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 $5.28 million, $2.29 million above book value. The farm is expected to produce revenue of $2.05 million each year, and annual cash flow from operations equals $1.89 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 $5.28 million, $2.29 million above book value. The farm is expected to produce revenue of $2.05 million each year, and annual cash flow from operations equals $1.89 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 this investment, we need to discount the cash flows from the investment and subtract the initial investment cost. Here's how you can calculate it step by step:

1. Calculate the annual cash flow from operations after tax:
Cash flow = Revenue - Expenses - Taxes
Cash flow = $2.05 million - $0.16 million - ($2.05 million - $0.16 million) * 0.35
Cash flow = $1.89 million

2. Calculate the annual cash flow after tax and depreciation:
Cash flow with depreciation = Cash flow + Depreciation
Depreciation = Initial investment cost - Salvage value / Useful life
Depreciation = ($9.40 million + $2.60 million - $5.28 million) / 10
Depreciation = $0.87 million
Cash flow with depreciation = $1.89 million + $0.87 million
Cash flow with depreciation = $2.76 million

3. Calculate the present value of the annual cash flows:
PV = Cash flow with depreciation / (1 + Discount rate)^Year
PV = $2.76 million / (1 + 0.09)^1 + $2.76 million / (1 + 0.09)^2 + ... + $2.76 million / (1 + 0.09)^10

To simplify the calculation, we can use the formula for the present value of an annuity:

PV = Cash flow with depreciation * [ (1 - (1 + Discount rate)^(-Number of years)) / Discount rate ]

PV = $2.76 million * [ (1 - (1 + 0.09)^(-10)) / 0.09 ]
PV = $2.76 million * [ (1 - (1.09)^(-10)) / 0.09 ]

PV ≈ $20.64 million

4. Calculate the NPV:
NPV = PV - Initial investment cost
NPV = $20.64 million - $12.00 million
NPV ≈ $8.64 million

So, the NPV of this investment is approximately $8.64 million.