.5406
= 38.98 (rounded to the nearest two decimals)
For Year 4:
PV4 = Cash Flow4 / (1 + Discount Rate)^4
= 60 / (1 + 0.18)^4
= 60 / 1.8135
= 33.04 (rounded to the nearest two decimals)
For Year 5:
PV5 = Cash Flow5 / (1 + Discount Rate)^5
= 75 / (1 + 0.18)^5
= 75 / 2.2519
= 33.30 (rounded to the nearest two decimals)
Step 3: Calculate the NPV
NPV = Sum of Present Values - Initial Investment
= PV1 + PV2 + PV3 + PV4 + PV5 - Initial Investment
= 33.90 + 32.35 + 38.98 + 33.04 + 33.30 - 2,00,000
= - 1,59,299.43 (rounded to the nearest two decimals)
Therefore, the net present value (NPV) of the project is approximately -Rs. 1,59,299.43. This negative value indicates that the project may not be financially viable as it is not expected to generate enough return to cover the initial investment and cost of capital.