Question

A project requires an initial investment of $10,000, straight-line depreciable to zero over 4 years. The discount rate is 10%. Your tax bracket is 34% and you receive a tax credit for negative earnings in the year in which the loss occurs. What is the net present value (NPV) of the project?

Answer 1

To calculate the net present value (NPV) of the project, we need to discount the cash flows to the present value and subtract the initial investment. In this case, the initial investment is $10,000, and the project is straight-line depreciable to zero over 4 years. The discount rate is 10% and the tax bracket is 34%. The net present value (NPV) of the project is -$3,769, indicating that the project is not financially viable.

Step-by-step explanation:

To calculate the net present value (NPV) of the project, we need to discount the cash flows to the present value and subtract the initial investment. In this case, the initial investment is $10,000, and the project is straight-line depreciable to zero over 4 years. The discount rate is 10% and the tax bracket is 34%.

First, we need to calculate the annual depreciation expense, which is the initial investment divided by the number of years. In this case, it is $10,000 divided by 4, which is $2,500 per year.

Next, we need to calculate the cash flows for each year. The cash flow in each year is the after-tax depreciation expense plus any additional savings or revenue generated by the project. In this case, let's assume there are no additional savings or revenue, so the cash flow in each year is the after-tax depreciation expense:

1. Year 1: $2,500 x (1 - tax rate) = $2,500 x (1 - 0.34) = $1,650
2. Year 2: $2,500 x (1 - tax rate) = $2,500 x (1 - 0.34) = $1,650
3. Year 3: $2,500 x (1 - tax rate) = $2,500 x (1 - 0.34) = $1,650
4. Year 4: $2,500 x (1 - tax rate) = $2,500 x (1 - 0.34) = $1,650

Now, we can calculate the present value of each cash flow by discounting it to the present value using the discount rate. The present value of each year's cash flow is:

1. Year 1: $1,650 / (1 + discount rate) = $1,650 / (1 + 0.10) = $1,500
2. Year 2: $1,650 / (1 + discount rate)^2 = $1,650 / (1 + 0.10)^2 = $1,359
3. Year 3: $1,650 / (1 + discount rate)^3 = $1,650 / (1 + 0.10)^3 = $1,244
4. Year 4: $1,650 / (1 + discount rate)^4 = $1,650 / (1 + 0.10)^4 = $1,134

Finally, we sum up the present values of all the cash flows and subtract the initial investment to get the net present value:

NPV = ($1,500 + $1,359 + $1,244 + $1,134) - $10,000 = $6,231 - $10,000 = -$3,769

Therefore, the net present value (NPV) of the project is -$3,769, indicating that the project is not financially viable.