An initial investment of $400,000 will produce an end of year cash flow of $480,000. What is the NPV of the project at a discount rate of 20%?

-400,000 + (480,000/ 1.2) = 0

NPV = 0

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To calculate the Net Present Value (NPV) of the project, we need to discount the cash flows at the given discount rate.

Step 1: Calculate the discounted cash flow for each year.
The cash flow at the end of the year is $480,000, and the discount rate is 20%. To calculate the discounted cash flow, divide the cash flow by (1 + discount rate) raised to the power of the year:
Year 1: $480,000 / (1 + 0.20)^1 = $400,000

Step 2: Calculate the present value of the initial investment.
Since the initial investment is made at the start of the project, there is no need to discount it. Therefore, the present value of the initial investment is $400,000.

Step 3: Calculate the NPV.
The NPV is calculated by summing the discounted cash flows and subtracting the initial investment:
NPV = Sum of discounted cash flows - Initial investment

In this case:
NPV = $400,000 - $400,000 = $0

Therefore, the NPV of the project at a discount rate of 20% is zero.

To calculate the net present value (NPV) of a project, you need to discount the future cash flows back to the present value using the given discount rate. The formula for calculating NPV is:

NPV = CF₁ / (1 + r)¹ + CF₂ / (1 + r)² + ... + CFₙ / (1 + r)ⁿ - Initial Investment

Where:
- CF₁, CF₂, ..., CFₙ are the future cash flows for each period.
- r is the discount rate.
- Initial Investment is the amount of money invested at the beginning.

In this case, the initial investment is $400,000, and the end of year cash flow is $480,000. The cash flow comes at the end of year one, so it will be discounted only once.

Using the formula, we have:

NPV = $480,000 / (1 + 0.20)¹ - $400,000

Let's calculate the NPV:

NPV = $480,000 / (1 + 0.20) - $400,000

Simplifying the calculations:

NPV = $480,000 / 1.20 - $400,000
NPV = $400,000 - $400,000
NPV = $0

Therefore, the NPV of the project at a discount rate of 20% is $0. This means that the project is not expected to generate any additional value beyond the initial investment.