Archer Daniels Midland Company is considering buying a new farm that it plans to

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 $12.10  million. This investment will consist of $2.30   million for land and $9.80  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 $1.88  million. The marginal tax rate is 35  percent, and the appropriate discount rate is 10  percent. Calculate the NPV of this investment.

To earn full points please show work so i can see how properly calulate this in the future.

Explanation / Answer

If the annual cash flow from operations includes taxes...
"CF" = cash flow
CF0 = (12.10m)
CFs 1 - 9 = 1.84m
CF10 = 1.84m + sale proceeds 5.06m - tax on gain over book (2.03m * 0.35 = 710,500)
= 6,189,500

PV of CFs 1 - 9, use Present Value ordinary annuity
PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]
= 1.84m[(1 - (1 / 1.09^9)) / 0.09]
= $11,031,254.28

PV of CF#10 = 6,189,500/1.09^10 = $2,614,511.69

NPV = (12,100,000) + 11,031,254.28 + 2,614,511.69 = $1,545,765.97
[or 1,545,765.98 depending on how/when you round]

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