Calculate the net present value (NPV) of the cash shown on the diagram at t = 0
year, if the interest rate is W % compounded annually. Initial capital is AED
300,000 [Choose any value for X,Y&Z from AED 200,000 to 900,000and W from
10% to 18%]
AED 100,000 AED X AED Y AED Z
0 1 2 3 4 5 6 Years
To calculate the net present value (NPV) of the cash shown on the diagram at t = 0, you will need to use the formula for calculating NPV, which takes into account the cash flows and the interest rate. Here's how you can calculate it step by step:
1. Identify the cash flows: In the given diagram, there are cash flows at different time periods (years). The cash flows are as follows:
- Year 0: Initial capital of AED 300,000 (outflow)
- Year 1: AED 100,000 (inflow)
- Year 2: AED X (inflow)
- Year 3: AED Y (inflow)
- Year 4: AED Z (inflow)
- Year 5: 0 (no cash flow)
- Year 6: 0 (no cash flow)
2. Determine the interest rate: In the question, it states that the interest rate is W% compounded annually. Choose any value for W between 10% and 18%.
3. Calculate the present value of each cash flow: To calculate the present value of each cash flow, you need to discount it back to its present value using the interest rate. The present value calculation formula is:
Present Value = Cash Flow / (1 + Interest Rate)^n
Where:
- Cash Flow: The cash flow in a specific year
- Interest Rate: The interest rate in decimal form (e.g., 10% = 0.10)
- n: The number of years into the future the cash flow occurs
Apply this formula to each cash flow from Year 1 to Year 4.
4. Calculate the NPV: Once you have calculated the present value for each cash flow, subtract the initial capital (Year 0) from the sum of the present values of the cash flows from Year 1 to Year 4.
NPV = (Present Value of Year 1) + (Present Value of Year 2) + (Present Value of Year 3) + (Present Value of Year 4) - Initial Capital
Substitute the appropriate values you have chosen for X, Y, Z, and W into the formula and calculate the NPV.
Note: The years with no cash flows (Year 5 and Year 6) do not affect the NPV calculation as their present values are zero.
Remember to adjust the values of X, Y, Z, and W within the given range for more accurate calculations based on the specific scenario provided.