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Calculate the NPV of a $100,000 investment project with cash inflows of $30,000 in year 1, $50,000 in year 2, and $80,000 in year 3, 120,000 in year 4. The cost of capita is 7%

Question

Calculate the NPV of a 100,000investmentprojectwithcashinflowsof100,000 investment project with cash inflows of 30,000 in year 1, 50,000inyear2,and50,000 in year 2, and 80,000 in year 3, 120,000 in year 4. The cost of capita is 7%

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Solution

To calculate the Net Present Value (NPV) of the investment project, we need to discount the cash inflows to their present value and subtract the initial investment.

Step 1: Determine the discount rate The given information states that the cost of capital is 7%. This will be used as the discount rate.

Step 2: Calculate the present value of each cash inflow To calculate the present value of each cash inflow, we will use the formula:

PV = CF / (1 + r)^n

Where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.

For year 1: PV1 = 30,000/(1+0.07)1=30,000 / (1 + 0.07)^1 = 30,000 / 1.07 = $28,037.38

For year 2: PV2 = 50,000/(1+0.07)2=50,000 / (1 + 0.07)^2 = 50,000 / 1.1449 = $43,664.12

For year 3: PV3 = 80,000/(1+0.07)3=80,000 / (1 + 0.07)^3 = 80,000 / 1.2250 = $65,306.12

For year 4: PV4 = 120,000/(1+0.07)4=120,000 / (1 + 0.07)^4 = 120,000 / 1.3108 = $91,457.58

Step 3: Calculate the NPV The NPV is calculated by subtracting the initial investment from the sum of the present values of the cash inflows.

NPV = PV1 + PV2 + PV3 + PV4 - Initial Investment

The initial investment is $100,000.

NPV = 28,037.38+28,037.38 + 43,664.12 + 65,306.12+65,306.12 + 91,457.58 - 100,000NPV=100,000 NPV = 128,465.20 - 100,000NPV=100,000 NPV = 28,465.20

Therefore, the NPV of the investment project is $28,465.20.

This problem has been solved

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