Archer Daniels Midland Company is considering buying a new farm that it plans to operate for 10 years. The farm will require an initial investment of $12.00 million. This investment will consist of $2.60 million for land and $9.40 million for trucks and other equipment. The land, all trucks, and all other equipment is expected to be sold at the end of 10 years at a price of $5.18 million, $2.29 million above book value. The farm is expected to produce revenue of $2.01 million each year, and annual cash flow from operations equals $1.84 million. The marginal tax rate is 35 percent, and the appropriate discount rate is 9 percent. Calculate the NPV of this investment

Question

Archer Daniels Midland Company is considering buying a new farm that it plans to operate for 10 years. The farm will require an initial investment of $12.00 million. This investment will consist of $2.60 million for land and $9.40 million for trucks and other equipment. The land, all trucks, and all other equipment is expected to be sold at the end of 10 years at a price of $5.18 million, $2.29 million above book value. The farm is expected to produce revenue of $2.01 million each year, and annual cash flow from operations equals $1.84 million. The marginal tax rate is 35 percent, and the appropriate discount rate is 9 percent. Calculate the NPV of this investment

Answer 1

To calculate the Net Present Value (NPV) of the investment, you need to determine the cash flows for each year and discount them to present value using the appropriate discount rate. NPV is the difference between the present value of cash inflows and outflows.

Here's how to calculate the NPV:

1. Determine the cash flows for each year:

Year 1:
Revenue: $2.01 million
Cash flow from operations: $1.84 million

Years 2-10:
Revenue: $2.01 million
Cash flow from operations: $1.84 million

2. Calculate the cash flow from the sale of assets at the end of 10 years:

Sale price: $5.18 million
Book value: $2.29 million (above book value)

Cash flow from sale: Sale price - Book value
Cash flow from sale = $5.18 million - $2.29 million = $2.89 million

3. Calculate the present value of each cash flow using the discount rate of 9 percent. The present value (PV) can be calculated using the formula:
PV = CF / (1 + r)^n
where CF is the cash flow, r is the discount rate, and n is the number of years.

Year 1:
PV_1 = $1.84 million / (1 + 0.09)^1 = $1.68 million

Years 2-10:
PV_2-10 = $1.84 million / (1 + 0.09)^2 + $2.01 million / (1 + 0.09)^2 + ... + $1.84 million / (1 + 0.09)^10

4. Calculate the present value of the cash flow from the sale:

PV_sale = $2.89 million / (1 + 0.09)^10 = $1.42 million

5. Calculate the NPV by summing up all the present values:

NPV = PV_1 + PV_2-10 + PV_sale - Initial investment

Initial investment (cash outflow) = $12 million

NPV = $1.68 million + PV_2-10 + $1.42 million - $12 million

To find the value for PV_2-10, you need to calculate the present value of an annuity, which is the sum of the present values of equal cash flows received each year:

PV_2-10 = (CF / (1 + r)^2) + (CF / (1 + r)^3) + ... + (CF / (1 + r)^10)

So, substitute CF = $1.84 million and r = 0.09 into the formula to calculate PV_2-10.

After calculating PV_2-10, substitute the values back into the NPV formula to find the final result.

I hope this helps you calculate the NPV of the investment correctly.