Question

Bentley Mews is considering a new 4-year expansion project that requires an initial fixed asset investment of $3 million. The fixed asset will be depreciated straight-line to zero over its 4-year tax life, after which time it will be sold. Assume it will be sold for $231,000, its estimated market value at the end of four years. The project requires an initial investment in net working capital of $330,000, all of which will be recovered at the end of the project. The project is estimated to generate $2,640,000 in annual sales, with costs of $1,056,000. The tax rate is 30 percent and the required return for the project is 11.0 percent. What is the net present value for this project

Answer 1

The net present value (NPV) for this project is $2,564,498.54. The cash flows include the annual sales and costs over the 4-year period, as well as the salvage value of the fixed asset at the end of the project.

Step-by-step explanation:

To calculate the net present value (NPV) for this project, we need to discount the future cash flows back to the present value using the required return rate. The net present value is calculated by subtracting the initial investment from the present value of the future cash flows. In this case, the cash flows include the annual sales and costs over the 4-year period, as well as the salvage value of the fixed asset at the end of the project. After discounting the cash flows and adding them up, we get the net present value of the project.

The formula to calculate the present value of the cash flows is:

PV = CF1 / (1+r) + CF2 / (1+r)^2 + ... + CFn / (1+r)^n

Where PV is the present value, CF is the cash flow for each period, r is the required return rate, and n is the number of periods.

In this case, the initial investment of $3 million is made at time zero, so its present value is $3 million. The annual sales of $2,640,000 and costs of $1,056,000 are assumed to be received and paid at the end of each year, so their present values need to be calculated using the formula above and added up for 4 periods. The salvage value of $231,000 is also received at the end of the 4-year period, so its present value is calculated using the formula above for one period.

Once the present values are calculated, the net present value is obtained by subtracting the initial investment from the sum of the present values.

In this case:

PV_sales = $2,640,000 / (1+0.11)^1 + $2,640,000 / (1+0.11)^2 + $2,640,000 / (1+0.11)^3 + $2,640,000 / (1+0.11)^4 = $8,658,907.98

PV_costs = $1,056,000 / (1+0.11)^1 + $1,056,000 / (1+0.11)^2 + $1,056,000 / (1+0.11)^3 + $1,056,000 / (1+0.11)^4 = $3,477,699.27

PV_salvage = $231,000 / (1+0.11)^4 = $152,289.83

NPV = $8,658,907.98 + $231,000 - $3,477,699.27 - $3,000,000 + $152,289.83 = $2,564,498.54

The net present value for this project is $2,564,498.54.