A firm with 50% debt to equity ratio has a cost of equity capital of 15%, a cost of debt of 9% and a tax rate of 33%. The firm is considering a project costing 5,000 that will generate an annual cash flow of 1,000 for the next 8 years. What is the projects NPV?

To calculate the project's NPV (Net Present Value), we need to determine the present value of the cash flows generated by the project and compare it to the initial cost of the project. Here's how you can calculate the NPV:

1. Calculate the weighted average cost of capital (WACC):
- The WACC takes into account the cost of equity and the cost of debt, weighted by the proportions of equity and debt in the company's capital structure.
- Since the firm has a 50% debt to equity ratio, the weights for equity and debt would be 0.5 each.
- The WACC formula is: WACC = (Weight of Equity * Cost of Equity) + (Weight of Debt * Cost of Debt * (1 - Tax Rate))

2. Calculate the present value of the cash flows:
- To calculate the present value (PV) of each cash flow, we need to discount them using the WACC.
- We use the formula: PV = Cash Flow / (1 + WACC)^n, where n is the time period.
- Repeat this calculation for each year's cash flow (in this case, for 8 years).

3. Calculate the NPV:
- The NPV is the sum of all the present values of the cash flows, minus the initial cost of the project.
- The formula for NPV is: NPV = Sum of PVs - Initial Cost

Now, let's calculate the NPV for the given project:

1. Calculate the WACC:
- Weight of Equity = 0.5
- Weight of Debt = 0.5
- Cost of Equity = 15%
- Cost of Debt = 9%
- Tax Rate = 33%
- WACC = (0.5 * 0.15) + (0.5 * 0.09 * (1 - 0.33))

2. Calculate the present value of the cash flows:
- For each year, divide the cash flow of $1,000 by (1 + WACC)^n, where n is the year.
- Repeat this calculation for each year: 1 to 8.

3. Calculate the NPV:
- Sum all the present values and subtract the initial cost of $5,000.

By following these steps, you will be able to calculate the project's NPV.